diff --git a/.all-contributorsrc b/.all-contributorsrc index 610c8223..a625ed92 100644 --- a/.all-contributorsrc +++ b/.all-contributorsrc @@ -240,6 +240,96 @@ "contributions": [ "example" ] + }, + { + "login": "FelixXu35", + "name": "Felix Xu", + "avatar_url": "https://avatars.githubusercontent.com/u/61252303?v=4", + "profile": "https://www.linkedin.com/in/felix-xu-16a153196/", + "contributions": [ + "tutorial", + "code", + "test" + ] + }, + { + "login": "hongyehu", + "name": "Hong-Ye Hu", + "avatar_url": "https://avatars.githubusercontent.com/u/50563225?v=4", + "profile": "https://scholar.harvard.edu/hongyehu/home", + "contributions": [ + "doc" + ] + }, + { + "login": "PeilinZHENG", + "name": "peilin", + "avatar_url": "https://avatars.githubusercontent.com/u/45784888?v=4", + "profile": "https://github.com/PeilinZHENG", + "contributions": [ + "tutorial", + "code", + "test", + "doc" + ] + }, + { + "login": "EmilianoG-byte", + "name": "Cristian Emiliano Godinez Ramirez", + "avatar_url": "https://avatars.githubusercontent.com/u/57567043?v=4", + "profile": "https://emilianog-byte.github.io", + "contributions": [ + "code", + "test" + ] + }, + { + "login": "ztzhu1", + "name": "ztzhu", + "avatar_url": "https://avatars.githubusercontent.com/u/111620128?v=4", + "profile": "https://github.com/ztzhu1", + "contributions": [ + "code" + ] + }, + { + "login": "royess", + "name": "Rabqubit", + "avatar_url": "https://avatars.githubusercontent.com/u/31059422?v=4", + "profile": "https://github.com/royess", + "contributions": [ + "example" + ] + }, + { + "login": "king-p3nguin", + "name": "Kazuki Tsuoka", + "avatar_url": "https://avatars.githubusercontent.com/u/103920010?v=4", + "profile": "https://github.com/king-p3nguin", + "contributions": [ + "code", + "test", + "doc", + "example" + ] + }, + { + "login": "Gopal-Dahale", + "name": "Gopal Ramesh Dahale", + "avatar_url": "https://avatars.githubusercontent.com/u/49199003?v=4", + "profile": "https://gopal-dahale.github.io/", + "contributions": [ + "example" + ] + }, + { + "login": "AbdullahKazi500", + "name": "Chanandellar Bong", + "avatar_url": "https://avatars.githubusercontent.com/u/75779966?v=4", + "profile": "https://github.com/AbdullahKazi500", + "contributions": [ + "example" + ] } ], "contributorsPerLine": 6, @@ -247,5 +337,6 @@ "repoType": "github", "repoHost": "https://github.com", "projectName": "tensorcircuit", - "projectOwner": "tencent-quantum-lab" + "projectOwner": "tencent-quantum-lab", + "commitType": "docs" } diff --git a/.gitattributes b/.gitattributes new file mode 100644 index 00000000..176a458f --- /dev/null +++ b/.gitattributes @@ -0,0 +1 @@ +* text=auto diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml index 7a0a7dff..964f9d67 100644 --- a/.github/workflows/ci.yml +++ b/.github/workflows/ci.yml @@ -7,7 +7,7 @@ jobs: strategy: matrix: os: [ubuntu-20.04, macos-latest] # macos-latest disabled to save quota - python-version: [3.8] + python-version: ["3.10"] fail-fast: false steps: - uses: actions/checkout@v2 diff --git a/.github/workflows/nightly_release.yml b/.github/workflows/nightly_release.yml index ce62cc9c..8a1dbda8 100644 --- a/.github/workflows/nightly_release.yml +++ b/.github/workflows/nightly_release.yml @@ -18,7 +18,7 @@ jobs: - name: Set up Python uses: actions/setup-python@v4 with: - python-version: 3.8 + python-version: "3.10" cache: "pip" - name: install dependencies run: | diff --git a/.gitignore b/.gitignore index c1649c55..c21b5efb 100644 --- a/.gitignore +++ b/.gitignore @@ -28,3 +28,4 @@ examples/Unified AD model.ipynb docs/source/locale/zh/LC_MESSAGES/textbook.po docs/source/locale/zh/LC_MESSAGES/whitepapertoc_cn.po docs/source/locale/zh/LC_MESSAGES/textbooktoc.po +test.qasm diff --git a/.readthedocs.yaml b/.readthedocs.yaml new file mode 100644 index 00000000..2acb1049 --- /dev/null +++ b/.readthedocs.yaml @@ -0,0 +1,24 @@ +# .readthedocs.yaml +# Read the Docs configuration file +# See https://docs.readthedocs.io/en/stable/config-file/v2.html for details + +# Required +version: 2 + +formats: + - pdf + +# Set the version of Python and other tools you might need +build: + os: ubuntu-20.04 + tools: + python: "3.8" + +# Build documentation in the docs/ directory with Sphinx +sphinx: + configuration: docs/source/conf.py +# We recommend specifying your dependencies to enable reproducible builds: +# https://docs.readthedocs.io/en/stable/guides/reproducible-builds.html +python: + install: + - requirements: requirements/requirements-rtd.txt diff --git a/CHANGELOG.md b/CHANGELOG.md index d922b381..3f072c9a 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -2,6 +2,110 @@ ## Unreleased +### Added + +- Add support for parameter expression in qiskit translation + +## 0.12.0 + +### Added + +- Add translation of r gate from qiskit + +- Add `det` method at backends + +- Add fermion Gaussian state simulator in `fgs.py` + +- Add `partial_transpose` and `entanglement_negativity` method in `quantum.py` + +- Add `reduced_wavefunction` method in `quantum.py` to get reduced pure state + +### Changed + +- move ensemble module to applications/ai (breaking changes) + +- tc2qiskit now record qiskit measure with incremental clbit from 0 + +### Fixed + +- Support degenerate eigenvalue for jax backend `eigh` method when using AD + +- Fixed `cu` gate translation from qiskit to avoid qiskit bug + +- Fixed jax refactoring (0.4.24) where SVD and QR return a namedtuple instead of a tuple + +- Fix qiskit<1.0 and tf<2.16 + +## 0.11.0 + +### Added + +- Add multiple GPU VQE examples using jax pmap + +- Add `with_prob` option to `general_kraus` so that the probability of each option can be returned together + +- Add benchmark example showcasing new way of implementing matrix product using vmap + +- Add keras3 example showcasing integration with tc + +- Add circuit copy method that avoid shallow copy issue `Circuit.copy()` + +- Add end to end infrastructures and methods for classical shadow in `shadows.py` + +- Add classical shadow tutorial + +- Add NN-VQE tutorial + +### Fixed + +- improve the `adaptive_vmap` to support internal jit and pytree output + +- fix `pauli_gates` dtype unchange issue when set new dtype (not recommend to use this attr anymore) + +- fix rem `apply_correction` bug when non-numpy backend is set + +- fix tf warning for `cast` with higher version of tf + +### Changed + +- The static method `BaseCircuit.copy` is renamed as `BaseCircuit.copy_nodes` (breaking changes) + +## 0.10.0 + +### Added + +- `c.measure_instruction(*qubits)` now supports multiple ints specified at the same time + +- `c.expectation_ps()` now also supports `ps` argument directly (pauli structures) + +- Add tc version print in `tc.about()` method + +- tc now supports fancy batch indexing for gates, e.g. `c.rxx([0, 1, 2], [1, 2, 3], theta=K.ones([3]))` + +- Task management via group tag (when `submit_task` and `list_tasks`) + +- `batch_expectation_ps` now supports local device without topology and thus unify the interface for numerical exact simulation, numerical simulation with measurement shots and QPU experiments + +- introduce two stage compiling for `batch_expectation_ps` to save some compiling overhead + +- Add experimental support for ODE backend pulse level control simulation/analog quantum computing + +- make the pulse level control support differentiating the end time + +- Add new qem module with qem methods: zne, dd and rc + +### Fixed + +- `tc.results.counts.plot_histogram` now can dispatch kws to corresponding qiskit method + +- New implementation for `c.inverse()` to partially avoid unrecognized gate name issue + +- Fixed bug for `batch_expectation_ps` for jax backend + +- Partially fix the SVD numerical stability bug on tf backend when using `MPSCircuit` + +- List syntax for gate now supports range + ## 0.9.1 ### Added diff --git a/README.md b/README.md index 0795945e..c46b54c7 100644 --- a/README.md +++ b/README.md @@ -31,13 +31,13 @@ TensorCircuit is the next generation of quantum software framework with support for automatic differentiation, just-in-time compiling, hardware acceleration, and vectorized parallelism. -TensorCircuit is built on top of modern machine learning frameworks and is machine learning backend agnostic. It is specifically suitable for highly efficient simulations of quantum-classical hybrid paradigm and variational quantum algorithms. It also supports real quantum hardware access and provides CPU/GPU/QPU hybrid deployment solutions since v0.9. +TensorCircuit is built on top of modern machine learning frameworks: Jax, TensorFlow, and PyTorch. It is specifically suitable for highly efficient simulations of quantum-classical hybrid paradigm and variational quantum algorithms in ideal, noisy and approximate cases. It also supports real quantum hardware access and provides CPU/GPU/QPU hybrid deployment solutions since v0.9. ## Getting Started -Please begin with [Quick Start](/docs/source/quickstart.rst). +Please begin with [Quick Start](/docs/source/quickstart.rst) in the [full documentation](https://tensorcircuit.readthedocs.io/). -For more information and introductions, please refer to helpful [example scripts](/examples) and [full documentation](https://tensorcircuit.readthedocs.io/). API docstrings and test cases in [tests](/tests) are also informative. +For more information on software usage, sota algorithm implementation and engineer paradigm demonstration, please refer to 70+ [example scripts](/examples) and 30+ [tutorial notebooks](https://tensorcircuit.readthedocs.io/en/latest/#tutorials). API docstrings and test cases in [tests](/tests) are also informative. The following are some minimal demos. @@ -76,6 +76,57 @@ theta = tc.array_to_tensor(1.0) print(g(theta)) ``` +
+ More highlight features for TensorCircuit (click for details) + +- Sparse Hamiltonian generation and expectation evaluation: + +```python +n = 6 +pauli_structures = [] +weights = [] +for i in range(n): + pauli_structures.append(tc.quantum.xyz2ps({"z": [i, (i + 1) % n]}, n=n)) + weights.append(1.0) +for i in range(n): + pauli_structures.append(tc.quantum.xyz2ps({"x": [i]}, n=n)) + weights.append(-1.0) +h = tc.quantum.PauliStringSum2COO(pauli_structures, weights) +print(h) +# BCOO(complex64[64, 64], nse=448) +c = tc.Circuit(n) +c.h(range(n)) +energy = tc.templates.measurements.operator_expectation(c, h) +# -6 +``` + +- Large-scale simulation with tensor network engine + +```python +# tc.set_contractor("cotengra-30-10") +n=500 +c = tc.Circuit(n) +c.h(0) +c.cx(range(n-1), range(1, n)) +c.expectation_ps(z=[0, n-1], reuse=False) +``` + +- Density matrix simulator and quantum info quantities + +```python +c = tc.DMCircuit(2) +c.h(0) +c.cx(0, 1) +c.depolarizing(1, px=0.1, py=0.1, pz=0.1) +dm = c.state() +print(tc.quantum.entropy(dm)) +print(tc.quantum.entanglement_entropy(dm, [0])) +print(tc.quantum.entanglement_negativity(dm, [0])) +print(tc.quantum.log_negativity(dm, [0])) +``` + +
+ ## Install The package is written in pure Python and can be obtained via pip as: @@ -92,13 +143,6 @@ pip install tensorcircuit[tensorflow] Other optional dependencies include `[torch]`, `[jax]`, `[qiskit]` and `[cloud]`. -For the nightly build of tensorcircuit with new features, try: - -```python -pip uninstall tensorcircuit -pip install tensorcircuit-nightly -``` - We also have [Docker support](/docker). ## Advantages @@ -117,24 +161,83 @@ We also have [Docker support](/docker). - Elegance - - Flexibility: customized contraction, multiple ML backend/interface choices, multiple dtype precisions + - Flexibility: customized contraction, multiple ML backend/interface choices, multiple dtype precisions, multiple QPU providers - API design: quantum for humans, less code, more power +- Batteries included + +
+ Tons of amazing features and built in tools for research (click for details) + + - Support **super large circuit simulation** using tensor network engine. + + - Support **noisy simulation** with both Monte Carlo and density matrix (tensor network powered) modes. + + - Support **approximate simulation** with MPS-TEBD modes. + + - Support **analog/digital hybrid simulation** (time dependent Hamiltonian evolution, **pulse** level simulation) with neural ode modes. + + - Support **Fermion Gaussian state** simulation with expectation, entanglement, measurement, ground state, real and imaginary time evolution. + + - Support **qudits simulation**. + + - Support **parallel** quantum circuit evaluation across **multiple GPUs**. + + - Highly customizable **noise model** with gate error and scalable readout error. + + - Support for **non-unitary** gate and post-selection simulation. + + - Support **real quantum devices access** from different providers. + + - **Scalable readout error mitigation** native to both bitstring and expectation level with automatic qubit mapping consideration. + + - **Advanced quantum error mitigation methods** and pipelines such as ZNE, DD, RC, etc. + + - Support **MPS/MPO** as representations for input states, quantum gates and observables to be measured. + + - Support **vectorized parallelism** on circuit inputs, circuit parameters, circuit structures, circuit measurements and these vectorization can be nested. + + - Gradients can be obtained with both **automatic differenation** and parameter shift (vmap accelerated) modes. + + - **Machine learning interface/layer/model** abstraction in both TensorFlow and PyTorch for both numerical simulation and real QPU experiments. + + - Circuit sampling supports both final state sampling and perfect sampling from tensor networks. + + - Light cone reduction support for local expectation calculation. + + - Highly customizable tensor network contraction path finder with opteinsum interface. + + - Observables are supported in measurement, sparse matrix, dense matrix and MPO format. + + - Super fast weighted sum Pauli string Hamiltonian matrix generation. + + - Reusable common circuit/measurement/problem templates and patterns. + + - Jittable classical shadow infrastructures. + + - SOTA quantum algorithm and model implementations. + + - Support hybrid workflows and pipelines with CPU/GPU/QPU hardware from local/cloud/hpc resources using tf/torch/jax/cupy/numpy frameworks all at the same time. + +
+ ## Contributing ### Status -This project is released by [Tencent Quantum Lab](https://quantum.tencent.com/) and is created and maintained by [Shi-Xin Zhang](https://github.com/refraction-ray) with current core authors [Shi-Xin Zhang](https://github.com/refraction-ray) and [Yu-Qin Chen](https://github.com/yutuer21). We also thank [contributions](https://github.com/tencent-quantum-lab/tensorcircuit/graphs/contributors) from the lab and the open source community. +This project is created and maintained by [Shi-Xin Zhang](https://github.com/refraction-ray) with current core authors [Shi-Xin Zhang](https://github.com/refraction-ray) and [Yu-Qin Chen](https://github.com/yutuer21). We also thank [contributions](https://github.com/tencent-quantum-lab/tensorcircuit/graphs/contributors) from the open source community. ### Citation -If this project helps in your research, please cite our software whitepaper published in Quantum: +If this project helps in your research, please cite our software whitepaper to acknowledge the work put into the development of TensorCircuit. -[TensorCircuit: a Quantum Software Framework for the NISQ Era](https://quantum-journal.org/papers/q-2023-02-02-912/) +[TensorCircuit: a Quantum Software Framework for the NISQ Era](https://quantum-journal.org/papers/q-2023-02-02-912/) (published in Quantum) which is also a good introduction to the software. +Research works citing TensorCircuit can be highlighted in [Research and Applications section](https://github.com/tencent-quantum-lab/tensorcircuit#research-and-applications). + ### Guidelines For contribution guidelines and notes, see [CONTRIBUTING](/CONTRIBUTING.md). @@ -179,6 +282,17 @@ TensorCircuit is open source, released under the Apache License, Version 2.0. 隐公观鱼
隐公观鱼
💻 ⚠️ WiuYuan
WiuYuan
💡 + Felix Xu
Felix Xu
✅ 💻 ⚠️ + Hong-Ye Hu
Hong-Ye Hu
📖 + peilin
peilin
✅ 💻 ⚠️ 📖 + Cristian Emiliano Godinez Ramirez
Cristian Emiliano Godinez Ramirez
💻 ⚠️ + + + ztzhu
ztzhu
💻 + Rabqubit
Rabqubit
💡 + Kazuki Tsuoka
Kazuki Tsuoka
💻 ⚠️ 📖 💡 + Gopal Ramesh Dahale
Gopal Ramesh Dahale
💡 + Chanandellar Bong
Chanandellar Bong
💡 @@ -207,7 +321,7 @@ Reference paper: https://arxiv.org/abs/2010.08561 (published in QST). For the application of Variational Quantum-Neural Hybrid Eigensolver, see [applications](/tensorcircuit/applications). -Reference paper: https://arxiv.org/abs/2106.05105 (published in PRL) and https://arxiv.org/abs/2112.10380. +Reference paper: https://arxiv.org/abs/2106.05105 (published in PRL) and https://arxiv.org/abs/2112.10380 (published in AQT). ### VQEX-MBL @@ -221,14 +335,71 @@ For the numerical demosntration of discrete time crystal enabled by Stark many-b Reference paper: https://arxiv.org/abs/2208.02866 (published in PRL). -### EMQAOA-DARBO +### RA-Training -For the numerical simulation and hardware experiments with error mitigation on QAOA, see the [project repo](https://github.com/sherrylixuecheng/EMQAOA-DARBO). +For the numerical simulation of variational quantum algorithm training using random gate activation strategy by us, see the [project repo](https://github.com/ls-iastu/RAtraining). -Reference paper: https://arxiv.org/abs/2303.14877. +Reference paper: https://arxiv.org/abs/2303.08154 (published in PRR as a Letter). ### TenCirChem [TenCirChem](https://github.com/tencent-quantum-lab/TenCirChem) is an efficient and versatile quantum computation package for molecular properties. TenCirChem is based on TensorCircuit and is optimized for chemistry applications. -Reference paper: https://arxiv.org/abs/2303.10825. +Reference paper: https://arxiv.org/abs/2303.10825 (published in JCTC). + +### EMQAOA-DARBO + +For the numerical simulation and hardware experiments with error mitigation on QAOA, see the [project repo](https://github.com/sherrylixuecheng/EMQAOA-DARBO). + +Reference paper: https://arxiv.org/abs/2303.14877 (published in Communications Physics). + +### NN-VQA + +For the setup and simulation code of neural network encoded variational quantum eigensolver, see the [demo](/docs/source/tutorials/nnvqe.ipynb). + +Reference paper: https://arxiv.org/abs/2308.01068 (published in PRApplied). + +### More works + +
+ More research works and code projects using TensorCircuit (click for details) + +- Neural Predictor based Quantum Architecture Search: https://arxiv.org/abs/2103.06524 (published in Machine Learning: Science and Technology). + +- Quantum imaginary-time control for accelerating the ground-state preparation: https://arxiv.org/abs/2112.11782 (published in PRR). + +- Efficient Quantum Simulation of Electron-Phonon Systems by Variational Basis State Encoder: https://arxiv.org/abs/2301.01442 (published in PRR). + +- Variational Quantum Simulations of Finite-Temperature Dynamical Properties via Thermofield Dynamics: https://arxiv.org/abs/2206.05571. + +- Understanding quantum machine learning also requires rethinking generalization: https://arxiv.org/abs/2306.13461 (published in Nature Communications). + +- Decentralized Quantum Federated Learning for Metaverse: Analysis, Design and Implementation: https://arxiv.org/abs/2306.11297. Code: https://github.com/s222416822/BQFL. + +- Non-IID quantum federated learning with one-shot communication complexity: https://arxiv.org/abs/2209.00768 (published in Quantum Machine Intelligence). Code: https://github.com/JasonZHM/quantum-fed-infer. + +- Quantum generative adversarial imitation learning: https://doi.org/10.1088/1367-2630/acc605 (published in New Journal of Physics). + +- GSQAS: Graph Self-supervised Quantum Architecture Search: https://arxiv.org/abs/2303.12381 (published in Physica A: Statistical Mechanics and its Applications). + +- Practical advantage of quantum machine learning in ghost imaging: https://www.nature.com/articles/s42005-023-01290-1 (published in Communications Physics). + +- Zero and Finite Temperature Quantum Simulations Powered by Quantum Magic: https://arxiv.org/abs/2308.11616. + +- Comparison of Quantum Simulators for Variational Quantum Search: A Benchmark Study: https://arxiv.org/abs/2309.05924. + +- Statistical analysis of quantum state learning process in quantum neural networks: https://arxiv.org/abs/2309.14980 (published in NeurIPS). + +- Generative quantum machine learning via denoising diffusion probabilistic models: https://arxiv.org/abs/2310.05866 (published in PRL). + +- Quantum imaginary time evolution and quantum annealing meet topological sector optimization: https://arxiv.org/abs/2310.04291. + +- Google Summer of Code 2023 Projects (QML4HEP): https://github.com/ML4SCI/QMLHEP, https://github.com/Gopal-Dahale/qgnn-hep, https://github.com/salcc/QuantumTransformers. + +- Absence of barren plateaus in finite local-depth circuits with long-range entanglement: https://arxiv.org/abs/2311.01393 (published in PRL). + +- Non-Markovianity benefits quantum dynamics simulation: https://arxiv.org/abs/2311.17622. + +
+ +If you want to highlight your research work or projects here, feel free to add by opening PR. diff --git a/README_cn.md b/README_cn.md index bc49327d..8137eb85 100644 --- a/README_cn.md +++ b/README_cn.md @@ -25,17 +25,17 @@

English | 简体中文

-TensorCircuit 是下一代量子软件框架，支持自动微分、即时编译、硬件加速和向量并行化。 +TensorCircuit 是下一代量子软件框架，完美支持自动微分、即时编译、硬件加速和向量并行化。 -TensorCircuit 建立在现代机器学习框架之上，并且与机器学习后端无关。 它特别适用于量子经典混合范式和变分量子算法的高效模拟。 +TensorCircuit 建立在现代机器学习框架 Jax, TensorFlow, PyTorch 之上，支持机器学习后端无关的统一界面。 其特别适用于理想情况、含噪声情况及可控近似情况下，大规模量子经典混合范式和变分量子算法的高效模拟。 -TensorCircuit 现在支持真实量子硬件连接和实验，并提供优雅的 CPU/GPU/QPU 混合部署方案（v0.9+）。 +TensorCircuit 现在支持真实量子硬件连接和实验，并提供优雅的 CPU/GPU/QPU 混合部署训练方案（v0.9+）。 ## 入门 -请从 [快速上手](/docs/source/quickstart.rst) 和 [Jupyter 教程](/docs/source/tutorials) 开始。 +请从 [完整文档](https://tensorcircuit.readthedocs.io/zh/latest/) 中的 [快速上手](/docs/source/quickstart.rst) 开始。 -有关更多信息和介绍，请参阅有用的 [示例脚本](/examples) 和 [完整文档](https://tensorcircuit.readthedocs.io/zh/latest/)。 [测试](/tests)用例和 API docstring 也提供了丰富的使用信息。 +有关软件用法，算法实现和工程范式演示的更多信息和介绍，请参阅 70+ [示例脚本](/examples) 和 30+ [案例教程](https://tensorcircuit.readthedocs.io/zh/latest/#tutorials)。 [测试](/tests) 用例和 API docstring 也提供了丰富的使用信息。 以下是一些最简易的演示。 @@ -52,7 +52,7 @@ print(c.expectation_ps(z=[0, 1])) print(c.sample(allow_state=True, batch=1024, format="count_dict_bin")) ``` -- 运行时特性定制: +- 运行时特性设置: ```python tc.set_backend("tensorflow") @@ -115,7 +115,7 @@ pip install tensorcircuit-nightly - 优雅 - - 灵活性：自定义张量收缩、多种 ML 后端/接口选择、多种数值精度 + - 灵活性：自定义张量收缩、多种 ML 后端/接口选择、多种数值精度、多种量子硬件 - API 设计：人类可理解的量子，更少的代码，更多的可能 @@ -123,11 +123,11 @@ pip install tensorcircuit-nightly ### 现况 -该项目由[腾讯量子实验室](https://quantum.tencent.com/)发布，由 [Shi-Xin Zhang](https://github.com/refraction-ray) 创造并维护。当前核心作者包括 [Shi-Xin Zhang](https://github.com/refraction-ray) 和 [Yu-Qin Chen](https://github.com/yutuer21)。我们也感谢来自实验室和开源社区的[贡献](https://github.com/tencent-quantum-lab/tensorcircuit/graphs/contributors)。 +该项目由 [Shi-Xin Zhang](https://github.com/refraction-ray) 创造并维护。当前核心作者包括 [Shi-Xin Zhang](https://github.com/refraction-ray) 和 [Yu-Qin Chen](https://github.com/yutuer21)。我们也感谢来自开源社区的[贡献](https://github.com/tencent-quantum-lab/tensorcircuit/graphs/contributors)。 ### 引用 -如果该软件对您的研究有帮助, 请引用我们发表在 Quantum 期刊的白皮书文章: +如果该软件对您的研究有帮助, 请引用我们发表在 Quantum 期刊的白皮书文章来支持我们的研发付出。 [TensorCircuit: a Quantum Software Framework for the NISQ Era](https://quantum-journal.org/papers/q-2023-02-02-912/). @@ -167,14 +167,26 @@ VQEX 在 MBL 相位识别上的应用见 [教程](/docs/source/tutorials/vqex_mb 参考论文: https://arxiv.org/abs/2208.02866 (PRL)。 +### RA-Training + +利用我们提出的随机量子门激活策略训练优化变分量子算法的实现请参考 [项目](https://github.com/ls-iastu/RAtraining). + +参考论文: https://arxiv.org/abs/2303.08154。 + +### TenCirChem + +[TenCirChem](https://github.com/tencent-quantum-lab/TenCirChem) 是高效的，专注于处理和计算分子性质的量子计算软件。其基于 TensorCircuit 并为量子化学任务进行了专门的优化。 + +参考论文: https://arxiv.org/abs/2303.10825 (JCTC)。 + ### EMQAOA-DARBO 数值模拟和带错误消除的真实量子硬件实验验证 QAOA 优化的代码请参考 [项目](https://github.com/sherrylixuecheng/EMQAOA-DARBO)。 参考论文: https://arxiv.org/abs/2303.14877。 -### TenCirChem +### NN-VQA -[TenCirChem](https://github.com/tencent-quantum-lab/TenCirChem) 是高效的，专注于处理和计算分子性质的量子计算软件。其基于 TensorCircuit 并为量子化学任务进行了专门的优化。 +关于神经网络编码的变分量子算法的实现和工作流, 见 [教程](/docs/source/tutorials/nnvqe.ipynb)。 -参考论文: https://arxiv.org/abs/2303.10825。 +参考论文: https://arxiv.org/abs/2308.01068。 diff --git a/check_all.sh b/check_all.sh old mode 100755 new mode 100644 diff --git a/docker/Dockerfile_v2 b/docker/Dockerfile_v2 new file mode 100644 index 00000000..9f2f4523 --- /dev/null +++ b/docker/Dockerfile_v2 @@ -0,0 +1,37 @@ +FROM nvidia/cuda:11.7.1-cudnn8-devel-ubuntu20.04 +# nvidia/cuda:11.6.0-cudnn8-devel-ubuntu20.04 + +RUN apt update && DEBIAN_FRONTEND=noninteractive apt install -y \ + wget \ + git \ + vim \ + pandoc + +RUN wget -q -P /tmp \ + https://repo.anaconda.com/miniconda/Miniconda3-latest-Linux-x86_64.sh \ + && bash /tmp/Miniconda3-latest-Linux-x86_64.sh -b -p /opt/conda \ + && rm /tmp/Miniconda3-latest-Linux-x86_64.sh + +ENV PATH="/opt/conda/bin:$PATH" + +RUN conda install -y \ + pip \ + python=3.10 + +COPY requirements/requirements-docker-v2.txt /requirements-docker-v2.txt + +# RUN pip install -r /requirements-docker-v2.txt -f https://storage.googleapis.com/jax-releases/jax_cuda_releases.html +RUN pip install -i https://pypi.tuna.tsinghua.edu.cn/simple -r /requirements-docker-v2.txt -f https://storage.googleapis.com/jax-releases/jax_cuda_releases.html + +# RUN pip install nvidia-cudnn-cu11==8.6.0.163 ray +RUN pip install -i https://pypi.tuna.tsinghua.edu.cn/simple nvidia-cudnn-cu11==8.6.0.163 ray + +RUN pip install tensorcircuit + +# requirements conflict for ray +# jax must have cudnn>8.6 otherwise fail when init array on gpu, +# while torch insists cudnn 8.5 in setup but 8.6 can also work for torch + +RUN echo export TF_CPP_MIN_LOG_LEVEL=3 >> ~/.bashrc + +CMD ["/bin/bash"] \ No newline at end of file diff --git a/docker/README.md b/docker/README.md index c9940635..1c5aea0d 100644 --- a/docker/README.md +++ b/docker/README.md @@ -4,6 +4,12 @@ Run the following command to build the docker for tensorcircuit at parent path: sudo docker build . -f docker/Dockerfile -t tensorcircuit ``` +Since v0.10 we introduce new docker env based on ubuntu20.04+cuda11.7+py3.10 (+ pip installed tensorcircuit package), build the new docker use + +```bash +sudo docker build . -f docker/Dockerfile_v2 -t tensorcircuit +``` + One can also pull the [official image](https://hub.docker.com/repository/docker/tensorcircuit/tensorcircuit) from DockerHub as ```bash @@ -15,14 +21,9 @@ Run the docker container by the following command: ```bash sudo docker run -it --network host --gpus all tensorcircuit -# if one also wants to mount local source code, also add args `-v "$(pwd)":/app` - -# using tensorcircuit/tensorcircuit to run the prebuild docker image from dockerhub +# if one also wants to mount local source code, also add args `-v "$(pwd)":/root` -# for old dockerfile with no runtime env setting -# sudo docker run -it --network host -e LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/usr/local/cuda-11.0/targets/x86_64-linux/lib -e PYTHONPATH=/app -v "$(pwd)":/app --gpus all tensorcircuit +# using tensorcircuit/tensorcircuit:latest to run the prebuild docker image from dockerhub ``` -`export TF_CPP_MIN_LOG_LEVEL=3` maybe necessary since jax suprisingly frequently complain about ptxas version problem. And `export CUDA_VISIBLE_DEVICES=-1` if you want to test only on CPU. - -The built docker has no tensorcircuit pip package installed but left with a tensorcircuit source code dir. So one can `python setup.py develop` to install tensorcircuit locally (one can also mount the tensorcircuit codebase on host) or `pip install tensorcircuit` within the running docker. +`export CUDA_VISIBLE_DEVICES=-1` if you want to test only on CPU. diff --git a/docs/source/api/about.rst b/docs/source/api/about.rst index 8f7bbf76..e065f1eb 100644 --- a/docs/source/api/about.rst +++ b/docs/source/api/about.rst @@ -1,5 +1,5 @@ tensorcircuit.about -================================================== +================================================================================ .. automodule:: tensorcircuit.about :members: :undoc-members: diff --git a/docs/source/api/abstractcircuit.rst b/docs/source/api/abstractcircuit.rst index 2caf0af1..3d67a499 100644 --- a/docs/source/api/abstractcircuit.rst +++ b/docs/source/api/abstractcircuit.rst @@ -1,5 +1,5 @@ tensorcircuit.abstractcircuit -================================================== +================================================================================ .. automodule:: tensorcircuit.abstractcircuit :members: :undoc-members: diff --git a/docs/source/api/applications.rst b/docs/source/api/applications.rst index ad329ccf..85c31126 100644 --- a/docs/source/api/applications.rst +++ b/docs/source/api/applications.rst @@ -1,9 +1,13 @@ tensorcircuit.applications -================================================== +================================================================================ .. toctree:: + applications/ai.rst applications/dqas.rst + applications/finance.rst applications/graphdata.rst applications/layers.rst + applications/optimization.rst + applications/physics.rst applications/utils.rst applications/vags.rst applications/van.rst diff --git a/docs/source/api/applications/ai.rst b/docs/source/api/applications/ai.rst new file mode 100644 index 00000000..96a22cdb --- /dev/null +++ b/docs/source/api/applications/ai.rst @@ -0,0 +1,4 @@ +tensorcircuit.applications.ai +================================================================================ +.. toctree:: + ai/ensemble.rst \ No newline at end of file diff --git a/docs/source/api/applications/ai/ensemble.rst b/docs/source/api/applications/ai/ensemble.rst new file mode 100644 index 00000000..0173ac00 --- /dev/null +++ b/docs/source/api/applications/ai/ensemble.rst @@ -0,0 +1,7 @@ +tensorcircuit.applications.ai.ensemble +================================================================================ +.. automodule:: tensorcircuit.applications.ai.ensemble + :members: + :undoc-members: + :show-inheritance: + :inherited-members: \ No newline at end of file diff --git a/docs/source/api/applications/dqas.rst b/docs/source/api/applications/dqas.rst index 32457e1f..73cacd43 100644 --- a/docs/source/api/applications/dqas.rst +++ b/docs/source/api/applications/dqas.rst @@ -1,5 +1,5 @@ tensorcircuit.applications.dqas -================================================== +================================================================================ .. automodule:: tensorcircuit.applications.dqas :members: :undoc-members: diff --git a/docs/source/api/applications/finance.rst b/docs/source/api/applications/finance.rst new file mode 100644 index 00000000..d3302b31 --- /dev/null +++ b/docs/source/api/applications/finance.rst @@ -0,0 +1,4 @@ +tensorcircuit.applications.finance +================================================================================ +.. toctree:: + finance/portfolio.rst \ No newline at end of file diff --git a/docs/source/api/applications/finance/portfolio.rst b/docs/source/api/applications/finance/portfolio.rst new file mode 100644 index 00000000..993b5754 --- /dev/null +++ b/docs/source/api/applications/finance/portfolio.rst @@ -0,0 +1,7 @@ +tensorcircuit.applications.finance.portfolio +================================================================================ +.. automodule:: tensorcircuit.applications.finance.portfolio + :members: + :undoc-members: + :show-inheritance: + :inherited-members: \ No newline at end of file diff --git a/docs/source/api/applications/graphdata.rst b/docs/source/api/applications/graphdata.rst index 22e1af13..44851513 100644 --- a/docs/source/api/applications/graphdata.rst +++ b/docs/source/api/applications/graphdata.rst @@ -1,5 +1,5 @@ tensorcircuit.applications.graphdata -================================================== +================================================================================ .. automodule:: tensorcircuit.applications.graphdata :members: :undoc-members: diff --git a/docs/source/api/applications/layers.rst b/docs/source/api/applications/layers.rst index 69303e98..d4f49e81 100644 --- a/docs/source/api/applications/layers.rst +++ b/docs/source/api/applications/layers.rst @@ -1,5 +1,5 @@ tensorcircuit.applications.layers -================================================== +================================================================================ .. automodule:: tensorcircuit.applications.layers :members: :undoc-members: diff --git a/docs/source/api/applications/optimization.rst b/docs/source/api/applications/optimization.rst new file mode 100644 index 00000000..87a0ffbb --- /dev/null +++ b/docs/source/api/applications/optimization.rst @@ -0,0 +1,7 @@ +tensorcircuit.applications.optimization +================================================================================ +.. automodule:: tensorcircuit.applications.optimization + :members: + :undoc-members: + :show-inheritance: + :inherited-members: \ No newline at end of file diff --git a/docs/source/api/applications/physics.rst b/docs/source/api/applications/physics.rst new file mode 100644 index 00000000..98d1a2ed --- /dev/null +++ b/docs/source/api/applications/physics.rst @@ -0,0 +1,5 @@ +tensorcircuit.applications.physics +================================================================================ +.. toctree:: + physics/baseline.rst + physics/fss.rst \ No newline at end of file diff --git a/docs/source/api/applications/physics/baseline.rst b/docs/source/api/applications/physics/baseline.rst new file mode 100644 index 00000000..2ac581ba --- /dev/null +++ b/docs/source/api/applications/physics/baseline.rst @@ -0,0 +1,7 @@ +tensorcircuit.applications.physics.baseline +================================================================================ +.. automodule:: tensorcircuit.applications.physics.baseline + :members: + :undoc-members: + :show-inheritance: + :inherited-members: \ No newline at end of file diff --git a/docs/source/api/applications/physics/fss.rst b/docs/source/api/applications/physics/fss.rst new file mode 100644 index 00000000..d65cd6c1 --- /dev/null +++ b/docs/source/api/applications/physics/fss.rst @@ -0,0 +1,7 @@ +tensorcircuit.applications.physics.fss +================================================================================ +.. automodule:: tensorcircuit.applications.physics.fss + :members: + :undoc-members: + :show-inheritance: + :inherited-members: \ No newline at end of file diff --git a/docs/source/api/applications/utils.rst b/docs/source/api/applications/utils.rst index d4549700..4114e7d8 100644 --- a/docs/source/api/applications/utils.rst +++ b/docs/source/api/applications/utils.rst @@ -1,5 +1,5 @@ tensorcircuit.applications.utils -================================================== +================================================================================ .. automodule:: tensorcircuit.applications.utils :members: :undoc-members: diff --git a/docs/source/api/applications/vags.rst b/docs/source/api/applications/vags.rst index 5b951bd3..af0f451f 100644 --- a/docs/source/api/applications/vags.rst +++ b/docs/source/api/applications/vags.rst @@ -1,5 +1,5 @@ tensorcircuit.applications.vags -================================================== +================================================================================ .. automodule:: tensorcircuit.applications.vags :members: :undoc-members: diff --git a/docs/source/api/applications/van.rst b/docs/source/api/applications/van.rst index 463e44d2..5c90f2e5 100644 --- a/docs/source/api/applications/van.rst +++ b/docs/source/api/applications/van.rst @@ -1,5 +1,5 @@ tensorcircuit.applications.van -================================================== +================================================================================ .. automodule:: tensorcircuit.applications.van :members: :undoc-members: diff --git a/docs/source/api/applications/vqes.rst b/docs/source/api/applications/vqes.rst index e3c775e5..d868c634 100644 --- a/docs/source/api/applications/vqes.rst +++ b/docs/source/api/applications/vqes.rst @@ -1,5 +1,5 @@ tensorcircuit.applications.vqes -================================================== +================================================================================ .. automodule:: tensorcircuit.applications.vqes :members: :undoc-members: diff --git a/docs/source/api/backends.rst b/docs/source/api/backends.rst index 4504e569..cfc63bec 100644 --- a/docs/source/api/backends.rst +++ b/docs/source/api/backends.rst @@ -1,5 +1,5 @@ tensorcircuit.backends -================================================== +================================================================================ .. toctree:: backends/backend_factory.rst backends/cupy_backend.rst diff --git a/docs/source/api/backends/backend_factory.rst b/docs/source/api/backends/backend_factory.rst index 8864abfe..6df6374e 100644 --- a/docs/source/api/backends/backend_factory.rst +++ b/docs/source/api/backends/backend_factory.rst @@ -1,5 +1,5 @@ tensorcircuit.backends.backend_factory -================================================== +================================================================================ .. automodule:: tensorcircuit.backends.backend_factory :members: :undoc-members: diff --git a/docs/source/api/backends/cupy_backend.rst b/docs/source/api/backends/cupy_backend.rst index 743fe8f3..1e2421eb 100644 --- a/docs/source/api/backends/cupy_backend.rst +++ b/docs/source/api/backends/cupy_backend.rst @@ -1,5 +1,5 @@ tensorcircuit.backends.cupy_backend -================================================== +================================================================================ .. automodule:: tensorcircuit.backends.cupy_backend :members: :undoc-members: diff --git a/docs/source/api/backends/jax_backend.rst b/docs/source/api/backends/jax_backend.rst index e0dfe7c3..209409bc 100644 --- a/docs/source/api/backends/jax_backend.rst +++ b/docs/source/api/backends/jax_backend.rst @@ -1,5 +1,5 @@ tensorcircuit.backends.jax_backend -================================================== +================================================================================ .. automodule:: tensorcircuit.backends.jax_backend :members: :undoc-members: diff --git a/docs/source/api/backends/numpy_backend.rst b/docs/source/api/backends/numpy_backend.rst index af19d26b..735f969f 100644 --- a/docs/source/api/backends/numpy_backend.rst +++ b/docs/source/api/backends/numpy_backend.rst @@ -1,5 +1,5 @@ tensorcircuit.backends.numpy_backend -================================================== +================================================================================ .. automodule:: tensorcircuit.backends.numpy_backend :members: :undoc-members: diff --git a/docs/source/api/backends/pytorch_backend.rst b/docs/source/api/backends/pytorch_backend.rst index df2712c6..0d10f664 100644 --- a/docs/source/api/backends/pytorch_backend.rst +++ b/docs/source/api/backends/pytorch_backend.rst @@ -1,5 +1,5 @@ tensorcircuit.backends.pytorch_backend -================================================== +================================================================================ .. automodule:: tensorcircuit.backends.pytorch_backend :members: :undoc-members: diff --git a/docs/source/api/backends/tensorflow_backend.rst b/docs/source/api/backends/tensorflow_backend.rst index 52663b1a..a595418e 100644 --- a/docs/source/api/backends/tensorflow_backend.rst +++ b/docs/source/api/backends/tensorflow_backend.rst @@ -1,5 +1,5 @@ tensorcircuit.backends.tensorflow_backend -================================================== +================================================================================ .. automodule:: tensorcircuit.backends.tensorflow_backend :members: :undoc-members: diff --git a/docs/source/api/basecircuit.rst b/docs/source/api/basecircuit.rst index 6b014bb1..79c2636e 100644 --- a/docs/source/api/basecircuit.rst +++ b/docs/source/api/basecircuit.rst @@ -1,5 +1,5 @@ tensorcircuit.basecircuit -================================================== +================================================================================ .. automodule:: tensorcircuit.basecircuit :members: :undoc-members: diff --git a/docs/source/api/channels.rst b/docs/source/api/channels.rst index 3a7cf3af..d9d6fd00 100644 --- a/docs/source/api/channels.rst +++ b/docs/source/api/channels.rst @@ -1,5 +1,5 @@ tensorcircuit.channels -================================================== +================================================================================ .. automodule:: tensorcircuit.channels :members: :undoc-members: diff --git a/docs/source/api/circuit.rst b/docs/source/api/circuit.rst index 910c5ef6..59c76ddd 100644 --- a/docs/source/api/circuit.rst +++ b/docs/source/api/circuit.rst @@ -1,5 +1,5 @@ tensorcircuit.circuit -================================================== +================================================================================ .. automodule:: tensorcircuit.circuit :members: :undoc-members: diff --git a/docs/source/api/cloud.rst b/docs/source/api/cloud.rst index 65b9c714..be2faf7d 100644 --- a/docs/source/api/cloud.rst +++ b/docs/source/api/cloud.rst @@ -1,5 +1,5 @@ tensorcircuit.cloud -================================================== +================================================================================ .. toctree:: cloud/abstraction.rst cloud/apis.rst diff --git a/docs/source/api/cloud/abstraction.rst b/docs/source/api/cloud/abstraction.rst index b0a50812..3f00247c 100644 --- a/docs/source/api/cloud/abstraction.rst +++ b/docs/source/api/cloud/abstraction.rst @@ -1,5 +1,5 @@ tensorcircuit.cloud.abstraction -================================================== +================================================================================ .. automodule:: tensorcircuit.cloud.abstraction :members: :undoc-members: diff --git a/docs/source/api/cloud/apis.rst b/docs/source/api/cloud/apis.rst index 648baa66..fe623eec 100644 --- a/docs/source/api/cloud/apis.rst +++ b/docs/source/api/cloud/apis.rst @@ -1,5 +1,5 @@ tensorcircuit.cloud.apis -================================================== +================================================================================ .. automodule:: tensorcircuit.cloud.apis :members: :undoc-members: diff --git a/docs/source/api/cloud/config.rst b/docs/source/api/cloud/config.rst index a4338784..8f6282a0 100644 --- a/docs/source/api/cloud/config.rst +++ b/docs/source/api/cloud/config.rst @@ -1,5 +1,5 @@ tensorcircuit.cloud.config -================================================== +================================================================================ .. automodule:: tensorcircuit.cloud.config :members: :undoc-members: diff --git a/docs/source/api/cloud/local.rst b/docs/source/api/cloud/local.rst index c3ae767d..649f66d6 100644 --- a/docs/source/api/cloud/local.rst +++ b/docs/source/api/cloud/local.rst @@ -1,5 +1,5 @@ tensorcircuit.cloud.local -================================================== +================================================================================ .. automodule:: tensorcircuit.cloud.local :members: :undoc-members: diff --git a/docs/source/api/cloud/quafu_provider.rst b/docs/source/api/cloud/quafu_provider.rst index eae158af..06d15eee 100644 --- a/docs/source/api/cloud/quafu_provider.rst +++ b/docs/source/api/cloud/quafu_provider.rst @@ -1,5 +1,5 @@ tensorcircuit.cloud.quafu_provider -================================================== +================================================================================ .. automodule:: tensorcircuit.cloud.quafu_provider :members: :undoc-members: diff --git a/docs/source/api/cloud/tencent.rst b/docs/source/api/cloud/tencent.rst index b38a7183..431c3294 100644 --- a/docs/source/api/cloud/tencent.rst +++ b/docs/source/api/cloud/tencent.rst @@ -1,5 +1,5 @@ tensorcircuit.cloud.tencent -================================================== +================================================================================ .. automodule:: tensorcircuit.cloud.tencent :members: :undoc-members: diff --git a/docs/source/api/cloud/utils.rst b/docs/source/api/cloud/utils.rst index 190ea5a4..a7e33fe4 100644 --- a/docs/source/api/cloud/utils.rst +++ b/docs/source/api/cloud/utils.rst @@ -1,5 +1,5 @@ tensorcircuit.cloud.utils -================================================== +================================================================================ .. automodule:: tensorcircuit.cloud.utils :members: :undoc-members: diff --git a/docs/source/api/cloud/wrapper.rst b/docs/source/api/cloud/wrapper.rst index bac6a502..d65d3c07 100644 --- a/docs/source/api/cloud/wrapper.rst +++ b/docs/source/api/cloud/wrapper.rst @@ -1,5 +1,5 @@ tensorcircuit.cloud.wrapper -================================================== +================================================================================ .. automodule:: tensorcircuit.cloud.wrapper :members: :undoc-members: diff --git a/docs/source/api/compiler.rst b/docs/source/api/compiler.rst index c83bc2bd..cb47419f 100644 --- a/docs/source/api/compiler.rst +++ b/docs/source/api/compiler.rst @@ -1,5 +1,5 @@ tensorcircuit.compiler -================================================== +================================================================================ .. toctree:: compiler/composed_compiler.rst compiler/qiskit_compiler.rst diff --git a/docs/source/api/compiler/composed_compiler.rst b/docs/source/api/compiler/composed_compiler.rst index c856636d..07f7f23e 100644 --- a/docs/source/api/compiler/composed_compiler.rst +++ b/docs/source/api/compiler/composed_compiler.rst @@ -1,5 +1,5 @@ tensorcircuit.compiler.composed_compiler -================================================== +================================================================================ .. automodule:: tensorcircuit.compiler.composed_compiler :members: :undoc-members: diff --git a/docs/source/api/compiler/qiskit_compiler.rst b/docs/source/api/compiler/qiskit_compiler.rst index 369b4740..b46ae8dc 100644 --- a/docs/source/api/compiler/qiskit_compiler.rst +++ b/docs/source/api/compiler/qiskit_compiler.rst @@ -1,5 +1,5 @@ tensorcircuit.compiler.qiskit_compiler -================================================== +================================================================================ .. automodule:: tensorcircuit.compiler.qiskit_compiler :members: :undoc-members: diff --git a/docs/source/api/compiler/simple_compiler.rst b/docs/source/api/compiler/simple_compiler.rst index 0578d8e5..941efba5 100644 --- a/docs/source/api/compiler/simple_compiler.rst +++ b/docs/source/api/compiler/simple_compiler.rst @@ -1,5 +1,5 @@ tensorcircuit.compiler.simple_compiler -================================================== +================================================================================ .. automodule:: tensorcircuit.compiler.simple_compiler :members: :undoc-members: diff --git a/docs/source/api/cons.rst b/docs/source/api/cons.rst index 6e077058..d4f48ab6 100644 --- a/docs/source/api/cons.rst +++ b/docs/source/api/cons.rst @@ -1,5 +1,5 @@ tensorcircuit.cons -================================================== +================================================================================ .. automodule:: tensorcircuit.cons :members: :undoc-members: diff --git a/docs/source/api/densitymatrix.rst b/docs/source/api/densitymatrix.rst index 571647d2..274dc323 100644 --- a/docs/source/api/densitymatrix.rst +++ b/docs/source/api/densitymatrix.rst @@ -1,5 +1,5 @@ tensorcircuit.densitymatrix -================================================== +================================================================================ .. automodule:: tensorcircuit.densitymatrix :members: :undoc-members: diff --git a/docs/source/api/experimental.rst b/docs/source/api/experimental.rst index 16761d4c..dbdfa068 100644 --- a/docs/source/api/experimental.rst +++ b/docs/source/api/experimental.rst @@ -1,5 +1,5 @@ tensorcircuit.experimental -================================================== +================================================================================ .. automodule:: tensorcircuit.experimental :members: :undoc-members: diff --git a/docs/source/api/fgs.rst b/docs/source/api/fgs.rst new file mode 100644 index 00000000..f00001b4 --- /dev/null +++ b/docs/source/api/fgs.rst @@ -0,0 +1,7 @@ +tensorcircuit.fgs +================================================================================ +.. automodule:: tensorcircuit.fgs + :members: + :undoc-members: + :show-inheritance: + :inherited-members: \ No newline at end of file diff --git a/docs/source/api/gates.rst b/docs/source/api/gates.rst index 8f72fbcc..71428553 100644 --- a/docs/source/api/gates.rst +++ b/docs/source/api/gates.rst @@ -1,5 +1,5 @@ tensorcircuit.gates -================================================== +================================================================================ .. automodule:: tensorcircuit.gates :members: :undoc-members: diff --git a/docs/source/api/interfaces.rst b/docs/source/api/interfaces.rst index 6371d824..5b234d0f 100644 --- a/docs/source/api/interfaces.rst +++ b/docs/source/api/interfaces.rst @@ -1,5 +1,5 @@ tensorcircuit.interfaces -================================================== +================================================================================ .. toctree:: interfaces/numpy.rst interfaces/scipy.rst diff --git a/docs/source/api/interfaces/numpy.rst b/docs/source/api/interfaces/numpy.rst index 5df8b0bb..5271b873 100644 --- a/docs/source/api/interfaces/numpy.rst +++ b/docs/source/api/interfaces/numpy.rst @@ -1,5 +1,5 @@ tensorcircuit.interfaces.numpy -================================================== +================================================================================ .. automodule:: tensorcircuit.interfaces.numpy :members: :undoc-members: diff --git a/docs/source/api/interfaces/scipy.rst b/docs/source/api/interfaces/scipy.rst index c263bd93..284dcbe9 100644 --- a/docs/source/api/interfaces/scipy.rst +++ b/docs/source/api/interfaces/scipy.rst @@ -1,5 +1,5 @@ tensorcircuit.interfaces.scipy -================================================== +================================================================================ .. automodule:: tensorcircuit.interfaces.scipy :members: :undoc-members: diff --git a/docs/source/api/interfaces/tensorflow.rst b/docs/source/api/interfaces/tensorflow.rst index e02981b9..8ac1a344 100644 --- a/docs/source/api/interfaces/tensorflow.rst +++ b/docs/source/api/interfaces/tensorflow.rst @@ -1,5 +1,5 @@ tensorcircuit.interfaces.tensorflow -================================================== +================================================================================ .. automodule:: tensorcircuit.interfaces.tensorflow :members: :undoc-members: diff --git a/docs/source/api/interfaces/tensortrans.rst b/docs/source/api/interfaces/tensortrans.rst index b666e177..a92b166d 100644 --- a/docs/source/api/interfaces/tensortrans.rst +++ b/docs/source/api/interfaces/tensortrans.rst @@ -1,5 +1,5 @@ tensorcircuit.interfaces.tensortrans -================================================== +================================================================================ .. automodule:: tensorcircuit.interfaces.tensortrans :members: :undoc-members: diff --git a/docs/source/api/interfaces/torch.rst b/docs/source/api/interfaces/torch.rst index 28090f54..5f7e3dea 100644 --- a/docs/source/api/interfaces/torch.rst +++ b/docs/source/api/interfaces/torch.rst @@ -1,5 +1,5 @@ tensorcircuit.interfaces.torch -================================================== +================================================================================ .. automodule:: tensorcircuit.interfaces.torch :members: :undoc-members: diff --git a/docs/source/api/keras.rst b/docs/source/api/keras.rst index 5ed313b2..9f2e4860 100644 --- a/docs/source/api/keras.rst +++ b/docs/source/api/keras.rst @@ -1,5 +1,5 @@ tensorcircuit.keras -================================================== +================================================================================ .. automodule:: tensorcircuit.keras :members: :undoc-members: diff --git a/docs/source/api/mps_base.rst b/docs/source/api/mps_base.rst index caf11b36..039da259 100644 --- a/docs/source/api/mps_base.rst +++ b/docs/source/api/mps_base.rst @@ -1,5 +1,5 @@ tensorcircuit.mps_base -================================================== +================================================================================ .. automodule:: tensorcircuit.mps_base :members: :undoc-members: diff --git a/docs/source/api/mpscircuit.rst b/docs/source/api/mpscircuit.rst index a4de8119..58a68f56 100644 --- a/docs/source/api/mpscircuit.rst +++ b/docs/source/api/mpscircuit.rst @@ -1,5 +1,5 @@ tensorcircuit.mpscircuit -================================================== +================================================================================ .. automodule:: tensorcircuit.mpscircuit :members: :undoc-members: diff --git a/docs/source/api/noisemodel.rst b/docs/source/api/noisemodel.rst index ab152857..4930d8f0 100644 --- a/docs/source/api/noisemodel.rst +++ b/docs/source/api/noisemodel.rst @@ -1,5 +1,5 @@ tensorcircuit.noisemodel -================================================== +================================================================================ .. automodule:: tensorcircuit.noisemodel :members: :undoc-members: diff --git a/docs/source/api/quantum.rst b/docs/source/api/quantum.rst index c9d13b6b..f25c8a5d 100644 --- a/docs/source/api/quantum.rst +++ b/docs/source/api/quantum.rst @@ -1,5 +1,5 @@ tensorcircuit.quantum -================================================== +================================================================================ .. automodule:: tensorcircuit.quantum :members: :undoc-members: diff --git a/docs/source/api/results.rst b/docs/source/api/results.rst index 0bea95e7..2e60327c 100644 --- a/docs/source/api/results.rst +++ b/docs/source/api/results.rst @@ -1,5 +1,6 @@ tensorcircuit.results -================================================== +================================================================================ .. toctree:: results/counts.rst + results/qem.rst results/readout_mitigation.rst \ No newline at end of file diff --git a/docs/source/api/results/counts.rst b/docs/source/api/results/counts.rst index 7542d722..7f145206 100644 --- a/docs/source/api/results/counts.rst +++ b/docs/source/api/results/counts.rst @@ -1,5 +1,5 @@ tensorcircuit.results.counts -================================================== +================================================================================ .. automodule:: tensorcircuit.results.counts :members: :undoc-members: diff --git a/docs/source/api/results/qem.rst b/docs/source/api/results/qem.rst new file mode 100644 index 00000000..160098f7 --- /dev/null +++ b/docs/source/api/results/qem.rst @@ -0,0 +1,5 @@ +tensorcircuit.results.qem +================================================================================ +.. toctree:: + qem/benchmark_circuits.rst + qem/qem_methods.rst \ No newline at end of file diff --git a/docs/source/api/results/qem/benchmark_circuits.rst b/docs/source/api/results/qem/benchmark_circuits.rst new file mode 100644 index 00000000..3c339884 --- /dev/null +++ b/docs/source/api/results/qem/benchmark_circuits.rst @@ -0,0 +1,7 @@ +tensorcircuit.results.qem.benchmark_circuits +================================================================================ +.. automodule:: tensorcircuit.results.qem.benchmark_circuits + :members: + :undoc-members: + :show-inheritance: + :inherited-members: \ No newline at end of file diff --git a/docs/source/api/results/qem/qem_methods.rst b/docs/source/api/results/qem/qem_methods.rst new file mode 100644 index 00000000..a95bdf95 --- /dev/null +++ b/docs/source/api/results/qem/qem_methods.rst @@ -0,0 +1,7 @@ +tensorcircuit.results.qem.qem_methods +================================================================================ +.. automodule:: tensorcircuit.results.qem.qem_methods + :members: + :undoc-members: + :show-inheritance: + :inherited-members: \ No newline at end of file diff --git a/docs/source/api/results/readout_mitigation.rst b/docs/source/api/results/readout_mitigation.rst index 0d9baa3d..325fe21a 100644 --- a/docs/source/api/results/readout_mitigation.rst +++ b/docs/source/api/results/readout_mitigation.rst @@ -1,5 +1,5 @@ tensorcircuit.results.readout_mitigation -================================================== +================================================================================ .. automodule:: tensorcircuit.results.readout_mitigation :members: :undoc-members: diff --git a/docs/source/api/shadows.rst b/docs/source/api/shadows.rst new file mode 100644 index 00000000..7aea082e --- /dev/null +++ b/docs/source/api/shadows.rst @@ -0,0 +1,7 @@ +tensorcircuit.shadows +================================================================================ +.. automodule:: tensorcircuit.shadows + :members: + :undoc-members: + :show-inheritance: + :inherited-members: \ No newline at end of file diff --git a/docs/source/api/simplify.rst b/docs/source/api/simplify.rst index c1816c31..22833f9f 100644 --- a/docs/source/api/simplify.rst +++ b/docs/source/api/simplify.rst @@ -1,5 +1,5 @@ tensorcircuit.simplify -================================================== +================================================================================ .. automodule:: tensorcircuit.simplify :members: :undoc-members: diff --git a/docs/source/api/templates.rst b/docs/source/api/templates.rst index 330fa6db..202b049d 100644 --- a/docs/source/api/templates.rst +++ b/docs/source/api/templates.rst @@ -1,9 +1,10 @@ tensorcircuit.templates -================================================== +================================================================================ .. toctree:: + templates/ansatz.rst templates/blocks.rst templates/chems.rst + templates/conversions.rst templates/dataset.rst - templates/ensemble.rst templates/graphs.rst templates/measurements.rst \ No newline at end of file diff --git a/docs/source/api/templates/ansatz.rst b/docs/source/api/templates/ansatz.rst new file mode 100644 index 00000000..15f19650 --- /dev/null +++ b/docs/source/api/templates/ansatz.rst @@ -0,0 +1,7 @@ +tensorcircuit.templates.ansatz +================================================================================ +.. automodule:: tensorcircuit.templates.ansatz + :members: + :undoc-members: + :show-inheritance: + :inherited-members: \ No newline at end of file diff --git a/docs/source/api/templates/blocks.rst b/docs/source/api/templates/blocks.rst index 0c88f3d9..b7a0945a 100644 --- a/docs/source/api/templates/blocks.rst +++ b/docs/source/api/templates/blocks.rst @@ -1,5 +1,5 @@ tensorcircuit.templates.blocks -================================================== +================================================================================ .. automodule:: tensorcircuit.templates.blocks :members: :undoc-members: diff --git a/docs/source/api/templates/chems.rst b/docs/source/api/templates/chems.rst index 8a31f9d3..d06d9e39 100644 --- a/docs/source/api/templates/chems.rst +++ b/docs/source/api/templates/chems.rst @@ -1,5 +1,5 @@ tensorcircuit.templates.chems -================================================== +================================================================================ .. automodule:: tensorcircuit.templates.chems :members: :undoc-members: diff --git a/docs/source/api/templates/conversions.rst b/docs/source/api/templates/conversions.rst new file mode 100644 index 00000000..38cbe47f --- /dev/null +++ b/docs/source/api/templates/conversions.rst @@ -0,0 +1,7 @@ +tensorcircuit.templates.conversions +================================================================================ +.. automodule:: tensorcircuit.templates.conversions + :members: + :undoc-members: + :show-inheritance: + :inherited-members: \ No newline at end of file diff --git a/docs/source/api/templates/dataset.rst b/docs/source/api/templates/dataset.rst index 36b9e510..aa6cdfa7 100644 --- a/docs/source/api/templates/dataset.rst +++ b/docs/source/api/templates/dataset.rst @@ -1,5 +1,5 @@ tensorcircuit.templates.dataset -================================================== +================================================================================ .. automodule:: tensorcircuit.templates.dataset :members: :undoc-members: diff --git a/docs/source/api/templates/ensemble.rst b/docs/source/api/templates/ensemble.rst deleted file mode 100644 index c7dd6f85..00000000 --- a/docs/source/api/templates/ensemble.rst +++ /dev/null @@ -1,7 +0,0 @@ -tensorcircuit.templates.ensemble -================================================== -.. automodule:: tensorcircuit.templates.ensemble - :members: - :undoc-members: - :show-inheritance: - :inherited-members: \ No newline at end of file diff --git a/docs/source/api/templates/graphs.rst b/docs/source/api/templates/graphs.rst index 0a2141f0..b86ab51e 100644 --- a/docs/source/api/templates/graphs.rst +++ b/docs/source/api/templates/graphs.rst @@ -1,5 +1,5 @@ tensorcircuit.templates.graphs -================================================== +================================================================================ .. automodule:: tensorcircuit.templates.graphs :members: :undoc-members: diff --git a/docs/source/api/templates/measurements.rst b/docs/source/api/templates/measurements.rst index 2113f03b..7e05673c 100644 --- a/docs/source/api/templates/measurements.rst +++ b/docs/source/api/templates/measurements.rst @@ -1,5 +1,5 @@ tensorcircuit.templates.measurements -================================================== +================================================================================ .. automodule:: tensorcircuit.templates.measurements :members: :undoc-members: diff --git a/docs/source/api/torchnn.rst b/docs/source/api/torchnn.rst index 5a5b2775..9f9c6598 100644 --- a/docs/source/api/torchnn.rst +++ b/docs/source/api/torchnn.rst @@ -1,5 +1,5 @@ tensorcircuit.torchnn -================================================== +================================================================================ .. automodule:: tensorcircuit.torchnn :members: :undoc-members: diff --git a/docs/source/api/translation.rst b/docs/source/api/translation.rst index a33667f7..f320c909 100644 --- a/docs/source/api/translation.rst +++ b/docs/source/api/translation.rst @@ -1,5 +1,5 @@ tensorcircuit.translation -================================================== +================================================================================ .. automodule:: tensorcircuit.translation :members: :undoc-members: diff --git a/docs/source/api/utils.rst b/docs/source/api/utils.rst index 3fa45319..93ee9496 100644 --- a/docs/source/api/utils.rst +++ b/docs/source/api/utils.rst @@ -1,5 +1,5 @@ tensorcircuit.utils -================================================== +================================================================================ .. automodule:: tensorcircuit.utils :members: :undoc-members: diff --git a/docs/source/api/vis.rst b/docs/source/api/vis.rst index f27680f1..2cdc89e2 100644 --- a/docs/source/api/vis.rst +++ b/docs/source/api/vis.rst @@ -1,5 +1,5 @@ tensorcircuit.vis -================================================== +================================================================================ .. automodule:: tensorcircuit.vis :members: :undoc-members: diff --git a/docs/source/cnconf.py b/docs/source/cnconf.py index 8b01d026..ceecf794 100644 --- a/docs/source/cnconf.py +++ b/docs/source/cnconf.py @@ -48,7 +48,9 @@ "sphinx_copybutton", "nbsphinx", "toctree_filter", + "sphinx.ext.napoleon", "myst_parser", + "sphinx_design", ] autosectionlabel_prefix_document = True diff --git a/docs/source/conf.py b/docs/source/conf.py index 181dda0e..9d8147d9 100644 --- a/docs/source/conf.py +++ b/docs/source/conf.py @@ -50,6 +50,7 @@ "toctree_filter", "sphinx.ext.napoleon", "myst_parser", + "sphinx_design", ] nbsphinx_allow_errors = True diff --git a/docs/source/contribs/development_Mac.md b/docs/source/contribs/development_Mac.md new file mode 100644 index 00000000..b2682f32 --- /dev/null +++ b/docs/source/contribs/development_Mac.md @@ -0,0 +1,113 @@ +# Tensorcircuit Installation Guide on MacOS + +Contributed by [_Mark (Zixuan) Song_](https://marksong.tech) + +Apple has updated Tensorflow (for MacOS) so that installation on M-series (until M2) and Intel-series Mac can follow the exact same procedure. + +## Starting From Scratch + +For completely new Macos or Macos without Xcode installed. + +If you have Xcode installed, skip to Install TC backends. + +### Install Xcode Command Line Tools + +Need graphical access to the machine. + +Run `xcode-select --install` to install if on optimal internet. + +Or Download it from [Apple](https://developer.apple.com/download/more/) Command Line Tools installation image then install it if the internet connection is weak. + +## Install TC Backends + +There are four backends to choose from, Numpy, Tensorflow, Jax, and Torch. + +### Install Jax, Pytorch (Optional) + +```bash +pip install [Package Name] +``` +### Install Tensorflow (Optional - Recommended) + +#### Install Miniconda (Optional - Recommended) + +If you wish to install Tensorflow optimized for MacOS (`tensorflow-macos`) or Tensorflow GPU optimized (`tensorflow-metal`) please install miniconda. + +If you wish to install Vanilla Tensorflow developed by Google (`tensorflow`) please skip this step. + +```bash +curl -o ~/miniconda.sh https://repo.anaconda.com/miniconda/Miniconda3-latest-MacOSX-arm64.sh +bash ~/miniconda.sh -b -p $HOME/miniconda +source ~/miniconda/bin/activate +conda install -c apple tensorflow-deps +``` + +#### Installation + +```bash +pip install tensorflow +``` + +If you wish to use tensorflow-metal PluggableDevice, then continue install (not recommended): + +```bash +pip install tensorflow-metal +``` + +#### Verify Tensorflow Installation + +```python +import tensorflow as tf + +cifar = tf.keras.datasets.cifar100 +(x_train, y_train), (x_test, y_test) = cifar.load_data() +model = tf.keras.applications.ResNet50( + include_top=True, + weights=None, + input_shape=(32, 32, 3), + classes=100,) + +loss_fn = tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True) +model.compile(optimizer="adam", loss=loss_fn, metrics=["accuracy"]) +model.fit(x_train, y_train, epochs=5, batch_size=64) +``` + +## Install Tensorcircuit + +```bash +pip install tensorcircuit +``` + +## Benchmarking + +This data is collected by running `benchmarks/scripts/vqe_tc.py` 10 times and average results. + + + + + + + + + + + + + + + + + + + + + + + + + + +
Vanilla TensorflowApple TensorflowApple Tensorflow with Metal Plugin
Construction Time11.49241641s11.31878941s11.6103961s
Iteration time0.002313011s0.002333004s0.046412581s
Total time11.72371747s11.55208979s16.25165417s
+ + +Until July 2023, this has been tested on Intel Macs running Ventura, M1 Macs running Ventura, M2 Macs running Ventura, and M2 Macs running Sonoma beta. \ No newline at end of file diff --git a/docs/source/contribs/development_MacARM.md b/docs/source/contribs/development_MacARM.md index ffddf582..73c63948 100644 --- a/docs/source/contribs/development_MacARM.md +++ b/docs/source/contribs/development_MacARM.md @@ -2,6 +2,9 @@ Contributed by Mark (Zixuan) Song +.. warning:: + This page is deprecated. Please visit `the update tutorial `_ for the latest information. + ## Starting From Scratch For completely new macos or macos without xcode and brew @@ -43,13 +46,7 @@ pip install [Package Name] ### Install Tensorflow (Optional) -#### Install Tensorflow (Recommended Approach) - -❗️ Tensorflow with MacOS optimization would not function correctly in version 2.11.0 and before. Do not use this version of tensorflow if you intented to train any machine learning model. - -FYI: Error can occur when machine learning training or gpu related code is involved. - -⚠️ Tensorflow without macos optimization does not support Metal API and utilizing GPU (both intel chips and M-series chips) until at least tensorflow 2.11. Tensorflow-macos would fail when running `tc.backend.to_dense()` +#### Install Tensorflow without MacOS optimization ``` conda config --add channels conda-forge @@ -75,13 +72,45 @@ model.compile(optimizer="adam", loss=loss_fn, metrics=["accuracy"]) model.fit(x_train, y_train, epochs=5, batch_size=64) ``` +#### Install Tensorflow with MacOS optimization (Recommended) + +For tensorflow version 2.13 or later: +``` +pip install tensorflow +pip install tensorflow-metal +``` + +For tensorflow version 2.12 or earlier: +``` +pip install tensorflow-macos +pip install tensorflow-metal +``` + +#### Verify Tensorflow Installation + +``` +import tensorflow as tf + +cifar = tf.keras.datasets.cifar100 +(x_train, y_train), (x_test, y_test) = cifar.load_data() +model = tf.keras.applications.ResNet50( + include_top=True, + weights=None, + input_shape=(32, 32, 3), + classes=100,) + +loss_fn = tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True) +model.compile(optimizer="adam", loss=loss_fn, metrics=["accuracy"]) +model.fit(x_train, y_train, epochs=5, batch_size=64) +``` + ## Install Tensorcircuit ``` pip install tensorcircuit ``` -Testing Platform (Tested Feb 2023) +Testing Platform (Tested Jun 2023) - Platform 1: - MacOS Ventura 13.1 (Build version 22C65) @@ -89,3 +118,6 @@ Testing Platform (Tested Feb 2023) - Platform 2: - MacOS Ventura 13.2 (Build version 22D49) - M1 Ultra (Virtual) +- Platform 4: + - MacOS Sonoma 14.0 Beta 2 (Build version 23A5276g) + - M2 Max \ No newline at end of file diff --git a/docs/source/contribs/development_MacM1.rst b/docs/source/contribs/development_MacM1.rst index 3df9c949..8ce9f058 100644 --- a/docs/source/contribs/development_MacM1.rst +++ b/docs/source/contribs/development_MacM1.rst @@ -4,7 +4,7 @@ Contributed by (Yuqin Chen) .. warning:: - This page is deprecated. Please visit `the update tutorial `_ for latest information. + This page is deprecated. Please visit `the update tutorial `_ for the latest information. Why We Can't Run TensorCircuit on TensorlowBackend with Apple M1 diff --git a/docs/source/contribs/development_MacM2.md b/docs/source/contribs/development_MacM2.md new file mode 100644 index 00000000..b3daf5fb --- /dev/null +++ b/docs/source/contribs/development_MacM2.md @@ -0,0 +1,53 @@ +# Tensorcircuit Installation Guide on MacOS + +Contributed by [Hong-Ye Hu](https://github.com/hongyehu) + +.. warning:: + This page is deprecated. Please visit `the update tutorial `_ for the latest information. + +The key issue addressed in this document is **how to install both TensorFlow and Jax on a M2 chip MacOS without conflict**. + +## Starting From Scratch + +### Install Xcode Command Line Tools + +Need graphical access to the machine. + +Run `xcode-select --install` to install if on optimal internet. + +Or Download from [Apple](https://developer.apple.com/download/more/) Command Line Tools installation image then install if internet connection is weak. + +## Install Miniconda + +Due to the limitation of MacOS and packages, the lastest version of python does not always function as desired, thus miniconda installation is advised to solve the issues. And use anaconda virtual environment is always a good habit. + +``` +curl -o ~/miniconda.sh https://repo.anaconda.com/miniconda/Miniconda3-latest-MacOSX-arm64.sh +bash ~/miniconda.sh -b -p $HOME/miniconda +source ~/miniconda/bin/activate +``` + +## Install Packages +First, create a virtual environment, and make sure the python version is 3.8.5 by +``` +conda create --name NewEnv python==3.8.5 +conda activate NewEnv +``` +Then, install the TensorFlow from `.whl` file (file can be downloaded from this [URL](https://drive.google.com/drive/folders/1oSipZLnoeQB0Awz8U68KYeCPsULy_dQ7)). This will install TensorFlow version 2.4.1 +``` +pip install ~/Downloads/tensorflow-2.4.1-py3-none-any.whl +``` +Next, one need to install **Jax** and **Optax** by +``` +conda install jax==0.3.0 +conda install optax==0.1.4 +``` +Now, hopefully, you should be able to use both Jax and TensorFlow in this environment. But sometimes, it may give you an error "ERROR: package Chardet not found.". +If that is the case, you can install it by `conda install chardet`. +Lastly, install tensorcircuit +``` +pip install tensorcircuit +``` +This is the solution that seems to work for M2-chip MacOS. Please let me know if there is a better solution! + + diff --git a/docs/source/contribs/development_Mac_cn.md b/docs/source/contribs/development_Mac_cn.md new file mode 100644 index 00000000..f23fd01f --- /dev/null +++ b/docs/source/contribs/development_Mac_cn.md @@ -0,0 +1,114 @@ +# MacOS Tensorcircuit 安装教程 + +[_Mark (Zixuan) Song_](https://marksong.tech) 撰写 + +由于苹果更新了Tensorflow，因此M系列（直到M2）和英特尔系列Mac上的安装可以遵循完全相同的过程。 + +## 从头开始 + +对于全新的Macos或未安装Xcode的Macos。 + +若您已安装Xcode，请跳转到安装TC后端。 + +### 安装Xcode命令行工具 + +需要对机器的图形访问 + +如果网络良好，请运行`xcode-select --install`进行安装。 + +或者，如果网络连接不理想，请从[苹果](https://developer.apple.com/download/more/)下载命令行工具安装映像，然后进行安装。 + +## 安装TC后端 + +有四个后端可供选择，Numpy，Tensorflow，Jax和Torch。 + +### 安装Jax、Pytorch（可选） + +```bash +pip install [Package Name] +``` + +### 安装Tensorflow（可选 - 推荐） + +#### 安装miniconda（可选 - 推荐） + +若您希望使用苹果为MacOS优化的Tensorflow（`tensorflow-macos`）或使用Tensorflow GPU优化（`tensorflow-metal`）请安装mimiconda。 + +若您希望使Google开发的原版Tensorflow（`tensorflow`）请跳过此步骤。 + +```bash +curl -o ~/miniconda.sh https://repo.anaconda.com/miniconda/Miniconda3-latest-MacOSX-arm64.sh +bash ~/miniconda.sh -b -p $HOME/miniconda +source ~/miniconda/bin/activate +conda install -c apple tensorflow-deps +``` + +#### 安装步骤 + +```bash +pip install tensorflow +``` + +若您希望使用苹果为Tensorflow优化的Metal后端，请继续运行（不建议）： + +```bash +pip install tensorflow-metal +``` + +#### 验证Tensorflow安装 + +```python +import tensorflow as tf + +cifar = tf.keras.datasets.cifar100 +(x_train, y_train), (x_test, y_test) = cifar.load_data() +model = tf.keras.applications.ResNet50( + include_top=True, + weights=None, + input_shape=(32, 32, 3), + classes=100,) + +loss_fn = tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True) +model.compile(optimizer="adam", loss=loss_fn, metrics=["accuracy"]) +model.fit(x_train, y_train, epochs=5, batch_size=64) +``` + +## 安装Tensorcircuit + +```bash +pip install tensorcircuit +``` + +## 测试与比较 + +以下数据由运行`benchmarks/scripts/vqe_tc.py` 10次并取平均值得到。 + + + + + + + + + + + + + + + + + + + + + + + + + + +
原版Tensorflow苹果优化版Tensorflow苹果优化版Tensorflow并安装Tensorflow Metal插件
构建时间11.49241641s11.31878941s11.6103961s
迭代时间0.002313011s0.002333004s0.046412581s
从时间11.72371747s11.55208979s16.25165417s
+ + +直到2023年7月，这已在运行Ventura的英特尔i9 Mac、运行Ventura的M1 Mac、运行Ventura的M2 Mac、运行Sonoma测试版的M2 Mac上进行了测试。 \ No newline at end of file diff --git a/docs/source/contribution.rst b/docs/source/contribution.rst index 5e8d7385..d8dbd493 100644 --- a/docs/source/contribution.rst +++ b/docs/source/contribution.rst @@ -146,7 +146,59 @@ We use `sphinx `__ to manage the document The source files for docs are .rst file in docs/source. -For English docs, ``sphinx-build source build/html`` in docs dir is enough. The html version of the docs are in docs/build/html. +For English docs, ``sphinx-build source build/html`` and ``make latexpdf LATEXMKOPTS="-silent"`` in docs dir are enough. +The html and pdf version of the docs are in docs/build/html and docs/build/latex, respectively. + +**Formula Environment Attention** + +It should be noted that the formula environment ``$$CONTENT$$`` in markdown is equivalent to the ``equation`` environment in latex. +Therefore, in the jupyter notebook documents, do not nest the formula environment in ``$$CONTENT$$`` that is incompatible with +``equation`` in latex, such as ``eqnarray``, which will cause errors in the pdf file built by ``nbsphinx``. +However, compatible formula environments can be used. For example, this legal code in markdown + +.. code-block:: markdown + + $$ + \begin{split} + X&=Y\\ + &=Z + \end{split} + $$ + +will be convert to + +.. code-block:: latex + + \begin{equation} + \begin{split} + X&=Y\\ + &=Z + \end{split} + \end{equation} + +in latex automatically by ``nbsphinx``, which is a legal latex code. However, this legal code in markdown + +.. code-block:: markdown + + $$ + \begin{eqnarray} + X&=&Y\\ + &=&Z + \end{eqnarray} + $$ + +will be convert to + +.. code-block:: latex + + \begin{equation} + \begin{eqnarray} + X&=&Y\\ + &=&Z + \end{eqnarray} + \end{equation} + +in latex, which is an illegal latex code. **Auto Generation of API Docs:** diff --git a/docs/source/generate_rst.py b/docs/source/generate_rst.py index 60fcf0de..9b112c46 100644 --- a/docs/source/generate_rst.py +++ b/docs/source/generate_rst.py @@ -5,7 +5,7 @@ class RSTGenerator: - title_line = "=" * 50 + title_line = "=" * 80 toctree = ".. toctree::\n {}" automodule = ".. automodule:: {}\n :members:\n :undoc-members:\n :show-inheritance:\n :inherited-members:" @@ -21,11 +21,14 @@ def __init__( def cleanup(self): if os.path.exists("modules.rst"): os.remove("modules.rst") - shutil.rmtree(self.dfolder) + try: + shutil.rmtree(self.dfolder) + except FileNotFoundError: + pass os.makedirs(self.dfolder) def write(self, path, content): - if type(content) == type([]): + if isinstance(content, list): content = "\n".join(content) with open(path, "w") as f: @@ -33,70 +36,68 @@ def write(self, path, content): print(f"Finish writing {path}") - def single_file_module(self): - """Process the module in the self.pfolder/*.py""" - - for module_name in glob.glob(pj(self.pfolder, "*.py")): + def _file_generate(self, package_parents): + file_list = [] + for module_name in glob.glob(pj(self.pfolder, *package_parents, "*.py")): module_name = os.path.basename(module_name)[:-3] if module_name in self.ingnored_modules: continue - rst_file = pj(self.dfolder, f"{module_name}.rst") + rst_file = pj(self.dfolder, *package_parents, f"{module_name}.rst") + name = f"{self.name}" + for n in package_parents: + name += f".{n}" + name += f".{module_name}" content = [ - f"{self.name}.{module_name}", + name, self.title_line, - self.automodule.format(f"{self.name}.{module_name}"), + self.automodule.format(name), ] - self.write(rst_file, content) - self.tree[rst_file] = [] - - def subdir_files_module(self): - """Write the rst files for modules with subdir or files""" - for subdir in glob.glob(pj(self.pfolder, "*/")): + if not package_parents: + upper = self.dfolder + else: + upper = package_parents[-1] + file_list.append(upper + f"/{module_name}.rst") + for subdir in glob.glob(pj(self.pfolder, *package_parents, "*/")): if "_" in subdir: continue - subdir = os.path.basename(os.path.normpath(subdir)) - os.makedirs(pj(self.dfolder, subdir), exist_ok=True) - rst_file = pj(self.dfolder, f"{subdir}.rst") - self.tree[rst_file] = [] - - for module_name in glob.glob(pj(self.pfolder, subdir, f"*.py")): - module_name = os.path.basename(module_name)[:-3] - if module_name in self.ingnored_modules: - continue - - content = [ - f"{self.name}.{subdir}.{module_name}", - self.title_line, - self.automodule.format(f"{self.name}.{subdir}.{module_name}"), - ] - - self.write(pj(self.dfolder, subdir, f"{module_name}.rst"), content) - self.tree[rst_file].append(f"{subdir}/{module_name}.rst") - + os.makedirs(pj(self.dfolder, *package_parents, subdir), exist_ok=True) + rst_file = pj(self.dfolder, *package_parents, f"{subdir}.rst") + subdir_filelist = self._file_generate(package_parents + [subdir]) + + name = f"{self.name}" + for n in package_parents: + name += f".{n}" + name += f".{subdir}" content = [ - f"{self.name}.{subdir}", + name, self.title_line, - self.toctree.format("\n ".join(sorted(self.tree[rst_file]))), + self.toctree.format("\n ".join(sorted(subdir_filelist))), ] self.write(rst_file, content) - def modules_file(self): + if not package_parents: + upper = self.dfolder + else: + upper = package_parents[-1] + file_list.append(upper + f"/{subdir}.rst") + return file_list + + def modules_file(self, file_list): """Write the modules.rst""" content = [ self.name, self.title_line, - self.toctree.format("\n ".join(sorted(self.tree.keys()))), + self.toctree.format("\n ".join(sorted(file_list))), ] self.write("modules.rst", content) def start(self): self.cleanup() - self.single_file_module() - self.subdir_files_module() - self.modules_file() + file_list = self._file_generate([]) + self.modules_file(file_list) if __name__ == "__main__": diff --git a/docs/source/index.rst b/docs/source/index.rst index 6732f8fc..bd055a60 100644 --- a/docs/source/index.rst +++ b/docs/source/index.rst @@ -7,6 +7,9 @@ TensorCircuit Documentation **Welcome and congratulations! You have found TensorCircuit.** 👏 +Introduction +--------------- + TensorCircuit is an open-source high-performance quantum computing software framework in Python. * It is built for humans. 👽 @@ -25,34 +28,168 @@ With the help of TensorCircuit, now get ready to efficiently and elegantly solve + Relevant Links -------------------- TensorCircuit is created and maintained by `Shi-Xin Zhang `_ and this version is released by `Tencent Quantum Lab `_. The current core authors of TensorCircuit are `Shi-Xin Zhang `_ and `Yu-Qin Chen `_. -We also thank `contributions `_ from the lab and the open source community. +We also thank `contributions `_ from the open source community. If you have any further questions or collaboration ideas, please use the issue tracker or forum below, or send email to shixinzhang#tencent.com. -* Source code: https://github.com/tencent-quantum-lab/tensorcircuit +.. card-carousel:: 2 + + .. card:: Source code + :link: https://github.com/tencent-quantum-lab/tensorcircuit + :shadow: md + + GitHub + + + .. card:: Documentation + :link: https://tensorcircuit.readthedocs.io + :shadow: md + + Readthedocs + + + .. card:: Whitepaper + :link: https://quantum-journal.org/papers/q-2023-02-02-912/ + :shadow: md + + *Quantum* journal + + + .. card:: Issue Tracker + :link: https://github.com/tencent-quantum-lab/tensorcircuit/issues + :shadow: md + + GitHub Issues + + + .. card:: Forum + :link: https://github.com/tencent-quantum-lab/tensorcircuit/discussions + :shadow: md + + GitHub Discussions + + + .. card:: PyPI + :link: https://pypi.org/project/tensorcircuit + :shadow: md + + ``pip install`` + + + .. card:: DockerHub + :link: https://hub.docker.com/repository/docker/tensorcircuit/tensorcircuit + :shadow: md + + ``docker pull`` + + + .. card:: Application + :link: https://github.com/tencent-quantum-lab/tensorcircuit#research-and-applications + :shadow: md + + Research using TC + + + .. card:: Cloud + :link: https://quantum.tencent.com/cloud + + Tencent Quantum Cloud + + + + +.. + * Source code: https://github.com/tencent-quantum-lab/tensorcircuit + + * Documentation: https://tensorcircuit.readthedocs.io + + * Software Whitepaper (published in Quantum): https://quantum-journal.org/papers/q-2023-02-02-912/ + + * Issue Tracker: https://github.com/tencent-quantum-lab/tensorcircuit/issues + + * Forum: https://github.com/tencent-quantum-lab/tensorcircuit/discussions + + * PyPI page: https://pypi.org/project/tensorcircuit + + * DockerHub page: https://hub.docker.com/repository/docker/tensorcircuit/tensorcircuit + + * Research and projects based on TensorCircuit: https://github.com/tencent-quantum-lab/tensorcircuit#research-and-applications + + * Tencent Quantum Cloud Service: https://quantum.tencent.com/cloud/ + + + +Unified Quantum Programming +------------------------------ + +TensorCircuit is unifying infrastructures and interfaces for quantum computing. + +.. grid:: 1 2 4 4 + :margin: 0 + :padding: 0 + :gutter: 2 + + .. grid-item-card:: Unified Backends + :columns: 12 6 3 3 + :shadow: md + + Jax/TensorFlow/PyTorch/Numpy/Cupy + + .. grid-item-card:: Unified Devices + :columns: 12 6 3 3 + :shadow: md + + CPU/GPU/TPU + + .. grid-item-card:: Unified Providers + :columns: 12 6 3 3 + :shadow: md + + QPUs from different vendors + + .. grid-item-card:: Unified Resources + :columns: 12 6 3 3 + :shadow: md + + local/cloud/HPC + + +.. grid:: 1 2 4 4 + :margin: 0 + :padding: 0 + :gutter: 2 -* Documentation: https://tensorcircuit.readthedocs.io + .. grid-item-card:: Unified Interfaces + :columns: 12 6 3 3 + :shadow: md -* Software Whitepaper (published in Quantum): https://quantum-journal.org/papers/q-2023-02-02-912/ + numerical sim/hardware exp -* Issue Tracker: https://github.com/tencent-quantum-lab/tensorcircuit/issues + .. grid-item-card:: Unified Engines + :columns: 12 6 3 3 + :shadow: md -* Forum: https://github.com/tencent-quantum-lab/tensorcircuit/discussions + ideal/noisy/approximate simulation -* PyPI page: https://pypi.org/project/tensorcircuit + .. grid-item-card:: Unified Representations + :columns: 12 6 3 3 + :shadow: md -* DockerHub page: https://hub.docker.com/repository/docker/tensorcircuit/tensorcircuit + from/to_IR/qiskit/openqasm/json -* Research and projects based on TensorCircuit: https://github.com/tencent-quantum-lab/tensorcircuit#research-and-applications + .. grid-item-card:: Unified Pipelines + :columns: 12 6 3 3 + :shadow: md -* Tencent Quantum Cloud Service: https://quantum.tencent.com/cloud/ + stateless functional programming/stateful ML models diff --git a/docs/source/locale/zh/LC_MESSAGES/api.po b/docs/source/locale/zh/LC_MESSAGES/api.po index c3ed832b..b7958e1e 100644 --- a/docs/source/locale/zh/LC_MESSAGES/api.po +++ b/docs/source/locale/zh/LC_MESSAGES/api.po @@ -8,7 +8,7 @@ msgid "" msgstr "" "Project-Id-Version: tensorcircuit\n" "Report-Msgid-Bugs-To: \n" -"POT-Creation-Date: 2023-05-10 22:01+0800\n" +"POT-Creation-Date: 2023-07-14 15:43+0800\n" "PO-Revision-Date: 2022-04-13 14:58+0800\n" "Last-Translator: Xinghan Yang\n" "Language: cn\n" @@ -16,7 +16,7 @@ msgstr "" "MIME-Version: 1.0\n" "Content-Type: text/plain; charset=utf-8\n" "Content-Transfer-Encoding: 8bit\n" -"Generated-By: Babel 2.9.1\n" +"Generated-By: Babel 2.12.1\n" #: ../../source/api/about.rst:2 msgid "tensorcircuit.about" @@ -65,45 +65,55 @@ msgstr "" msgid "example" msgstr "" -#: keras.engine.base_layer.Layer.add_loss -#: keras.engine.base_layer.Layer.add_metric -#: keras.engine.base_layer.Layer.add_update -#: keras.engine.base_layer.Layer.add_weight keras.engine.base_layer.Layer.apply -#: keras.engine.base_layer.Layer.build -#: keras.engine.base_layer.Layer.compute_mask -#: keras.engine.base_layer.Layer.compute_output_shape -#: keras.engine.base_layer.Layer.compute_output_signature -#: keras.engine.base_layer.Layer.from_config -#: keras.engine.base_layer.Layer.get_input_at -#: keras.engine.base_layer.Layer.get_input_mask_at -#: keras.engine.base_layer.Layer.get_input_shape_at -#: keras.engine.base_layer.Layer.get_losses_for -#: keras.engine.base_layer.Layer.get_output_at -#: keras.engine.base_layer.Layer.get_output_mask_at -#: keras.engine.base_layer.Layer.get_output_shape_at -#: keras.engine.base_layer.Layer.get_updates_for -#: keras.engine.base_layer.Layer.set_weights keras.engine.training.Model.build -#: keras.engine.training.Model.compile keras.engine.training.Model.evaluate -#: keras.engine.training.Model.fit keras.engine.training.Model.from_config -#: keras.engine.training.Model.get_layer -#: keras.engine.training.Model.load_weights -#: keras.engine.training.Model.make_predict_function -#: keras.engine.training.Model.make_test_function -#: keras.engine.training.Model.make_train_function -#: keras.engine.training.Model.predict -#: keras.engine.training.Model.predict_on_batch -#: keras.engine.training.Model.predict_step keras.engine.training.Model.save -#: keras.engine.training.Model.save_weights keras.engine.training.Model.summary -#: keras.engine.training.Model.test_on_batch -#: keras.engine.training.Model.test_step keras.engine.training.Model.to_json -#: keras.engine.training.Model.to_yaml -#: keras.engine.training.Model.train_on_batch -#: keras.engine.training.Model.train_step -#: keras.optimizer_v2.learning_rate_schedule.LearningRateSchedule.from_config +#: keras.src.engine.base_layer.Layer.add_loss +#: keras.src.engine.base_layer.Layer.add_metric +#: keras.src.engine.base_layer.Layer.add_update +#: keras.src.engine.base_layer.Layer.add_weight +#: keras.src.engine.base_layer.Layer.build +#: keras.src.engine.base_layer.Layer.build_from_config +#: keras.src.engine.base_layer.Layer.compute_mask +#: keras.src.engine.base_layer.Layer.compute_output_shape +#: keras.src.engine.base_layer.Layer.compute_output_signature +#: keras.src.engine.base_layer.Layer.from_config +#: keras.src.engine.base_layer.Layer.get_input_at +#: keras.src.engine.base_layer.Layer.get_input_mask_at +#: keras.src.engine.base_layer.Layer.get_input_shape_at +#: keras.src.engine.base_layer.Layer.get_output_at +#: keras.src.engine.base_layer.Layer.get_output_mask_at +#: keras.src.engine.base_layer.Layer.get_output_shape_at +#: keras.src.engine.base_layer.Layer.load_own_variables +#: keras.src.engine.base_layer.Layer.save_own_variables +#: keras.src.engine.base_layer.Layer.set_weights +#: keras.src.engine.training.Model.build +#: keras.src.engine.training.Model.compile +#: keras.src.engine.training.Model.compile_from_config +#: keras.src.engine.training.Model.compute_loss +#: keras.src.engine.training.Model.compute_metrics +#: keras.src.engine.training.Model.evaluate +#: keras.src.engine.training.Model.export keras.src.engine.training.Model.fit +#: keras.src.engine.training.Model.from_config +#: keras.src.engine.training.Model.get_layer +#: keras.src.engine.training.Model.load_weights +#: keras.src.engine.training.Model.make_predict_function +#: keras.src.engine.training.Model.make_test_function +#: keras.src.engine.training.Model.make_train_function +#: keras.src.engine.training.Model.predict +#: keras.src.engine.training.Model.predict_on_batch +#: keras.src.engine.training.Model.predict_step +#: keras.src.engine.training.Model.save +#: keras.src.engine.training.Model.save_weights +#: keras.src.engine.training.Model.summary +#: keras.src.engine.training.Model.test_on_batch +#: keras.src.engine.training.Model.test_step +#: keras.src.engine.training.Model.to_json +#: keras.src.engine.training.Model.to_yaml +#: keras.src.engine.training.Model.train_on_batch +#: keras.src.engine.training.Model.train_step +#: keras.src.optimizers.schedules.learning_rate_schedule.LearningRateSchedule.from_config #: of tensorcircuit.abstractcircuit.AbstractCircuit.append #: tensorcircuit.abstractcircuit.AbstractCircuit.append_from_qir -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply_list #: tensorcircuit.abstractcircuit.AbstractCircuit.barrier_instruction #: tensorcircuit.abstractcircuit.AbstractCircuit.cond_measurement #: tensorcircuit.abstractcircuit.AbstractCircuit.expectation_ps @@ -601,6 +611,7 @@ msgstr "" #: tensorcircuit.densitymatrix.DMCircuit.expectation #: tensorcircuit.densitymatrix.DMCircuit.to_circuit #: tensorcircuit.densitymatrix.DMCircuit2.apply_general_kraus_delayed..apply +#: tensorcircuit.experimental.evol_global tensorcircuit.experimental.evol_local #: tensorcircuit.experimental.hamiltonian_evol #: tensorcircuit.experimental.parameter_shift_grad #: tensorcircuit.experimental.parameter_shift_grad_v2 @@ -693,6 +704,12 @@ msgstr "" #: tensorcircuit.quantum.truncated_free_energy tensorcircuit.quantum.xyz2ps #: tensorcircuit.results.counts.expectation #: tensorcircuit.results.counts.plot_histogram +#: tensorcircuit.results.qem.qem_methods.add_dd +#: tensorcircuit.results.qem.qem_methods.apply_dd +#: tensorcircuit.results.qem.qem_methods.apply_rc +#: tensorcircuit.results.qem.qem_methods.apply_zne +#: tensorcircuit.results.qem.qem_methods.prune_ddcircuit +#: tensorcircuit.results.qem.qem_methods.used_qubits #: tensorcircuit.results.readout_mitigation.ReadoutMit.__init__ #: tensorcircuit.results.readout_mitigation.ReadoutMit.apply_correction #: tensorcircuit.results.readout_mitigation.ReadoutMit.apply_readout_mitigation @@ -710,7 +727,6 @@ msgstr "" #: tensorcircuit.templates.blocks.example_block #: tensorcircuit.templates.blocks.qft #: tensorcircuit.templates.blocks.state_centric -#: tensorcircuit.templates.chems.get_ps #: tensorcircuit.templates.graphs.Grid2DCoord.__init__ #: tensorcircuit.templates.graphs.Grid2DCoord.all_cols #: tensorcircuit.templates.graphs.Grid2DCoord.all_rows @@ -816,7 +832,6 @@ msgstr "" #: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.shape_tuple #: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.sign #: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.slice -#: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.svd #: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.trace #: tensornetwork.matrixproductstates.base_mps.BaseMPS.apply_transfer_operator #: tensornetwork.matrixproductstates.base_mps.BaseMPS.check_orthonormality @@ -871,39 +886,44 @@ msgid "" "means plain concatenation." msgstr "" -#: keras.engine.base_layer.Layer.add_weight keras.engine.base_layer.Layer.apply -#: keras.engine.base_layer.Layer.compute_mask -#: keras.engine.base_layer.Layer.compute_output_shape -#: keras.engine.base_layer.Layer.compute_output_signature -#: keras.engine.base_layer.Layer.count_params -#: keras.engine.base_layer.Layer.from_config -#: keras.engine.base_layer.Layer.get_config -#: keras.engine.base_layer.Layer.get_input_at -#: keras.engine.base_layer.Layer.get_input_mask_at -#: keras.engine.base_layer.Layer.get_input_shape_at -#: keras.engine.base_layer.Layer.get_losses_for -#: keras.engine.base_layer.Layer.get_output_at -#: keras.engine.base_layer.Layer.get_output_mask_at -#: keras.engine.base_layer.Layer.get_output_shape_at -#: keras.engine.base_layer.Layer.get_updates_for -#: keras.engine.base_layer.Layer.get_weights -#: keras.engine.training.Model.evaluate keras.engine.training.Model.fit -#: keras.engine.training.Model.from_config -#: keras.engine.training.Model.get_config keras.engine.training.Model.get_layer -#: keras.engine.training.Model.get_weights -#: keras.engine.training.Model.load_weights -#: keras.engine.training.Model.make_predict_function -#: keras.engine.training.Model.make_test_function -#: keras.engine.training.Model.make_train_function -#: keras.engine.training.Model.predict -#: keras.engine.training.Model.predict_on_batch -#: keras.engine.training.Model.predict_step -#: keras.engine.training.Model.test_on_batch -#: keras.engine.training.Model.test_step keras.engine.training.Model.to_json -#: keras.engine.training.Model.to_yaml -#: keras.engine.training.Model.train_on_batch -#: keras.engine.training.Model.train_step -#: keras.optimizer_v2.learning_rate_schedule.LearningRateSchedule.from_config +#: keras.src.engine.base_layer.Layer.add_weight +#: keras.src.engine.base_layer.Layer.compute_mask +#: keras.src.engine.base_layer.Layer.compute_output_shape +#: keras.src.engine.base_layer.Layer.compute_output_signature +#: keras.src.engine.base_layer.Layer.count_params +#: keras.src.engine.base_layer.Layer.from_config +#: keras.src.engine.base_layer.Layer.get_build_config +#: keras.src.engine.base_layer.Layer.get_config +#: keras.src.engine.base_layer.Layer.get_input_at +#: keras.src.engine.base_layer.Layer.get_input_mask_at +#: keras.src.engine.base_layer.Layer.get_input_shape_at +#: keras.src.engine.base_layer.Layer.get_output_at +#: keras.src.engine.base_layer.Layer.get_output_mask_at +#: keras.src.engine.base_layer.Layer.get_output_shape_at +#: keras.src.engine.base_layer.Layer.get_weights +#: keras.src.engine.training.Model.compute_loss +#: keras.src.engine.training.Model.compute_metrics +#: keras.src.engine.training.Model.evaluate keras.src.engine.training.Model.fit +#: keras.src.engine.training.Model.from_config +#: keras.src.engine.training.Model.get_compile_config +#: keras.src.engine.training.Model.get_config +#: keras.src.engine.training.Model.get_layer +#: keras.src.engine.training.Model.get_metrics_result +#: keras.src.engine.training.Model.get_weight_paths +#: keras.src.engine.training.Model.get_weights +#: keras.src.engine.training.Model.make_predict_function +#: keras.src.engine.training.Model.make_test_function +#: keras.src.engine.training.Model.make_train_function +#: keras.src.engine.training.Model.predict +#: keras.src.engine.training.Model.predict_on_batch +#: keras.src.engine.training.Model.predict_step +#: keras.src.engine.training.Model.test_on_batch +#: keras.src.engine.training.Model.test_step +#: keras.src.engine.training.Model.to_json +#: keras.src.engine.training.Model.to_yaml +#: keras.src.engine.training.Model.train_on_batch +#: keras.src.engine.training.Model.train_step +#: keras.src.optimizers.schedules.learning_rate_schedule.LearningRateSchedule.from_config #: of tensorcircuit.abstractcircuit.AbstractCircuit.append #: tensorcircuit.abstractcircuit.AbstractCircuit.cond_measurement #: tensorcircuit.abstractcircuit.AbstractCircuit.expectation_ps @@ -1540,6 +1560,7 @@ msgstr "" #: tensorcircuit.densitymatrix.DMCircuit.get_dm_as_quoperator #: tensorcircuit.densitymatrix.DMCircuit.to_circuit #: tensorcircuit.densitymatrix.DMCircuit.wavefunction +#: tensorcircuit.experimental.evol_global tensorcircuit.experimental.evol_local #: tensorcircuit.experimental.hamiltonian_evol #: tensorcircuit.experimental.parameter_shift_grad #: tensorcircuit.experimental.parameter_shift_grad_v2 @@ -1664,6 +1685,12 @@ msgstr "" #: tensorcircuit.quantum.truncated_free_energy tensorcircuit.quantum.xyz2ps #: tensorcircuit.results.counts.expectation #: tensorcircuit.results.counts.plot_histogram +#: tensorcircuit.results.qem.qem_methods.add_dd +#: tensorcircuit.results.qem.qem_methods.apply_dd +#: tensorcircuit.results.qem.qem_methods.apply_rc +#: tensorcircuit.results.qem.qem_methods.apply_zne +#: tensorcircuit.results.qem.qem_methods.prune_ddcircuit +#: tensorcircuit.results.qem.qem_methods.used_qubits #: tensorcircuit.results.readout_mitigation.ReadoutMit.apply_readout_mitigation #: tensorcircuit.results.readout_mitigation.ReadoutMit.expectation #: tensorcircuit.results.readout_mitigation.ReadoutMit.get_matrix @@ -1679,7 +1706,6 @@ msgstr "" #: tensorcircuit.templates.blocks.example_block #: tensorcircuit.templates.blocks.qft #: tensorcircuit.templates.blocks.state_centric -#: tensorcircuit.templates.chems.get_ps #: tensorcircuit.templates.graphs.Grid2DCoord.all_cols #: tensorcircuit.templates.graphs.Grid2DCoord.all_rows #: tensorcircuit.templates.graphs.Grid2DCoord.lattice_graph @@ -1824,7 +1850,6 @@ msgstr "" #: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.shape_tuple #: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.subtraction #: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.sum -#: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.svd #: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.trace #: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.transpose #: tensornetwork.matrixproductstates.base_mps.BaseMPS.apply_transfer_operator @@ -2324,6 +2349,7 @@ msgstr "" #: tensorcircuit.densitymatrix.DMCircuit.get_dm_as_quoperator #: tensorcircuit.densitymatrix.DMCircuit.to_circuit #: tensorcircuit.densitymatrix.DMCircuit.wavefunction +#: tensorcircuit.experimental.evol_global tensorcircuit.experimental.evol_local #: tensorcircuit.experimental.hamiltonian_evol #: tensorcircuit.experimental.parameter_shift_grad #: tensorcircuit.experimental.parameter_shift_grad_v2 @@ -2414,6 +2440,12 @@ msgstr "" #: tensorcircuit.quantum.truncated_free_energy tensorcircuit.quantum.xyz2ps #: tensorcircuit.results.counts.expectation #: tensorcircuit.results.counts.plot_histogram +#: tensorcircuit.results.qem.qem_methods.add_dd +#: tensorcircuit.results.qem.qem_methods.apply_dd +#: tensorcircuit.results.qem.qem_methods.apply_rc +#: tensorcircuit.results.qem.qem_methods.apply_zne +#: tensorcircuit.results.qem.qem_methods.prune_ddcircuit +#: tensorcircuit.results.qem.qem_methods.used_qubits #: tensorcircuit.results.readout_mitigation.ReadoutMit.apply_readout_mitigation #: tensorcircuit.results.readout_mitigation.ReadoutMit.expectation #: tensorcircuit.results.readout_mitigation.ReadoutMit.get_matrix @@ -2429,7 +2461,6 @@ msgstr "" #: tensorcircuit.templates.blocks.example_block #: tensorcircuit.templates.blocks.qft #: tensorcircuit.templates.blocks.state_centric -#: tensorcircuit.templates.chems.get_ps #: tensorcircuit.templates.graphs.Grid2DCoord.all_cols #: tensorcircuit.templates.graphs.Grid2DCoord.all_rows #: tensorcircuit.templates.graphs.Grid2DCoord.lattice_graph @@ -2508,7 +2539,6 @@ msgstr "" #: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.inv #: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.random_uniform #: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.sum -#: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.svd #: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.trace #: tensornetwork.matrixproductstates.base_mps.BaseMPS.apply_transfer_operator #: tensornetwork.matrixproductstates.base_mps.BaseMPS.check_orthonormality @@ -2632,6 +2662,8 @@ msgid "add a barrier instruction flag, no effect on numerical simulation" msgstr "" #: of tensorcircuit.abstractcircuit.AbstractCircuit.barrier_instruction:3 +#: tensorcircuit.abstractcircuit.AbstractCircuit.measure_instruction:3 +#: tensorcircuit.abstractcircuit.AbstractCircuit.reset_instruction:3 msgid "the corresponding qubits" msgstr "" @@ -2682,6 +2714,7 @@ msgid "" "Visualise the circuit. This method recevies the keywords as same as " "qiskit.circuit.QuantumCircuit.draw. More details can be found here: " "https://qiskit.org/documentation/stubs/qiskit.circuit.QuantumCircuit.draw.html." +" Interesting kws options include: ``idle_wires``(bool)" msgstr "" #: of tensorcircuit.abstractcircuit.AbstractCircuit.expectation_ps:1 @@ -2706,10 +2739,17 @@ msgid "sites to apply Z gate, defaults to None" msgstr "" #: of tensorcircuit.abstractcircuit.AbstractCircuit.expectation_ps:32 +msgid "" +"or one can apply a ps structures instead of ``x``, ``y``, ``z``, e.g. [0," +" 1, 3, 0, 2, 2] for X_1Z_2Y_4Y_5 defaults to None, ``ps`` can overwrite " +"``x``, ``y`` and ``z``" +msgstr "" + +#: of tensorcircuit.abstractcircuit.AbstractCircuit.expectation_ps:36 msgid "whether to cache and reuse the wavefunction, defaults to True" msgstr "" -#: of tensorcircuit.abstractcircuit.AbstractCircuit.expectation_ps:34 +#: of tensorcircuit.abstractcircuit.AbstractCircuit.expectation_ps:38 #: tensorcircuit.basecircuit.BaseCircuit.sample_expectation_ps:46 #: tensorcircuit.circuit.Circuit.expectation:32 #: tensorcircuit.densitymatrix.DMCircuit.expectation:8 @@ -2718,7 +2758,7 @@ msgstr "" msgid "Noise Configuration, defaults to None" msgstr "" -#: of tensorcircuit.abstractcircuit.AbstractCircuit.expectation_ps:36 +#: of tensorcircuit.abstractcircuit.AbstractCircuit.expectation_ps:40 #: tensorcircuit.basecircuit.BaseCircuit.sample_expectation_ps:48 #: tensorcircuit.circuit.Circuit.expectation:34 #: tensorcircuit.noisemodel.expectation_noisfy:7 @@ -2727,7 +2767,7 @@ msgid "" " to 1000" msgstr "" -#: of tensorcircuit.abstractcircuit.AbstractCircuit.expectation_ps:38 +#: of tensorcircuit.abstractcircuit.AbstractCircuit.expectation_ps:42 #: tensorcircuit.basecircuit.BaseCircuit.sample_expectation_ps:50 #: tensorcircuit.circuit.Circuit.expectation:36 #: tensorcircuit.densitymatrix.DMCircuit.expectation:10 @@ -2738,7 +2778,7 @@ msgid "" "None, used for noisfy circuit sampling" msgstr "" -#: of tensorcircuit.abstractcircuit.AbstractCircuit.expectation_ps:41 +#: of tensorcircuit.abstractcircuit.AbstractCircuit.expectation_ps:45 msgid "Expectation value" msgstr "" @@ -2815,6 +2855,12 @@ msgstr "" #: tensorcircuit.cloud.apis.set_token:13 #: tensorcircuit.cons.runtime_contractor:3 #: tensorcircuit.cons.set_function_contractor:3 +#: tensorcircuit.experimental.evol_global:4 +#: tensorcircuit.experimental.evol_global:9 +#: tensorcircuit.experimental.evol_global:11 +#: tensorcircuit.experimental.evol_local:4 +#: tensorcircuit.experimental.evol_local:6 +#: tensorcircuit.experimental.evol_local:13 #: tensorcircuit.experimental.hamiltonian_evol:4 #: tensorcircuit.experimental.hamiltonian_evol:6 #: tensorcircuit.experimental.hamiltonian_evol:8 tensorcircuit.gates.u_gate:16 @@ -2824,8 +2870,8 @@ msgstr "" #: tensorcircuit.quantum.ps2xyz:7 tensorcircuit.quantum.sample2count:3 #: tensorcircuit.quantum.sample2count:5 tensorcircuit.quantum.sample2count:9 #: tensorcircuit.quantum.xyz2ps:3 tensorcircuit.quantum.xyz2ps:7 -#: tensorcircuit.results.counts.plot_histogram:4 #: tensorcircuit.results.counts.plot_histogram:6 +#: tensorcircuit.results.counts.plot_histogram:8 #: tensorcircuit.templates.graphs.Grid2DCoord.lattice_graph:6 #: tensorcircuit.translation.eqasm2tc:3 tensorcircuit.translation.eqasm2tc:9 #: tensorcircuit.translation.qir2json:3 tensorcircuit.translation.qir2json:8 @@ -3006,11 +3052,6 @@ msgstr "" msgid "add a measurement instruction flag, no effect on numerical simulation" msgstr "" -#: of tensorcircuit.abstractcircuit.AbstractCircuit.measure_instruction:3 -#: tensorcircuit.abstractcircuit.AbstractCircuit.reset_instruction:3 -msgid "the corresponding qubit" -msgstr "" - #: of tensorcircuit.abstractcircuit.AbstractCircuit.prepend:1 msgid "prepend circuit ``c`` before" msgstr "" @@ -3766,7 +3807,7 @@ msgstr "" #: of tensorcircuit.applications.van.MADE:1 #: tensorcircuit.applications.van.NMF:1 #: tensorcircuit.applications.van.PixelCNN:1 -msgid "Bases: :py:class:`~keras.engine.training.Model`" +msgid "Bases: :py:class:`~keras.src.engine.training.Model`" msgstr "" #: of tensorcircuit.applications.van.MADE.activity_regularizer:1 @@ -3781,11 +3822,11 @@ msgstr "" msgid "Optional regularizer function for the output of this layer." msgstr "" -#: keras.engine.base_layer.Layer.add_loss:1 of +#: keras.src.engine.base_layer.Layer.add_loss:1 of msgid "Add loss tensor(s), potentially dependent on layer inputs." msgstr "" -#: keras.engine.base_layer.Layer.add_loss:3 of +#: keras.src.engine.base_layer.Layer.add_loss:3 of msgid "" "Some losses (for instance, activity regularization losses) may be " "dependent on the inputs passed when calling a layer. Hence, when reusing " @@ -3794,16 +3835,19 @@ msgid "" "automatically keeps track of dependencies." msgstr "" -#: keras.engine.base_layer.Layer.add_loss:9 of +#: keras.src.engine.base_layer.Layer.add_loss:9 of msgid "" "This method can be used inside a subclassed layer or model's `call` " "function, in which case `losses` should be a Tensor or list of Tensors." msgstr "" -#: keras.engine.base_layer.Layer.add_loss:12 -#: keras.engine.base_layer.Layer.add_loss:26 -#: keras.engine.base_layer.Layer.add_loss:42 -#: keras.engine.training.Model.compile:3 keras.engine.training.Model.save:28 of +#: keras.src.engine.base_layer.Layer.add_loss:12 +#: keras.src.engine.base_layer.Layer.add_loss:32 +#: keras.src.engine.base_layer.Layer.add_loss:48 +#: keras.src.engine.training.Model.compile:3 +#: keras.src.engine.training.Model.export:15 +#: keras.src.engine.training.Model.get_weight_paths:18 +#: keras.src.engine.training.Model.save:38 of #: tensorcircuit.applications.van.MaskedConv2D.metrics:3 #: tensorcircuit.applications.van.MaskedLinear.metrics:3 #: tensorcircuit.applications.van.ResidualBlock.metrics:3 @@ -3813,22 +3857,24 @@ msgstr "" msgid "Example:" msgstr "" -#: keras.engine.base_layer.Layer.add_loss:14 of +#: keras.src.engine.base_layer.Layer.add_loss:14 of msgid "```python class MyLayer(tf.keras.layers.Layer):" msgstr "" -#: keras.engine.base_layer.Layer.add_loss:17 -#: keras.engine.base_layer.Layer.add_metric:14 of +#: keras.src.engine.base_layer.Layer.add_loss:17 +#: keras.src.engine.base_layer.Layer.add_metric:14 +#: keras.src.engine.training.Model.get_weight_paths:30 of msgid "def call(self, inputs):" msgstr "" -#: keras.engine.base_layer.Layer.add_loss:17 of +#: keras.src.engine.base_layer.Layer.add_loss:17 of msgid "self.add_loss(tf.abs(tf.reduce_mean(inputs))) return inputs" msgstr "" -#: keras.engine.base_layer.Layer.add_loss:19 -#: keras.engine.base_layer.Layer.add_metric:16 -#: keras.engine.training.Model.compile:10 of +#: keras.src.engine.base_layer.Layer.add_loss:19 +#: keras.src.engine.base_layer.Layer.add_metric:16 +#: keras.src.engine.training.Model.compile:10 +#: keras.src.engine.training.Model.compute_metrics:21 of #: tensornetwork.backends.jax.jax_backend.JaxBackend.eigs:21 #: tensornetwork.backends.jax.jax_backend.JaxBackend.eigs:35 #: tensornetwork.backends.jax.jax_backend.JaxBackend.eigsh:21 @@ -3838,16 +3884,24 @@ msgstr "" msgid "```" msgstr "" -#: keras.engine.base_layer.Layer.add_loss:21 of +#: keras.src.engine.base_layer.Layer.add_loss:21 of msgid "" -"This method can also be called directly on a Functional Model during " -"construction. In this case, any loss Tensors passed to this Model must be" -" symbolic and be able to be traced back to the model's `Input`s. These " -"losses become part of the model's topology and are tracked in " +"The same code works in distributed training: the input to `add_loss()` is" +" treated like a regularization loss and averaged across replicas by the " +"training loop (both built-in `Model.fit()` and compliant custom training " +"loops)." +msgstr "" + +#: keras.src.engine.base_layer.Layer.add_loss:26 of +msgid "" +"The `add_loss` method can also be called directly on a Functional Model " +"during construction. In this case, any loss Tensors passed to this Model " +"must be symbolic and be able to be traced back to the model's `Input`s. " +"These losses become part of the model's topology and are tracked in " "`get_config`." msgstr "" -#: keras.engine.base_layer.Layer.add_loss:28 of +#: keras.src.engine.base_layer.Layer.add_loss:34 of msgid "" "```python inputs = tf.keras.Input(shape=(10,)) x = " "tf.keras.layers.Dense(10)(inputs) outputs = tf.keras.layers.Dense(1)(x) " @@ -3855,7 +3909,7 @@ msgid "" "model.add_loss(tf.abs(tf.reduce_mean(x))) ```" msgstr "" -#: keras.engine.base_layer.Layer.add_loss:37 of +#: keras.src.engine.base_layer.Layer.add_loss:43 of msgid "" "If this is not the case for your loss (if, for example, your loss " "references a `Variable` of one of the model's layers), you can wrap your " @@ -3863,7 +3917,7 @@ msgid "" "the model's topology since they can't be serialized." msgstr "" -#: keras.engine.base_layer.Layer.add_loss:44 of +#: keras.src.engine.base_layer.Layer.add_loss:50 of msgid "" "```python inputs = tf.keras.Input(shape=(10,)) d = " "tf.keras.layers.Dense(10) x = d(inputs) outputs = " @@ -3872,57 +3926,47 @@ msgid "" "```" msgstr "" -#: keras.engine.base_layer.Layer.add_loss:54 of +#: keras.src.engine.base_layer.Layer.add_loss:60 of msgid "" "Loss tensor, or list/tuple of tensors. Rather than tensors, losses may " "also be zero-argument callables which create a loss tensor." msgstr "" -#: keras.engine.base_layer.Layer.add_loss:56 of -msgid "" -"Additional keyword arguments for backward compatibility. Accepted values:" -" inputs - Deprecated, will be automatically inferred." -msgstr "" - -#: keras.engine.base_layer.Layer.add_loss:56 of -msgid "Additional keyword arguments for backward compatibility. Accepted values:" -msgstr "" - -#: keras.engine.base_layer.Layer.add_loss:58 of -msgid "inputs - Deprecated, will be automatically inferred." +#: keras.src.engine.base_layer.Layer.add_loss:63 of +msgid "Used for backwards compatibility only." msgstr "" -#: keras.engine.base_layer.Layer.add_metric:1 of +#: keras.src.engine.base_layer.Layer.add_metric:1 of msgid "Adds metric tensor to the layer." msgstr "" -#: keras.engine.base_layer.Layer.add_metric:3 of +#: keras.src.engine.base_layer.Layer.add_metric:3 of msgid "" "This method can be used inside the `call()` method of a subclassed layer " "or model." msgstr "" -#: keras.engine.base_layer.Layer.add_metric:6 of +#: keras.src.engine.base_layer.Layer.add_metric:6 of msgid "```python class MyMetricLayer(tf.keras.layers.Layer):" msgstr "" -#: keras.engine.base_layer.Layer.add_metric:10 of +#: keras.src.engine.base_layer.Layer.add_metric:10 of msgid "def __init__(self):" msgstr "" -#: keras.engine.base_layer.Layer.add_metric:9 of +#: keras.src.engine.base_layer.Layer.add_metric:9 of msgid "" "super(MyMetricLayer, self).__init__(name='my_metric_layer') self.mean = " "tf.keras.metrics.Mean(name='metric_1')" msgstr "" -#: keras.engine.base_layer.Layer.add_metric:13 of +#: keras.src.engine.base_layer.Layer.add_metric:13 of msgid "" "self.add_metric(self.mean(inputs)) self.add_metric(tf.reduce_sum(inputs)," " name='metric_2') return inputs" msgstr "" -#: keras.engine.base_layer.Layer.add_metric:18 of +#: keras.src.engine.base_layer.Layer.add_metric:18 of msgid "" "This method can also be called directly on a Functional Model during " "construction. In this case, any tensor passed to this Model must be " @@ -3931,7 +3975,7 @@ msgid "" " the model via `save()`." msgstr "" -#: keras.engine.base_layer.Layer.add_metric:24 of +#: keras.src.engine.base_layer.Layer.add_metric:24 of msgid "" "```python inputs = tf.keras.Input(shape=(10,)) x = " "tf.keras.layers.Dense(10)(inputs) outputs = tf.keras.layers.Dense(1)(x) " @@ -3939,7 +3983,7 @@ msgid "" "model.add_metric(math_ops.reduce_sum(x), name='metric_1') ```" msgstr "" -#: keras.engine.base_layer.Layer.add_metric:32 of +#: keras.src.engine.base_layer.Layer.add_metric:32 of msgid "" "Note: Calling `add_metric()` with the result of a metric object on a " "Functional Model, as shown in the example below, is not supported. This " @@ -3947,7 +3991,7 @@ msgid "" "inputs." msgstr "" -#: keras.engine.base_layer.Layer.add_metric:36 of +#: keras.src.engine.base_layer.Layer.add_metric:37 of msgid "" "```python inputs = tf.keras.Input(shape=(10,)) x = " "tf.keras.layers.Dense(10)(inputs) outputs = tf.keras.layers.Dense(1)(x) " @@ -3955,15 +3999,15 @@ msgid "" "model.add_metric(tf.keras.metrics.Mean()(x), name='metric_1') ```" msgstr "" -#: keras.engine.base_layer.Layer.add_metric:44 of +#: keras.src.engine.base_layer.Layer.add_metric:45 of msgid "Metric tensor." msgstr "" -#: keras.engine.base_layer.Layer.add_metric:45 of +#: keras.src.engine.base_layer.Layer.add_metric:46 of msgid "String metric name." msgstr "" -#: keras.engine.base_layer.Layer.add_metric:46 of +#: keras.src.engine.base_layer.Layer.add_metric:47 of msgid "" "Additional keyword arguments for backward compatibility. Accepted values:" " `aggregation` - When the `value` tensor provided is not the result of " @@ -3971,11 +4015,11 @@ msgid "" " a `keras.Metric.Mean`." msgstr "" -#: keras.engine.base_layer.Layer.add_update:1 of +#: keras.src.engine.base_layer.Layer.add_update:1 of msgid "Add update op(s), potentially dependent on layer inputs." msgstr "" -#: keras.engine.base_layer.Layer.add_update:3 of +#: keras.src.engine.base_layer.Layer.add_update:3 of msgid "" "Weight updates (for instance, the updates of the moving mean and variance" " in a BatchNormalization layer) may be dependent on the inputs passed " @@ -3985,14 +4029,14 @@ msgid "" "dependencies." msgstr "" -#: keras.engine.base_layer.Layer.add_update:10 of +#: keras.src.engine.base_layer.Layer.add_update:10 of msgid "" "This call is ignored when eager execution is enabled (in that case, " "variable updates are run on the fly and thus do not need to be tracked " "for later execution)." msgstr "" -#: keras.engine.base_layer.Layer.add_update:14 of +#: keras.src.engine.base_layer.Layer.add_update:14 of msgid "" "Update op, or list/tuple of update ops, or zero-arg callable that returns" " an update op. A zero-arg callable should be passed in order to disable " @@ -4000,39 +4044,35 @@ msgid "" "executing in Eager mode." msgstr "" -#: keras.engine.base_layer.Layer.add_update:18 of -msgid "Deprecated, will be automatically inferred." -msgstr "" - -#: keras.engine.base_layer.Layer.add_variable:1 of +#: keras.src.engine.base_layer.Layer.add_variable:1 of msgid "Deprecated, do NOT use! Alias for `add_weight`." msgstr "" -#: keras.engine.base_layer.Layer.add_weight:1 of +#: keras.src.engine.base_layer.Layer.add_weight:1 of msgid "Adds a new variable to the layer." msgstr "" -#: keras.engine.base_layer.Layer.add_weight:3 of +#: keras.src.engine.base_layer.Layer.add_weight:3 of msgid "Variable name." msgstr "" -#: keras.engine.base_layer.Layer.add_weight:4 of +#: keras.src.engine.base_layer.Layer.add_weight:4 of msgid "Variable shape. Defaults to scalar if unspecified." msgstr "" -#: keras.engine.base_layer.Layer.add_weight:5 of +#: keras.src.engine.base_layer.Layer.add_weight:5 of msgid "The type of the variable. Defaults to `self.dtype`." msgstr "" -#: keras.engine.base_layer.Layer.add_weight:6 of +#: keras.src.engine.base_layer.Layer.add_weight:6 of msgid "Initializer instance (callable)." msgstr "" -#: keras.engine.base_layer.Layer.add_weight:7 of +#: keras.src.engine.base_layer.Layer.add_weight:7 of msgid "Regularizer instance (callable)." msgstr "" -#: keras.engine.base_layer.Layer.add_weight:8 of +#: keras.src.engine.base_layer.Layer.add_weight:8 of msgid "" "Boolean, whether the variable should be part of the layer's " "\"trainable_variables\" (e.g. variables, biases) or " @@ -4040,15 +4080,28 @@ msgid "" " `trainable` cannot be `True` if `synchronization` is set to `ON_READ`." msgstr "" -#: keras.engine.base_layer.Layer.add_weight:13 of +#: keras.src.engine.base_layer.Layer.add_weight:13 of msgid "Constraint instance (callable)." msgstr "" -#: keras.engine.base_layer.Layer.add_weight:14 of -msgid "Whether to use `ResourceVariable`." +#: keras.src.engine.base_layer.Layer.add_weight:14 of +msgid "" +"Whether to use a `ResourceVariable` or not. See [this guide]( " +"https://www.tensorflow.org/guide/migrate/tf1_vs_tf2#resourcevariables_instead_of_referencevariables)" +" for more information." +msgstr "" + +#: keras.src.engine.base_layer.Layer.add_weight:14 of +msgid "" +"Whether to use a `ResourceVariable` or not. See [this guide]( " +"https://www.tensorflow.org/guide/migrate/tf1_vs_tf2#resourcevariables_instead_of_referencevariables)" +msgstr "" + +#: keras.src.engine.base_layer.Layer.add_weight:17 of +msgid "for more information." msgstr "" -#: keras.engine.base_layer.Layer.add_weight:15 of +#: keras.src.engine.base_layer.Layer.add_weight:18 of msgid "" "Indicates when a distributed a variable will be aggregated. Accepted " "values are constants defined in the class `tf.VariableSynchronization`. " @@ -4057,37 +4110,39 @@ msgid "" "is set to `ON_READ`, `trainable` must not be set to `True`." msgstr "" -#: keras.engine.base_layer.Layer.add_weight:21 of +#: keras.src.engine.base_layer.Layer.add_weight:24 of msgid "" "Indicates how a distributed variable will be aggregated. Accepted values " "are constants defined in the class `tf.VariableAggregation`." msgstr "" -#: keras.engine.base_layer.Layer.add_weight:24 of +#: keras.src.engine.base_layer.Layer.add_weight:27 of msgid "" "Additional keyword arguments. Accepted values are `getter`, " "`collections`, `experimental_autocast` and `caching_device`." msgstr "" -#: keras.engine.base_layer.Layer.add_weight:27 of +#: keras.src.engine.base_layer.Layer.add_weight:30 of msgid "The variable created." msgstr "" -#: keras.engine.base_layer.Layer.add_weight -#: keras.engine.base_layer.Layer.compute_output_signature -#: keras.engine.base_layer.Layer.count_params -#: keras.engine.base_layer.Layer.get_input_at -#: keras.engine.base_layer.Layer.get_input_shape_at -#: keras.engine.base_layer.Layer.get_output_at -#: keras.engine.base_layer.Layer.get_output_shape_at -#: keras.engine.base_layer.Layer.set_weights keras.engine.training.Model.build -#: keras.engine.training.Model.evaluate keras.engine.training.Model.fit -#: keras.engine.training.Model.load_weights keras.engine.training.Model.predict -#: keras.engine.training.Model.predict_on_batch -#: keras.engine.training.Model.save_weights keras.engine.training.Model.summary -#: keras.engine.training.Model.test_on_batch -#: keras.engine.training.Model.to_yaml -#: keras.engine.training.Model.train_on_batch of +#: keras.src.engine.base_layer.Layer.add_weight +#: keras.src.engine.base_layer.Layer.compute_output_signature +#: keras.src.engine.base_layer.Layer.count_params +#: keras.src.engine.base_layer.Layer.get_input_at +#: keras.src.engine.base_layer.Layer.get_input_shape_at +#: keras.src.engine.base_layer.Layer.get_output_at +#: keras.src.engine.base_layer.Layer.get_output_shape_at +#: keras.src.engine.base_layer.Layer.set_weights +#: keras.src.engine.training.Model.build +#: keras.src.engine.training.Model.evaluate keras.src.engine.training.Model.fit +#: keras.src.engine.training.Model.predict +#: keras.src.engine.training.Model.predict_on_batch +#: keras.src.engine.training.Model.save_weights +#: keras.src.engine.training.Model.summary +#: keras.src.engine.training.Model.test_on_batch +#: keras.src.engine.training.Model.to_yaml +#: keras.src.engine.training.Model.train_on_batch of #: tensorcircuit.applications.van.MADE.input #: tensorcircuit.applications.van.MADE.input_mask #: tensorcircuit.applications.van.MADE.input_shape @@ -4170,52 +4225,23 @@ msgstr "" msgid "Raises" msgstr "" -#: keras.engine.base_layer.Layer.add_weight:29 of +#: keras.src.engine.base_layer.Layer.add_weight:32 of msgid "" "When giving unsupported dtype and no initializer or when trainable " -"has been set to True with synchronization set as `ON_READ`." -msgstr "" - -#: keras.engine.base_layer.Layer.apply:1 -#: keras.engine.base_layer.Layer.get_losses_for:1 -#: keras.engine.base_layer.Layer.get_updates_for:1 of -#: tensorcircuit.applications.van.MADE.state_updates:1 -#: tensorcircuit.applications.van.NMF.state_updates:1 -#: tensorcircuit.applications.van.PixelCNN.state_updates:1 -msgid "Deprecated, do NOT use!" -msgstr "" - -#: keras.engine.base_layer.Layer.apply:3 of -msgid "This is an alias of `self.__call__`." -msgstr "" - -#: keras.engine.base_layer.Layer.apply:5 of -msgid "Input tensor(s)." -msgstr "" - -#: keras.engine.base_layer.Layer.apply:6 of -msgid "additional positional arguments to be passed to `self.call`." +"has been set to True with synchronization set as `ON_READ`." msgstr "" -#: keras.engine.base_layer.Layer.apply:7 of -msgid "additional keyword arguments to be passed to `self.call`." -msgstr "" - -#: keras.engine.base_layer.Layer.apply:9 of -msgid "Output tensor(s)." -msgstr "" - -#: keras.engine.training.Model.build:1 of +#: keras.src.engine.training.Model.build:1 of msgid "Builds the model based on input shapes received." msgstr "" -#: keras.engine.training.Model.build:3 of +#: keras.src.engine.training.Model.build:3 of msgid "" "This is to be used for subclassed models, which do not know at " "instantiation time what their inputs look like." msgstr "" -#: keras.engine.training.Model.build:6 of +#: keras.src.engine.training.Model.build:6 of msgid "" "This method only exists for users who want to call `model.build()` in a " "standalone way (as a substitute for calling the model on real data to " @@ -4223,28 +4249,44 @@ msgid "" "never throw unexpected errors in an unrelated workflow)." msgstr "" -#: keras.engine.training.Model.build:11 of +#: keras.src.engine.training.Model.build:11 of msgid "" "Single tuple, `TensorShape` instance, or list/dict of shapes, where " "shapes are tuples, integers, or `TensorShape` instances." msgstr "" -#: keras.engine.training.Model.build:14 of +#: keras.src.engine.training.Model.build:15 of msgid "" "1. In case of invalid user-provided data (not of type tuple, list," " `TensorShape`, or dict). 2. If the model requires call arguments " "that are agnostic to the input shapes (positional or keyword arg " -"in call signature). 3. If not all layers were properly built. 4. " -"If float type inputs are not supported within the layers." +"in call signature). 3. If not all layers were properly built." +" 4. If float type inputs are not supported within the layers." msgstr "" -#: keras.engine.training.Model.build:14 of +#: keras.src.engine.training.Model.build:15 of msgid "" "In case of invalid user-provided data (not of type tuple, list, " "`TensorShape`, or dict). 2. If the model requires call arguments that" " are agnostic to the input shapes (positional or keyword arg in " -"call signature). 3. If not all layers were properly built. 4. If " -"float type inputs are not supported within the layers." +"call signature). 3. If not all layers were properly built." +" 4. If float type inputs are not supported within the layers." +msgstr "" + +#: keras.src.engine.base_layer.Layer.build_from_config:1 of +msgid "Builds the layer's states with the supplied config dict." +msgstr "" + +#: keras.src.engine.base_layer.Layer.build_from_config:3 of +msgid "" +"By default, this method calls the `build(config[\"input_shape\"])` " +"method, which creates weights based on the layer's input shape in the " +"supplied config. If your config contains other information needed to load" +" the layer's state, you should override this method." +msgstr "" + +#: keras.src.engine.base_layer.Layer.build_from_config:8 of +msgid "Dict containing the input shape associated with this layer." msgstr "" #: of tensorcircuit.applications.van.MADE.call:1 @@ -4290,24 +4332,10 @@ msgstr "" #: tensorcircuit.applications.van.PixelCNN.call:15 msgid "" "A mask or list of masks. A mask can be either a boolean tensor or None " -"(no mask). For more details, check the guide " +"(no mask). For more details, check the guide " "[here](https://www.tensorflow.org/guide/keras/masking_and_padding)." msgstr "" -#: of tensorcircuit.applications.van.MADE.call:15 -#: tensorcircuit.applications.van.NMF.call:15 -#: tensorcircuit.applications.van.PixelCNN.call:15 -msgid "" -"A mask or list of masks. A mask can be either a boolean tensor or None " -"(no mask). For more details, check the guide" -msgstr "" - -#: of tensorcircuit.applications.van.MADE.call:17 -#: tensorcircuit.applications.van.NMF.call:17 -#: tensorcircuit.applications.van.PixelCNN.call:17 -msgid "[here](https://www.tensorflow.org/guide/keras/masking_and_padding)." -msgstr "" - #: of tensorcircuit.applications.van.MADE.call:19 #: tensorcircuit.applications.van.NMF.call:19 #: tensorcircuit.applications.van.PixelCNN.call:19 @@ -4316,35 +4344,35 @@ msgid "" "more than one outputs." msgstr "" -#: keras.engine.training.Model.compile:1 of +#: keras.src.engine.training.Model.compile:1 of msgid "Configures the model for training." msgstr "" -#: keras.engine.training.Model.compile:5 of +#: keras.src.engine.training.Model.compile:5 of msgid "" "```python " "model.compile(optimizer=tf.keras.optimizers.Adam(learning_rate=1e-3)," msgstr "" -#: keras.engine.training.Model.compile:7 of +#: keras.src.engine.training.Model.compile:7 of msgid "" "loss=tf.keras.losses.BinaryCrossentropy(), " "metrics=[tf.keras.metrics.BinaryAccuracy()," msgstr "" -#: keras.engine.training.Model.compile:9 of +#: keras.src.engine.training.Model.compile:9 of msgid "tf.keras.metrics.FalseNegatives()])" msgstr "" -#: keras.engine.training.Model.compile:12 of +#: keras.src.engine.training.Model.compile:12 of msgid "" "String (name of optimizer) or optimizer instance. See " "`tf.keras.optimizers`." msgstr "" -#: keras.engine.training.Model.compile:14 of +#: keras.src.engine.training.Model.compile:14 of msgid "" -"Loss function. Maybe be a string (name of loss function), or a " +"Loss function. May be a string (name of loss function), or a " "`tf.keras.losses.Loss` instance. See `tf.keras.losses`. A loss function " "is any callable with the signature `loss = fn(y_true, y_pred)`, where " "`y_true` are the ground truth values, and `y_pred` are the model's " @@ -4361,7 +4389,7 @@ msgid "" "individual losses, unless `loss_weights` is specified." msgstr "" -#: keras.engine.training.Model.compile:34 of +#: keras.src.engine.training.Model.compile:34 of msgid "" "List of metrics to be evaluated by the model during training and testing." " Each of this can be a string (name of a built-in function), function or " @@ -4369,80 +4397,117 @@ msgid "" "you will use `metrics=['accuracy']`. A function is any callable with the " "signature `result = fn(y_true, y_pred)`. To specify different metrics for" " different outputs of a multi-output model, you could also pass a " -"dictionary, such as `metrics={'output_a': 'accuracy', 'output_b': " -"['accuracy', 'mse']}`. You can also pass a list to specify a metric or a " -"list of metrics for each output, such as `metrics=[['accuracy'], " -"['accuracy', 'mse']]` or `metrics=['accuracy', ['accuracy', 'mse']]`. " -"When you pass the strings 'accuracy' or 'acc', we convert this to one of " -"`tf.keras.metrics.BinaryAccuracy`, " +"dictionary, such as `metrics={'output_a':'accuracy', " +"'output_b':['accuracy', 'mse']}`. You can also pass a list to specify a " +"metric or a list of metrics for each output, such as " +"`metrics=[['accuracy'], ['accuracy', 'mse']]` or `metrics=['accuracy', " +"['accuracy', 'mse']]`. When you pass the strings 'accuracy' or 'acc', we " +"convert this to one of `tf.keras.metrics.BinaryAccuracy`, " "`tf.keras.metrics.CategoricalAccuracy`, " -"`tf.keras.metrics.SparseCategoricalAccuracy` based on the loss function " -"used and the model output shape. We do a similar conversion for the " -"strings 'crossentropy' and 'ce' as well." +"`tf.keras.metrics.SparseCategoricalAccuracy` based on the shapes of the " +"targets and of the model output. We do a similar conversion for the " +"strings 'crossentropy' and 'ce' as well. The metrics passed here are " +"evaluated without sample weighting; if you would like sample weighting to" +" apply, you can specify your metrics via the `weighted_metrics` argument " +"instead." msgstr "" -#: keras.engine.training.Model.compile:51 of +#: keras.src.engine.training.Model.compile:56 of msgid "" "Optional list or dictionary specifying scalar coefficients (Python " "floats) to weight the loss contributions of different model outputs. The " "loss value that will be minimized by the model will then be the *weighted" " sum* of all individual losses, weighted by the `loss_weights` " -"coefficients. If a list, it is expected to have a 1:1 mapping to the " -"model's outputs. If a dict, it is expected to map output names " -"(strings) to scalar coefficients." +"coefficients. If a list, it is expected to have a 1:1 mapping to the " +"model's outputs. If a dict, it is expected to map output names (strings) " +"to scalar coefficients." msgstr "" -#: keras.engine.training.Model.compile:51 of +#: keras.src.engine.training.Model.compile:64 of msgid "" -"Optional list or dictionary specifying scalar coefficients (Python " -"floats) to weight the loss contributions of different model outputs. The " -"loss value that will be minimized by the model will then be the *weighted" -" sum* of all individual losses, weighted by the `loss_weights` " -"coefficients." +"List of metrics to be evaluated and weighted by `sample_weight` or " +"`class_weight` during training and testing." msgstr "" -#: keras.engine.training.Model.compile:57 of -msgid "If a list, it is expected to have a 1:1 mapping to the model's" +#: keras.src.engine.training.Model.compile:66 of +msgid "" +"Bool. If `True`, this `Model`'s logic will not be wrapped in a " +"`tf.function`. Recommended to leave this as `None` unless your `Model` " +"cannot be run inside a `tf.function`. `run_eagerly=True` is not supported" +" when using `tf.distribute.experimental.ParameterServerStrategy`. " +"Defaults to `False`." msgstr "" -#: keras.engine.training.Model.compile:57 of +#: keras.src.engine.training.Model.compile:66 of msgid "" -"outputs. If a dict, it is expected to map output names (strings) to " -"scalar coefficients." +"Bool. If `True`, this `Model`'s logic will not be wrapped in a " +"`tf.function`. Recommended to leave this as `None` unless your `Model` " +"cannot be run inside a `tf.function`. `run_eagerly=True` is not supported" +" when using `tf.distribute.experimental.ParameterServerStrategy`. " +"Defaults to" +msgstr "" + +#: keras.src.engine.training.Model.compile:71 of +msgid "`False`." msgstr "" -#: keras.engine.training.Model.compile:59 of +#: keras.src.engine.training.Model.compile:72 of msgid "" -"List of metrics to be evaluated and weighted by `sample_weight` or " -"`class_weight` during training and testing." +"Int. The number of batches to run during each `tf.function` call. Running" +" multiple batches inside a single `tf.function` call can greatly improve " +"performance on TPUs or small models with a large Python overhead. At " +"most, one full epoch will be run each execution. If a number larger than " +"the size of the epoch is passed, the execution will be truncated to the " +"size of the epoch. Note that if `steps_per_execution` is set to `N`, " +"`Callback.on_batch_begin` and `Callback.on_batch_end` methods will only " +"be called every `N` batches (i.e. before/after each `tf.function` " +"execution). Defaults to `1`." msgstr "" -#: keras.engine.training.Model.compile:61 of +#: keras.src.engine.training.Model.compile:82 of msgid "" -"Bool. Defaults to `False`. If `True`, this `Model`'s logic will not be " -"wrapped in a `tf.function`. Recommended to leave this as `None` unless " -"your `Model` cannot be run inside a `tf.function`. `run_eagerly=True` is " -"not supported when using " -"`tf.distribute.experimental.ParameterServerStrategy`." +"If `True`, compile the model training step with XLA. " +"[XLA](https://www.tensorflow.org/xla) is an optimizing compiler for " +"machine learning. `jit_compile` is not enabled for by default. Note that " +"`jit_compile=True` may not necessarily work for all models. For more " +"information on supported operations please refer to the [XLA " +"documentation](https://www.tensorflow.org/xla). Also refer to [known XLA " +"issues](https://www.tensorflow.org/xla/known_issues) for more details." msgstr "" -#: keras.engine.training.Model.compile:66 of +#: keras.src.engine.training.Model.compile:93 of msgid "" -"Int. Defaults to 1. The number of batches to run during each " -"`tf.function` call. Running multiple batches inside a single " -"`tf.function` call can greatly improve performance on TPUs or small " -"models with a large Python overhead. At most, one full epoch will be run " -"each execution. If a number larger than the size of the epoch is passed, " -"the execution will be truncated to the size of the epoch. Note that if " -"`steps_per_execution` is set to `N`, `Callback.on_batch_begin` and " -"`Callback.on_batch_end` methods will only be called every `N` batches " -"(i.e. before/after each `tf.function` execution)." +"Integer or 'auto'. Used for `tf.distribute.ParameterServerStrategy` " +"training only. This arg sets the number of shards to split the dataset " +"into, to enable an exact visitation guarantee for evaluation, meaning the" +" model will be applied to each dataset element exactly once, even if " +"workers fail. The dataset must be sharded to ensure separate workers do " +"not process the same data. The number of shards should be at least the " +"number of workers for good performance. A value of 'auto' turns on exact " +"evaluation and uses a heuristic for the number of shards based on the " +"number of workers. 0, meaning no visitation guarantee is provided. NOTE: " +"Custom implementations of `Model.test_step` will be ignored when doing " +"exact evaluation. Defaults to `0`." msgstr "" -#: keras.engine.training.Model.compile:77 of +#: keras.src.engine.training.Model.compile:106 of msgid "Arguments supported for backwards compatibility only." msgstr "" +#: keras.src.engine.training.Model.compile_from_config:1 of +msgid "Compiles the model with the information given in config." +msgstr "" + +#: keras.src.engine.training.Model.compile_from_config:3 of +msgid "" +"This method uses the information in the config (optimizer, loss, metrics," +" etc.) to compile the model." +msgstr "" + +#: keras.src.engine.training.Model.compile_from_config:6 of +msgid "Dict containing information for compiling the model." +msgstr "" + #: of tensorcircuit.applications.van.MADE.compute_dtype:1 #: tensorcircuit.applications.van.MaskedConv2D.compute_dtype:1 #: tensorcircuit.applications.van.MaskedLinear.compute_dtype:1 @@ -4513,56 +4578,202 @@ msgstr "" msgid "The layer's compute dtype." msgstr "" -#: keras.engine.base_layer.Layer.compute_mask:1 of +#: keras.src.engine.training.Model.compute_loss:1 of +msgid "Compute the total loss, validate it, and return it." +msgstr "" + +#: keras.src.engine.training.Model.compute_loss:3 of +msgid "" +"Subclasses can optionally override this method to provide custom loss " +"computation logic." +msgstr "" + +#: keras.src.engine.training.Model.compute_loss:6 of +msgid "Example: ```python class MyModel(tf.keras.Model):" +msgstr "" + +#: keras.src.engine.training.Model.compute_loss:12 of +msgid "def __init__(self, *args, **kwargs):" +msgstr "" + +#: keras.src.engine.training.Model.compute_loss:11 of +msgid "" +"super(MyModel, self).__init__(*args, **kwargs) self.loss_tracker = " +"tf.keras.metrics.Mean(name='loss')" +msgstr "" + +#: keras.src.engine.training.Model.compute_loss:18 of +msgid "def compute_loss(self, x, y, y_pred, sample_weight):" +msgstr "" + +#: keras.src.engine.training.Model.compute_loss:15 of +msgid "" +"loss = tf.reduce_mean(tf.math.squared_difference(y_pred, y)) loss += " +"tf.add_n(self.losses) self.loss_tracker.update_state(loss) return loss" +msgstr "" + +#: keras.src.engine.training.Model.compute_loss:21 of +msgid "def reset_metrics(self):" +msgstr "" + +#: keras.src.engine.training.Model.compute_loss:21 of +msgid "self.loss_tracker.reset_states()" +msgstr "" + +#: keras.src.engine.training.Model.compute_loss:23 of +msgid "@property def metrics(self):" +msgstr "" + +#: keras.src.engine.training.Model.compute_loss:25 of +msgid "return [self.loss_tracker]" +msgstr "" + +#: keras.src.engine.training.Model.compute_loss:27 of +msgid "" +"tensors = tf.random.uniform((10, 10)), tf.random.uniform((10,)) dataset =" +" tf.data.Dataset.from_tensor_slices(tensors).repeat().batch(1)" +msgstr "" + +#: keras.src.engine.training.Model.compute_loss:30 of +msgid "" +"inputs = tf.keras.layers.Input(shape=(10,), name='my_input') outputs = " +"tf.keras.layers.Dense(10)(inputs) model = MyModel(inputs, outputs) " +"model.add_loss(tf.reduce_sum(outputs))" +msgstr "" + +#: keras.src.engine.training.Model.compute_loss:35 of +msgid "" +"optimizer = tf.keras.optimizers.SGD() model.compile(optimizer, " +"loss='mse', steps_per_execution=10) model.fit(dataset, epochs=2, " +"steps_per_epoch=10) print('My custom loss: ', " +"model.loss_tracker.result().numpy()) ```" +msgstr "" + +#: keras.src.engine.training.Model.compute_loss:41 +#: keras.src.engine.training.Model.compute_metrics:23 of +msgid "Input data." +msgstr "" + +#: keras.src.engine.training.Model.compute_loss:42 +#: keras.src.engine.training.Model.compute_metrics:24 of +msgid "Target data." +msgstr "" + +#: keras.src.engine.training.Model.compute_loss:43 of +msgid "Predictions returned by the model (output of `model(x)`)" +msgstr "" + +#: keras.src.engine.training.Model.compute_loss:44 +#: keras.src.engine.training.Model.compute_metrics:26 of +msgid "Sample weights for weighting the loss function." +msgstr "" + +#: keras.src.engine.training.Model.compute_loss:46 of +msgid "" +"The total loss as a `tf.Tensor`, or `None` if no loss results (which is " +"the case when called by `Model.test_step`)." +msgstr "" + +#: keras.src.engine.base_layer.Layer.compute_mask:1 of msgid "Computes an output mask tensor." msgstr "" -#: keras.engine.base_layer.Layer.compute_mask:3 -#: keras.engine.base_layer.Layer.compute_mask:4 of +#: keras.src.engine.base_layer.Layer.compute_mask:3 +#: keras.src.engine.base_layer.Layer.compute_mask:4 of msgid "Tensor or list of tensors." msgstr "" -#: keras.engine.base_layer.Layer.compute_mask:6 of +#: keras.src.engine.base_layer.Layer.compute_mask:6 of msgid "" "None or a tensor (or list of tensors, one per output tensor of the " "layer)." msgstr "" -#: keras.engine.base_layer.Layer.compute_mask:8 of +#: keras.src.engine.base_layer.Layer.compute_mask:8 of msgid "None or a tensor (or list of tensors," msgstr "" -#: keras.engine.base_layer.Layer.compute_mask:9 of +#: keras.src.engine.base_layer.Layer.compute_mask:9 of msgid "one per output tensor of the layer)." msgstr "" -#: keras.engine.base_layer.Layer.compute_output_shape:1 of +#: keras.src.engine.training.Model.compute_metrics:1 of +msgid "Update metric states and collect all metrics to be returned." +msgstr "" + +#: keras.src.engine.training.Model.compute_metrics:3 of +msgid "" +"Subclasses can optionally override this method to provide custom metric " +"updating and collection logic." +msgstr "" + +#: keras.src.engine.training.Model.compute_metrics:6 of +msgid "Example: ```python class MyModel(tf.keras.Sequential):" +msgstr "" + +#: keras.src.engine.training.Model.compute_metrics:10 of +msgid "def compute_metrics(self, x, y, y_pred, sample_weight):" +msgstr "" + +#: keras.src.engine.training.Model.compute_metrics:12 of +msgid "" +"# This super call updates `self.compiled_metrics` and returns # results " +"for all metrics listed in `self.metrics`. metric_results = super(MyModel," +" self).compute_metrics(" +msgstr "" + +#: keras.src.engine.training.Model.compute_metrics:15 of +msgid "x, y, y_pred, sample_weight)" +msgstr "" + +#: keras.src.engine.training.Model.compute_metrics:17 of +msgid "" +"# Note that `self.custom_metric` is not listed in `self.metrics`. " +"self.custom_metric.update_state(x, y, y_pred, sample_weight) " +"metric_results['custom_metric_name'] = self.custom_metric.result() return" +" metric_results" +msgstr "" + +#: keras.src.engine.training.Model.compute_metrics:25 of +msgid "Predictions returned by the model (output of `model.call(x)`)" +msgstr "" + +#: keras.src.engine.training.Model.compute_metrics:28 of +msgid "" +"A `dict` containing values that will be passed to " +"`tf.keras.callbacks.CallbackList.on_train_batch_end()`. Typically, the " +"values of the metrics listed in `self.metrics` are returned. Example: " +"`{'loss': 0.2, 'accuracy': 0.7}`." +msgstr "" + +#: keras.src.engine.base_layer.Layer.compute_output_shape:1 of msgid "Computes the output shape of the layer." msgstr "" -#: keras.engine.base_layer.Layer.compute_output_shape:3 of +#: keras.src.engine.base_layer.Layer.compute_output_shape:3 of msgid "" -"If the layer has not been built, this method will call `build` on the " -"layer. This assumes that the layer will later be used with inputs that " -"match the input shape provided here." +"This method will cause the layer's state to be built, if that has not " +"happened before. This requires that the layer will later be used with " +"inputs that match the input shape provided here." msgstr "" -#: keras.engine.base_layer.Layer.compute_output_shape:7 of +#: keras.src.engine.base_layer.Layer.compute_output_shape:7 of msgid "" -"Shape tuple (tuple of integers) or list of shape tuples (one per output " -"tensor of the layer). Shape tuples can include None for free dimensions, " -"instead of an integer." +"Shape tuple (tuple of integers) or `tf.TensorShape`, or structure of " +"shape tuples / `tf.TensorShape` instances (one per output tensor of the " +"layer). Shape tuples can include None for free dimensions, instead of an " +"integer." msgstr "" -#: keras.engine.base_layer.Layer.compute_output_shape:12 of -msgid "An input shape tuple." +#: keras.src.engine.base_layer.Layer.compute_output_shape:13 of +msgid "A `tf.TensorShape` instance or structure of `tf.TensorShape` instances." msgstr "" -#: keras.engine.base_layer.Layer.compute_output_signature:1 of +#: keras.src.engine.base_layer.Layer.compute_output_signature:1 of msgid "Compute the output tensor signature of the layer based on the inputs." msgstr "" -#: keras.engine.base_layer.Layer.compute_output_signature:3 of +#: keras.src.engine.base_layer.Layer.compute_output_signature:3 of msgid "" "Unlike a TensorShape object, a TensorSpec object contains both shape and " "dtype information for a tensor. This method allows layers to provide " @@ -4572,44 +4783,59 @@ msgid "" "matches the input dtype." msgstr "" -#: keras.engine.base_layer.Layer.compute_output_signature:10 of +#: keras.src.engine.base_layer.Layer.compute_output_signature:10 of msgid "" "Single TensorSpec or nested structure of TensorSpec objects, describing a" " candidate input for the layer." msgstr "" -#: keras.engine.base_layer.Layer.compute_output_signature:13 of +#: keras.src.engine.base_layer.Layer.compute_output_signature:13 of msgid "" -"Single TensorSpec or nested structure of TensorSpec objects, describing" -" how the layer would transform the provided input." +"Single TensorSpec or nested structure of TensorSpec objects, describing" +" how the layer would transform the provided input." msgstr "" -#: keras.engine.base_layer.Layer.compute_output_signature:16 of -msgid "Single TensorSpec or nested structure of TensorSpec objects, describing" +#: keras.src.engine.base_layer.Layer.compute_output_signature:16 of +msgid "Single TensorSpec or nested structure of TensorSpec objects," msgstr "" -#: keras.engine.base_layer.Layer.compute_output_signature:16 of -msgid "how the layer would transform the provided input." +#: keras.src.engine.base_layer.Layer.compute_output_signature:16 of +msgid "describing how the layer would transform the provided input." msgstr "" -#: keras.engine.base_layer.Layer.compute_output_signature:18 of +#: keras.src.engine.base_layer.Layer.compute_output_signature:18 of msgid "If input_signature contains a non-TensorSpec object." msgstr "" -#: keras.engine.base_layer.Layer.count_params:1 of +#: keras.src.engine.base_layer.Layer.count_params:1 of msgid "Count the total number of scalars composing the weights." msgstr "" -#: keras.engine.base_layer.Layer.count_params:3 of +#: keras.src.engine.base_layer.Layer.count_params:3 of msgid "An integer count." msgstr "" -#: keras.engine.base_layer.Layer.count_params:5 of +#: keras.src.engine.base_layer.Layer.count_params:5 of msgid "" "if the layer isn't yet built (in which case its weights aren't yet " "defined)." msgstr "" +#: of tensorcircuit.applications.van.MADE.distribute_reduction_method:1 +#: tensorcircuit.applications.van.NMF.distribute_reduction_method:1 +#: tensorcircuit.applications.van.PixelCNN.distribute_reduction_method:1 +msgid "The method employed to reduce per-replica values during training." +msgstr "" + +#: of tensorcircuit.applications.van.MADE.distribute_reduction_method:3 +#: tensorcircuit.applications.van.NMF.distribute_reduction_method:3 +#: tensorcircuit.applications.van.PixelCNN.distribute_reduction_method:3 +msgid "" +"Unless specified, the value \"auto\" will be assumed, indicating that the" +" reduction strategy should be chosen based on the current running " +"environment. See `reduce_per_replica` function for more details." +msgstr "" + #: of tensorcircuit.applications.van.MADE.distribute_strategy:1 #: tensorcircuit.applications.van.NMF.distribute_strategy:1 #: tensorcircuit.applications.van.PixelCNN.distribute_strategy:1 @@ -4679,15 +4905,15 @@ msgstr "" msgid "Whether the layer is dynamic (eager-only); set in the constructor." msgstr "" -#: keras.engine.training.Model.evaluate:1 of +#: keras.src.engine.training.Model.evaluate:1 of msgid "Returns the loss value & metrics values for the model in test mode." msgstr "" -#: keras.engine.training.Model.evaluate:3 of +#: keras.src.engine.training.Model.evaluate:3 of msgid "Computation is done in batches (see the `batch_size` arg.)" msgstr "" -#: keras.engine.training.Model.evaluate:5 of +#: keras.src.engine.training.Model.evaluate:5 of msgid "" "Input data. It could be: - A Numpy array (or array-like), or a list of " "arrays (in case the model has multiple inputs). - A TensorFlow tensor, " @@ -4695,63 +4921,67 @@ msgid "" "mapping input names to the corresponding array/tensors, if the model " "has named inputs. - A `tf.data` dataset. Should return a tuple of " "either `(inputs, targets)` or `(inputs, targets, sample_weights)`. - A " -"generator or `keras.utils.Sequence` returning `(inputs, targets)` or " +"generator or `keras.utils.Sequence` returning `(inputs, targets)` or " "`(inputs, targets, sample_weights)`. A more detailed description of " "unpacking behavior for iterator types (Dataset, generator, Sequence) is " "given in the `Unpacking behavior for iterator-like inputs` section of " "`Model.fit`." msgstr "" -#: keras.engine.training.Model.evaluate:5 keras.engine.training.Model.fit:3 -#: keras.engine.training.Model.train_on_batch:3 of +#: keras.src.engine.training.Model.evaluate:5 +#: keras.src.engine.training.Model.fit:3 +#: keras.src.engine.training.Model.train_on_batch:3 of msgid "" "Input data. It could be: - A Numpy array (or array-like), or a list of " "arrays" msgstr "" -#: keras.engine.training.Model.evaluate:7 keras.engine.training.Model.fit:5 -#: keras.engine.training.Model.predict:13 -#: keras.engine.training.Model.train_on_batch:5 -#: keras.engine.training.Model.train_on_batch:7 of +#: keras.src.engine.training.Model.evaluate:7 +#: keras.src.engine.training.Model.fit:5 +#: keras.src.engine.training.Model.predict:28 +#: keras.src.engine.training.Model.train_on_batch:5 +#: keras.src.engine.training.Model.train_on_batch:7 of msgid "(in case the model has multiple inputs)." msgstr "" -#: keras.engine.training.Model.evaluate:8 keras.engine.training.Model.fit:6 -#: keras.engine.training.Model.predict:14 of +#: keras.src.engine.training.Model.evaluate:8 +#: keras.src.engine.training.Model.fit:6 +#: keras.src.engine.training.Model.predict:29 of msgid "" "A TensorFlow tensor, or a list of tensors (in case the model has multiple" " inputs)." msgstr "" -#: keras.engine.training.Model.evaluate:10 keras.engine.training.Model.fit:8 of +#: keras.src.engine.training.Model.evaluate:10 +#: keras.src.engine.training.Model.fit:8 of msgid "" "A dict mapping input names to the corresponding array/tensors, if the " "model has named inputs." msgstr "" -#: keras.engine.training.Model.evaluate:12 keras.engine.training.Model.fit:10 -#: of +#: keras.src.engine.training.Model.evaluate:12 +#: keras.src.engine.training.Model.fit:10 of msgid "" "A `tf.data` dataset. Should return a tuple of either `(inputs, targets)` " "or `(inputs, targets, sample_weights)`." msgstr "" -#: keras.engine.training.Model.evaluate:15 keras.engine.training.Model.fit:13 -#: of +#: keras.src.engine.training.Model.evaluate:15 +#: keras.src.engine.training.Model.fit:13 of msgid "" "A generator or `keras.utils.Sequence` returning `(inputs, targets)` or " "`(inputs, targets, sample_weights)`." msgstr "" -#: keras.engine.training.Model.evaluate:17 -#: keras.engine.training.Model.predict:18 of +#: keras.src.engine.training.Model.evaluate:17 +#: keras.src.engine.training.Model.predict:33 of msgid "" "A more detailed description of unpacking behavior for iterator types " "(Dataset, generator, Sequence) is given in the `Unpacking behavior for " "iterator-like inputs` section of `Model.fit`." msgstr "" -#: keras.engine.training.Model.evaluate:20 of +#: keras.src.engine.training.Model.evaluate:20 of msgid "" "Target data. Like the input data `x`, it could be either Numpy array(s) " "or TensorFlow tensor(s). It should be consistent with `x` (you cannot " @@ -4760,7 +4990,7 @@ msgid "" "specified (since targets will be obtained from the iterator/dataset)." msgstr "" -#: keras.engine.training.Model.evaluate:26 of +#: keras.src.engine.training.Model.evaluate:26 of msgid "" "Integer or `None`. Number of samples per batch of computation. If " "unspecified, `batch_size` will default to 32. Do not specify the " @@ -4768,34 +4998,41 @@ msgid "" "`keras.utils.Sequence` instances (since they generate batches)." msgstr "" -#: keras.engine.training.Model.evaluate:31 of -msgid "0 or 1. Verbosity mode. 0 = silent, 1 = progress bar." +#: keras.src.engine.training.Model.evaluate:31 +#: keras.src.engine.training.Model.predict:42 of +msgid "" +"`\"auto\"`, 0, 1, or 2. Verbosity mode. 0 = silent, 1 = progress bar, 2 =" +" single line. `\"auto\"` becomes 1 for most cases, and to 2 when used " +"with `ParameterServerStrategy`. Note that the progress bar is not " +"particularly useful when logged to a file, so `verbose=2` is recommended " +"when not running interactively (e.g. in a production environment). " +"Defaults to 'auto'." msgstr "" -#: keras.engine.training.Model.evaluate:32 of +#: keras.src.engine.training.Model.evaluate:38 of msgid "" "Optional Numpy array of weights for the test samples, used for weighting " "the loss function. You can either pass a flat (1D) Numpy array with the " "same length as the input samples (1:1 mapping between weights and " "samples), or in the case of temporal data, you can pass a 2D array " "with shape `(samples, sequence_length)`, to apply a different weight " -"to every timestep of every sample. This argument is not supported " -"when `x` is a dataset, instead pass sample weights as the third " +"to every timestep of every sample. This argument is not supported " +"when `x` is a dataset, instead pass sample weights as the third " "element of `x`." msgstr "" -#: keras.engine.training.Model.evaluate:32 of +#: keras.src.engine.training.Model.evaluate:38 of msgid "" "Optional Numpy array of weights for the test samples, used for weighting " "the loss function. You can either pass a flat (1D) Numpy array with the " "same length as the input samples" msgstr "" -#: keras.engine.training.Model.evaluate:38 of +#: keras.src.engine.training.Model.evaluate:45 of msgid "(1:1 mapping between weights and samples), or in the case of" msgstr "" -#: keras.engine.training.Model.evaluate:36 of +#: keras.src.engine.training.Model.evaluate:42 of msgid "" "temporal data, you can pass a 2D array with shape `(samples, " "sequence_length)`, to apply a different weight to every timestep of every" @@ -4803,7 +5040,7 @@ msgid "" "pass sample weights as the third element of `x`." msgstr "" -#: keras.engine.training.Model.evaluate:40 of +#: keras.src.engine.training.Model.evaluate:47 of msgid "" "Integer or `None`. Total number of steps (batches of samples) before " "declaring the evaluation round finished. Ignored with the default value " @@ -4812,30 +5049,33 @@ msgid "" "with array inputs." msgstr "" -#: keras.engine.training.Model.evaluate:45 of +#: keras.src.engine.training.Model.evaluate:52 of msgid "" "List of `keras.callbacks.Callback` instances. List of callbacks to apply " -"during evaluation. See [callbacks](/api_docs/python/tf/keras/callbacks)." +"during evaluation. See " +"[callbacks](https://www.tensorflow.org/api_docs/python/tf/keras/callbacks)." msgstr "" -#: keras.engine.training.Model.evaluate:48 keras.engine.training.Model.fit:160 -#: keras.engine.training.Model.predict:36 of +#: keras.src.engine.training.Model.evaluate:55 +#: keras.src.engine.training.Model.predict:58 of msgid "" "Integer. Used for generator or `keras.utils.Sequence` input only. Maximum" " size for the generator queue. If unspecified, `max_queue_size` will " "default to 10." msgstr "" -#: keras.engine.training.Model.evaluate:51 keras.engine.training.Model.fit:163 -#: keras.engine.training.Model.predict:39 of +#: keras.src.engine.training.Model.evaluate:58 +#: keras.src.engine.training.Model.fit:178 +#: keras.src.engine.training.Model.predict:62 of msgid "" "Integer. Used for generator or `keras.utils.Sequence` input only. Maximum" " number of processes to spin up when using process-based threading. If " "unspecified, `workers` will default to 1." msgstr "" -#: keras.engine.training.Model.evaluate:54 keras.engine.training.Model.fit:167 -#: keras.engine.training.Model.predict:43 of +#: keras.src.engine.training.Model.evaluate:62 +#: keras.src.engine.training.Model.fit:182 +#: keras.src.engine.training.Model.predict:66 of msgid "" "Boolean. Used for generator or `keras.utils.Sequence` input only. If " "`True`, use process-based threading. If unspecified, " @@ -4845,32 +5085,26 @@ msgid "" "children processes." msgstr "" -#: keras.engine.training.Model.evaluate:60 -#: keras.engine.training.Model.test_on_batch:21 -#: keras.engine.training.Model.train_on_batch:25 of +#: keras.src.engine.training.Model.evaluate:69 +#: keras.src.engine.training.Model.test_on_batch:21 +#: keras.src.engine.training.Model.train_on_batch:27 of msgid "" "If `True`, loss and metric results are returned as a dict, with each key " "being the name of the metric. If `False`, they are returned as a list." msgstr "" -#: keras.engine.training.Model.evaluate:63 of +#: keras.src.engine.training.Model.evaluate:72 of msgid "Unused at this time." msgstr "" -#: keras.engine.training.Model.evaluate:65 of +#: keras.src.engine.training.Model.evaluate:74 of msgid "" "See the discussion of `Unpacking behavior for iterator-like inputs` for " "`Model.fit`." msgstr "" -#: keras.engine.training.Model.evaluate:68 of -msgid "" -"`Model.evaluate` is not yet supported with " -"`tf.distribute.experimental.ParameterServerStrategy`." -msgstr "" - -#: keras.engine.training.Model.evaluate:71 -#: keras.engine.training.Model.test_on_batch:25 of +#: keras.src.engine.training.Model.evaluate:77 +#: keras.src.engine.training.Model.test_on_batch:25 of msgid "" "Scalar test loss (if the model has a single output and no metrics) or " "list of scalars (if the model has multiple outputs and/or metrics). The " @@ -4878,42 +5112,89 @@ msgid "" "scalar outputs." msgstr "" -#: keras.engine.training.Model.evaluate:76 of +#: keras.src.engine.training.Model.evaluate:82 of msgid "If `model.evaluate` is wrapped in a `tf.function`." msgstr "" -#: keras.engine.training.Model.evaluate_generator:1 of +#: keras.src.engine.training.Model.evaluate_generator:1 of msgid "Evaluates the model on a data generator." msgstr "" -#: keras.engine.training.Model.evaluate_generator:4 -#: keras.engine.training.Model.fit_generator:4 -#: keras.engine.training.Model.predict_generator:4 of +#: keras.src.engine.training.Model.evaluate_generator:4 +#: keras.src.engine.training.Model.fit_generator:4 +#: keras.src.engine.training.Model.predict_generator:4 of msgid "DEPRECATED:" msgstr "" -#: keras.engine.training.Model.evaluate_generator:4 of +#: keras.src.engine.training.Model.evaluate_generator:4 of msgid "" "`Model.evaluate` now supports generators, so there is no longer any need " "to use this endpoint." msgstr "" -#: keras.engine.base_layer.Layer.finalize_state:1 of +#: keras.src.engine.training.Model.export:1 of +msgid "Create a SavedModel artifact for inference (e.g. via TF-Serving)." +msgstr "" + +#: keras.src.engine.training.Model.export:3 of +msgid "" +"This method lets you export a model to a lightweight SavedModel artifact " +"that contains the model's forward pass only (its `call()` method) and can" +" be served via e.g. TF-Serving. The forward pass is registered under the " +"name `serve()` (see example below)." +msgstr "" + +#: keras.src.engine.training.Model.export:8 of +msgid "" +"The original code of the model (including any custom layers you may have " +"used) is *no longer* necessary to reload the artifact -- it is entirely " +"standalone." +msgstr "" + +#: keras.src.engine.training.Model.export:12 of +msgid "`str` or `pathlib.Path` object. Path where to save the artifact." +msgstr "" + +#: keras.src.engine.training.Model.export:17 of +msgid "```python # Create the artifact model.export(\"path/to/location\")" +msgstr "" + +#: keras.src.engine.training.Model.export:21 of +msgid "" +"# Later, in a different process / environment... reloaded_artifact = " +"tf.saved_model.load(\"path/to/location\") predictions = " +"reloaded_artifact.serve(input_data) ```" +msgstr "" + +#: keras.src.engine.training.Model.export:26 of +msgid "" +"If you would like to customize your serving endpoints, you can use the " +"lower-level `keras.export.ExportArchive` class. The `export()` method " +"relies on `ExportArchive` internally." +msgstr "" + +#: keras.src.engine.base_layer.Layer.finalize_state:1 of msgid "Finalizes the layers state after updating layer weights." msgstr "" -#: keras.engine.base_layer.Layer.finalize_state:3 of +#: keras.src.engine.base_layer.Layer.finalize_state:3 of msgid "" "This function can be subclassed in a layer and will be called after " "updating a layer weights. It can be overridden to finalize any additional" " layer state after a weight update." msgstr "" -#: keras.engine.training.Model.fit:1 of -msgid "Trains the model for a fixed number of epochs (iterations on a dataset)." +#: keras.src.engine.base_layer.Layer.finalize_state:7 of +msgid "" +"This function will be called after weights of a layer have been restored " +"from a loaded model." +msgstr "" + +#: keras.src.engine.training.Model.fit:1 of +msgid "Trains the model for a fixed number of epochs (dataset iterations)." msgstr "" -#: keras.engine.training.Model.fit:3 of +#: keras.src.engine.training.Model.fit:3 of msgid "" "Input data. It could be: - A Numpy array (or array-like), or a list of " "arrays (in case the model has multiple inputs). - A TensorFlow tensor, " @@ -4921,7 +5202,7 @@ msgid "" "mapping input names to the corresponding array/tensors, if the model " "has named inputs. - A `tf.data` dataset. Should return a tuple of " "either `(inputs, targets)` or `(inputs, targets, sample_weights)`. - A " -"generator or `keras.utils.Sequence` returning `(inputs, targets)` or " +"generator or `keras.utils.Sequence` returning `(inputs, targets)` or " "`(inputs, targets, sample_weights)`. - A " "`tf.keras.utils.experimental.DatasetCreator`, which wraps a callable " "that takes a single argument of type `tf.distribute.InputContext`, and " @@ -4929,12 +5210,15 @@ msgid "" " prefer to specify the per-replica batching and sharding logic for the " "`Dataset`. See `tf.keras.utils.experimental.DatasetCreator` doc for " "more information. A more detailed description of unpacking behavior for" -" iterator types (Dataset, generator, Sequence) is given below. If using " +" iterator types (Dataset, generator, Sequence) is given below. If these " +"include `sample_weights` as a third component, note that sample weighting" +" applies to the `weighted_metrics` argument but not the `metrics` " +"argument in `compile()`. If using " "`tf.distribute.experimental.ParameterServerStrategy`, only " "`DatasetCreator` type is supported for `x`." msgstr "" -#: keras.engine.training.Model.fit:15 of +#: keras.src.engine.training.Model.fit:15 of msgid "" "A `tf.keras.utils.experimental.DatasetCreator`, which wraps a callable " "that takes a single argument of type `tf.distribute.InputContext`, and " @@ -4944,15 +5228,18 @@ msgid "" "information." msgstr "" -#: keras.engine.training.Model.fit:22 of +#: keras.src.engine.training.Model.fit:22 of msgid "" "A more detailed description of unpacking behavior for iterator types " -"(Dataset, generator, Sequence) is given below. If using " +"(Dataset, generator, Sequence) is given below. If these include " +"`sample_weights` as a third component, note that sample weighting applies" +" to the `weighted_metrics` argument but not the `metrics` argument in " +"`compile()`. If using " "`tf.distribute.experimental.ParameterServerStrategy`, only " "`DatasetCreator` type is supported for `x`." msgstr "" -#: keras.engine.training.Model.fit:26 of +#: keras.src.engine.training.Model.fit:29 of msgid "" "Target data. Like the input data `x`, it could be either Numpy array(s) " "or TensorFlow tensor(s). It should be consistent with `x` (you cannot " @@ -4961,7 +5248,7 @@ msgid "" "specified (since targets will be obtained from `x`)." msgstr "" -#: keras.engine.training.Model.fit:32 of +#: keras.src.engine.training.Model.fit:35 of msgid "" "Integer or `None`. Number of samples per gradient update. If unspecified," " `batch_size` will default to 32. Do not specify the `batch_size` if your" @@ -4969,7 +5256,7 @@ msgid "" "instances (since they generate batches)." msgstr "" -#: keras.engine.training.Model.fit:38 of +#: keras.src.engine.training.Model.fit:41 of msgid "" "Integer. Number of epochs to train the model. An epoch is an iteration " "over the entire `x` and `y` data provided (unless the `steps_per_epoch` " @@ -4979,16 +5266,17 @@ msgid "" "merely until the epoch of index `epochs` is reached." msgstr "" -#: keras.engine.training.Model.fit:48 of +#: keras.src.engine.training.Model.fit:51 of msgid "" "'auto', 0, 1, or 2. Verbosity mode. 0 = silent, 1 = progress bar, 2 = one" -" line per epoch. 'auto' defaults to 1 for most cases, but 2 when used " -"with `ParameterServerStrategy`. Note that the progress bar is not " -"particularly useful when logged to a file, so verbose=2 is recommended " -"when not running interactively (eg, in a production environment)." +" line per epoch. 'auto' becomes 1 for most cases, but 2 when used with " +"`ParameterServerStrategy`. Note that the progress bar is not particularly" +" useful when logged to a file, so verbose=2 is recommended when not " +"running interactively (eg, in a production environment). Defaults to " +"'auto'." msgstr "" -#: keras.engine.training.Model.fit:55 of +#: keras.src.engine.training.Model.fit:58 of msgid "" "List of `keras.callbacks.Callback` instances. List of callbacks to apply " "during training. See `tf.keras.callbacks`. Note " @@ -5002,43 +5290,21 @@ msgid "" "`steps_per_epoch` value." msgstr "" -#: keras.engine.training.Model.fit:66 of -msgid "" -"Float between 0 and 1. Fraction of the training data to be used as " -"validation data. The model will set apart this fraction of the training " -"data, will not train on it, and will evaluate the loss and any model " -"metrics on this data at the end of each epoch. The validation data is " -"selected from the last samples in the `x` and `y` data provided, before " -"shuffling. This argument is not supported when `x` is a dataset, " -"generator or `keras.utils.Sequence` instance. `validation_split` is not " -"yet supported with `tf.distribute.experimental.ParameterServerStrategy`." -msgstr "" - -#: keras.engine.training.Model.fit:74 of -msgid "Float between 0 and 1." -msgstr "" - -#: keras.engine.training.Model.fit:68 of -msgid "" -"Fraction of the training data to be used as validation data. The model " -"will set apart this fraction of the training data, will not train on it, " -"and will evaluate the loss and any model metrics on this data at the end " -"of each epoch. The validation data is selected from the last samples in " -"the `x` and `y` data provided, before shuffling. This argument is not " -"supported when `x` is a dataset, generator or" -msgstr "" - -#: keras.engine.training.Model.fit:77 of -msgid "`keras.utils.Sequence` instance." -msgstr "" - -#: keras.engine.training.Model.fit:77 of +#: keras.src.engine.training.Model.fit:70 of msgid "" -"`validation_split` is not yet supported with " +"Float between 0 and 1. Fraction of the training data to be used as " +"validation data. The model will set apart this fraction of the training " +"data, will not train on it, and will evaluate the loss and any model " +"metrics on this data at the end of each epoch. The validation data is " +"selected from the last samples in the `x` and `y` data provided, before " +"shuffling. This argument is not supported when `x` is a dataset, " +"generator or `keras.utils.Sequence` instance. If both `validation_data` " +"and `validation_split` are provided, `validation_data` will override " +"`validation_split`. `validation_split` is not yet supported with " "`tf.distribute.experimental.ParameterServerStrategy`." msgstr "" -#: keras.engine.training.Model.fit:79 of +#: keras.src.engine.training.Model.fit:84 of msgid "" "Data on which to evaluate the loss and any model metrics at the end of " "each epoch. The model will not be trained on this data. Thus, note the " @@ -5046,14 +5312,14 @@ msgid "" "or `validation_data` is not affected by regularization layers like noise " "and dropout. `validation_data` will override `validation_split`. " "`validation_data` could be: - A tuple `(x_val, y_val)` of Numpy arrays " -"or tensors. - A tuple `(x_val, y_val, val_sample_weights)` of NumPy " -"arrays. - A `tf.data.Dataset`. - A Python generator or " +"or tensors. - A tuple `(x_val, y_val, val_sample_weights)` of NumPy" +" arrays. - A `tf.data.Dataset`. - A Python generator or " "`keras.utils.Sequence` returning `(inputs, targets)` or `(inputs, " "targets, sample_weights)`. `validation_data` is not yet supported with " "`tf.distribute.experimental.ParameterServerStrategy`." msgstr "" -#: keras.engine.training.Model.fit:79 of +#: keras.src.engine.training.Model.fit:84 of msgid "" "Data on which to evaluate the loss and any model metrics at the end of " "each epoch. The model will not be trained on this data. Thus, note the " @@ -5063,33 +5329,33 @@ msgid "" "`validation_data` could be:" msgstr "" -#: keras.engine.training.Model.fit:87 of +#: keras.src.engine.training.Model.fit:92 of msgid "A tuple `(x_val, y_val)` of Numpy arrays or tensors." msgstr "" -#: keras.engine.training.Model.fit:88 of +#: keras.src.engine.training.Model.fit:93 of msgid "A tuple `(x_val, y_val, val_sample_weights)` of NumPy arrays." msgstr "" -#: keras.engine.training.Model.fit:89 of +#: keras.src.engine.training.Model.fit:95 of msgid "A `tf.data.Dataset`." msgstr "" -#: keras.engine.training.Model.fit:90 of +#: keras.src.engine.training.Model.fit:96 of msgid "A Python generator or `keras.utils.Sequence` returning" msgstr "" -#: keras.engine.training.Model.fit:91 of +#: keras.src.engine.training.Model.fit:97 of msgid "`(inputs, targets)` or `(inputs, targets, sample_weights)`." msgstr "" -#: keras.engine.training.Model.fit:92 of +#: keras.src.engine.training.Model.fit:98 of msgid "" "`validation_data` is not yet supported with " "`tf.distribute.experimental.ParameterServerStrategy`." msgstr "" -#: keras.engine.training.Model.fit:94 of +#: keras.src.engine.training.Model.fit:100 of msgid "" "Boolean (whether to shuffle the training data before each epoch) or str " "(for 'batch'). This argument is ignored when `x` is a generator or an " @@ -5098,57 +5364,39 @@ msgid "" "effect when `steps_per_epoch` is not `None`." msgstr "" -#: keras.engine.training.Model.fit:100 of +#: keras.src.engine.training.Model.fit:106 of msgid "" "Optional dictionary mapping class indices (integers) to a weight (float) " "value, used for weighting the loss function (during training only). This " "can be useful to tell the model to \"pay more attention\" to samples from" -" an under-represented class." +" an under-represented class. When `class_weight` is specified and targets" +" have a rank of 2 or greater, either `y` must be one-hot encoded, or an " +"explicit final dimension of `1` must be included for sparse class labels." msgstr "" -#: keras.engine.training.Model.fit:106 of +#: keras.src.engine.training.Model.fit:115 of msgid "" -"Optional Numpy array of weights for the training samples, used for " -"weighting the loss function (during training only). You can either pass " -"a flat (1D) Numpy array with the same length as the input samples (1:1 " -"mapping between weights and samples), or in the case of temporal data, " -"you can pass a 2D array with shape `(samples, sequence_length)`, to " -"apply a different weight to every timestep of every sample. This " -"argument is not supported when `x` is a dataset, generator, or " -"`keras.utils.Sequence` instance, instead provide the sample_weights as " -"the third element of `x`." +"Optional Numpy array of weights for the training samples, used for " +"weighting the loss function (during training only). You can either pass a" +" flat (1D) Numpy array with the same length as the input samples (1:1 " +"mapping between weights and samples), or in the case of temporal data, " +"you can pass a 2D array with shape `(samples, sequence_length)`, to apply" +" a different weight to every timestep of every sample. This argument is " +"not supported when `x` is a dataset, generator, or `keras.utils.Sequence`" +" instance, instead provide the sample_weights as the third element of " +"`x`. Note that sample weighting does not apply to metrics specified via " +"the `metrics` argument in `compile()`. To apply sample weighting to your " +"metrics, you can specify them via the `weighted_metrics` in `compile()` " +"instead." msgstr "" -#: keras.engine.training.Model.fit:115 of -msgid "Optional Numpy array of weights for" -msgstr "" - -#: keras.engine.training.Model.fit:108 of -msgid "" -"the training samples, used for weighting the loss function (during " -"training only). You can either pass a flat (1D) Numpy array with the same" -" length as the input samples (1:1 mapping between weights and samples), " -"or in the case of temporal data, you can pass a 2D array with shape " -"`(samples, sequence_length)`, to apply a different weight to every " -"timestep of every sample. This argument is not supported when `x` is a " -"dataset, generator, or" -msgstr "" - -#: keras.engine.training.Model.fit:117 of -msgid "`keras.utils.Sequence` instance, instead provide the sample_weights" -msgstr "" - -#: keras.engine.training.Model.fit:118 of -msgid "as the third element of `x`." -msgstr "" - -#: keras.engine.training.Model.fit:119 of +#: keras.src.engine.training.Model.fit:131 of msgid "" "Integer. Epoch at which to start training (useful for resuming a previous" " training run)." msgstr "" -#: keras.engine.training.Model.fit:122 of +#: keras.src.engine.training.Model.fit:134 of msgid "" "Integer or `None`. Total number of steps (batches of samples) before " "declaring one epoch finished and starting the next epoch. When training " @@ -5156,15 +5404,15 @@ msgid "" " equal to the number of samples in your dataset divided by the batch " "size, or 1 if that cannot be determined. If x is a `tf.data` dataset, and" " 'steps_per_epoch' is None, the epoch will run until the input dataset is" -" exhausted. When passing an infinitely repeating dataset, you must " +" exhausted. When passing an infinitely repeating dataset, you must " "specify the `steps_per_epoch` argument. If `steps_per_epoch=-1` the " -"training will run indefinitely with an infinitely repeating dataset. This" -" argument is not supported with array inputs. When using " +"training will run indefinitely with an infinitely repeating dataset. " +"This argument is not supported with array inputs. When using " "`tf.distribute.experimental.ParameterServerStrategy`: * " "`steps_per_epoch=None` is not supported." msgstr "" -#: keras.engine.training.Model.fit:122 of +#: keras.src.engine.training.Model.fit:134 of msgid "" "Integer or `None`. Total number of steps (batches of samples) before " "declaring one epoch finished and starting the next epoch. When training " @@ -5172,18 +5420,18 @@ msgid "" " equal to the number of samples in your dataset divided by the batch " "size, or 1 if that cannot be determined. If x is a `tf.data` dataset, and" " 'steps_per_epoch' is None, the epoch will run until the input dataset is" -" exhausted. When passing an infinitely repeating dataset, you must " +" exhausted. When passing an infinitely repeating dataset, you must " "specify the `steps_per_epoch` argument. If `steps_per_epoch=-1` the " -"training will run indefinitely with an infinitely repeating dataset. This" -" argument is not supported with array inputs. When using " +"training will run indefinitely with an infinitely repeating dataset. " +"This argument is not supported with array inputs. When using " "`tf.distribute.experimental.ParameterServerStrategy`:" msgstr "" -#: keras.engine.training.Model.fit:136 of +#: keras.src.engine.training.Model.fit:149 of msgid "`steps_per_epoch=None` is not supported." msgstr "" -#: keras.engine.training.Model.fit:137 of +#: keras.src.engine.training.Model.fit:150 of msgid "" "Only relevant if `validation_data` is provided and is a `tf.data` " "dataset. Total number of steps (batches of samples) to draw before " @@ -5197,7 +5445,7 @@ msgid "" "time." msgstr "" -#: keras.engine.training.Model.fit:147 of +#: keras.src.engine.training.Model.fit:161 of msgid "" "Integer or `None`. Number of samples per validation batch. If " "unspecified, will default to `batch_size`. Do not specify the " @@ -5206,10 +5454,10 @@ msgid "" "batches)." msgstr "" -#: keras.engine.training.Model.fit:153 of +#: keras.src.engine.training.Model.fit:167 of msgid "" "Only relevant if validation data is provided. Integer or " -"`collections.abc.Container` instance (e.g. list, tuple, etc.). If an " +"`collections.abc.Container` instance (e.g. list, tuple, etc.). If an " "integer, specifies how many training epochs to run before a new " "validation run is performed, e.g. `validation_freq=2` runs validation " "every 2 epochs. If a Container, specifies the epochs on which to run " @@ -5217,19 +5465,26 @@ msgid "" "of the 1st, 2nd, and 10th epochs." msgstr "" -#: keras.engine.training.Model.fit:196 of +#: keras.src.engine.training.Model.fit:175 of +msgid "" +"Integer. Used for generator or `keras.utils.Sequence` input only. Maximum" +" size for the generator queue. If unspecified, `max_queue_size` will " +"default to 10." +msgstr "" + +#: keras.src.engine.training.Model.fit:214 of msgid "Unpacking behavior for iterator-like inputs:" msgstr "" -#: keras.engine.training.Model.fit:175 of +#: keras.src.engine.training.Model.fit:191 of msgid "A common pattern is to pass a tf.data.Dataset, generator, or" msgstr "" -#: keras.engine.training.Model.fit:176 of +#: keras.src.engine.training.Model.fit:192 of msgid "" "tf.keras.utils.Sequence to the `x` argument of fit, which will in fact " "yield not only features (x) but optionally targets (y) and sample " -"weights. Keras requires that the output of such iterator-likes be " +"weights. Keras requires that the output of such iterator-likes be " "unambiguous. The iterator should return a tuple of length 1, 2, or 3, " "where the optional second and third elements will be used for y and " "sample_weight respectively. Any other type provided will be wrapped in a " @@ -5239,31 +5494,31 @@ msgid "" "features, targets, and weights from the keys of a single dict." msgstr "" -#: keras.engine.training.Model.fit:186 of -msgid "A notable unsupported data type is the namedtuple. The reason is that" +#: keras.src.engine.training.Model.fit:203 of +msgid "A notable unsupported data type is the namedtuple. The reason is" msgstr "" -#: keras.engine.training.Model.fit:187 of +#: keras.src.engine.training.Model.fit:204 of msgid "" -"it behaves like both an ordered datatype (tuple) and a mapping datatype " -"(dict). So given a namedtuple of the form:" +"that it behaves like both an ordered datatype (tuple) and a mapping " +"datatype (dict). So given a namedtuple of the form:" msgstr "" -#: keras.engine.training.Model.fit:189 of +#: keras.src.engine.training.Model.fit:206 of msgid "`namedtuple(\"example_tuple\", [\"y\", \"x\"])`" msgstr "" -#: keras.engine.training.Model.fit:190 of +#: keras.src.engine.training.Model.fit:207 of msgid "" "it is ambiguous whether to reverse the order of the elements when " "interpreting the value. Even worse is a tuple of the form:" msgstr "" -#: keras.engine.training.Model.fit:192 of +#: keras.src.engine.training.Model.fit:209 of msgid "`namedtuple(\"other_tuple\", [\"x\", \"y\", \"z\"])`" msgstr "" -#: keras.engine.training.Model.fit:193 of +#: keras.src.engine.training.Model.fit:210 of msgid "" "where it is unclear if the tuple was intended to be unpacked into x, y, " "and sample_weight or passed through as a single element to `x`. As a " @@ -5271,44 +5526,44 @@ msgid "" "encounters a namedtuple. (Along with instructions to remedy the issue.)" msgstr "" -#: keras.engine.training.Model.fit:198 of +#: keras.src.engine.training.Model.fit:216 of msgid "" "A `History` object. Its `History.history` attribute is a record of " "training loss values and metrics values at successive epochs, as well as " "validation loss values and validation metrics values (if applicable)." msgstr "" -#: keras.engine.training.Model.fit:203 of +#: keras.src.engine.training.Model.fit:221 of msgid "1. If the model was never compiled or," msgstr "" -#: keras.engine.training.Model.fit:203 of +#: keras.src.engine.training.Model.fit:221 of msgid "If the model was never compiled or," msgstr "" -#: keras.engine.training.Model.fit:205 of +#: keras.src.engine.training.Model.fit:223 of msgid "" "In case of mismatch between the provided input data and what the " "model expects or when the input data is empty." msgstr "" -#: keras.engine.training.Model.fit_generator:1 of +#: keras.src.engine.training.Model.fit_generator:1 of msgid "Fits the model on data yielded batch-by-batch by a Python generator." msgstr "" -#: keras.engine.training.Model.fit_generator:4 of +#: keras.src.engine.training.Model.fit_generator:4 of msgid "" "`Model.fit` now supports generators, so there is no longer any need to " "use this endpoint." msgstr "" -#: keras.engine.base_layer.Layer.from_config:1 -#: keras.engine.training.Model.from_config:1 of +#: keras.src.engine.base_layer.Layer.from_config:1 +#: keras.src.engine.training.Model.from_config:1 of msgid "Creates a layer from its config." msgstr "" -#: keras.engine.base_layer.Layer.from_config:3 -#: keras.engine.training.Model.from_config:3 of +#: keras.src.engine.base_layer.Layer.from_config:3 +#: keras.src.engine.training.Model.from_config:3 of msgid "" "This method is the reverse of `get_config`, capable of instantiating the " "same layer from the config dictionary. It does not handle layer " @@ -5316,69 +5571,106 @@ msgid "" "`set_weights`)." msgstr "" -#: keras.engine.base_layer.Layer.from_config:8 -#: keras.engine.training.Model.from_config:8 of +#: keras.src.engine.base_layer.Layer.from_config:8 +#: keras.src.engine.training.Model.from_config:8 of msgid "A Python dictionary, typically the output of get_config." msgstr "" -#: keras.engine.base_layer.Layer.from_config:11 -#: keras.engine.training.Model.from_config:11 -#: keras.engine.training.Model.get_layer:9 of +#: keras.src.engine.base_layer.Layer.from_config:11 +#: keras.src.engine.training.Model.from_config:11 +#: keras.src.engine.training.Model.get_layer:9 of msgid "A layer instance." msgstr "" -#: keras.engine.base_layer.Layer.get_config:1 -#: keras.engine.training.Model.get_config:1 of -msgid "Returns the config of the layer." +#: keras.src.engine.base_layer.Layer.get_build_config:1 of +msgid "Returns a dictionary with the layer's input shape." msgstr "" -#: keras.engine.base_layer.Layer.get_config:3 -#: keras.engine.training.Model.get_config:3 of +#: keras.src.engine.base_layer.Layer.get_build_config:3 of msgid "" -"A layer config is a Python dictionary (serializable) containing the " -"configuration of a layer. The same layer can be reinstantiated later " -"(without its trained weights) from this configuration." +"This method returns a config dict that can be used by " +"`build_from_config(config)` to create all states (e.g. Variables and " +"Lookup tables) needed by the layer." msgstr "" -#: keras.engine.base_layer.Layer.get_config:8 -#: keras.engine.training.Model.get_config:8 of +#: keras.src.engine.base_layer.Layer.get_build_config:7 of msgid "" -"The config of a layer does not include connectivity information, nor the " -"layer class name. These are handled by `Network` (one layer of " -"abstraction above)." +"By default, the config only contains the input shape that the layer was " +"built with. If you're writing a custom layer that creates state in an " +"unusual way, you should override this method to make sure this state is " +"already created when Keras attempts to load its value upon model loading." +msgstr "" + +#: keras.src.engine.base_layer.Layer.get_build_config:13 of +msgid "A dict containing the input shape associated with the layer." +msgstr "" + +#: keras.src.engine.training.Model.get_compile_config:1 of +msgid "Returns a serialized config with information for compiling the model." +msgstr "" + +#: keras.src.engine.training.Model.get_compile_config:3 of +msgid "" +"This method returns a config dictionary containing all the information " +"(optimizer, loss, metrics, etc.) with which the model was compiled." +msgstr "" + +#: keras.src.engine.training.Model.get_compile_config:6 of +msgid "A dict containing information for compiling the model." +msgstr "" + +#: keras.src.engine.training.Model.get_config:1 of +msgid "Returns the config of the `Model`." msgstr "" -#: keras.engine.base_layer.Layer.get_config:12 -#: keras.engine.training.Model.get_config:12 of +#: keras.src.engine.training.Model.get_config:3 of +msgid "" +"Config is a Python dictionary (serializable) containing the configuration" +" of an object, which in this case is a `Model`. This allows the `Model` " +"to be be reinstantiated later (without its trained weights) from this " +"configuration." +msgstr "" + +#: keras.src.engine.base_layer.Layer.get_config:12 +#: keras.src.engine.training.Model.get_config:8 of msgid "" "Note that `get_config()` does not guarantee to return a fresh copy of " "dict every time it is called. The callers should make a copy of the " "returned dict if they want to modify it." msgstr "" -#: keras.engine.base_layer.Layer.get_config:16 -#: keras.engine.training.Model.get_config:16 of -msgid "Python dictionary." +#: keras.src.engine.training.Model.get_config:12 of +msgid "" +"Developers of subclassed `Model` are advised to override this method, and" +" continue to update the dict from `super(MyModel, self).get_config()` to " +"provide the proper configuration of this `Model`. The default config will" +" return config dict for init parameters if they are basic types. Raises " +"`NotImplementedError` when in cases where a custom `get_config()` " +"implementation is required for the subclassed model." +msgstr "" + +#: keras.src.engine.training.Model.get_config:19 of +msgid "Python dictionary containing the configuration of this `Model`." msgstr "" -#: keras.engine.base_layer.Layer.get_input_at:1 of +#: keras.src.engine.base_layer.Layer.get_input_at:1 of msgid "Retrieves the input tensor(s) of a layer at a given node." msgstr "" -#: keras.engine.base_layer.Layer.get_input_at:3 of +#: keras.src.engine.base_layer.Layer.get_input_at:3 of msgid "" "Integer, index of the node from which to retrieve the attribute. E.g. " "`node_index=0` will correspond to the first input node of the layer." msgstr "" -#: keras.engine.base_layer.Layer.get_input_at:8 of +#: keras.src.engine.base_layer.Layer.get_input_at:8 of msgid "A tensor (or list of tensors if the layer has multiple inputs)." msgstr "" -#: keras.engine.base_layer.Layer.get_input_at:10 -#: keras.engine.base_layer.Layer.get_input_shape_at:11 -#: keras.engine.base_layer.Layer.get_output_at:10 -#: keras.engine.base_layer.Layer.get_output_shape_at:11 of +#: keras.src.engine.base_layer.Layer.get_input_at:10 +#: keras.src.engine.base_layer.Layer.get_input_shape_at:11 +#: keras.src.engine.base_layer.Layer.get_output_at:10 +#: keras.src.engine.base_layer.Layer.get_output_shape_at:11 of #: tensorcircuit.applications.van.MADE.input:8 #: tensorcircuit.applications.van.MaskedConv2D.input:8 #: tensorcircuit.applications.van.MaskedLinear.input:8 @@ -5391,127 +5683,187 @@ msgstr "" msgid "If called in Eager mode." msgstr "" -#: keras.engine.base_layer.Layer.get_input_mask_at:1 of +#: keras.src.engine.base_layer.Layer.get_input_mask_at:1 of msgid "Retrieves the input mask tensor(s) of a layer at a given node." msgstr "" -#: keras.engine.base_layer.Layer.get_input_mask_at:3 -#: keras.engine.base_layer.Layer.get_input_shape_at:3 -#: keras.engine.base_layer.Layer.get_output_mask_at:3 -#: keras.engine.base_layer.Layer.get_output_shape_at:3 of +#: keras.src.engine.base_layer.Layer.get_input_mask_at:3 +#: keras.src.engine.base_layer.Layer.get_input_shape_at:3 +#: keras.src.engine.base_layer.Layer.get_output_mask_at:3 +#: keras.src.engine.base_layer.Layer.get_output_shape_at:3 of msgid "" "Integer, index of the node from which to retrieve the attribute. E.g. " "`node_index=0` will correspond to the first time the layer was called." msgstr "" -#: keras.engine.base_layer.Layer.get_input_mask_at:8 of +#: keras.src.engine.base_layer.Layer.get_input_mask_at:8 of msgid "A mask tensor (or list of tensors if the layer has multiple inputs)." msgstr "" -#: keras.engine.base_layer.Layer.get_input_shape_at:1 of +#: keras.src.engine.base_layer.Layer.get_input_shape_at:1 of msgid "Retrieves the input shape(s) of a layer at a given node." msgstr "" -#: keras.engine.base_layer.Layer.get_input_shape_at:8 of +#: keras.src.engine.base_layer.Layer.get_input_shape_at:8 of msgid "A shape tuple (or list of shape tuples if the layer has multiple inputs)." msgstr "" -#: keras.engine.training.Model.get_layer:1 of +#: keras.src.engine.training.Model.get_layer:1 of msgid "Retrieves a layer based on either its name (unique) or index." msgstr "" -#: keras.engine.training.Model.get_layer:3 of +#: keras.src.engine.training.Model.get_layer:3 of msgid "" "If `name` and `index` are both provided, `index` will take precedence. " "Indices are based on order of horizontal graph traversal (bottom-up)." msgstr "" -#: keras.engine.training.Model.get_layer:6 of +#: keras.src.engine.training.Model.get_layer:6 of msgid "String, name of layer." msgstr "" -#: keras.engine.training.Model.get_layer:7 of +#: keras.src.engine.training.Model.get_layer:7 of msgid "Integer, index of layer." msgstr "" -#: keras.engine.base_layer.Layer.get_losses_for:3 of -msgid "Retrieves losses relevant to a specific set of inputs." +#: keras.src.engine.training.Model.get_metrics_result:1 of +msgid "Returns the model's metrics values as a dict." msgstr "" -#: keras.engine.base_layer.Layer.get_losses_for:5 -#: keras.engine.base_layer.Layer.get_updates_for:5 of -msgid "Input tensor or list/tuple of input tensors." +#: keras.src.engine.training.Model.get_metrics_result:3 of +msgid "" +"If any of the metric result is a dict (containing multiple metrics), each" +" of them gets added to the top level returned dict of this method." msgstr "" -#: keras.engine.base_layer.Layer.get_losses_for:7 of -msgid "List of loss tensors of the layer that depend on `inputs`." +#: keras.src.engine.training.Model.get_metrics_result:6 of +msgid "" +"A `dict` containing values of the metrics listed in `self.metrics`. " +"Example: `{'loss': 0.2, 'accuracy': 0.7}`." msgstr "" -#: keras.engine.base_layer.Layer.get_output_at:1 of +#: keras.src.engine.base_layer.Layer.get_output_at:1 of msgid "Retrieves the output tensor(s) of a layer at a given node." msgstr "" -#: keras.engine.base_layer.Layer.get_output_at:3 of +#: keras.src.engine.base_layer.Layer.get_output_at:3 of msgid "" "Integer, index of the node from which to retrieve the attribute. E.g. " "`node_index=0` will correspond to the first output node of the layer." msgstr "" -#: keras.engine.base_layer.Layer.get_output_at:8 of +#: keras.src.engine.base_layer.Layer.get_output_at:8 of msgid "A tensor (or list of tensors if the layer has multiple outputs)." msgstr "" -#: keras.engine.base_layer.Layer.get_output_mask_at:1 of +#: keras.src.engine.base_layer.Layer.get_output_mask_at:1 of msgid "Retrieves the output mask tensor(s) of a layer at a given node." msgstr "" -#: keras.engine.base_layer.Layer.get_output_mask_at:8 of +#: keras.src.engine.base_layer.Layer.get_output_mask_at:8 of msgid "A mask tensor (or list of tensors if the layer has multiple outputs)." msgstr "" -#: keras.engine.base_layer.Layer.get_output_shape_at:1 of +#: keras.src.engine.base_layer.Layer.get_output_shape_at:1 of msgid "Retrieves the output shape(s) of a layer at a given node." msgstr "" -#: keras.engine.base_layer.Layer.get_output_shape_at:8 of +#: keras.src.engine.base_layer.Layer.get_output_shape_at:8 of msgid "A shape tuple (or list of shape tuples if the layer has multiple outputs)." msgstr "" -#: keras.engine.base_layer.Layer.get_updates_for:3 of -msgid "Retrieves updates relevant to a specific set of inputs." +#: keras.src.engine.training.Model.get_weight_paths:1 of +msgid "Retrieve all the variables and their paths for the model." msgstr "" -#: keras.engine.base_layer.Layer.get_updates_for:7 of -msgid "List of update ops of the layer that depend on `inputs`." +#: keras.src.engine.training.Model.get_weight_paths:3 of +msgid "" +"The variable path (string) is a stable key to identify a `tf.Variable` " +"instance owned by the model. It can be used to specify variable-specific " +"configurations (e.g. DTensor, quantization) from a global view." msgstr "" -#: keras.engine.training.Model.get_weights:1 of -msgid "Retrieves the weights of the model." +#: keras.src.engine.training.Model.get_weight_paths:7 of +msgid "" +"This method returns a dict with weight object paths as keys and the " +"corresponding `tf.Variable` instances as values." msgstr "" -#: keras.engine.training.Model.get_weights:3 of -msgid "A flat list of Numpy arrays." +#: keras.src.engine.training.Model.get_weight_paths:10 of +msgid "" +"Note that if the model is a subclassed model and the weights haven't been" +" initialized, an empty dict will be returned." msgstr "" -#: of tensorcircuit.applications.van.MADE.inbound_nodes:1 -#: tensorcircuit.applications.van.MADE.outbound_nodes:1 -#: tensorcircuit.applications.van.MaskedConv2D.inbound_nodes:1 -#: tensorcircuit.applications.van.MaskedConv2D.outbound_nodes:1 -#: tensorcircuit.applications.van.MaskedLinear.inbound_nodes:1 -#: tensorcircuit.applications.van.MaskedLinear.outbound_nodes:1 -#: tensorcircuit.applications.van.NMF.inbound_nodes:1 -#: tensorcircuit.applications.van.NMF.outbound_nodes:1 -#: tensorcircuit.applications.van.PixelCNN.inbound_nodes:1 -#: tensorcircuit.applications.van.PixelCNN.outbound_nodes:1 -#: tensorcircuit.applications.van.ResidualBlock.inbound_nodes:1 -#: tensorcircuit.applications.van.ResidualBlock.outbound_nodes:1 -#: tensorcircuit.applications.vqes.Linear.inbound_nodes:1 -#: tensorcircuit.applications.vqes.Linear.outbound_nodes:1 -#: tensorcircuit.keras.HardwareLayer.inbound_nodes:1 -#: tensorcircuit.keras.HardwareLayer.outbound_nodes:1 -#: tensorcircuit.keras.QuantumLayer.inbound_nodes:1 -#: tensorcircuit.keras.QuantumLayer.outbound_nodes:1 -msgid "Deprecated, do NOT use! Only for compatibility with external Keras." +#: keras.src.engine.training.Model.get_weight_paths:13 of +msgid "" +"A dict where keys are variable paths and values are `tf.Variable` " +"instances." +msgstr "" + +#: keras.src.engine.training.Model.get_weight_paths:16 of +msgid "A dict where keys are variable paths and values are `tf.Variable`" +msgstr "" + +#: keras.src.engine.training.Model.get_weight_paths:16 of +msgid "instances." +msgstr "" + +#: keras.src.engine.training.Model.get_weight_paths:20 of +msgid "```python class SubclassModel(tf.keras.Model):" +msgstr "" + +#: keras.src.engine.training.Model.get_weight_paths:26 of +msgid "def __init__(self, name=None):" +msgstr "" + +#: keras.src.engine.training.Model.get_weight_paths:24 of +msgid "" +"super().__init__(name=name) self.d1 = tf.keras.layers.Dense(10) self.d2 =" +" tf.keras.layers.Dense(20)" +msgstr "" + +#: keras.src.engine.training.Model.get_weight_paths:29 of +msgid "x = self.d1(inputs) return self.d2(x)" +msgstr "" + +#: keras.src.engine.training.Model.get_weight_paths:32 of +msgid "" +"model = SubclassModel() model(tf.zeros((10, 10))) weight_paths = " +"model.get_weight_paths() # weight_paths: # { # 'd1.kernel': " +"model.d1.kernel, # 'd1.bias': model.d1.bias, # 'd2.kernel': " +"model.d2.kernel, # 'd2.bias': model.d2.bias, # }" +msgstr "" + +#: keras.src.engine.training.Model.get_weight_paths:43 of +msgid "" +"# Functional model inputs = tf.keras.Input((10,), batch_size=10) x = " +"tf.keras.layers.Dense(20, name='d1')(inputs) output = " +"tf.keras.layers.Dense(30, name='d2')(x) model = tf.keras.Model(inputs, " +"output) d1 = model.layers[1] d2 = model.layers[2] weight_paths = " +"model.get_weight_paths() # weight_paths: # { # 'd1.kernel': d1.kernel," +" # 'd1.bias': d1.bias, # 'd2.kernel': d2.kernel, # 'd2.bias': " +"d2.bias, # } ```" +msgstr "" + +#: keras.src.engine.training.Model.get_weights:1 of +msgid "Retrieves the weights of the model." +msgstr "" + +#: keras.src.engine.training.Model.get_weights:3 of +msgid "A flat list of Numpy arrays." +msgstr "" + +#: of tensorcircuit.applications.van.MADE.inbound_nodes:1 +#: tensorcircuit.applications.van.MaskedConv2D.inbound_nodes:1 +#: tensorcircuit.applications.van.MaskedLinear.inbound_nodes:1 +#: tensorcircuit.applications.van.NMF.inbound_nodes:1 +#: tensorcircuit.applications.van.PixelCNN.inbound_nodes:1 +#: tensorcircuit.applications.van.ResidualBlock.inbound_nodes:1 +#: tensorcircuit.applications.vqes.Linear.inbound_nodes:1 +#: tensorcircuit.keras.HardwareLayer.inbound_nodes:1 +#: tensorcircuit.keras.QuantumLayer.inbound_nodes:1 +msgid "Return Functional API nodes upstream of this layer." msgstr "" #: of tensorcircuit.applications.van.MADE.input:1 @@ -5822,92 +6174,125 @@ msgstr "" msgid "A `tf.keras.layers.InputSpec` instance, or nested structure thereof." msgstr "" -#: keras.engine.training.Model.load_weights:1 of -msgid "Loads all layer weights, either from a TensorFlow or an HDF5 weight file." +#: of tensorcircuit.applications.van.MADE.jit_compile:1 +#: tensorcircuit.applications.van.NMF.jit_compile:1 +#: tensorcircuit.applications.van.PixelCNN.jit_compile:1 +msgid "Specify whether to compile the model with XLA." msgstr "" -#: keras.engine.training.Model.load_weights:3 of +#: of tensorcircuit.applications.van.MADE.jit_compile:3 +#: tensorcircuit.applications.van.NMF.jit_compile:3 +#: tensorcircuit.applications.van.PixelCNN.jit_compile:3 msgid "" -"If `by_name` is False weights are loaded based on the network's topology." -" This means the architecture should be the same as when the weights were " -"saved. Note that layers that don't have weights are not taken into " -"account in the topological ordering, so adding or removing layers is fine" -" as long as they don't have weights." +"[XLA](https://www.tensorflow.org/xla) is an optimizing compiler for " +"machine learning. `jit_compile` is not enabled by default. Note that " +"`jit_compile=True` may not necessarily work for all models." msgstr "" -#: keras.engine.training.Model.load_weights:9 of +#: of tensorcircuit.applications.van.MADE.jit_compile:7 +#: tensorcircuit.applications.van.NMF.jit_compile:7 +#: tensorcircuit.applications.van.PixelCNN.jit_compile:7 msgid "" -"If `by_name` is True, weights are loaded into layers only if they share " -"the same name. This is useful for fine-tuning or transfer-learning models" -" where some of the layers have changed." +"For more information on supported operations please refer to the [XLA " +"documentation](https://www.tensorflow.org/xla). Also refer to [known XLA " +"issues](https://www.tensorflow.org/xla/known_issues) for more details." msgstr "" -#: keras.engine.training.Model.load_weights:13 of +#: keras.src.engine.base_layer.Layer.load_own_variables:1 of +msgid "Loads the state of the layer." +msgstr "" + +#: keras.src.engine.base_layer.Layer.load_own_variables:3 of msgid "" -"Only topological loading (`by_name=False`) is supported when loading " -"weights from the TensorFlow format. Note that topological loading differs" -" slightly between TensorFlow and HDF5 formats for user-defined classes " -"inheriting from `tf.keras.Model`: HDF5 loads based on a flattened list of" -" weights, while the TensorFlow format loads based on the object-local " -"names of attributes to which layers are assigned in the `Model`'s " -"constructor." +"You can override this method to take full control of how the state of the" +" layer is loaded upon calling `keras.models.load_model()`." +msgstr "" + +#: keras.src.engine.base_layer.Layer.load_own_variables:6 of +msgid "Dict from which the state of the model will be loaded." msgstr "" -#: keras.engine.training.Model.load_weights:20 of +#: keras.src.engine.training.Model.load_weights:1 of +msgid "Loads all layer weights from a saved files." +msgstr "" + +#: keras.src.engine.training.Model.load_weights:3 of msgid "" -"String, path to the weights file to load. For weight files in TensorFlow " -"format, this is the file prefix (the same as was passed to " -"`save_weights`). This can also be a path to a SavedModel saved from " -"`model.save`." +"The saved file could be a SavedModel file, a `.keras` file (v3 saving " +"format), or a file created via `model.save_weights()`." msgstr "" -#: keras.engine.training.Model.load_weights:24 of +#: keras.src.engine.training.Model.load_weights:6 of msgid "" -"Boolean, whether to load weights by name or by topological order. Only " -"topological loading is supported for weight files in TensorFlow format." +"By default, weights are loaded based on the network's topology. This " +"means the architecture should be the same as when the weights were saved." +" Note that layers that don't have weights are not taken into account in " +"the topological ordering, so adding or removing layers is fine as long as" +" they don't have weights." +msgstr "" + +#: keras.src.engine.training.Model.load_weights:12 of +msgid "**Partial weight loading**" msgstr "" -#: keras.engine.training.Model.load_weights:27 of +#: keras.src.engine.training.Model.load_weights:14 of msgid "" -"Boolean, whether to skip loading of layers where there is a mismatch in " -"the number of weights, or a mismatch in the shape of the weight (only " -"valid when `by_name=True`)." +"If you have modified your model, for instance by adding a new layer (with" +" weights) or by changing the shape of the weights of a layer, you can " +"choose to ignore errors and continue loading by setting " +"`skip_mismatch=True`. In this case any layer with mismatching weights " +"will be skipped. A warning will be displayed for each skipped layer." msgstr "" -#: keras.engine.training.Model.load_weights:30 of +#: keras.src.engine.training.Model.load_weights:21 of +msgid "**Weight loading by name**" +msgstr "" + +#: keras.src.engine.training.Model.load_weights:23 of msgid "" -"Optional `tf.train.CheckpointOptions` object that specifies options for " -"loading weights." +"If your weights are saved as a `.h5` file created via " +"`model.save_weights()`, you can use the argument `by_name=True`." +msgstr "" + +#: keras.src.engine.training.Model.load_weights:26 of +msgid "" +"In this case, weights are loaded into layers only if they share the same " +"name. This is useful for fine-tuning or transfer-learning models where " +"some of the layers have changed." msgstr "" -#: keras.engine.training.Model.load_weights:33 of +#: keras.src.engine.training.Model.load_weights:30 of msgid "" -"When loading a weight file in TensorFlow format, returns the same status " -"object as `tf.train.Checkpoint.restore`. When graph building, restore ops" -" are run automatically as soon as the network is built (on first call for" -" user-defined classes inheriting from `Model`, immediately if it is " -"already built). When loading weights in HDF5 format, returns `None`." +"Note that only topological loading (`by_name=False`) is supported when " +"loading weights from the `.keras` v3 format or from the TensorFlow " +"SavedModel format." msgstr "" -#: keras.engine.training.Model.load_weights:33 of +#: keras.src.engine.training.Model.load_weights:34 of msgid "" -"When loading a weight file in TensorFlow format, returns the same status " -"object as `tf.train.Checkpoint.restore`. When graph building, restore ops" -" are run automatically as soon as the network is built (on first call for" -" user-defined classes inheriting from `Model`, immediately if it is " -"already built)." +"String, path to the weights file to load. For weight files in TensorFlow " +"format, this is the file prefix (the same as was passed to " +"`save_weights()`). This can also be a path to a SavedModel or a `.keras` " +"file (v3 saving format) saved via `model.save()`." msgstr "" -#: keras.engine.training.Model.load_weights:39 of -msgid "When loading weights in HDF5 format, returns `None`." +#: keras.src.engine.training.Model.load_weights:39 of +msgid "" +"Boolean, whether to skip loading of layers where there is a mismatch in " +"the number of weights, or a mismatch in the shape of the weights." msgstr "" -#: keras.engine.training.Model.load_weights:41 of -msgid "If `h5py` is not available and the weight file is in HDF5 format." +#: keras.src.engine.training.Model.load_weights:42 of +msgid "" +"Boolean, whether to load weights by name or by topological order. Only " +"topological loading is supported for weight files in the `.keras` v3 " +"format or in the TensorFlow SavedModel format." msgstr "" -#: keras.engine.training.Model.load_weights:42 of -msgid "If `skip_mismatch` is set to `True` when `by_name` is `False`." +#: keras.src.engine.training.Model.load_weights:45 of +msgid "" +"Optional `tf.train.CheckpointOptions` object that specifies options for " +"loading weights (only valid for a SavedModel file)." msgstr "" #: of tensorcircuit.applications.van.MADE.losses:1 @@ -5938,55 +6323,55 @@ msgid "" "variables." msgstr "" -#: keras.engine.training.Model.reset_metrics:3 of -#: tensorcircuit.applications.van.MADE.losses:7 +#: keras.src.engine.training.Model.reset_metrics:3 of +#: tensorcircuit.applications.van.MADE.losses:8 #: tensorcircuit.applications.van.MADE.metrics:6 #: tensorcircuit.applications.van.MADE.metrics_names:6 -#: tensorcircuit.applications.van.MaskedConv2D.losses:7 -#: tensorcircuit.applications.van.MaskedLinear.losses:7 -#: tensorcircuit.applications.van.NMF.losses:7 +#: tensorcircuit.applications.van.MaskedConv2D.losses:8 +#: tensorcircuit.applications.van.MaskedLinear.losses:8 +#: tensorcircuit.applications.van.NMF.losses:8 #: tensorcircuit.applications.van.NMF.metrics:6 #: tensorcircuit.applications.van.NMF.metrics_names:6 -#: tensorcircuit.applications.van.PixelCNN.losses:7 +#: tensorcircuit.applications.van.PixelCNN.losses:8 #: tensorcircuit.applications.van.PixelCNN.metrics:6 #: tensorcircuit.applications.van.PixelCNN.metrics_names:6 -#: tensorcircuit.applications.van.ResidualBlock.losses:7 -#: tensorcircuit.applications.vqes.Linear.losses:7 -#: tensorcircuit.keras.HardwareLayer.losses:7 -#: tensorcircuit.keras.QuantumLayer.losses:7 +#: tensorcircuit.applications.van.ResidualBlock.losses:8 +#: tensorcircuit.applications.vqes.Linear.losses:8 +#: tensorcircuit.keras.HardwareLayer.losses:8 +#: tensorcircuit.keras.QuantumLayer.losses:8 msgid "Examples:" msgstr "" -#: of tensorcircuit.applications.van.MADE.losses:39 -#: tensorcircuit.applications.van.MaskedConv2D.losses:39 -#: tensorcircuit.applications.van.MaskedLinear.losses:39 -#: tensorcircuit.applications.van.NMF.losses:39 -#: tensorcircuit.applications.van.PixelCNN.losses:39 -#: tensorcircuit.applications.van.ResidualBlock.losses:39 -#: tensorcircuit.applications.vqes.Linear.losses:39 -#: tensorcircuit.keras.HardwareLayer.losses:39 -#: tensorcircuit.keras.QuantumLayer.losses:39 +#: of tensorcircuit.applications.van.MADE.losses:40 +#: tensorcircuit.applications.van.MaskedConv2D.losses:40 +#: tensorcircuit.applications.van.MaskedLinear.losses:40 +#: tensorcircuit.applications.van.NMF.losses:40 +#: tensorcircuit.applications.van.PixelCNN.losses:40 +#: tensorcircuit.applications.van.ResidualBlock.losses:40 +#: tensorcircuit.applications.vqes.Linear.losses:40 +#: tensorcircuit.keras.HardwareLayer.losses:40 +#: tensorcircuit.keras.QuantumLayer.losses:40 msgid "A list of tensors." msgstr "" -#: keras.engine.training.Model.make_predict_function:1 of +#: keras.src.engine.training.Model.make_predict_function:1 of msgid "Creates a function that executes one step of inference." msgstr "" -#: keras.engine.training.Model.make_predict_function:3 of +#: keras.src.engine.training.Model.make_predict_function:3 of msgid "" "This method can be overridden to support custom inference logic. This " "method is called by `Model.predict` and `Model.predict_on_batch`." msgstr "" -#: keras.engine.training.Model.make_predict_function:6 of +#: keras.src.engine.training.Model.make_predict_function:6 of msgid "" "Typically, this method directly controls `tf.function` and " "`tf.distribute.Strategy` settings, and delegates the actual evaluation " "logic to `Model.predict_step`." msgstr "" -#: keras.engine.training.Model.make_predict_function:10 of +#: keras.src.engine.training.Model.make_predict_function:10 of msgid "" "This function is cached the first time `Model.predict` or " "`Model.predict_on_batch` is called. The cache is cleared whenever " @@ -5994,36 +6379,36 @@ msgid "" "function with `force=True`." msgstr "" -#: keras.engine.training.Model.make_predict_function:15 of +#: keras.src.engine.training.Model.make_predict_function:15 of msgid "" "Whether to regenerate the predict function and skip the cached function " "if available." msgstr "" -#: keras.engine.training.Model.make_predict_function:18 of +#: keras.src.engine.training.Model.make_predict_function:18 of msgid "" "Function. The function created by this method should accept a " "`tf.data.Iterator`, and return the outputs of the `Model`." msgstr "" -#: keras.engine.training.Model.make_test_function:1 of +#: keras.src.engine.training.Model.make_test_function:1 of msgid "Creates a function that executes one step of evaluation." msgstr "" -#: keras.engine.training.Model.make_test_function:3 of +#: keras.src.engine.training.Model.make_test_function:3 of msgid "" "This method can be overridden to support custom evaluation logic. This " "method is called by `Model.evaluate` and `Model.test_on_batch`." msgstr "" -#: keras.engine.training.Model.make_test_function:6 of +#: keras.src.engine.training.Model.make_test_function:6 of msgid "" "Typically, this method directly controls `tf.function` and " "`tf.distribute.Strategy` settings, and delegates the actual evaluation " "logic to `Model.test_step`." msgstr "" -#: keras.engine.training.Model.make_test_function:10 of +#: keras.src.engine.training.Model.make_test_function:10 of msgid "" "This function is cached the first time `Model.evaluate` or " "`Model.test_on_batch` is called. The cache is cleared whenever " @@ -6031,37 +6416,37 @@ msgid "" "function with `force=True`." msgstr "" -#: keras.engine.training.Model.make_test_function:15 of +#: keras.src.engine.training.Model.make_test_function:15 of msgid "" "Whether to regenerate the test function and skip the cached function if " "available." msgstr "" -#: keras.engine.training.Model.make_test_function:18 of +#: keras.src.engine.training.Model.make_test_function:18 of msgid "" "Function. The function created by this method should accept a " "`tf.data.Iterator`, and return a `dict` containing values that will be " "passed to `tf.keras.Callbacks.on_test_batch_end`." msgstr "" -#: keras.engine.training.Model.make_train_function:1 of +#: keras.src.engine.training.Model.make_train_function:1 of msgid "Creates a function that executes one step of training." msgstr "" -#: keras.engine.training.Model.make_train_function:3 of +#: keras.src.engine.training.Model.make_train_function:3 of msgid "" "This method can be overridden to support custom training logic. This " "method is called by `Model.fit` and `Model.train_on_batch`." msgstr "" -#: keras.engine.training.Model.make_train_function:6 of +#: keras.src.engine.training.Model.make_train_function:6 of msgid "" "Typically, this method directly controls `tf.function` and " "`tf.distribute.Strategy` settings, and delegates the actual training " "logic to `Model.train_step`." msgstr "" -#: keras.engine.training.Model.make_train_function:10 of +#: keras.src.engine.training.Model.make_train_function:10 of msgid "" "This function is cached the first time `Model.fit` or " "`Model.train_on_batch` is called. The cache is cleared whenever " @@ -6069,13 +6454,13 @@ msgid "" "function with `force=True`." msgstr "" -#: keras.engine.training.Model.make_train_function:15 of +#: keras.src.engine.training.Model.make_train_function:15 of msgid "" "Whether to regenerate the train function and skip the cached function if " "available." msgstr "" -#: keras.engine.training.Model.make_train_function:18 of +#: keras.src.engine.training.Model.make_train_function:18 of msgid "" "Function. The function created by this method should accept a " "`tf.data.Iterator`, and return a `dict` containing values that will be " @@ -6086,7 +6471,7 @@ msgstr "" #: of tensorcircuit.applications.van.MADE.metrics:1 #: tensorcircuit.applications.van.NMF.metrics:1 #: tensorcircuit.applications.van.PixelCNN.metrics:1 -msgid "Returns the model's metrics added using `compile()`, `add_metric()` APIs." +msgid "Return metrics added using `compile()` or `add_metric()`." msgstr "" #: of tensorcircuit.applications.van.MADE.metrics:3 @@ -6235,6 +6620,18 @@ msgstr "" msgid "A list of non-trainable variables." msgstr "" +#: of tensorcircuit.applications.van.MADE.outbound_nodes:1 +#: tensorcircuit.applications.van.MaskedConv2D.outbound_nodes:1 +#: tensorcircuit.applications.van.MaskedLinear.outbound_nodes:1 +#: tensorcircuit.applications.van.NMF.outbound_nodes:1 +#: tensorcircuit.applications.van.PixelCNN.outbound_nodes:1 +#: tensorcircuit.applications.van.ResidualBlock.outbound_nodes:1 +#: tensorcircuit.applications.vqes.Linear.outbound_nodes:1 +#: tensorcircuit.keras.HardwareLayer.outbound_nodes:1 +#: tensorcircuit.keras.QuantumLayer.outbound_nodes:1 +msgid "Return Functional API nodes downstream of this layer." +msgstr "" + #: of tensorcircuit.applications.van.MADE.output:1 #: tensorcircuit.applications.van.MaskedConv2D.output:1 #: tensorcircuit.applications.van.MaskedLinear.output:1 @@ -6361,22 +6758,45 @@ msgstr "" msgid "if the layer has no defined output shape." msgstr "" -#: keras.engine.training.Model.predict:1 of +#: keras.src.engine.training.Model.predict:1 of msgid "Generates output predictions for the input samples." msgstr "" -#: keras.engine.training.Model.predict:3 of +#: keras.src.engine.training.Model.predict:3 of +msgid "" +"Computation is done in batches. This method is designed for batch " +"processing of large numbers of inputs. It is not intended for use inside " +"of loops that iterate over your data and process small numbers of inputs " +"at a time." +msgstr "" + +#: keras.src.engine.training.Model.predict:8 of +msgid "" +"For small numbers of inputs that fit in one batch, directly use " +"`__call__()` for faster execution, e.g., `model(x)`, or `model(x, " +"training=False)` if you have layers such as " +"`tf.keras.layers.BatchNormalization` that behave differently during " +"inference. You may pair the individual model call with a `tf.function` " +"for additional performance inside your inner loop. If you need access to " +"numpy array values instead of tensors after your model call, you can use " +"`tensor.numpy()` to get the numpy array value of an eager tensor." +msgstr "" + +#: keras.src.engine.training.Model.predict:18 of +msgid "" +"Also, note the fact that test loss is not affected by regularization " +"layers like noise and dropout." +msgstr "" + +#: keras.src.engine.training.Model.predict:21 of msgid "" -"Computation is done in batches. This method is designed for performance " -"in large scale inputs. For small amount of inputs that fit in one batch, " -"directly using `__call__()` is recommended for faster execution, e.g., " -"`model(x)`, or `model(x, training=False)` if you have layers such as " -"`tf.keras.layers.BatchNormalization` that behaves differently during " -"inference. Also, note the fact that test loss is not affected by " -"regularization layers like noise and dropout." +"Note: See [this FAQ entry]( https://keras.io/getting_started/faq/#whats-" +"the-difference-between-model-methods-predict-and-call) for more details " +"about the difference between `Model` methods `predict()` and " +"`__call__()`." msgstr "" -#: keras.engine.training.Model.predict:11 of +#: keras.src.engine.training.Model.predict:26 of msgid "" "Input samples. It could be: - A Numpy array (or array-like), or a list of" " arrays (in case the model has multiple inputs). - A TensorFlow tensor," @@ -6387,21 +6807,21 @@ msgid "" "iterator-like inputs` section of `Model.fit`." msgstr "" -#: keras.engine.training.Model.predict:11 of +#: keras.src.engine.training.Model.predict:26 of msgid "" "Input samples. It could be: - A Numpy array (or array-like), or a list of" " arrays" msgstr "" -#: keras.engine.training.Model.predict:16 of +#: keras.src.engine.training.Model.predict:31 of msgid "A `tf.data` dataset." msgstr "" -#: keras.engine.training.Model.predict:17 of +#: keras.src.engine.training.Model.predict:32 of msgid "A generator or `keras.utils.Sequence` instance." msgstr "" -#: keras.engine.training.Model.predict:21 of +#: keras.src.engine.training.Model.predict:36 of msgid "" "Integer or `None`. Number of samples per batch. If unspecified, " "`batch_size` will default to 32. Do not specify the `batch_size` if your " @@ -6409,11 +6829,7 @@ msgid "" "instances (since they generate batches)." msgstr "" -#: keras.engine.training.Model.predict:27 of -msgid "Verbosity mode, 0 or 1." -msgstr "" - -#: keras.engine.training.Model.predict:28 of +#: keras.src.engine.training.Model.predict:49 of msgid "" "Total number of steps (batches of samples) before declaring the " "prediction round finished. Ignored with the default value of `None`. If x" @@ -6421,13 +6837,14 @@ msgid "" "the input dataset is exhausted." msgstr "" -#: keras.engine.training.Model.predict:33 of +#: keras.src.engine.training.Model.predict:54 of msgid "" "List of `keras.callbacks.Callback` instances. List of callbacks to apply " -"during prediction. See [callbacks](/api_docs/python/tf/keras/callbacks)." +"during prediction. See [callbacks]( " +"https://www.tensorflow.org/api_docs/python/tf/keras/callbacks)." msgstr "" -#: keras.engine.training.Model.predict:50 of +#: keras.src.engine.training.Model.predict:74 of msgid "" "See the discussion of `Unpacking behavior for iterator-like inputs` for " "`Model.fit`. Note that Model.predict uses the same interpretation rules " @@ -6435,105 +6852,105 @@ msgid "" "all three methods." msgstr "" -#: keras.engine.training.Model.predict:55 -#: keras.engine.training.Model.predict_on_batch:9 of +#: keras.src.engine.training.Model.predict:79 +#: keras.src.engine.training.Model.predict_on_batch:9 of msgid "Numpy array(s) of predictions." msgstr "" -#: keras.engine.training.Model.predict:57 of +#: keras.src.engine.training.Model.predict:81 of msgid "If `model.predict` is wrapped in a `tf.function`." msgstr "" -#: keras.engine.training.Model.predict:58 of +#: keras.src.engine.training.Model.predict:82 of msgid "" "In case of mismatch between the provided input data and the model's " "expectations, or in case a stateful model receives a number of " "samples that is not a multiple of the batch size." msgstr "" -#: keras.engine.training.Model.predict_generator:1 of +#: keras.src.engine.training.Model.predict_generator:1 of msgid "Generates predictions for the input samples from a data generator." msgstr "" -#: keras.engine.training.Model.predict_generator:4 of +#: keras.src.engine.training.Model.predict_generator:4 of msgid "" "`Model.predict` now supports generators, so there is no longer any need " "to use this endpoint." msgstr "" -#: keras.engine.training.Model.predict_on_batch:1 of +#: keras.src.engine.training.Model.predict_on_batch:1 of msgid "Returns predictions for a single batch of samples." msgstr "" -#: keras.engine.training.Model.predict_on_batch:3 of +#: keras.src.engine.training.Model.predict_on_batch:3 of msgid "" "Input data. It could be: - A Numpy array (or array-like), or a list of " "arrays (in case the model has multiple inputs). - A TensorFlow " "tensor, or a list of tensors (in case the model has multiple inputs)." msgstr "" -#: keras.engine.training.Model.predict_on_batch:3 -#: keras.engine.training.Model.test_on_batch:3 of +#: keras.src.engine.training.Model.predict_on_batch:3 +#: keras.src.engine.training.Model.test_on_batch:3 of msgid "" "Input data. It could be: - A Numpy array (or array-like), or a list of " "arrays (in case the" msgstr "" -#: keras.engine.training.Model.predict_on_batch:5 -#: keras.engine.training.Model.test_on_batch:5 of +#: keras.src.engine.training.Model.predict_on_batch:5 +#: keras.src.engine.training.Model.test_on_batch:5 of msgid "model has multiple inputs)." msgstr "" -#: keras.engine.training.Model.predict_on_batch:7 -#: keras.engine.training.Model.test_on_batch:6 of +#: keras.src.engine.training.Model.predict_on_batch:7 +#: keras.src.engine.training.Model.test_on_batch:6 of msgid "A TensorFlow tensor, or a list of tensors (in case the model has" msgstr "" -#: keras.engine.training.Model.predict_on_batch:7 -#: keras.engine.training.Model.test_on_batch:7 of +#: keras.src.engine.training.Model.predict_on_batch:7 +#: keras.src.engine.training.Model.test_on_batch:7 of msgid "multiple inputs)." msgstr "" -#: keras.engine.training.Model.predict_on_batch:11 of -msgid "If `model.predict_on_batch` is wrapped in a `tf.function`." +#: keras.src.engine.training.Model.predict_on_batch:11 of +msgid "If `model.predict_on_batch` is wrapped in a `tf.function`." msgstr "" -#: keras.engine.training.Model.predict_step:1 of +#: keras.src.engine.training.Model.predict_step:1 of msgid "The logic for one inference step." msgstr "" -#: keras.engine.training.Model.predict_step:3 of +#: keras.src.engine.training.Model.predict_step:3 of msgid "" "This method can be overridden to support custom inference logic. This " "method is called by `Model.make_predict_function`." msgstr "" -#: keras.engine.training.Model.predict_step:6 of +#: keras.src.engine.training.Model.predict_step:6 of msgid "" "This method should contain the mathematical logic for one step of " -"inference. This typically includes the forward pass." +"inference. This typically includes the forward pass." msgstr "" -#: keras.engine.training.Model.predict_step:9 of +#: keras.src.engine.training.Model.predict_step:9 of msgid "" "Configuration details for *how* this logic is run (e.g. `tf.function` and" " `tf.distribute.Strategy` settings), should be left to " "`Model.make_predict_function`, which can also be overridden." msgstr "" -#: keras.engine.training.Model.predict_step:13 -#: keras.engine.training.Model.test_step:15 -#: keras.engine.training.Model.train_step:16 of +#: keras.src.engine.training.Model.predict_step:13 +#: keras.src.engine.training.Model.test_step:15 +#: keras.src.engine.training.Model.train_step:17 of msgid "A nested structure of `Tensor`s." msgstr "" -#: keras.engine.training.Model.predict_step:15 of +#: keras.src.engine.training.Model.predict_step:15 of msgid "" "The result of one inference step, typically the output of calling the " "`Model` on data." msgstr "" -#: keras.engine.training.Model.reset_metrics:1 of +#: keras.src.engine.training.Model.reset_metrics:1 of msgid "Resets the state of all the metrics in the model." msgstr "" @@ -6566,124 +6983,170 @@ msgstr "" msgid "Boolean, whether the model should run eagerly." msgstr "" -#: keras.engine.training.Model.save:1 of -msgid "Saves the model to Tensorflow SavedModel or a single HDF5 file." +#: keras.src.engine.training.Model.save:1 of +msgid "Saves a model as a TensorFlow SavedModel or HDF5 file." msgstr "" -#: keras.engine.training.Model.save:3 of -msgid "" -"Please see `tf.keras.models.save_model` or the [Serialization and Saving " -"guide](https://keras.io/guides/serialization_and_saving/) for details." +#: keras.src.engine.training.Model.save:4 of +msgid "See the [Serialization and Saving guide](" msgstr "" -#: keras.engine.training.Model.save:7 of -msgid "String, PathLike, path to SavedModel or H5 file to save the model." +#: keras.src.engine.training.Model.save:4 of +msgid "https://keras.io/guides/serialization_and_saving/) for details." msgstr "" -#: keras.engine.training.Model.save:9 -#: keras.engine.training.Model.save_weights:47 of -msgid "" -"Whether to silently overwrite any existing file at the target location, " -"or provide the user with a manual prompt." +#: keras.src.engine.training.Model.save:6 of +msgid "Keras model instance to be saved." +msgstr "" + +#: keras.src.engine.training.Model.save:7 of +msgid "`str` or `pathlib.Path` object. Path where to save the model." msgstr "" -#: keras.engine.training.Model.save:11 of -msgid "If True, save optimizer's state together." +#: keras.src.engine.training.Model.save:9 of +msgid "" +"Whether we should overwrite any existing model at the target location, or" +" instead ask the user via an interactive prompt." msgstr "" -#: keras.engine.training.Model.save:12 of +#: keras.src.engine.training.Model.save:12 of msgid "" -"Either `'tf'` or `'h5'`, indicating whether to save the model to " -"Tensorflow SavedModel or HDF5. Defaults to 'tf' in TF 2.X, and 'h5' in TF" -" 1.X." +"Either `\"keras\"`, `\"tf\"`, `\"h5\"`, indicating whether to save the " +"model in the native Keras format (`.keras`), in the TensorFlow SavedModel" +" format (referred to as \"SavedModel\" below), or in the legacy HDF5 " +"format (`.h5`). Defaults to `\"tf\"` in TF 2.X, and `\"h5\"` in TF 1.X." +msgstr "" + +#: keras.src.engine.training.Model.save:36 of +msgid "SavedModel format arguments:" +msgstr "" + +#: keras.src.engine.training.Model.save:22 of +msgid "include_optimizer: Only applied to SavedModel and legacy HDF5" +msgstr "" + +#: keras.src.engine.training.Model.save:22 of +msgid "formats. If False, do not save the optimizer state. Defaults to `True`." msgstr "" -#: keras.engine.training.Model.save:15 of +#: keras.src.engine.training.Model.save:25 of +msgid "signatures: Only applies to SavedModel format. Signatures to save" +msgstr "" + +#: keras.src.engine.training.Model.save:25 of msgid "" -"Signatures to save with the SavedModel. Applicable to the 'tf' format " -"only. Please see the `signatures` argument in `tf.saved_model.save` for " -"details." +"with the SavedModel. See the `signatures` argument in " +"`tf.saved_model.save` for details." +msgstr "" + +#: keras.src.engine.training.Model.save:28 of +msgid "options: Only applies to SavedModel format." msgstr "" -#: keras.engine.training.Model.save:18 of +#: keras.src.engine.training.Model.save:28 of msgid "" -"(only applies to SavedModel format) `tf.saved_model.SaveOptions` object " -"that specifies options for saving to SavedModel." +"`tf.saved_model.SaveOptions` object that specifies SavedModel saving " +"options." msgstr "" -#: keras.engine.training.Model.save:21 of +#: keras.src.engine.training.Model.save:36 of +msgid "save_traces: Only applies to SavedModel format. When enabled, the" +msgstr "" + +#: keras.src.engine.training.Model.save:31 of msgid "" -"(only applies to SavedModel format) When enabled, the SavedModel will " -"store the function traces for each layer. This can be disabled, so that " -"only the configs of each layer are stored. Defaults to `True`. Disabling " -"this will decrease serialization time and reduce file size, but it " -"requires that all custom layers/models implement a `get_config()` method." +"SavedModel will store the function traces for each layer. This can be " +"disabled, so that only the configs of each layer are stored. Defaults to " +"`True`. Disabling this will decrease serialization time and reduce file " +"size, but it requires that all custom layers/models implement a " +"`get_config()` method." +msgstr "" + +#: keras.src.engine.training.Model.save:40 of +msgid "```python model = tf.keras.Sequential([" msgstr "" -#: keras.engine.training.Model.save:30 of -msgid "```python from keras.models import load_model" +#: keras.src.engine.training.Model.save:42 of +msgid "tf.keras.layers.Dense(5, input_shape=(3,)), tf.keras.layers.Softmax()])" msgstr "" -#: keras.engine.training.Model.save:33 of +#: keras.src.engine.training.Model.save:44 of msgid "" -"model.save('my_model.h5') # creates a HDF5 file 'my_model.h5' del model" -" # deletes the existing model" +"model.save(\"model.keras\") loaded_model = " +"tf.keras.models.load_model(\"model.keras\") x = tf.random.uniform((10, " +"3)) assert np.allclose(model.predict(x), loaded_model.predict(x)) ```" msgstr "" -#: keras.engine.training.Model.save:36 of +#: keras.src.engine.training.Model.save:50 of +msgid "Note that `model.save()` is an alias for `tf.keras.models.save_model()`." +msgstr "" + +#: keras.src.engine.base_layer.Layer.save_own_variables:1 of +msgid "Saves the state of the layer." +msgstr "" + +#: keras.src.engine.base_layer.Layer.save_own_variables:3 of msgid "" -"# returns a compiled model # identical to the previous one model = " -"load_model('my_model.h5') ```" +"You can override this method to take full control of how the state of the" +" layer is saved upon calling `model.save()`." msgstr "" -#: keras.engine.training.Model.save_spec:1 of -msgid "Returns the `tf.TensorSpec` of call inputs as a tuple `(args, kwargs)`." +#: keras.src.engine.base_layer.Layer.save_own_variables:6 of +msgid "Dict where the state of the model will be saved." msgstr "" -#: keras.engine.training.Model.save_spec:3 of +#: keras.src.engine.training.Model.save_spec:1 of +msgid "Returns the `tf.TensorSpec` of call args as a tuple `(args, kwargs)`." +msgstr "" + +#: keras.src.engine.training.Model.save_spec:3 of msgid "" "This value is automatically defined after calling the model for the first" " time. Afterwards, you can use it when exporting the model for serving:" msgstr "" -#: keras.engine.training.Model.save_spec:6 of +#: keras.src.engine.training.Model.save_spec:7 of msgid "```python model = tf.keras.Model(...)" msgstr "" -#: keras.engine.training.Model.save_spec:9 of +#: keras.src.engine.training.Model.save_spec:10 of msgid "@tf.function def serve(*args, **kwargs):" msgstr "" -#: keras.engine.training.Model.save_spec:11 of +#: keras.src.engine.training.Model.save_spec:12 of msgid "" "outputs = model(*args, **kwargs) # Apply postprocessing steps, or add " "additional outputs. ... return outputs" msgstr "" -#: keras.engine.training.Model.save_spec:16 of +#: keras.src.engine.training.Model.save_spec:17 of msgid "" -"# arg_specs is `[tf.TensorSpec(...), ...]`. kwarg_specs, in this example," -" is # an empty dict since functional models do not use keyword arguments." -" arg_specs, kwarg_specs = model.save_spec()" +"# arg_specs is `[tf.TensorSpec(...), ...]`. kwarg_specs, in this # " +"example, is an empty dict since functional models do not use keyword # " +"arguments. arg_specs, kwarg_specs = model.save_spec()" msgstr "" -#: keras.engine.training.Model.save_spec:20 of +#: keras.src.engine.training.Model.save_spec:23 of msgid "model.save(path, signatures={" msgstr "" -#: keras.engine.training.Model.save_spec:21 of -msgid "'serving_default': serve.get_concrete_function(*arg_specs, **kwarg_specs)" +#: keras.src.engine.training.Model.save_spec:23 of +msgid "'serving_default': serve.get_concrete_function(*arg_specs," +msgstr "" + +#: keras.src.engine.training.Model.save_spec:24 of +msgid "**kwarg_specs)" msgstr "" -#: keras.engine.training.Model.save_spec:23 of +#: keras.src.engine.training.Model.save_spec:26 of msgid "})" msgstr "" -#: keras.engine.training.Model.save_spec of +#: keras.src.engine.training.Model.save_spec of msgid "param dynamic_batch" msgstr "" -#: keras.engine.training.Model.save_spec:25 of +#: keras.src.engine.training.Model.save_spec:28 of msgid "" "Whether to set the batch sizes of all the returned `tf.TensorSpec` to " "`None`. (Note that when defining functional or Sequential models with " @@ -6691,11 +7154,11 @@ msgid "" "preserved). Defaults to `True`." msgstr "" -#: keras.engine.training.Model.save_spec of +#: keras.src.engine.training.Model.save_spec of msgid "returns" msgstr "" -#: keras.engine.training.Model.save_spec:30 of +#: keras.src.engine.training.Model.save_spec:33 of msgid "" "If the model inputs are defined, returns a tuple `(args, kwargs)`. All " "elements in `args` and `kwargs` are `tf.TensorSpec`. If the model inputs " @@ -6703,49 +7166,49 @@ msgid "" "when calling the model, `model.fit`, `model.evaluate` or `model.predict`." msgstr "" -#: keras.engine.training.Model.save_weights:1 of +#: keras.src.engine.training.Model.save_weights:1 of msgid "Saves all layer weights." msgstr "" -#: keras.engine.training.Model.save_weights:3 of +#: keras.src.engine.training.Model.save_weights:3 of msgid "" "Either saves in HDF5 or in TensorFlow format based on the `save_format` " "argument." msgstr "" -#: keras.engine.training.Model.save_weights:14 of +#: keras.src.engine.training.Model.save_weights:14 of msgid "When saving in HDF5 format, the weight file has:" msgstr "" -#: keras.engine.training.Model.save_weights:7 of +#: keras.src.engine.training.Model.save_weights:7 of msgid "`layer_names` (attribute), a list of strings" msgstr "" -#: keras.engine.training.Model.save_weights:8 of +#: keras.src.engine.training.Model.save_weights:8 of msgid "(ordered names of model layers)." msgstr "" -#: keras.engine.training.Model.save_weights:14 of +#: keras.src.engine.training.Model.save_weights:14 of msgid "For every layer, a `group` named `layer.name`" msgstr "" -#: keras.engine.training.Model.save_weights:11 of +#: keras.src.engine.training.Model.save_weights:11 of msgid "For every such layer group, a group attribute `weight_names`," msgstr "" -#: keras.engine.training.Model.save_weights:11 of +#: keras.src.engine.training.Model.save_weights:11 of msgid "a list of strings (ordered names of weights tensor of the layer)." msgstr "" -#: keras.engine.training.Model.save_weights:14 of +#: keras.src.engine.training.Model.save_weights:14 of msgid "For every weight in the layer, a dataset" msgstr "" -#: keras.engine.training.Model.save_weights:14 of +#: keras.src.engine.training.Model.save_weights:14 of msgid "storing the weight value, named after the weight tensor." msgstr "" -#: keras.engine.training.Model.save_weights:16 of +#: keras.src.engine.training.Model.save_weights:16 of msgid "" "When saving in TensorFlow format, all objects referenced by the network " "are saved in the same format as `tf.train.Checkpoint`, including any " @@ -6758,7 +7221,7 @@ msgid "" "`tf.train.Checkpoint` and `tf.keras.Model` for details." msgstr "" -#: keras.engine.training.Model.save_weights:26 of +#: keras.src.engine.training.Model.save_weights:26 of msgid "" "While the formats are the same, do not mix `save_weights` and " "`tf.train.Checkpoint`. Checkpoints saved by `Model.save_weights` should " @@ -6768,7 +7231,7 @@ msgid "" "`save_weights` for training checkpoints." msgstr "" -#: keras.engine.training.Model.save_weights:33 of +#: keras.src.engine.training.Model.save_weights:33 of msgid "" "The TensorFlow format matches objects and variables by starting at a root" " object, `self` for `save_weights`, and greedily matching attribute " @@ -6777,11 +7240,11 @@ msgid "" "This means saving a `tf.keras.Model` using `save_weights` and loading " "into a `tf.train.Checkpoint` with a `Model` attached (or vice versa) will" " not match the `Model`'s variables. See the [guide to training " -"checkpoints](https://www.tensorflow.org/guide/checkpoint) for details on " -"the TensorFlow format." +"checkpoints]( https://www.tensorflow.org/guide/checkpoint) for details on" +" the TensorFlow format." msgstr "" -#: keras.engine.training.Model.save_weights:43 of +#: keras.src.engine.training.Model.save_weights:44 of msgid "" "String or PathLike, path to the file to save the weights to. When saving " "in TensorFlow format, this is the prefix used for checkpoint files " @@ -6789,28 +7252,34 @@ msgid "" " to be saved in HDF5 format." msgstr "" -#: keras.engine.training.Model.save_weights:49 of +#: keras.src.engine.training.Model.save_weights:48 of +msgid "" +"Whether to silently overwrite any existing file at the target location, " +"or provide the user with a manual prompt." +msgstr "" + +#: keras.src.engine.training.Model.save_weights:50 of msgid "" "Either 'tf' or 'h5'. A `filepath` ending in '.h5' or '.keras' will " -"default to HDF5 if `save_format` is `None`. Otherwise `None` defaults to " -"'tf'." +"default to HDF5 if `save_format` is `None`. Otherwise, `None` becomes " +"'tf'. Defaults to `None`." msgstr "" -#: keras.engine.training.Model.save_weights:52 of +#: keras.src.engine.training.Model.save_weights:53 of msgid "" "Optional `tf.train.CheckpointOptions` object that specifies options for " "saving weights." msgstr "" -#: keras.engine.training.Model.save_weights:55 of -msgid "If `h5py` is not available when attempting to save in HDF5 format." +#: keras.src.engine.training.Model.save_weights:56 of +msgid "If `h5py` is not available when attempting to save in HDF5 format." msgstr "" -#: keras.engine.base_layer.Layer.set_weights:1 of +#: keras.src.engine.base_layer.Layer.set_weights:1 of msgid "Sets the weights of the layer, from NumPy arrays." msgstr "" -#: keras.engine.base_layer.Layer.set_weights:3 of +#: keras.src.engine.base_layer.Layer.set_weights:3 of msgid "" "The weights of a layer represent the state of the layer. This function " "sets the weight values from numpy arrays. The weight values should be " @@ -6819,27 +7288,33 @@ msgid "" " layer." msgstr "" -#: keras.engine.base_layer.Layer.get_weights:8 -#: keras.engine.base_layer.Layer.set_weights:9 of +#: keras.src.engine.base_layer.Layer.get_weights:8 +#: keras.src.engine.base_layer.Layer.set_weights:9 of msgid "" "For example, a `Dense` layer returns a list of two values: the kernel " "matrix and the bias vector. These can be used to set the weights of " "another `Dense` layer:" msgstr "" -#: keras.engine.base_layer.Layer.set_weights:33 of +#: keras.src.engine.base_layer.Layer.set_weights:33 of msgid "" "a list of NumPy arrays. The number of arrays and their shape must match " "number of the dimensions of the weights of the layer (i.e. it should " "match the output of `get_weights`)." msgstr "" -#: keras.engine.base_layer.Layer.set_weights:39 of +#: keras.src.engine.base_layer.Layer.set_weights:39 of msgid "" "If the provided weights list does not match the layer's " "specifications." msgstr "" +#: of tensorcircuit.applications.van.MADE.state_updates:1 +#: tensorcircuit.applications.van.NMF.state_updates:1 +#: tensorcircuit.applications.van.PixelCNN.state_updates:1 +msgid "Deprecated, do NOT use!" +msgstr "" + #: of tensorcircuit.applications.van.MADE.state_updates:3 #: tensorcircuit.applications.van.NMF.state_updates:3 #: tensorcircuit.applications.van.PixelCNN.state_updates:3 @@ -6898,34 +7373,50 @@ msgstr "" msgid "A sequence of all submodules." msgstr "" -#: keras.engine.training.Model.summary:1 of +#: keras.src.engine.training.Model.summary:1 of msgid "Prints a string summary of the network." msgstr "" -#: keras.engine.training.Model.summary:3 of +#: keras.src.engine.training.Model.summary:3 of msgid "" "Total length of printed lines (e.g. set this to adapt the display to " "different terminal window sizes)." msgstr "" -#: keras.engine.training.Model.summary:6 of +#: keras.src.engine.training.Model.summary:6 of msgid "" "Relative or absolute positions of log elements in each line. If not " -"provided, defaults to `[.33, .55, .67, 1.]`." +"provided, becomes `[0.3, 0.6, 0.70, 1.]`. Defaults to `None`." msgstr "" -#: keras.engine.training.Model.summary:9 of +#: keras.src.engine.training.Model.summary:9 of msgid "" -"Print function to use. Defaults to `print`. It will be called on each " -"line of the summary. You can set it to a custom function in order to " -"capture the string summary." +"Print function to use. By default, prints to `stdout`. If `stdout` " +"doesn't work in your environment, change to `print`. It will be called on" +" each line of the summary. You can set it to a custom function in order " +"to capture the string summary." +msgstr "" + +#: keras.src.engine.training.Model.summary:14 of +msgid "Whether to expand the nested models. Defaults to `False`." msgstr "" -#: keras.engine.training.Model.summary:13 of -msgid "Whether to expand the nested models. If not provided, defaults to `False`." +#: keras.src.engine.training.Model.summary:16 of +msgid "Whether to show if a layer is trainable. Defaults to `False`." msgstr "" -#: keras.engine.training.Model.summary:16 of +#: keras.src.engine.training.Model.summary:18 of +msgid "" +"a list or tuple of 2 strings, which is the starting layer name and ending" +" layer name (both inclusive) indicating the range of layers to be printed" +" in summary. It also accepts regex patterns instead of exact name. In " +"such case, start predicate will be the first element it matches to " +"`layer_range[0]` and the end predicate will be the last element it " +"matches to `layer_range[1]`. By default `None` which considers all layers" +" of model." +msgstr "" + +#: keras.src.engine.training.Model.summary:27 of msgid "if `summary()` is called before the model is built." msgstr "" @@ -6941,37 +7432,38 @@ msgstr "" msgid "Whether this layer supports computing a mask using `compute_mask`." msgstr "" -#: keras.engine.training.Model.test_on_batch:1 of +#: keras.src.engine.training.Model.test_on_batch:1 of msgid "Test the model on a single batch of samples." msgstr "" -#: keras.engine.training.Model.test_on_batch:3 of +#: keras.src.engine.training.Model.test_on_batch:3 of msgid "" "Input data. It could be: - A Numpy array (or array-like), or a list of " "arrays (in case the model has multiple inputs). - A TensorFlow " "tensor, or a list of tensors (in case the model has multiple inputs)." -" - A dict mapping input names to the corresponding array/tensors, if " +" - A dict mapping input names to the corresponding array/tensors, if " "the model has named inputs." msgstr "" -#: keras.engine.training.Model.test_on_batch:8 of -msgid "A dict mapping input names to the corresponding array/tensors, if" +#: keras.src.engine.training.Model.test_on_batch:8 +#: keras.src.engine.training.Model.train_on_batch:8 of +msgid "A dict mapping input names to the corresponding array/tensors," msgstr "" -#: keras.engine.training.Model.test_on_batch:9 of -msgid "the model has named inputs." +#: keras.src.engine.training.Model.test_on_batch:9 +#: keras.src.engine.training.Model.train_on_batch:9 of +msgid "if the model has named inputs." msgstr "" -#: keras.engine.training.Model.test_on_batch:10 -#: keras.engine.training.Model.train_on_batch:10 of +#: keras.src.engine.training.Model.test_on_batch:10 of msgid "" "Target data. Like the input data `x`, it could be either Numpy array(s) " "or TensorFlow tensor(s). It should be consistent with `x` (you cannot " "have Numpy inputs and tensor targets, or inversely)." msgstr "" -#: keras.engine.training.Model.test_on_batch:13 -#: keras.engine.training.Model.train_on_batch:13 of +#: keras.src.engine.training.Model.test_on_batch:13 +#: keras.src.engine.training.Model.train_on_batch:12 of msgid "" "Optional array of the same length as x, containing weights to apply to " "the model's loss for each sample. In the case of temporal data, you can " @@ -6979,105 +7471,105 @@ msgid "" "different weight to every timestep of every sample." msgstr "" -#: keras.engine.training.Model.test_on_batch:18 -#: keras.engine.training.Model.train_on_batch:22 of +#: keras.src.engine.training.Model.test_on_batch:18 +#: keras.src.engine.training.Model.train_on_batch:24 of msgid "" "If `True`, the metrics returned will be only for this batch. If `False`, " "the metrics will be statefully accumulated across batches." msgstr "" -#: keras.engine.training.Model.test_on_batch:30 of -msgid "If `model.test_on_batch` is wrapped in a `tf.function`." +#: keras.src.engine.training.Model.test_on_batch:30 of +msgid "If `model.test_on_batch` is wrapped in a `tf.function`." msgstr "" -#: keras.engine.training.Model.test_step:1 of +#: keras.src.engine.training.Model.test_step:1 of msgid "The logic for one evaluation step." msgstr "" -#: keras.engine.training.Model.test_step:3 of +#: keras.src.engine.training.Model.test_step:3 of msgid "" "This method can be overridden to support custom evaluation logic. This " "method is called by `Model.make_test_function`." msgstr "" -#: keras.engine.training.Model.test_step:6 of +#: keras.src.engine.training.Model.test_step:6 of msgid "" "This function should contain the mathematical logic for one step of " "evaluation. This typically includes the forward pass, loss calculation, " "and metrics updates." msgstr "" -#: keras.engine.training.Model.test_step:11 of +#: keras.src.engine.training.Model.test_step:11 of msgid "" "Configuration details for *how* this logic is run (e.g. `tf.function` and" " `tf.distribute.Strategy` settings), should be left to " "`Model.make_test_function`, which can also be overridden." msgstr "" -#: keras.engine.training.Model.test_step:17 of +#: keras.src.engine.training.Model.test_step:17 of msgid "" "A `dict` containing values that will be passed to " "`tf.keras.callbacks.CallbackList.on_train_batch_end`. Typically, the " "values of the `Model`'s metrics are returned." msgstr "" -#: keras.engine.training.Model.to_json:1 of +#: keras.src.engine.training.Model.to_json:1 of msgid "Returns a JSON string containing the network configuration." msgstr "" -#: keras.engine.training.Model.to_json:3 of +#: keras.src.engine.training.Model.to_json:3 of msgid "" "To load a network from a JSON save file, use " "`keras.models.model_from_json(json_string, custom_objects={})`." msgstr "" -#: keras.engine.training.Model.to_json:6 of -msgid "Additional keyword arguments to be passed to `json.dumps()`." +#: keras.src.engine.training.Model.to_json:6 of +msgid "Additional keyword arguments to be passed to *`json.dumps()`." msgstr "" -#: keras.engine.training.Model.to_json:9 of +#: keras.src.engine.training.Model.to_json:9 of msgid "A JSON string." msgstr "" -#: keras.engine.training.Model.to_yaml:1 of +#: keras.src.engine.training.Model.to_yaml:1 of msgid "Returns a yaml string containing the network configuration." msgstr "" -#: keras.engine.training.Model.to_yaml:3 of +#: keras.src.engine.training.Model.to_yaml:3 of msgid "" "Note: Since TF 2.6, this method is no longer supported and will raise a " "RuntimeError." msgstr "" -#: keras.engine.training.Model.to_yaml:6 of +#: keras.src.engine.training.Model.to_yaml:6 of msgid "" "To load a network from a yaml save file, use " "`keras.models.model_from_yaml(yaml_string, custom_objects={})`." msgstr "" -#: keras.engine.training.Model.to_yaml:9 of +#: keras.src.engine.training.Model.to_yaml:9 of msgid "" "`custom_objects` should be a dictionary mapping the names of custom " "losses / layers / etc to the corresponding functions / classes." msgstr "" -#: keras.engine.training.Model.to_yaml:13 of +#: keras.src.engine.training.Model.to_yaml:13 of msgid "Additional keyword arguments to be passed to `yaml.dump()`." msgstr "" -#: keras.engine.training.Model.to_yaml:16 of +#: keras.src.engine.training.Model.to_yaml:16 of msgid "A YAML string." msgstr "" -#: keras.engine.training.Model.to_yaml:18 of +#: keras.src.engine.training.Model.to_yaml:18 of msgid "announces that the method poses a security risk" msgstr "" -#: keras.engine.training.Model.train_on_batch:1 of +#: keras.src.engine.training.Model.train_on_batch:1 of msgid "Runs a single gradient update on a single batch of data." msgstr "" -#: keras.engine.training.Model.train_on_batch:3 of +#: keras.src.engine.training.Model.train_on_batch:3 of msgid "" "Input data. It could be: - A Numpy array (or array-like), or a list of " "arrays (in case the model has multiple inputs). - A TensorFlow " @@ -7086,27 +7578,28 @@ msgid "" "the model has named inputs." msgstr "" -#: keras.engine.training.Model.train_on_batch:6 of +#: keras.src.engine.training.Model.train_on_batch:6 of msgid "A TensorFlow tensor, or a list of tensors" msgstr "" -#: keras.engine.training.Model.train_on_batch:8 of -msgid "A dict mapping input names to the corresponding array/tensors," -msgstr "" - -#: keras.engine.training.Model.train_on_batch:9 of -msgid "if the model has named inputs." +#: keras.src.engine.training.Model.train_on_batch:10 of +msgid "" +"Target data. Like the input data `x`, it could be either Numpy array(s) " +"or TensorFlow tensor(s)." msgstr "" -#: keras.engine.training.Model.train_on_batch:18 of +#: keras.src.engine.training.Model.train_on_batch:17 of msgid "" "Optional dictionary mapping class indices (integers) to a weight (float) " "to apply to the model's loss for the samples from this class during " "training. This can be useful to tell the model to \"pay more attention\" " -"to samples from an under-represented class." +"to samples from an under-represented class. When `class_weight` is " +"specified and targets have a rank of 2 or greater, either `y` must be " +"one-hot encoded, or an explicit final dimension of `1` must be included " +"for sparse class labels." msgstr "" -#: keras.engine.training.Model.train_on_batch:29 of +#: keras.src.engine.training.Model.train_on_batch:31 of msgid "" "Scalar training loss (if the model has a single output and no metrics) or" " list of scalars (if the model has multiple outputs and/or metrics). The " @@ -7114,38 +7607,38 @@ msgid "" "scalar outputs." msgstr "" -#: keras.engine.training.Model.train_on_batch:35 of +#: keras.src.engine.training.Model.train_on_batch:37 of msgid "If `model.train_on_batch` is wrapped in a `tf.function`." msgstr "" -#: keras.engine.training.Model.train_step:1 of +#: keras.src.engine.training.Model.train_step:1 of msgid "The logic for one training step." msgstr "" -#: keras.engine.training.Model.train_step:3 of +#: keras.src.engine.training.Model.train_step:3 of msgid "" "This method can be overridden to support custom training logic. For " "concrete examples of how to override this method see [Customizing what " -"happends in " -"fit](https://www.tensorflow.org/guide/keras/customizing_what_happens_in_fit)." -" This method is called by `Model.make_train_function`." +"happens in fit]( " +"https://www.tensorflow.org/guide/keras/customizing_what_happens_in_fit). " +"This method is called by `Model.make_train_function`." msgstr "" -#: keras.engine.training.Model.train_step:8 of +#: keras.src.engine.training.Model.train_step:9 of msgid "" "This method should contain the mathematical logic for one step of " -"training. This typically includes the forward pass, loss calculation, " +"training. This typically includes the forward pass, loss calculation, " "backpropagation, and metric updates." msgstr "" -#: keras.engine.training.Model.train_step:12 of +#: keras.src.engine.training.Model.train_step:13 of msgid "" "Configuration details for *how* this logic is run (e.g. `tf.function` and" " `tf.distribute.Strategy` settings), should be left to " "`Model.make_train_function`, which can also be overridden." msgstr "" -#: keras.engine.training.Model.train_step:18 of +#: keras.src.engine.training.Model.train_step:19 of msgid "" "A `dict` containing values that will be passed to " "`tf.keras.callbacks.CallbackList.on_train_batch_end`. Typically, the " @@ -7306,33 +7799,36 @@ msgstr "" #: tensorcircuit.applications.van.MaskedLinear:1 #: tensorcircuit.applications.van.ResidualBlock:1 #: tensorcircuit.applications.vqes.Linear:1 tensorcircuit.keras.QuantumLayer:1 -msgid "Bases: :py:class:`~keras.engine.base_layer.Layer`" +msgid "Bases: :py:class:`~keras.src.engine.base_layer.Layer`" msgstr "" -#: keras.engine.base_layer.Layer.build:1 of +#: keras.src.engine.base_layer.Layer.build:1 of #: tensorcircuit.applications.van.MaskedConv2D.build:1 #: tensorcircuit.keras.QuantumLayer.build:1 -msgid "Creates the variables of the layer (optional, for subclass implementers)." +msgid "Creates the variables of the layer (for subclass implementers)." msgstr "" -#: keras.engine.base_layer.Layer.build:3 of +#: keras.src.engine.base_layer.Layer.build:3 of #: tensorcircuit.applications.van.MaskedConv2D.build:3 #: tensorcircuit.keras.QuantumLayer.build:3 msgid "" "This is a method that implementers of subclasses of `Layer` or `Model` " "can override if they need a state-creation step in-between layer " -"instantiation and layer call." +"instantiation and layer call. It is invoked automatically before the " +"first execution of `call()`." msgstr "" -#: keras.engine.base_layer.Layer.build:7 of -#: tensorcircuit.applications.van.MaskedConv2D.build:7 -#: tensorcircuit.keras.QuantumLayer.build:7 -msgid "This is typically used to create the weights of `Layer` subclasses." +#: keras.src.engine.base_layer.Layer.build:8 of +#: tensorcircuit.applications.van.MaskedConv2D.build:8 +#: tensorcircuit.keras.QuantumLayer.build:8 +msgid "" +"This is typically used to create the weights of `Layer` subclasses (at " +"the discretion of the subclass implementer)." msgstr "" -#: keras.engine.base_layer.Layer.build:9 of -#: tensorcircuit.applications.van.MaskedConv2D.build:9 -#: tensorcircuit.keras.QuantumLayer.build:9 +#: keras.src.engine.base_layer.Layer.build:11 of +#: tensorcircuit.applications.van.MaskedConv2D.build:11 +#: tensorcircuit.keras.QuantumLayer.build:11 msgid "" "Instance of `TensorShape`, or list of instances of `TensorShape` if the " "layer expects a list of inputs (one instance per input)." @@ -7350,81 +7846,79 @@ msgstr "" #: tensorcircuit.applications.van.ResidualBlock.call:3 #: tensorcircuit.applications.vqes.Linear.call:3 msgid "" -"Note here that `call()` method in `tf.keras` is little bit different from" -" `keras` API. In `keras` API, you can pass support masking for layers as " -"additional arguments. Whereas `tf.keras` has `compute_mask()` method to " -"support masking." +"The `call()` method may not create state (except in its first invocation," +" wrapping the creation of variables or other resources in " +"`tf.init_scope()`). It is recommended to create state, including " +"`tf.Variable` instances and nested `Layer` instances," +msgstr "" + +#: of tensorcircuit.applications.van.MaskedConv2D.call:7 +#: tensorcircuit.applications.van.MaskedLinear.call:7 +#: tensorcircuit.applications.van.ResidualBlock.call:7 +#: tensorcircuit.applications.vqes.Linear.call:7 +msgid "in `__init__()`, or in the `build()` method that is" msgstr "" #: of tensorcircuit.applications.van.MaskedConv2D.call:8 #: tensorcircuit.applications.van.MaskedLinear.call:8 #: tensorcircuit.applications.van.ResidualBlock.call:8 #: tensorcircuit.applications.vqes.Linear.call:8 +msgid "called automatically before `call()` executes for the first time." +msgstr "" + +#: of tensorcircuit.applications.van.MaskedConv2D.call:10 +#: tensorcircuit.applications.van.MaskedLinear.call:10 +#: tensorcircuit.applications.van.ResidualBlock.call:10 +#: tensorcircuit.applications.vqes.Linear.call:10 msgid "" "Input tensor, or dict/list/tuple of input tensors. The first positional " "`inputs` argument is subject to special rules: - `inputs` must be " "explicitly passed. A layer cannot have zero arguments, and `inputs` " "cannot be provided via the default value of a keyword argument. - NumPy" -" array or Python scalar values in `inputs` get cast as tensors. - Keras " -"mask metadata is only collected from `inputs`. - Layers are built " +" array or Python scalar values in `inputs` get cast as tensors. - Keras" +" mask metadata is only collected from `inputs`. - Layers are built " "(`build(input_shape)` method) using shape info from `inputs` only. - " "`input_spec` compatibility is only checked against `inputs`. - Mixed " "precision input casting is only applied to `inputs`. If a layer has " "tensor arguments in `*args` or `**kwargs`, their casting behavior in " "mixed precision should be handled manually. - The SavedModel input " -"specification is generated using `inputs` only. - Integration with " +"specification is generated using `inputs` only. - Integration with " "various ecosystem packages like TFMOT, TFLite, TF.js, etc is only " "supported for `inputs` and not for tensors in positional and keyword " "arguments." msgstr "" -#: of tensorcircuit.applications.van.MaskedConv2D.call:8 -#: tensorcircuit.applications.van.MaskedLinear.call:8 -#: tensorcircuit.applications.van.ResidualBlock.call:8 -#: tensorcircuit.applications.vqes.Linear.call:8 +#: of tensorcircuit.applications.van.MaskedConv2D.call:10 +#: tensorcircuit.applications.van.MaskedLinear.call:10 +#: tensorcircuit.applications.van.ResidualBlock.call:10 +#: tensorcircuit.applications.vqes.Linear.call:10 msgid "" "Input tensor, or dict/list/tuple of input tensors. The first positional " "`inputs` argument is subject to special rules: - `inputs` must be " "explicitly passed. A layer cannot have zero" msgstr "" -#: of tensorcircuit.applications.van.MaskedConv2D.call:11 -#: tensorcircuit.applications.van.MaskedLinear.call:11 -#: tensorcircuit.applications.van.ResidualBlock.call:11 -#: tensorcircuit.applications.vqes.Linear.call:11 -msgid "" -"arguments, and `inputs` cannot be provided via the default value of a " -"keyword argument." -msgstr "" - #: of tensorcircuit.applications.van.MaskedConv2D.call:13 #: tensorcircuit.applications.van.MaskedLinear.call:13 #: tensorcircuit.applications.van.ResidualBlock.call:13 #: tensorcircuit.applications.vqes.Linear.call:13 -msgid "NumPy array or Python scalar values in `inputs` get cast as tensors." -msgstr "" - -#: of tensorcircuit.applications.van.MaskedConv2D.call:14 -#: tensorcircuit.applications.van.MaskedLinear.call:14 -#: tensorcircuit.applications.van.ResidualBlock.call:14 -#: tensorcircuit.applications.vqes.Linear.call:14 -msgid "Keras mask metadata is only collected from `inputs`." +msgid "" +"arguments, and `inputs` cannot be provided via the default value of a " +"keyword argument." msgstr "" #: of tensorcircuit.applications.van.MaskedConv2D.call:15 #: tensorcircuit.applications.van.MaskedLinear.call:15 #: tensorcircuit.applications.van.ResidualBlock.call:15 #: tensorcircuit.applications.vqes.Linear.call:15 -msgid "" -"Layers are built (`build(input_shape)` method) using shape info from " -"`inputs` only." +msgid "NumPy array or Python scalar values in `inputs` get cast as tensors." msgstr "" #: of tensorcircuit.applications.van.MaskedConv2D.call:17 #: tensorcircuit.applications.van.MaskedLinear.call:17 #: tensorcircuit.applications.van.ResidualBlock.call:17 #: tensorcircuit.applications.vqes.Linear.call:17 -msgid "`input_spec` compatibility is only checked against `inputs`." +msgid "Keras mask metadata is only collected from `inputs`." msgstr "" #: of tensorcircuit.applications.van.MaskedConv2D.call:18 @@ -7432,57 +7926,73 @@ msgstr "" #: tensorcircuit.applications.van.ResidualBlock.call:18 #: tensorcircuit.applications.vqes.Linear.call:18 msgid "" -"Mixed precision input casting is only applied to `inputs`. If a layer has" -" tensor arguments in `*args` or `**kwargs`, their casting behavior in " -"mixed precision should be handled manually." +"Layers are built (`build(input_shape)` method) using shape info from " +"`inputs` only." +msgstr "" + +#: of tensorcircuit.applications.van.MaskedConv2D.call:20 +#: tensorcircuit.applications.van.MaskedLinear.call:20 +#: tensorcircuit.applications.van.ResidualBlock.call:20 +#: tensorcircuit.applications.vqes.Linear.call:20 +msgid "`input_spec` compatibility is only checked against `inputs`." msgstr "" #: of tensorcircuit.applications.van.MaskedConv2D.call:21 #: tensorcircuit.applications.van.MaskedLinear.call:21 #: tensorcircuit.applications.van.ResidualBlock.call:21 #: tensorcircuit.applications.vqes.Linear.call:21 +msgid "" +"Mixed precision input casting is only applied to `inputs`. If a layer has" +" tensor arguments in `*args` or `**kwargs`, their casting behavior in " +"mixed precision should be handled manually." +msgstr "" + +#: of tensorcircuit.applications.van.MaskedConv2D.call:24 +#: tensorcircuit.applications.van.MaskedLinear.call:24 +#: tensorcircuit.applications.van.ResidualBlock.call:24 +#: tensorcircuit.applications.vqes.Linear.call:24 msgid "The SavedModel input specification is generated using `inputs` only." msgstr "" -#: of tensorcircuit.applications.van.MaskedConv2D.call:22 -#: tensorcircuit.applications.van.MaskedLinear.call:22 -#: tensorcircuit.applications.van.ResidualBlock.call:22 -#: tensorcircuit.applications.vqes.Linear.call:22 +#: of tensorcircuit.applications.van.MaskedConv2D.call:26 +#: tensorcircuit.applications.van.MaskedLinear.call:26 +#: tensorcircuit.applications.van.ResidualBlock.call:26 +#: tensorcircuit.applications.vqes.Linear.call:26 msgid "" "Integration with various ecosystem packages like TFMOT, TFLite, TF.js, " "etc is only supported for `inputs` and not for tensors in positional and " "keyword arguments." msgstr "" -#: of tensorcircuit.applications.van.MaskedConv2D.call:25 -#: tensorcircuit.applications.van.MaskedLinear.call:25 -#: tensorcircuit.applications.van.ResidualBlock.call:25 -#: tensorcircuit.applications.vqes.Linear.call:25 +#: of tensorcircuit.applications.van.MaskedConv2D.call:29 +#: tensorcircuit.applications.van.MaskedLinear.call:29 +#: tensorcircuit.applications.van.ResidualBlock.call:29 +#: tensorcircuit.applications.vqes.Linear.call:29 msgid "" "Additional positional arguments. May contain tensors, although this is " "not recommended, for the reasons above." msgstr "" -#: of tensorcircuit.applications.van.MaskedConv2D.call:27 -#: tensorcircuit.applications.van.MaskedLinear.call:27 -#: tensorcircuit.applications.van.ResidualBlock.call:27 -#: tensorcircuit.applications.vqes.Linear.call:27 +#: of tensorcircuit.applications.van.MaskedConv2D.call:31 +#: tensorcircuit.applications.van.MaskedLinear.call:31 +#: tensorcircuit.applications.van.ResidualBlock.call:31 +#: tensorcircuit.applications.vqes.Linear.call:31 msgid "" "Additional keyword arguments. May contain tensors, although this is not " "recommended, for the reasons above. The following optional keyword " "arguments are reserved: - `training`: Boolean scalar tensor of Python " "boolean indicating whether the `call` is meant for training or " "inference. - `mask`: Boolean input mask. If the layer's `call()` method " -"takes a `mask` argument, its default value will be set to the mask " -"generated for `inputs` by the previous layer (if `input` did come from " -"a layer that generated a corresponding mask, i.e. if it came from a " -"Keras layer with masking support)." +"takes a `mask` argument, its default value will be set to the mask " +"generated for `inputs` by the previous layer (if `input` did come from " +"a layer that generated a corresponding mask, i.e. if it came from a " +"Keras layer with masking support)." msgstr "" -#: of tensorcircuit.applications.van.MaskedConv2D.call:27 -#: tensorcircuit.applications.van.MaskedLinear.call:27 -#: tensorcircuit.applications.van.ResidualBlock.call:27 -#: tensorcircuit.applications.vqes.Linear.call:27 +#: of tensorcircuit.applications.van.MaskedConv2D.call:31 +#: tensorcircuit.applications.van.MaskedLinear.call:31 +#: tensorcircuit.applications.van.ResidualBlock.call:31 +#: tensorcircuit.applications.vqes.Linear.call:31 msgid "" "Additional keyword arguments. May contain tensors, although this is not " "recommended, for the reasons above. The following optional keyword " @@ -7490,17 +8000,17 @@ msgid "" "boolean indicating" msgstr "" -#: of tensorcircuit.applications.van.MaskedConv2D.call:31 -#: tensorcircuit.applications.van.MaskedLinear.call:31 -#: tensorcircuit.applications.van.ResidualBlock.call:31 -#: tensorcircuit.applications.vqes.Linear.call:31 +#: of tensorcircuit.applications.van.MaskedConv2D.call:35 +#: tensorcircuit.applications.van.MaskedLinear.call:35 +#: tensorcircuit.applications.van.ResidualBlock.call:35 +#: tensorcircuit.applications.vqes.Linear.call:35 msgid "whether the `call` is meant for training or inference." msgstr "" -#: of tensorcircuit.applications.van.MaskedConv2D.call:32 -#: tensorcircuit.applications.van.MaskedLinear.call:32 -#: tensorcircuit.applications.van.ResidualBlock.call:32 -#: tensorcircuit.applications.vqes.Linear.call:32 +#: of tensorcircuit.applications.van.MaskedConv2D.call:36 +#: tensorcircuit.applications.van.MaskedLinear.call:36 +#: tensorcircuit.applications.van.ResidualBlock.call:36 +#: tensorcircuit.applications.vqes.Linear.call:36 msgid "" "`mask`: Boolean input mask. If the layer's `call()` method takes a `mask`" " argument, its default value will be set to the mask generated for " @@ -7509,18 +8019,40 @@ msgid "" "masking support)." msgstr "" -#: of tensorcircuit.applications.van.MaskedConv2D.call:38 -#: tensorcircuit.applications.van.MaskedLinear.call:38 -#: tensorcircuit.applications.van.ResidualBlock.call:38 -#: tensorcircuit.applications.vqes.Linear.call:38 +#: of tensorcircuit.applications.van.MaskedConv2D.call:42 +#: tensorcircuit.applications.van.MaskedLinear.call:42 +#: tensorcircuit.applications.van.ResidualBlock.call:42 +#: tensorcircuit.applications.vqes.Linear.call:42 msgid "A tensor or list/tuple of tensors." msgstr "" -#: keras.engine.base_layer.Layer.get_weights:1 of +#: keras.src.engine.base_layer.Layer.get_config:1 of +msgid "Returns the config of the layer." +msgstr "" + +#: keras.src.engine.base_layer.Layer.get_config:3 of +msgid "" +"A layer config is a Python dictionary (serializable) containing the " +"configuration of a layer. The same layer can be reinstantiated later " +"(without its trained weights) from this configuration." +msgstr "" + +#: keras.src.engine.base_layer.Layer.get_config:8 of +msgid "" +"The config of a layer does not include connectivity information, nor the " +"layer class name. These are handled by `Network` (one layer of " +"abstraction above)." +msgstr "" + +#: keras.src.engine.base_layer.Layer.get_config:16 of +msgid "Python dictionary." +msgstr "" + +#: keras.src.engine.base_layer.Layer.get_weights:1 of msgid "Returns the current weights of the layer, as NumPy arrays." msgstr "" -#: keras.engine.base_layer.Layer.get_weights:3 of +#: keras.src.engine.base_layer.Layer.get_weights:3 of msgid "" "The weights of a layer represent the state of the layer. This function " "returns both trainable and non-trainable weight values associated with " @@ -7528,7 +8060,7 @@ msgid "" "state into similarly parameterized layers." msgstr "" -#: keras.engine.base_layer.Layer.get_weights:32 of +#: keras.src.engine.base_layer.Layer.get_weights:32 of msgid "Weights values as a list of NumPy arrays." msgstr "" @@ -7561,20 +8093,20 @@ msgstr "" #: of tensorcircuit.applications.vqes.JointSchedule:1 msgid "" "Bases: " -":py:class:`~keras.optimizer_v2.learning_rate_schedule.LearningRateSchedule`" +":py:class:`~keras.src.optimizers.schedules.learning_rate_schedule.LearningRateSchedule`" msgstr "" -#: keras.optimizer_v2.learning_rate_schedule.LearningRateSchedule.from_config:1 +#: keras.src.optimizers.schedules.learning_rate_schedule.LearningRateSchedule.from_config:1 #: of msgid "Instantiates a `LearningRateSchedule` from its config." msgstr "" -#: keras.optimizer_v2.learning_rate_schedule.LearningRateSchedule.from_config:3 +#: keras.src.optimizers.schedules.learning_rate_schedule.LearningRateSchedule.from_config:3 #: of msgid "Output of `get_config()`." msgstr "" -#: keras.optimizer_v2.learning_rate_schedule.LearningRateSchedule.from_config:5 +#: keras.src.optimizers.schedules.learning_rate_schedule.LearningRateSchedule.from_config:5 #: of msgid "A `LearningRateSchedule` instance." msgstr "" @@ -10823,18 +11355,18 @@ msgid "will be reduced by 1." msgstr "" #: of tensorcircuit.backends.jax_backend._svd_jax:1 +#: tensorcircuit.backends.tensorflow_backend._svd_tf:1 #: tensornetwork.backends.abstract_backend.AbstractBackend.svd:1 #: tensornetwork.backends.numpy.numpy_backend.NumPyBackend.svd:1 #: tensornetwork.backends.pytorch.pytorch_backend.PyTorchBackend.svd:1 -#: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.svd:1 msgid "Computes the singular value decomposition (SVD) of a tensor." msgstr "" #: of tensorcircuit.backends.jax_backend._svd_jax:3 +#: tensorcircuit.backends.tensorflow_backend._svd_tf:3 #: tensornetwork.backends.abstract_backend.AbstractBackend.svd:3 #: tensornetwork.backends.numpy.numpy_backend.NumPyBackend.svd:3 #: tensornetwork.backends.pytorch.pytorch_backend.PyTorchBackend.svd:3 -#: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.svd:3 msgid "" "The SVD is performed by treating the tensor as a matrix, with an " "effective left (row) index resulting from combining the axes " @@ -10843,10 +11375,10 @@ msgid "" msgstr "" #: of tensorcircuit.backends.jax_backend._svd_jax:8 +#: tensorcircuit.backends.tensorflow_backend._svd_tf:8 #: tensornetwork.backends.abstract_backend.AbstractBackend.svd:8 #: tensornetwork.backends.numpy.numpy_backend.NumPyBackend.svd:8 #: tensornetwork.backends.pytorch.pytorch_backend.PyTorchBackend.svd:8 -#: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.svd:8 msgid "" "For example, if `tensor` had a shape (2, 3, 4, 5) and `pivot_axis` was 2," " then `u` would have shape (2, 3, 6), `s` would have shape (6), and `vh` " @@ -10854,20 +11386,20 @@ msgid "" msgstr "" #: of tensorcircuit.backends.jax_backend._svd_jax:12 +#: tensorcircuit.backends.tensorflow_backend._svd_tf:12 #: tensornetwork.backends.abstract_backend.AbstractBackend.svd:12 #: tensornetwork.backends.numpy.numpy_backend.NumPyBackend.svd:12 #: tensornetwork.backends.pytorch.pytorch_backend.PyTorchBackend.svd:12 -#: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.svd:12 msgid "" "If `max_singular_values` is set to an integer, the SVD is truncated to " "keep at most this many singular values." msgstr "" #: of tensorcircuit.backends.jax_backend._svd_jax:15 +#: tensorcircuit.backends.tensorflow_backend._svd_tf:15 #: tensornetwork.backends.abstract_backend.AbstractBackend.svd:15 #: tensornetwork.backends.numpy.numpy_backend.NumPyBackend.svd:15 #: tensornetwork.backends.pytorch.pytorch_backend.PyTorchBackend.svd:15 -#: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.svd:15 msgid "" "If `max_truncation_error > 0`, as many singular values will be truncated " "as possible, so that the truncation error (the norm of discarded singular" @@ -10880,7 +11412,6 @@ msgstr "" #: tensornetwork.backends.abstract_backend.AbstractBackend.svd:21 #: tensornetwork.backends.numpy.numpy_backend.NumPyBackend.svd:21 #: tensornetwork.backends.pytorch.pytorch_backend.PyTorchBackend.svd:21 -#: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.svd:21 msgid "" "If both `max_singular_values` and `max_truncation_error` are specified, " "the number of retained singular values will be `min(max_singular_values, " @@ -10893,7 +11424,6 @@ msgstr "" #: tensornetwork.backends.abstract_backend.AbstractBackend.svd:27 #: tensornetwork.backends.numpy.numpy_backend.NumPyBackend.svd:27 #: tensornetwork.backends.pytorch.pytorch_backend.PyTorchBackend.svd:27 -#: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.svd:27 msgid "The output consists of three tensors `u, s, vh` such that: ```python" msgstr "" @@ -10901,7 +11431,6 @@ msgstr "" #: tensornetwork.backends.abstract_backend.AbstractBackend.svd:29 #: tensornetwork.backends.numpy.numpy_backend.NumPyBackend.svd:29 #: tensornetwork.backends.pytorch.pytorch_backend.PyTorchBackend.svd:29 -#: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.svd:29 msgid "u[i1,...,iN, j] * s[j] * vh[j, k1,...,kM] == tensor[i1,...,iN, k1,...,kM]" msgstr "" @@ -10909,7 +11438,6 @@ msgstr "" #: tensornetwork.backends.abstract_backend.AbstractBackend.svd:30 #: tensornetwork.backends.numpy.numpy_backend.NumPyBackend.svd:30 #: tensornetwork.backends.pytorch.pytorch_backend.PyTorchBackend.svd:30 -#: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.svd:30 msgid "" "``` Note that the output ordering matches numpy.linalg.svd rather than " "tf.svd." @@ -10923,7 +11451,6 @@ msgstr "" #: tensornetwork.backends.abstract_backend.AbstractBackend.svd:33 #: tensornetwork.backends.numpy.numpy_backend.NumPyBackend.svd:33 #: tensornetwork.backends.pytorch.pytorch_backend.PyTorchBackend.svd:33 -#: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.svd:33 msgid "A tensor to be decomposed." msgstr "" @@ -10935,7 +11462,6 @@ msgstr "" #: tensornetwork.backends.abstract_backend.AbstractBackend.svd:34 #: tensornetwork.backends.numpy.numpy_backend.NumPyBackend.svd:34 #: tensornetwork.backends.pytorch.pytorch_backend.PyTorchBackend.svd:34 -#: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.svd:34 msgid "Where to split the tensor's axes before flattening into a matrix." msgstr "" @@ -10943,7 +11469,6 @@ msgstr "" #: tensornetwork.backends.abstract_backend.AbstractBackend.svd:36 #: tensornetwork.backends.numpy.numpy_backend.NumPyBackend.svd:36 #: tensornetwork.backends.pytorch.pytorch_backend.PyTorchBackend.svd:36 -#: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.svd:36 msgid "The number of singular values to keep, or `None` to keep them all." msgstr "" @@ -10951,7 +11476,6 @@ msgstr "" #: tensornetwork.backends.abstract_backend.AbstractBackend.svd:38 #: tensornetwork.backends.numpy.numpy_backend.NumPyBackend.svd:38 #: tensornetwork.backends.pytorch.pytorch_backend.PyTorchBackend.svd:38 -#: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.svd:38 msgid "The maximum allowed truncation error or `None` to not do any truncation." msgstr "" @@ -10961,7 +11485,6 @@ msgstr "" #: tensornetwork.backends.abstract_backend.AbstractBackend.svd:40 #: tensornetwork.backends.numpy.numpy_backend.NumPyBackend.svd:40 #: tensornetwork.backends.pytorch.pytorch_backend.PyTorchBackend.svd:40 -#: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.svd:40 msgid "Multiply `max_truncation_err` with the largest singular value." msgstr "" @@ -10969,7 +11492,6 @@ msgstr "" #: tensornetwork.backends.abstract_backend.AbstractBackend.svd:42 #: tensornetwork.backends.numpy.numpy_backend.NumPyBackend.svd:42 #: tensornetwork.backends.pytorch.pytorch_backend.PyTorchBackend.svd:42 -#: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.svd:42 msgid "" "Left tensor factor. s: Vector of ordered singular values from largest to " "smallest. vh: Right tensor factor. s_rest: Vector of discarded singular " @@ -10980,7 +11502,6 @@ msgstr "" #: tensornetwork.backends.abstract_backend.AbstractBackend.svd:42 #: tensornetwork.backends.numpy.numpy_backend.NumPyBackend.svd:42 #: tensornetwork.backends.pytorch.pytorch_backend.PyTorchBackend.svd:42 -#: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.svd:42 msgid "" "Left tensor factor. s: Vector of ordered singular values from largest to " "smallest. vh: Right tensor factor. s_rest: Vector of discarded singular " @@ -10988,10 +11509,10 @@ msgid "" msgstr "" #: of tensorcircuit.backends.jax_backend._svd_jax:46 +#: tensorcircuit.backends.tensorflow_backend._svd_tf:49 #: tensornetwork.backends.abstract_backend.AbstractBackend.svd:46 #: tensornetwork.backends.numpy.numpy_backend.NumPyBackend.svd:46 #: tensornetwork.backends.pytorch.pytorch_backend.PyTorchBackend.svd:46 -#: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.svd:46 msgid "truncation)." msgstr "" @@ -12039,6 +12560,62 @@ msgid "" "backend. The TensorFlow version returns y[i] = x[i] / abs(x[i])." msgstr "" +#: of tensorcircuit.backends.tensorflow_backend._svd_tf:21 +msgid "" +"If both `max_singular_values` snd `max_truncation_error` are specified, " +"the number of retained singular values will be `min(max_singular_values, " +"nsv_auto_trunc)`, where `nsv_auto_trunc` is the number of singular values" +" that must be kept to maintain a truncation error smaller than " +"`max_truncation_error`." +msgstr "" + +#: of tensorcircuit.backends.tensorflow_backend._svd_tf:27 +msgid "" +"The output consists of three tensors `u, s, vh` such that: ```python " +"u[i1,...,iN, j] * s[j] * vh[j, k1,...,kM] == tensor[i1,...,iN, k1,...,kM]" +" ``` Note that the output ordering matches numpy.linalg.svd rather than " +"tf.svd." +msgstr "" + +#: of tensorcircuit.backends.tensorflow_backend._svd_tf:33 +msgid "" +"Args: tf: The tensorflow module. tensor: A tensor to be decomposed. " +"pivot_axis: Where to split the tensor's axes before flattening into a" +msgstr "" + +#: of tensorcircuit.backends.tensorflow_backend._svd_tf:37 +msgid "matrix." +msgstr "" + +#: of tensorcircuit.backends.tensorflow_backend._svd_tf:38 +msgid "max_singular_values: The number of singular values to keep, or `None` to" +msgstr "" + +#: of tensorcircuit.backends.tensorflow_backend._svd_tf:39 +msgid "keep them all." +msgstr "" + +#: of tensorcircuit.backends.tensorflow_backend._svd_tf:40 +msgid "" +"max_truncation_error: The maximum allowed truncation error or `None` to " +"not" +msgstr "" + +#: of tensorcircuit.backends.tensorflow_backend._svd_tf:41 +msgid "do any truncation." +msgstr "" + +#: of tensorcircuit.backends.tensorflow_backend._svd_tf:42 +msgid "relative: Multiply `max_truncation_err` with the largest singular value." +msgstr "" + +#: of tensorcircuit.backends.tensorflow_backend._svd_tf:44 +msgid "" +"Returns: u: Left tensor factor. s: Vector of ordered singular values from" +" largest to smallest. vh: Right tensor factor. s_rest: Vector of " +"discarded singular values (length zero if no" +msgstr "" + #: of #: tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.trace:11 msgid "" @@ -12907,15 +13484,15 @@ msgid "``Circuit`` class. Simple usage demo below." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply_list:1 msgid "" "Apply **ANY** gate with parameters on the circuit. See " ":py:meth:`tensorcircuit.gates.any_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply:4 -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply:5 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply_list:4 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply_list:5 #: tensorcircuit.circuit.Circuit.apply_general_kraus_delayed..apply:4 #: tensorcircuit.densitymatrix.DMCircuit.apply_general_kraus_delayed..apply:4 #: tensorcircuit.densitymatrix.DMCircuit2.apply_general_kraus_delayed..apply:4 @@ -12923,20 +13500,20 @@ msgid "Qubit number that the gate applies on." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply:6 -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply:7 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply_list:6 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply_list:7 msgid "Parameters for the gate." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:1 msgid "" "Apply **CNOT** gate on the circuit. See " ":py:meth:`tensorcircuit.gates.cnot_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:5 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:5 msgid "" "Qubit number that the gate applies on. The matrix for the gate is .. " "math:: \\begin{bmatrix} 1.+0.j & 0.+0.j & 0.+0.j & 0.+0.j\\\\" @@ -12945,12 +13522,12 @@ msgid "" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:5 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:5 msgid "Qubit number that the gate applies on. The matrix for the gate is" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:8 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:8 msgid "" "\\begin{bmatrix} 1.+0.j & 0.+0.j & 0.+0.j & 0.+0.j\\\\ 0.+0.j & " "1.+0.j & 0.+0.j & 0.+0.j\\\\ 0.+0.j & 0.+0.j & 0.+0.j & 1.+0.j\\\\ " @@ -12958,56 +13535,56 @@ msgid "" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply_list:1 msgid "" "Apply **CPHASE** gate with parameters on the circuit. See " ":py:meth:`tensorcircuit.gates.cphase_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply_list:1 msgid "" "Apply **CR** gate with parameters on the circuit. See " ":py:meth:`tensorcircuit.gates.cr_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply_list:1 msgid "" "Apply **CRX** gate with parameters on the circuit. See " ":py:meth:`tensorcircuit.gates.crx_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply_list:1 msgid "" "Apply **CRY** gate with parameters on the circuit. See " ":py:meth:`tensorcircuit.gates.cry_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply_list:1 msgid "" "Apply **CRZ** gate with parameters on the circuit. See " ":py:meth:`tensorcircuit.gates.crz_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply_list:1 msgid "" "Apply **CU** gate with parameters on the circuit. See " ":py:meth:`tensorcircuit.gates.cu_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:1 msgid "" "Apply **CY** gate on the circuit. See " ":py:meth:`tensorcircuit.gates.cy_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:5 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:5 msgid "" "Qubit number that the gate applies on. The matrix for the gate is .. " "math:: \\begin{bmatrix} 1.+0.j & 0.+0.j & 0.+0.j & 0.+0.j\\\\" @@ -13016,7 +13593,7 @@ msgid "" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:8 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:8 msgid "" "\\begin{bmatrix} 1.+0.j & 0.+0.j & 0.+0.j & 0.+0.j\\\\ 0.+0.j & " "1.+0.j & 0.+0.j & 0.+0.j\\\\ 0.+0.j & 0.+0.j & 0.+0.j & 0.-1.j\\\\ " @@ -13024,14 +13601,14 @@ msgid "" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:1 msgid "" "Apply **CZ** gate on the circuit. See " ":py:meth:`tensorcircuit.gates.cz_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:5 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:5 msgid "" "Qubit number that the gate applies on. The matrix for the gate is .. " "math:: \\begin{bmatrix} 1.+0.j & 0.+0.j & 0.+0.j & 0.+0.j\\\\" @@ -13040,7 +13617,7 @@ msgid "" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:8 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:8 msgid "" "\\begin{bmatrix} 1.+0.j & 0.+0.j & 0.+0.j & 0.+0.j\\\\ 0.+0.j & " "1.+0.j & 0.+0.j & 0.+0.j\\\\ 0.+0.j & 0.+0.j & 1.+0.j & 0.+0.j\\\\ " @@ -13048,28 +13625,28 @@ msgid "" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply_list:1 msgid "" "Apply **EXP** gate with parameters on the circuit. See " ":py:meth:`tensorcircuit.gates.exp_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply_list:1 msgid "" "Apply **EXP1** gate with parameters on the circuit. See " ":py:meth:`tensorcircuit.gates.exp1_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:1 msgid "" "Apply **FREDKIN** gate on the circuit. See " ":py:meth:`tensorcircuit.gates.fredkin_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:5 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:5 msgid "" "Qubit number that the gate applies on. The matrix for the gate is .. " "math:: \\begin{bmatrix} 1.+0.j & 0.+0.j & 0.+0.j & 0.+0.j & " @@ -13085,7 +13662,7 @@ msgid "" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:8 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:8 msgid "" "\\begin{bmatrix} 1.+0.j & 0.+0.j & 0.+0.j & 0.+0.j & 0.+0.j & 0.+0.j &" " 0.+0.j & 0.+0.j\\\\ 0.+0.j & 1.+0.j & 0.+0.j & 0.+0.j & 0.+0.j & " @@ -13100,14 +13677,14 @@ msgid "" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:1 msgid "" "Apply **H** gate on the circuit. See " ":py:meth:`tensorcircuit.gates.h_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:5 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:5 msgid "" "Qubit number that the gate applies on. The matrix for the gate is .. " "math:: \\begin{bmatrix} 0.70710677+0.j & 0.70710677+0.j\\\\ " @@ -13115,21 +13692,21 @@ msgid "" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:8 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:8 msgid "" "\\begin{bmatrix} 0.70710677+0.j & 0.70710677+0.j\\\\ 0.70710677+0.j" " & -0.70710677+0.j \\end{bmatrix}" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:1 msgid "" "Apply **I** gate on the circuit. See " ":py:meth:`tensorcircuit.gates.i_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:5 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:5 msgid "" "Qubit number that the gate applies on. The matrix for the gate is .. " "math:: \\begin{bmatrix} 1.+0.j & 0.+0.j\\\\ 0.+0.j & 1.+0.j " @@ -13137,61 +13714,61 @@ msgid "" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:8 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:8 msgid "\\begin{bmatrix} 1.+0.j & 0.+0.j\\\\ 0.+0.j & 1.+0.j \\end{bmatrix}" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply_list:1 msgid "" "Apply **ISWAP** gate with parameters on the circuit. See " ":py:meth:`tensorcircuit.gates.iswap_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply_list:1 msgid "" "Apply mpo gate in MPO format on the circuit. See " ":py:meth:`tensorcircuit.gates.mpo_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply_list:1 msgid "" "Apply multicontrol gate in MPO format on the circuit. See " ":py:meth:`tensorcircuit.gates.multicontrol_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply_list:1 msgid "" "Apply **ORX** gate with parameters on the circuit. See " ":py:meth:`tensorcircuit.gates.orx_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply_list:1 msgid "" "Apply **ORY** gate with parameters on the circuit. See " ":py:meth:`tensorcircuit.gates.ory_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply_list:1 msgid "" "Apply **ORZ** gate with parameters on the circuit. See " ":py:meth:`tensorcircuit.gates.orz_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:1 msgid "" "Apply **OX** gate on the circuit. See " ":py:meth:`tensorcircuit.gates.ox_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:5 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:5 msgid "" "Qubit number that the gate applies on. The matrix for the gate is .. " "math:: \\begin{bmatrix} 0.+0.j & 1.+0.j & 0.+0.j & 0.+0.j\\\\" @@ -13200,7 +13777,7 @@ msgid "" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:8 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:8 msgid "" "\\begin{bmatrix} 0.+0.j & 1.+0.j & 0.+0.j & 0.+0.j\\\\ 1.+0.j & " "0.+0.j & 0.+0.j & 0.+0.j\\\\ 0.+0.j & 0.+0.j & 1.+0.j & 0.+0.j\\\\ " @@ -13208,14 +13785,14 @@ msgid "" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:1 msgid "" "Apply **OY** gate on the circuit. See " ":py:meth:`tensorcircuit.gates.oy_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:5 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:5 msgid "" "Qubit number that the gate applies on. The matrix for the gate is .. " "math:: \\begin{bmatrix} 0.+0.j & 0.-1.j & 0.+0.j & 0.+0.j\\\\" @@ -13224,7 +13801,7 @@ msgid "" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:8 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:8 msgid "" "\\begin{bmatrix} 0.+0.j & 0.-1.j & 0.+0.j & 0.+0.j\\\\ 0.+1.j & " "0.+0.j & 0.+0.j & 0.+0.j\\\\ 0.+0.j & 0.+0.j & 1.+0.j & 0.+0.j\\\\ " @@ -13232,14 +13809,14 @@ msgid "" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:1 msgid "" "Apply **OZ** gate on the circuit. See " ":py:meth:`tensorcircuit.gates.oz_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:5 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:5 msgid "" "Qubit number that the gate applies on. The matrix for the gate is .. " "math:: \\begin{bmatrix} 1.+0.j & 0.+0.j & 0.+0.j & 0.+0.j\\\\" @@ -13248,7 +13825,7 @@ msgid "" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:8 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:8 msgid "" "\\begin{bmatrix} 1.+0.j & 0.+0.j & 0.+0.j & 0.+0.j\\\\ 0.+0.j & " "-1.+0.j & 0.+0.j & 0.+0.j\\\\ 0.+0.j & 0.+0.j & 1.+0.j & 0.+0.j\\\\" @@ -13256,70 +13833,70 @@ msgid "" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply_list:1 msgid "" "Apply **PHASE** gate with parameters on the circuit. See " ":py:meth:`tensorcircuit.gates.phase_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply_list:1 msgid "" "Apply **R** gate with parameters on the circuit. See " ":py:meth:`tensorcircuit.gates.r_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply_list:1 msgid "" "Apply **RX** gate with parameters on the circuit. See " ":py:meth:`tensorcircuit.gates.rx_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply_list:1 msgid "" "Apply **RXX** gate with parameters on the circuit. See " ":py:meth:`tensorcircuit.gates.rxx_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply_list:1 msgid "" "Apply **RY** gate with parameters on the circuit. See " ":py:meth:`tensorcircuit.gates.ry_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply_list:1 msgid "" "Apply **RYY** gate with parameters on the circuit. See " ":py:meth:`tensorcircuit.gates.ryy_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply_list:1 msgid "" "Apply **RZ** gate with parameters on the circuit. See " ":py:meth:`tensorcircuit.gates.rz_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply_list:1 msgid "" "Apply **RZZ** gate with parameters on the circuit. See " ":py:meth:`tensorcircuit.gates.rzz_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:1 msgid "" "Apply **S** gate on the circuit. See " ":py:meth:`tensorcircuit.gates.s_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:5 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:5 msgid "" "Qubit number that the gate applies on. The matrix for the gate is .. " "math:: \\begin{bmatrix} 1.+0.j & 0.+0.j\\\\ 0.+0.j & 0.+1.j " @@ -13327,19 +13904,19 @@ msgid "" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:8 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:8 msgid "\\begin{bmatrix} 1.+0.j & 0.+0.j\\\\ 0.+0.j & 0.+1.j \\end{bmatrix}" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:1 msgid "" "Apply **SD** gate on the circuit. See " ":py:meth:`tensorcircuit.gates.sd_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:5 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:5 msgid "" "Qubit number that the gate applies on. The matrix for the gate is .. " "math:: \\begin{bmatrix} 1.+0.j & 0.+0.j\\\\ 0.+0.j & 0.-1.j " @@ -13347,19 +13924,19 @@ msgid "" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:8 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:8 msgid "\\begin{bmatrix} 1.+0.j & 0.+0.j\\\\ 0.+0.j & 0.-1.j \\end{bmatrix}" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:1 msgid "" "Apply **SWAP** gate on the circuit. See " ":py:meth:`tensorcircuit.gates.swap_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:5 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:5 msgid "" "Qubit number that the gate applies on. The matrix for the gate is .. " "math:: \\begin{bmatrix} 1.+0.j & 0.+0.j & 0.+0.j & 0.+0.j\\\\" @@ -13368,7 +13945,7 @@ msgid "" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:8 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:8 msgid "" "\\begin{bmatrix} 1.+0.j & 0.+0.j & 0.+0.j & 0.+0.j\\\\ 0.+0.j & " "0.+0.j & 1.+0.j & 0.+0.j\\\\ 0.+0.j & 1.+0.j & 0.+0.j & 0.+0.j\\\\ " @@ -13376,14 +13953,14 @@ msgid "" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:1 msgid "" "Apply **T** gate on the circuit. See " ":py:meth:`tensorcircuit.gates.t_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:5 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:5 msgid "" "Qubit number that the gate applies on. The matrix for the gate is .. " "math:: \\begin{bmatrix} 1. & +0.j & 0. & +0.j\\\\ 0. & +0.j " @@ -13391,21 +13968,21 @@ msgid "" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:8 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:8 msgid "" "\\begin{bmatrix} 1. & +0.j & 0. & +0.j\\\\ 0. & +0.j & " "0.70710677+0.70710677j \\end{bmatrix}" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:1 msgid "" "Apply **TD** gate on the circuit. See " ":py:meth:`tensorcircuit.gates.td_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:5 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:5 msgid "" "Qubit number that the gate applies on. The matrix for the gate is .. " "math:: \\begin{bmatrix} 1. & +0.j & 0. & +0.j\\\\ 0. & +0.j " @@ -13413,21 +13990,21 @@ msgid "" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:8 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:8 msgid "" "\\begin{bmatrix} 1. & +0.j & 0. & +0.j\\\\ 0. & +0.j & " "0.70710677-0.70710677j \\end{bmatrix}" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:1 msgid "" "Apply **TOFFOLI** gate on the circuit. See " ":py:meth:`tensorcircuit.gates.toffoli_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:5 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:5 msgid "" "Qubit number that the gate applies on. The matrix for the gate is .. " "math:: \\begin{bmatrix} 1.+0.j & 0.+0.j & 0.+0.j & 0.+0.j & " @@ -13443,7 +14020,7 @@ msgid "" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:8 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:8 msgid "" "\\begin{bmatrix} 1.+0.j & 0.+0.j & 0.+0.j & 0.+0.j & 0.+0.j & 0.+0.j &" " 0.+0.j & 0.+0.j\\\\ 0.+0.j & 1.+0.j & 0.+0.j & 0.+0.j & 0.+0.j & " @@ -13458,21 +14035,21 @@ msgid "" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_variable_gate_delayed..apply_list:1 msgid "" "Apply **U** gate with parameters on the circuit. See " ":py:meth:`tensorcircuit.gates.u_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:1 msgid "" "Apply **WROOT** gate on the circuit. See " ":py:meth:`tensorcircuit.gates.wroot_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:5 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:5 msgid "" "Qubit number that the gate applies on. The matrix for the gate is .. " "math:: \\begin{bmatrix} 0.70710677+0.j & -0.5 & -0.5j\\\\ " @@ -13480,21 +14057,21 @@ msgid "" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:8 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:8 msgid "" "\\begin{bmatrix} 0.70710677+0.j & -0.5 & -0.5j\\\\ 0.5 & -0.5j & " "0.70710677+0.j \\end{bmatrix}" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:1 msgid "" "Apply **X** gate on the circuit. See " ":py:meth:`tensorcircuit.gates.x_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:5 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:5 msgid "" "Qubit number that the gate applies on. The matrix for the gate is .. " "math:: \\begin{bmatrix} 0.+0.j & 1.+0.j\\\\ 1.+0.j & 0.+0.j " @@ -13502,19 +14079,19 @@ msgid "" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:8 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:8 msgid "\\begin{bmatrix} 0.+0.j & 1.+0.j\\\\ 1.+0.j & 0.+0.j \\end{bmatrix}" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:1 msgid "" "Apply **Y** gate on the circuit. See " ":py:meth:`tensorcircuit.gates.y_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:5 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:5 msgid "" "Qubit number that the gate applies on. The matrix for the gate is .. " "math:: \\begin{bmatrix} 0.+0.j & 0.-1.j\\\\ 0.+1.j & 0.+0.j " @@ -13522,19 +14099,19 @@ msgid "" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:8 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:8 msgid "\\begin{bmatrix} 0.+0.j & 0.-1.j\\\\ 0.+1.j & 0.+0.j \\end{bmatrix}" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:1 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:1 msgid "" "Apply **Z** gate on the circuit. See " ":py:meth:`tensorcircuit.gates.z_gate`." msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:5 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:5 msgid "" "Qubit number that the gate applies on. The matrix for the gate is .. " "math:: \\begin{bmatrix} 1.+0.j & 0.+0.j\\\\ 0.+0.j & -1.+0.j" @@ -13542,7 +14119,7 @@ msgid "" msgstr "" #: of -#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply:8 +#: tensorcircuit.abstractcircuit.AbstractCircuit.apply_general_gate_delayed..apply_list:8 msgid "\\begin{bmatrix} 1.+0.j & 0.+0.j\\\\ 0.+0.j & -1.+0.j \\end{bmatrix}" msgstr "" @@ -14659,6 +15236,34 @@ msgstr "" msgid "Experimental features" msgstr "" +#: of tensorcircuit.experimental.evol_global:1 +msgid "" +"ode evolution of time dependent Hamiltonian on circuit of all qubits " +"[only jax backend support for now]" +msgstr "" + +#: of tensorcircuit.experimental.evol_global:6 +msgid "" +"h_fun should return a **SPARSE** Hamiltonian matrix with input arguments " +"time and *args" +msgstr "" + +#: of tensorcircuit.experimental.evol_local:1 +msgid "" +"ode evolution of time dependent Hamiltonian on circuit of given indices " +"[only jax backend support for now]" +msgstr "" + +#: of tensorcircuit.experimental.evol_local:8 +msgid "" +"h_fun should return a dense Hamiltonian matrix with input arguments time " +"and *args" +msgstr "" + +#: of tensorcircuit.experimental.evol_local:11 +msgid "evolution time" +msgstr "" + #: of tensorcircuit.experimental.hamiltonian_evol:1 msgid "" "Fast implementation of static full Hamiltonian evolution (default as " @@ -17478,15 +18083,184 @@ msgid "" "https://qiskit.org/documentation/stubs/qiskit.visualization.plot_histogram.html" msgstr "" -#: ../../source/api/results/readout_mitigation.rst:2 -msgid "tensorcircuit.results.readout_mitigation" +#: of tensorcircuit.results.counts.plot_histogram:4 +msgid "interesting kw options include: ``number_to_keep`` (int)" msgstr "" -#: of tensorcircuit.results.readout_mitigation:1 -msgid "readout error mitigation functionalities" +#: ../../source/api/results/qem.rst:2 +msgid "tensorcircuit.results.qem" msgstr "" -#: of tensorcircuit.results.readout_mitigation.ReadoutMit.__init__:1 +#: ../../source/api/results/qem/benchmark_circuits.rst:2 +msgid "tensorcircuit.results.qem.benchmark_circuits" +msgstr "" + +#: of tensorcircuit.results.qem.benchmark_circuits:1 +msgid "circuits for quantum chip benchmark" +msgstr "" + +#: ../../source/api/results/qem/qem_methods.rst:2 +msgid "tensorcircuit.results.qem.qem_methods" +msgstr "" + +#: of tensorcircuit.results.qem.qem_methods:1 +msgid "quantum error mitigation functionalities" +msgstr "" + +#: of tensorcircuit.results.qem.qem_methods.add_dd:1 +msgid "Add DD sequence to A circuit" +msgstr "" + +#: of tensorcircuit.results.qem.qem_methods.add_dd:3 +#: tensorcircuit.results.qem.qem_methods.prune_ddcircuit:4 +msgid "circuit" +msgstr "" + +#: of tensorcircuit.results.qem.qem_methods.add_dd:5 +msgid "The rule to conduct the DD sequence" +msgstr "" + +#: of tensorcircuit.results.qem.qem_methods.add_dd:7 +#: tensorcircuit.results.qem.qem_methods.prune_ddcircuit:8 +msgid "new circuit" +msgstr "" + +#: of tensorcircuit.results.qem.qem_methods.apply_dd:1 +msgid "Apply dynamic decoupling (DD) and return the mitigated results." +msgstr "" + +#: of tensorcircuit.results.qem.qem_methods.apply_dd:4 +#: tensorcircuit.results.qem.qem_methods.apply_zne:3 +msgid "The aim circuit." +msgstr "" + +#: of tensorcircuit.results.qem.qem_methods.apply_dd:6 +#: tensorcircuit.results.qem.qem_methods.apply_rc:5 +msgid "A executor that executes a circuit and return results." +msgstr "" + +#: of tensorcircuit.results.qem.qem_methods.apply_dd:8 +msgid "" +"The rule to construct DD sequence, can use default rule " +"\"dd_option.rules.xx\"" +msgstr "" + +#: of tensorcircuit.results.qem.qem_methods.apply_dd:9 +msgid "" +"or custom rule \"['X','X']\" :type rule: Union[Callable[[int], Any], " +"List[str]] :param rule_args:An optional dictionary of keyword arguments " +"for ``rule``, defaults to {}. :type rule_args: Dict[str, Any], optional " +":param num_trials: The number of independent experiments to average over," +" defaults to 1 :type num_trials: int, optional :param full_output: If " +"``False`` only the mitigated expectation value is" +msgstr "" + +#: of tensorcircuit.results.qem.qem_methods.apply_dd:16 +msgid "" +"returned. If ``True`` a dictionary containing all DD data is returned " +"too, defaults to False" +msgstr "" + +#: of tensorcircuit.results.qem.qem_methods.apply_dd:19 +msgid "ignore the DD sequences that added to unused qubits, defaults to True" +msgstr "" + +#: of tensorcircuit.results.qem.qem_methods.apply_dd:21 +msgid "dd sequence full fill the idle circuits, defaults to False" +msgstr "" + +#: of tensorcircuit.results.qem.qem_methods.apply_dd:23 +#: tensorcircuit.results.qem.qem_methods.apply_rc:11 +msgid "whether the output is bit string, defaults to False" +msgstr "" + +#: of tensorcircuit.results.qem.qem_methods.apply_dd:25 +msgid "" +"mitigated expectation value or mitigated expectation value and DD circuit" +" information" +msgstr "" + +#: of tensorcircuit.results.qem.qem_methods.apply_rc:1 +msgid "Apply Randomized Compiling or Pauli twirling on two-qubit gates." +msgstr "" + +#: of tensorcircuit.results.qem.qem_methods.apply_rc:3 +msgid "Input circuit" +msgstr "" + +#: of tensorcircuit.results.qem.qem_methods.apply_rc:7 +msgid "Number of circuits for RC, defaults to 1" +msgstr "" + +#: of tensorcircuit.results.qem.qem_methods.apply_rc:9 +msgid "" +"Whether simplify the circuits by merging single qubit gates, defaults to " +"True" +msgstr "" + +#: of tensorcircuit.results.qem.qem_methods.apply_rc:13 +msgid "Mitigated results by RC" +msgstr "" + +#: of tensorcircuit.results.qem.qem_methods.apply_zne:1 +msgid "Apply zero-noise extrapolation (ZNE) and return the mitigated results." +msgstr "" + +#: of tensorcircuit.results.qem.qem_methods.apply_zne:5 +msgid "" +"A executor that executes a single circuit or a batch of circuits and " +"return results." +msgstr "" + +#: of tensorcircuit.results.qem.qem_methods.apply_zne:7 +msgid "Determines the extropolation method." +msgstr "" + +#: of tensorcircuit.results.qem.qem_methods.apply_zne:9 +msgid "The scaling function for the aim circuit, defaults to fold_gates_at_random" +msgstr "" + +#: of tensorcircuit.results.qem.qem_methods.apply_zne:11 +msgid "" +"Number of times expectation values are computed by the executor, average " +"each point, defaults to 1." +msgstr "" + +#: of tensorcircuit.results.qem.qem_methods.apply_zne:14 +msgid "Mitigated average value by ZNE." +msgstr "" + +#: of tensorcircuit.results.qem.qem_methods.prune_ddcircuit:1 +msgid "" +"Discard DD sequence on idle qubits and Discard identity gate (no " +"identity/idle gate on device now) filled in DD sequence." +msgstr "" + +#: of tensorcircuit.results.qem.qem_methods.prune_ddcircuit:6 +msgid "qubit list to apply DD sequence" +msgstr "" + +#: of tensorcircuit.results.qem.qem_methods.used_qubits:1 +msgid "Create a qubit list that includes all qubits having gate manipulation." +msgstr "" + +#: of tensorcircuit.results.qem.qem_methods.used_qubits:3 +msgid "a circuit" +msgstr "" + +#: of tensorcircuit.results.qem.qem_methods.used_qubits:5 +msgid "qubit list" +msgstr "" + +#: ../../source/api/results/readout_mitigation.rst:2 +msgid "tensorcircuit.results.readout_mitigation" +msgstr "" + +#: of tensorcircuit.results.readout_mitigation:1 +msgid "readout error mitigation functionalities" +msgstr "" + +#: of tensorcircuit.results.readout_mitigation.ReadoutMit.__init__:1 msgid "The Class for readout error mitigation" msgstr "" @@ -17846,24 +18620,6 @@ msgstr "" msgid "Useful utilities for quantum chemistry related task" msgstr "" -#: of tensorcircuit.templates.chems.get_ps:1 -msgid "" -"Get Pauli string array and weights array for a qubit Hamiltonian as a sum" -" of Pauli strings defined in openfermion ``QubitOperator``." -msgstr "" - -#: of tensorcircuit.templates.chems.get_ps:4 -msgid "``openfermion.ops.operators.qubit_operator.QubitOperator``" -msgstr "" - -#: of tensorcircuit.templates.chems.get_ps:6 -msgid "The number of qubits" -msgstr "" - -#: of tensorcircuit.templates.chems.get_ps:8 -msgid "Pauli String array and weights array" -msgstr "" - #: ../../source/api/templates/dataset.rst:2 msgid "tensorcircuit.templates.dataset" msgstr "" @@ -24097,3 +24853,1044 @@ msgstr "" #~ msgid "Returns a dictionary containing a whole state of the module." #~ msgstr "" +#~ msgid "" +#~ "Visualise the circuit. This method " +#~ "recevies the keywords as same as " +#~ "qiskit.circuit.QuantumCircuit.draw. More details can" +#~ " be found here: " +#~ "https://qiskit.org/documentation/stubs/qiskit.circuit.QuantumCircuit.draw.html." +#~ msgstr "" + +#~ msgid "the corresponding qubit" +#~ msgstr "" + +#~ msgid "Bases: :py:class:`~keras.engine.training.Model`" +#~ msgstr "" + +#~ msgid "" +#~ "This method can also be called " +#~ "directly on a Functional Model during" +#~ " construction. In this case, any loss" +#~ " Tensors passed to this Model must" +#~ " be symbolic and be able to be" +#~ " traced back to the model's `Input`s." +#~ " These losses become part of the " +#~ "model's topology and are tracked in " +#~ "`get_config`." +#~ msgstr "" + +#~ msgid "" +#~ "Additional keyword arguments for backward " +#~ "compatibility. Accepted values: inputs - " +#~ "Deprecated, will be automatically inferred." +#~ msgstr "" + +#~ msgid "" +#~ "Additional keyword arguments for backward " +#~ "compatibility. Accepted values:" +#~ msgstr "" + +#~ msgid "inputs - Deprecated, will be automatically inferred." +#~ msgstr "" + +#~ msgid "Deprecated, will be automatically inferred." +#~ msgstr "" + +#~ msgid "Whether to use `ResourceVariable`." +#~ msgstr "" + +#~ msgid "" +#~ "When giving unsupported dtype and no " +#~ "initializer or when trainable has " +#~ "been set to True with synchronization" +#~ " set as `ON_READ`." +#~ msgstr "" + +#~ msgid "This is an alias of `self.__call__`." +#~ msgstr "" + +#~ msgid "Input tensor(s)." +#~ msgstr "" + +#~ msgid "additional positional arguments to be passed to `self.call`." +#~ msgstr "" + +#~ msgid "additional keyword arguments to be passed to `self.call`." +#~ msgstr "" + +#~ msgid "Output tensor(s)." +#~ msgstr "" + +#~ msgid "" +#~ "1. In case of invalid user-" +#~ "provided data (not of type tuple," +#~ " list, `TensorShape`, or dict). " +#~ "2. If the model requires call " +#~ "arguments that are agnostic to " +#~ "the input shapes (positional or keyword" +#~ " arg in call signature). 3. If" +#~ " not all layers were properly built." +#~ " 4. If float type inputs are " +#~ "not supported within the layers." +#~ msgstr "" + +#~ msgid "" +#~ "In case of invalid user-provided " +#~ "data (not of type tuple, list," +#~ " `TensorShape`, or dict). 2. If " +#~ "the model requires call arguments that" +#~ " are agnostic to the input " +#~ "shapes (positional or keyword arg in " +#~ "call signature). 3. If not all " +#~ "layers were properly built. 4. If" +#~ " float type inputs are not supported" +#~ " within the layers." +#~ msgstr "" + +#~ msgid "" +#~ "A mask or list of masks. A " +#~ "mask can be either a boolean " +#~ "tensor or None (no mask). For more" +#~ " details, check the guide " +#~ "[here](https://www.tensorflow.org/guide/keras/masking_and_padding)." +#~ msgstr "" + +#~ msgid "" +#~ "A mask or list of masks. A " +#~ "mask can be either a boolean " +#~ "tensor or None (no mask). For more" +#~ " details, check the guide" +#~ msgstr "" + +#~ msgid "" +#~ "Loss function. Maybe be a string " +#~ "(name of loss function), or a " +#~ "`tf.keras.losses.Loss` instance. See " +#~ "`tf.keras.losses`. A loss function is " +#~ "any callable with the signature `loss" +#~ " = fn(y_true, y_pred)`, where `y_true` " +#~ "are the ground truth values, and " +#~ "`y_pred` are the model's predictions. " +#~ "`y_true` should have shape `(batch_size, " +#~ "d0, .. dN)` (except in the case" +#~ " of sparse loss functions such as " +#~ "sparse categorical crossentropy which expects" +#~ " integer arrays of shape `(batch_size, " +#~ "d0, .. dN-1)`). `y_pred` should have " +#~ "shape `(batch_size, d0, .. dN)`. The " +#~ "loss function should return a float " +#~ "tensor. If a custom `Loss` instance " +#~ "is used and reduction is set to" +#~ " `None`, return value has shape " +#~ "`(batch_size, d0, .. dN-1)` i.e. per-" +#~ "sample or per-timestep loss values; " +#~ "otherwise, it is a scalar. If the" +#~ " model has multiple outputs, you can" +#~ " use a different loss on each " +#~ "output by passing a dictionary or " +#~ "a list of losses. The loss value" +#~ " that will be minimized by the " +#~ "model will then be the sum of " +#~ "all individual losses, unless `loss_weights`" +#~ " is specified." +#~ msgstr "" + +#~ msgid "" +#~ "List of metrics to be evaluated by" +#~ " the model during training and " +#~ "testing. Each of this can be a " +#~ "string (name of a built-in " +#~ "function), function or a " +#~ "`tf.keras.metrics.Metric` instance. See " +#~ "`tf.keras.metrics`. Typically you will use " +#~ "`metrics=['accuracy']`. A function is any " +#~ "callable with the signature `result =" +#~ " fn(y_true, y_pred)`. To specify different" +#~ " metrics for different outputs of a" +#~ " multi-output model, you could also" +#~ " pass a dictionary, such as " +#~ "`metrics={'output_a': 'accuracy', 'output_b': " +#~ "['accuracy', 'mse']}`. You can also pass" +#~ " a list to specify a metric or" +#~ " a list of metrics for each " +#~ "output, such as `metrics=[['accuracy'], " +#~ "['accuracy', 'mse']]` or `metrics=['accuracy', " +#~ "['accuracy', 'mse']]`. When you pass the" +#~ " strings 'accuracy' or 'acc', we " +#~ "convert this to one of " +#~ "`tf.keras.metrics.BinaryAccuracy`, " +#~ "`tf.keras.metrics.CategoricalAccuracy`, " +#~ "`tf.keras.metrics.SparseCategoricalAccuracy` based on " +#~ "the loss function used and the " +#~ "model output shape. We do a " +#~ "similar conversion for the strings " +#~ "'crossentropy' and 'ce' as well." +#~ msgstr "" + +#~ msgid "" +#~ "Optional list or dictionary specifying " +#~ "scalar coefficients (Python floats) to " +#~ "weight the loss contributions of " +#~ "different model outputs. The loss value" +#~ " that will be minimized by the " +#~ "model will then be the *weighted " +#~ "sum* of all individual losses, weighted" +#~ " by the `loss_weights` coefficients. If" +#~ " a list, it is expected to have" +#~ " a 1:1 mapping to the model's " +#~ "outputs. If a dict, it is expected" +#~ " to map output names (strings) to" +#~ " scalar coefficients." +#~ msgstr "" + +#~ msgid "" +#~ "Optional list or dictionary specifying " +#~ "scalar coefficients (Python floats) to " +#~ "weight the loss contributions of " +#~ "different model outputs. The loss value" +#~ " that will be minimized by the " +#~ "model will then be the *weighted " +#~ "sum* of all individual losses, weighted" +#~ " by the `loss_weights` coefficients." +#~ msgstr "" + +#~ msgid "If a list, it is expected to have a 1:1 mapping to the model's" +#~ msgstr "" + +#~ msgid "" +#~ "outputs. If a dict, it is expected" +#~ " to map output names (strings) to " +#~ "scalar coefficients." +#~ msgstr "" + +#~ msgid "" +#~ "Bool. Defaults to `False`. If `True`," +#~ " this `Model`'s logic will not be " +#~ "wrapped in a `tf.function`. Recommended " +#~ "to leave this as `None` unless " +#~ "your `Model` cannot be run inside " +#~ "a `tf.function`. `run_eagerly=True` is not " +#~ "supported when using " +#~ "`tf.distribute.experimental.ParameterServerStrategy`." +#~ msgstr "" + +#~ msgid "" +#~ "Int. Defaults to 1. The number of" +#~ " batches to run during each " +#~ "`tf.function` call. Running multiple batches" +#~ " inside a single `tf.function` call " +#~ "can greatly improve performance on TPUs" +#~ " or small models with a large " +#~ "Python overhead. At most, one full " +#~ "epoch will be run each execution. " +#~ "If a number larger than the size" +#~ " of the epoch is passed, the " +#~ "execution will be truncated to the " +#~ "size of the epoch. Note that if" +#~ " `steps_per_execution` is set to `N`, " +#~ "`Callback.on_batch_begin` and `Callback.on_batch_end` " +#~ "methods will only be called every " +#~ "`N` batches (i.e. before/after each " +#~ "`tf.function` execution)." +#~ msgstr "" + +#~ msgid "" +#~ "If the layer has not been built," +#~ " this method will call `build` on " +#~ "the layer. This assumes that the " +#~ "layer will later be used with " +#~ "inputs that match the input shape " +#~ "provided here." +#~ msgstr "" + +#~ msgid "" +#~ "Shape tuple (tuple of integers) or " +#~ "list of shape tuples (one per " +#~ "output tensor of the layer). Shape " +#~ "tuples can include None for free " +#~ "dimensions, instead of an integer." +#~ msgstr "" + +#~ msgid "An input shape tuple." +#~ msgstr "" + +#~ msgid "" +#~ "Single TensorSpec or nested structure of" +#~ " TensorSpec objects, describing how the" +#~ " layer would transform the provided " +#~ "input." +#~ msgstr "" + +#~ msgid "Single TensorSpec or nested structure of TensorSpec objects, describing" +#~ msgstr "" + +#~ msgid "how the layer would transform the provided input." +#~ msgstr "" + +#~ msgid "" +#~ "Input data. It could be: - A " +#~ "Numpy array (or array-like), or a" +#~ " list of arrays (in case the " +#~ "model has multiple inputs). - A " +#~ "TensorFlow tensor, or a list of " +#~ "tensors (in case the model has " +#~ "multiple inputs). - A dict mapping " +#~ "input names to the corresponding " +#~ "array/tensors, if the model has named" +#~ " inputs. - A `tf.data` dataset. " +#~ "Should return a tuple of either " +#~ "`(inputs, targets)` or `(inputs, targets," +#~ " sample_weights)`. - A generator or " +#~ "`keras.utils.Sequence` returning `(inputs, targets)`" +#~ " or `(inputs, targets, sample_weights)`. " +#~ "A more detailed description of unpacking" +#~ " behavior for iterator types (Dataset, " +#~ "generator, Sequence) is given in the " +#~ "`Unpacking behavior for iterator-like " +#~ "inputs` section of `Model.fit`." +#~ msgstr "" + +#~ msgid "0 or 1. Verbosity mode. 0 = silent, 1 = progress bar." +#~ msgstr "" + +#~ msgid "" +#~ "Optional Numpy array of weights for " +#~ "the test samples, used for weighting " +#~ "the loss function. You can either " +#~ "pass a flat (1D) Numpy array with" +#~ " the same length as the input " +#~ "samples (1:1 mapping between weights " +#~ "and samples), or in the case of" +#~ " temporal data, you can pass a" +#~ " 2D array with shape `(samples, " +#~ "sequence_length)`, to apply a different " +#~ "weight to every timestep of every" +#~ " sample. This argument is not " +#~ "supported when `x` is a dataset, " +#~ "instead pass sample weights as the " +#~ "third element of `x`." +#~ msgstr "" + +#~ msgid "" +#~ "List of `keras.callbacks.Callback` instances. " +#~ "List of callbacks to apply during " +#~ "evaluation. See " +#~ "[callbacks](/api_docs/python/tf/keras/callbacks)." +#~ msgstr "" + +#~ msgid "" +#~ "`Model.evaluate` is not yet supported " +#~ "with `tf.distribute.experimental.ParameterServerStrategy`." +#~ msgstr "" + +#~ msgid "" +#~ "Trains the model for a fixed " +#~ "number of epochs (iterations on a " +#~ "dataset)." +#~ msgstr "" + +#~ msgid "" +#~ "Input data. It could be: - A " +#~ "Numpy array (or array-like), or a" +#~ " list of arrays (in case the " +#~ "model has multiple inputs). - A " +#~ "TensorFlow tensor, or a list of " +#~ "tensors (in case the model has " +#~ "multiple inputs). - A dict mapping " +#~ "input names to the corresponding " +#~ "array/tensors, if the model has named" +#~ " inputs. - A `tf.data` dataset. " +#~ "Should return a tuple of either " +#~ "`(inputs, targets)` or `(inputs, targets," +#~ " sample_weights)`. - A generator or " +#~ "`keras.utils.Sequence` returning `(inputs, targets)`" +#~ " or `(inputs, targets, sample_weights)`. " +#~ "- A `tf.keras.utils.experimental.DatasetCreator`, " +#~ "which wraps a callable that takes " +#~ "a single argument of type " +#~ "`tf.distribute.InputContext`, and returns a " +#~ "`tf.data.Dataset`. `DatasetCreator` should be " +#~ "used when users prefer to specify " +#~ "the per-replica batching and sharding" +#~ " logic for the `Dataset`. See " +#~ "`tf.keras.utils.experimental.DatasetCreator` doc for " +#~ "more information. A more detailed " +#~ "description of unpacking behavior for " +#~ "iterator types (Dataset, generator, Sequence)" +#~ " is given below. If using " +#~ "`tf.distribute.experimental.ParameterServerStrategy`, only " +#~ "`DatasetCreator` type is supported for " +#~ "`x`." +#~ msgstr "" + +#~ msgid "" +#~ "A more detailed description of unpacking" +#~ " behavior for iterator types (Dataset, " +#~ "generator, Sequence) is given below. If" +#~ " using `tf.distribute.experimental.ParameterServerStrategy`," +#~ " only `DatasetCreator` type is supported" +#~ " for `x`." +#~ msgstr "" + +#~ msgid "" +#~ "'auto', 0, 1, or 2. Verbosity " +#~ "mode. 0 = silent, 1 = progress " +#~ "bar, 2 = one line per epoch. " +#~ "'auto' defaults to 1 for most " +#~ "cases, but 2 when used with " +#~ "`ParameterServerStrategy`. Note that the " +#~ "progress bar is not particularly useful" +#~ " when logged to a file, so " +#~ "verbose=2 is recommended when not " +#~ "running interactively (eg, in a " +#~ "production environment)." +#~ msgstr "" + +#~ msgid "" +#~ "Float between 0 and 1. Fraction " +#~ "of the training data to be used" +#~ " as validation data. The model will" +#~ " set apart this fraction of the " +#~ "training data, will not train on " +#~ "it, and will evaluate the loss " +#~ "and any model metrics on this " +#~ "data at the end of each epoch." +#~ " The validation data is selected " +#~ "from the last samples in the `x`" +#~ " and `y` data provided, before " +#~ "shuffling. This argument is not " +#~ "supported when `x` is a dataset, " +#~ "generator or `keras.utils.Sequence` instance. " +#~ "`validation_split` is not yet supported " +#~ "with `tf.distribute.experimental.ParameterServerStrategy`." +#~ msgstr "" + +#~ msgid "Float between 0 and 1." +#~ msgstr "" + +#~ msgid "" +#~ "Fraction of the training data to " +#~ "be used as validation data. The " +#~ "model will set apart this fraction " +#~ "of the training data, will not " +#~ "train on it, and will evaluate the" +#~ " loss and any model metrics on " +#~ "this data at the end of each " +#~ "epoch. The validation data is selected" +#~ " from the last samples in the " +#~ "`x` and `y` data provided, before " +#~ "shuffling. This argument is not " +#~ "supported when `x` is a dataset, " +#~ "generator or" +#~ msgstr "" + +#~ msgid "`keras.utils.Sequence` instance." +#~ msgstr "" + +#~ msgid "" +#~ "`validation_split` is not yet supported " +#~ "with `tf.distribute.experimental.ParameterServerStrategy`." +#~ msgstr "" + +#~ msgid "" +#~ "Data on which to evaluate the loss" +#~ " and any model metrics at the " +#~ "end of each epoch. The model will" +#~ " not be trained on this data. " +#~ "Thus, note the fact that the " +#~ "validation loss of data provided using" +#~ " `validation_split` or `validation_data` is " +#~ "not affected by regularization layers " +#~ "like noise and dropout. `validation_data` " +#~ "will override `validation_split`. `validation_data`" +#~ " could be: - A tuple `(x_val, " +#~ "y_val)` of Numpy arrays or tensors." +#~ " - A tuple `(x_val, y_val, " +#~ "val_sample_weights)` of NumPy arrays. - " +#~ "A `tf.data.Dataset`. - A Python " +#~ "generator or `keras.utils.Sequence` returning " +#~ "`(inputs, targets)` or `(inputs, targets, " +#~ "sample_weights)`. `validation_data` is not yet" +#~ " supported with " +#~ "`tf.distribute.experimental.ParameterServerStrategy`." +#~ msgstr "" + +#~ msgid "" +#~ "Optional dictionary mapping class indices " +#~ "(integers) to a weight (float) value," +#~ " used for weighting the loss function" +#~ " (during training only). This can be" +#~ " useful to tell the model to " +#~ "\"pay more attention\" to samples from" +#~ " an under-represented class." +#~ msgstr "" + +#~ msgid "" +#~ "Optional Numpy array of weights for " +#~ "the training samples, used for weighting" +#~ " the loss function (during training " +#~ "only). You can either pass a flat" +#~ " (1D) Numpy array with the same " +#~ "length as the input samples (1:1 " +#~ "mapping between weights and samples), " +#~ "or in the case of temporal data," +#~ " you can pass a 2D array with" +#~ " shape `(samples, sequence_length)`, to " +#~ "apply a different weight to every " +#~ "timestep of every sample. This argument" +#~ " is not supported when `x` is a" +#~ " dataset, generator, or `keras.utils.Sequence`" +#~ " instance, instead provide the " +#~ "sample_weights as the third element of" +#~ " `x`." +#~ msgstr "" + +#~ msgid "Optional Numpy array of weights for" +#~ msgstr "" + +#~ msgid "" +#~ "the training samples, used for weighting" +#~ " the loss function (during training " +#~ "only). You can either pass a flat" +#~ " (1D) Numpy array with the same " +#~ "length as the input samples (1:1 " +#~ "mapping between weights and samples), or" +#~ " in the case of temporal data, " +#~ "you can pass a 2D array with " +#~ "shape `(samples, sequence_length)`, to apply" +#~ " a different weight to every timestep" +#~ " of every sample. This argument is" +#~ " not supported when `x` is a " +#~ "dataset, generator, or" +#~ msgstr "" + +#~ msgid "`keras.utils.Sequence` instance, instead provide the sample_weights" +#~ msgstr "" + +#~ msgid "as the third element of `x`." +#~ msgstr "" + +#~ msgid "" +#~ "Integer or `None`. Total number of " +#~ "steps (batches of samples) before " +#~ "declaring one epoch finished and " +#~ "starting the next epoch. When training" +#~ " with input tensors such as " +#~ "TensorFlow data tensors, the default " +#~ "`None` is equal to the number of" +#~ " samples in your dataset divided by" +#~ " the batch size, or 1 if that" +#~ " cannot be determined. If x is " +#~ "a `tf.data` dataset, and 'steps_per_epoch' " +#~ "is None, the epoch will run until" +#~ " the input dataset is exhausted. When" +#~ " passing an infinitely repeating dataset," +#~ " you must specify the `steps_per_epoch` " +#~ "argument. If `steps_per_epoch=-1` the training" +#~ " will run indefinitely with an " +#~ "infinitely repeating dataset. This argument" +#~ " is not supported with array inputs." +#~ " When using " +#~ "`tf.distribute.experimental.ParameterServerStrategy`: * " +#~ "`steps_per_epoch=None` is not supported." +#~ msgstr "" + +#~ msgid "" +#~ "Integer or `None`. Total number of " +#~ "steps (batches of samples) before " +#~ "declaring one epoch finished and " +#~ "starting the next epoch. When training" +#~ " with input tensors such as " +#~ "TensorFlow data tensors, the default " +#~ "`None` is equal to the number of" +#~ " samples in your dataset divided by" +#~ " the batch size, or 1 if that" +#~ " cannot be determined. If x is " +#~ "a `tf.data` dataset, and 'steps_per_epoch' " +#~ "is None, the epoch will run until" +#~ " the input dataset is exhausted. When" +#~ " passing an infinitely repeating dataset," +#~ " you must specify the `steps_per_epoch` " +#~ "argument. If `steps_per_epoch=-1` the training" +#~ " will run indefinitely with an " +#~ "infinitely repeating dataset. This argument" +#~ " is not supported with array inputs." +#~ " When using " +#~ "`tf.distribute.experimental.ParameterServerStrategy`:" +#~ msgstr "" + +#~ msgid "" +#~ "Only relevant if validation data is " +#~ "provided. Integer or `collections.abc.Container` " +#~ "instance (e.g. list, tuple, etc.). If" +#~ " an integer, specifies how many " +#~ "training epochs to run before a " +#~ "new validation run is performed, e.g." +#~ " `validation_freq=2` runs validation every " +#~ "2 epochs. If a Container, specifies " +#~ "the epochs on which to run " +#~ "validation, e.g. `validation_freq=[1, 2, 10]`" +#~ " runs validation at the end of " +#~ "the 1st, 2nd, and 10th epochs." +#~ msgstr "" + +#~ msgid "" +#~ "tf.keras.utils.Sequence to the `x` argument" +#~ " of fit, which will in fact " +#~ "yield not only features (x) but " +#~ "optionally targets (y) and sample " +#~ "weights. Keras requires that the output" +#~ " of such iterator-likes be " +#~ "unambiguous. The iterator should return " +#~ "a tuple of length 1, 2, or " +#~ "3, where the optional second and " +#~ "third elements will be used for y" +#~ " and sample_weight respectively. Any other" +#~ " type provided will be wrapped in " +#~ "a length one tuple, effectively treating" +#~ " everything as 'x'. When yielding " +#~ "dicts, they should still adhere to " +#~ "the top-level tuple structure. e.g. " +#~ "`({\"x0\": x0, \"x1\": x1}, y)`. Keras" +#~ " will not attempt to separate " +#~ "features, targets, and weights from the" +#~ " keys of a single dict." +#~ msgstr "" + +#~ msgid "A notable unsupported data type is the namedtuple. The reason is that" +#~ msgstr "" + +#~ msgid "" +#~ "it behaves like both an ordered " +#~ "datatype (tuple) and a mapping datatype" +#~ " (dict). So given a namedtuple of " +#~ "the form:" +#~ msgstr "" + +#~ msgid "Retrieves losses relevant to a specific set of inputs." +#~ msgstr "" + +#~ msgid "Input tensor or list/tuple of input tensors." +#~ msgstr "" + +#~ msgid "List of loss tensors of the layer that depend on `inputs`." +#~ msgstr "" + +#~ msgid "Retrieves updates relevant to a specific set of inputs." +#~ msgstr "" + +#~ msgid "List of update ops of the layer that depend on `inputs`." +#~ msgstr "" + +#~ msgid "Deprecated, do NOT use! Only for compatibility with external Keras." +#~ msgstr "" + +#~ msgid "" +#~ "Loads all layer weights, either from " +#~ "a TensorFlow or an HDF5 weight " +#~ "file." +#~ msgstr "" + +#~ msgid "" +#~ "If `by_name` is False weights are " +#~ "loaded based on the network's topology." +#~ " This means the architecture should " +#~ "be the same as when the weights" +#~ " were saved. Note that layers that" +#~ " don't have weights are not taken " +#~ "into account in the topological " +#~ "ordering, so adding or removing layers" +#~ " is fine as long as they don't" +#~ " have weights." +#~ msgstr "" + +#~ msgid "" +#~ "If `by_name` is True, weights are " +#~ "loaded into layers only if they " +#~ "share the same name. This is " +#~ "useful for fine-tuning or transfer-" +#~ "learning models where some of the " +#~ "layers have changed." +#~ msgstr "" + +#~ msgid "" +#~ "Only topological loading (`by_name=False`) is" +#~ " supported when loading weights from " +#~ "the TensorFlow format. Note that " +#~ "topological loading differs slightly between" +#~ " TensorFlow and HDF5 formats for " +#~ "user-defined classes inheriting from " +#~ "`tf.keras.Model`: HDF5 loads based on a" +#~ " flattened list of weights, while the" +#~ " TensorFlow format loads based on the" +#~ " object-local names of attributes to" +#~ " which layers are assigned in the " +#~ "`Model`'s constructor." +#~ msgstr "" + +#~ msgid "" +#~ "String, path to the weights file " +#~ "to load. For weight files in " +#~ "TensorFlow format, this is the file " +#~ "prefix (the same as was passed to" +#~ " `save_weights`). This can also be a" +#~ " path to a SavedModel saved from " +#~ "`model.save`." +#~ msgstr "" + +#~ msgid "" +#~ "Boolean, whether to load weights by " +#~ "name or by topological order. Only " +#~ "topological loading is supported for " +#~ "weight files in TensorFlow format." +#~ msgstr "" + +#~ msgid "" +#~ "Boolean, whether to skip loading of " +#~ "layers where there is a mismatch " +#~ "in the number of weights, or a " +#~ "mismatch in the shape of the " +#~ "weight (only valid when `by_name=True`)." +#~ msgstr "" + +#~ msgid "" +#~ "Optional `tf.train.CheckpointOptions` object that" +#~ " specifies options for loading weights." +#~ msgstr "" + +#~ msgid "" +#~ "When loading a weight file in " +#~ "TensorFlow format, returns the same " +#~ "status object as `tf.train.Checkpoint.restore`. " +#~ "When graph building, restore ops are " +#~ "run automatically as soon as the " +#~ "network is built (on first call " +#~ "for user-defined classes inheriting from" +#~ " `Model`, immediately if it is " +#~ "already built). When loading weights in" +#~ " HDF5 format, returns `None`." +#~ msgstr "" + +#~ msgid "" +#~ "When loading a weight file in " +#~ "TensorFlow format, returns the same " +#~ "status object as `tf.train.Checkpoint.restore`. " +#~ "When graph building, restore ops are " +#~ "run automatically as soon as the " +#~ "network is built (on first call " +#~ "for user-defined classes inheriting from" +#~ " `Model`, immediately if it is " +#~ "already built)." +#~ msgstr "" + +#~ msgid "When loading weights in HDF5 format, returns `None`." +#~ msgstr "" + +#~ msgid "If `h5py` is not available and the weight file is in HDF5 format." +#~ msgstr "" + +#~ msgid "If `skip_mismatch` is set to `True` when `by_name` is `False`." +#~ msgstr "" + +#~ msgid "" +#~ "Returns the model's metrics added using" +#~ " `compile()`, `add_metric()` APIs." +#~ msgstr "" + +#~ msgid "" +#~ "Computation is done in batches. This " +#~ "method is designed for performance in" +#~ " large scale inputs. For small amount" +#~ " of inputs that fit in one " +#~ "batch, directly using `__call__()` is " +#~ "recommended for faster execution, e.g., " +#~ "`model(x)`, or `model(x, training=False)` if" +#~ " you have layers such as " +#~ "`tf.keras.layers.BatchNormalization` that behaves " +#~ "differently during inference. Also, note " +#~ "the fact that test loss is not " +#~ "affected by regularization layers like " +#~ "noise and dropout." +#~ msgstr "" + +#~ msgid "Verbosity mode, 0 or 1." +#~ msgstr "" + +#~ msgid "" +#~ "List of `keras.callbacks.Callback` instances. " +#~ "List of callbacks to apply during " +#~ "prediction. See " +#~ "[callbacks](/api_docs/python/tf/keras/callbacks)." +#~ msgstr "" + +#~ msgid "If `model.predict_on_batch` is wrapped in a `tf.function`." +#~ msgstr "" + +#~ msgid "" +#~ "This method should contain the " +#~ "mathematical logic for one step of " +#~ "inference. This typically includes the " +#~ "forward pass." +#~ msgstr "" + +#~ msgid "Saves the model to Tensorflow SavedModel or a single HDF5 file." +#~ msgstr "" + +#~ msgid "" +#~ "Please see `tf.keras.models.save_model` or the" +#~ " [Serialization and Saving " +#~ "guide](https://keras.io/guides/serialization_and_saving/) for" +#~ " details." +#~ msgstr "" + +#~ msgid "String, PathLike, path to SavedModel or H5 file to save the model." +#~ msgstr "" + +#~ msgid "If True, save optimizer's state together." +#~ msgstr "" + +#~ msgid "" +#~ "Either `'tf'` or `'h5'`, indicating " +#~ "whether to save the model to " +#~ "Tensorflow SavedModel or HDF5. Defaults " +#~ "to 'tf' in TF 2.X, and 'h5' " +#~ "in TF 1.X." +#~ msgstr "" + +#~ msgid "" +#~ "Signatures to save with the SavedModel." +#~ " Applicable to the 'tf' format only." +#~ " Please see the `signatures` argument " +#~ "in `tf.saved_model.save` for details." +#~ msgstr "" + +#~ msgid "" +#~ "(only applies to SavedModel format) " +#~ "`tf.saved_model.SaveOptions` object that specifies" +#~ " options for saving to SavedModel." +#~ msgstr "" + +#~ msgid "" +#~ "(only applies to SavedModel format) When" +#~ " enabled, the SavedModel will store " +#~ "the function traces for each layer. " +#~ "This can be disabled, so that only" +#~ " the configs of each layer are " +#~ "stored. Defaults to `True`. Disabling " +#~ "this will decrease serialization time " +#~ "and reduce file size, but it " +#~ "requires that all custom layers/models " +#~ "implement a `get_config()` method." +#~ msgstr "" + +#~ msgid "```python from keras.models import load_model" +#~ msgstr "" + +#~ msgid "" +#~ "model.save('my_model.h5') # creates a HDF5" +#~ " file 'my_model.h5' del model # " +#~ "deletes the existing model" +#~ msgstr "" + +#~ msgid "" +#~ "# returns a compiled model # " +#~ "identical to the previous one model " +#~ "= load_model('my_model.h5') ```" +#~ msgstr "" + +#~ msgid "Returns the `tf.TensorSpec` of call inputs as a tuple `(args, kwargs)`." +#~ msgstr "" + +#~ msgid "" +#~ "# arg_specs is `[tf.TensorSpec(...), ...]`." +#~ " kwarg_specs, in this example, is #" +#~ " an empty dict since functional " +#~ "models do not use keyword arguments. " +#~ "arg_specs, kwarg_specs = model.save_spec()" +#~ msgstr "" + +#~ msgid "" +#~ "'serving_default': serve.get_concrete_function(*arg_specs, " +#~ "**kwarg_specs)" +#~ msgstr "" + +#~ msgid "" +#~ "The TensorFlow format matches objects " +#~ "and variables by starting at a " +#~ "root object, `self` for `save_weights`, " +#~ "and greedily matching attribute names. " +#~ "For `Model.save` this is the `Model`," +#~ " and for `Checkpoint.save` this is " +#~ "the `Checkpoint` even if the " +#~ "`Checkpoint` has a model attached. This" +#~ " means saving a `tf.keras.Model` using " +#~ "`save_weights` and loading into a " +#~ "`tf.train.Checkpoint` with a `Model` attached" +#~ " (or vice versa) will not match " +#~ "the `Model`'s variables. See the [guide" +#~ " to training " +#~ "checkpoints](https://www.tensorflow.org/guide/checkpoint) for" +#~ " details on the TensorFlow format." +#~ msgstr "" + +#~ msgid "" +#~ "Either 'tf' or 'h5'. A `filepath` " +#~ "ending in '.h5' or '.keras' will " +#~ "default to HDF5 if `save_format` is " +#~ "`None`. Otherwise `None` defaults to " +#~ "'tf'." +#~ msgstr "" + +#~ msgid "If `h5py` is not available when attempting to save in HDF5 format." +#~ msgstr "" + +#~ msgid "" +#~ "Relative or absolute positions of log" +#~ " elements in each line. If not " +#~ "provided, defaults to `[.33, .55, .67," +#~ " 1.]`." +#~ msgstr "" + +#~ msgid "" +#~ "Print function to use. Defaults to " +#~ "`print`. It will be called on each" +#~ " line of the summary. You can " +#~ "set it to a custom function in " +#~ "order to capture the string summary." +#~ msgstr "" + +#~ msgid "" +#~ "Whether to expand the nested models. " +#~ "If not provided, defaults to `False`." +#~ msgstr "" + +#~ msgid "" +#~ "Input data. It could be: - A " +#~ "Numpy array (or array-like), or a" +#~ " list of arrays (in case the " +#~ "model has multiple inputs). - A " +#~ "TensorFlow tensor, or a list of " +#~ "tensors (in case the model has " +#~ "multiple inputs). - A dict mapping " +#~ "input names to the corresponding " +#~ "array/tensors, if the model has " +#~ "named inputs." +#~ msgstr "" + +#~ msgid "A dict mapping input names to the corresponding array/tensors, if" +#~ msgstr "" + +#~ msgid "the model has named inputs." +#~ msgstr "" + +#~ msgid "If `model.test_on_batch` is wrapped in a `tf.function`." +#~ msgstr "" + +#~ msgid "Additional keyword arguments to be passed to `json.dumps()`." +#~ msgstr "" + +#~ msgid "" +#~ "Optional dictionary mapping class indices " +#~ "(integers) to a weight (float) to " +#~ "apply to the model's loss for the" +#~ " samples from this class during " +#~ "training. This can be useful to " +#~ "tell the model to \"pay more " +#~ "attention\" to samples from an under-" +#~ "represented class." +#~ msgstr "" + +#~ msgid "" +#~ "This method can be overridden to " +#~ "support custom training logic. For " +#~ "concrete examples of how to override " +#~ "this method see [Customizing what " +#~ "happends in " +#~ "fit](https://www.tensorflow.org/guide/keras/customizing_what_happens_in_fit)." +#~ " This method is called by " +#~ "`Model.make_train_function`." +#~ msgstr "" + +#~ msgid "" +#~ "This method should contain the " +#~ "mathematical logic for one step of " +#~ "training. This typically includes the " +#~ "forward pass, loss calculation, " +#~ "backpropagation, and metric updates." +#~ msgstr "" + +#~ msgid "Bases: :py:class:`~keras.engine.base_layer.Layer`" +#~ msgstr "" + +#~ msgid "" +#~ "Input tensor, or dict/list/tuple of " +#~ "input tensors. The first positional " +#~ "`inputs` argument is subject to special" +#~ " rules: - `inputs` must be explicitly" +#~ " passed. A layer cannot have zero" +#~ " arguments, and `inputs` cannot be " +#~ "provided via the default value of " +#~ "a keyword argument. - NumPy array " +#~ "or Python scalar values in `inputs` " +#~ "get cast as tensors. - Keras mask" +#~ " metadata is only collected from " +#~ "`inputs`. - Layers are built " +#~ "(`build(input_shape)` method) using shape " +#~ "info from `inputs` only. - `input_spec`" +#~ " compatibility is only checked against " +#~ "`inputs`. - Mixed precision input " +#~ "casting is only applied to `inputs`." +#~ " If a layer has tensor arguments" +#~ " in `*args` or `**kwargs`, their " +#~ "casting behavior in mixed precision " +#~ "should be handled manually. - The " +#~ "SavedModel input specification is generated" +#~ " using `inputs` only. - Integration " +#~ "with various ecosystem packages like " +#~ "TFMOT, TFLite, TF.js, etc is only " +#~ "supported for `inputs` and not for " +#~ "tensors in positional and keyword " +#~ "arguments." +#~ msgstr "" + +#~ msgid "" +#~ "Additional keyword arguments. May contain " +#~ "tensors, although this is not " +#~ "recommended, for the reasons above. The" +#~ " following optional keyword arguments are" +#~ " reserved: - `training`: Boolean scalar " +#~ "tensor of Python boolean indicating " +#~ "whether the `call` is meant for " +#~ "training or inference. - `mask`: Boolean" +#~ " input mask. If the layer's `call()`" +#~ " method takes a `mask` argument, " +#~ "its default value will be set to" +#~ " the mask generated for `inputs` by" +#~ " the previous layer (if `input` did" +#~ " come from a layer that generated" +#~ " a corresponding mask, i.e. if it " +#~ "came from a Keras layer with " +#~ "masking support)." +#~ msgstr "" + +#~ msgid "" +#~ "Bases: " +#~ ":py:class:`~keras.optimizer_v2.learning_rate_schedule.LearningRateSchedule`" +#~ msgstr "" + +#~ msgid "" +#~ "Get Pauli string array and weights " +#~ "array for a qubit Hamiltonian as a" +#~ " sum of Pauli strings defined in " +#~ "openfermion ``QubitOperator``." +#~ msgstr "" + +#~ msgid "``openfermion.ops.operators.qubit_operator.QubitOperator``" +#~ msgstr "" + +#~ msgid "The number of qubits" +#~ msgstr "" + +#~ msgid "Pauli String array and weights array" +#~ msgstr "" + diff --git a/docs/source/locale/zh/LC_MESSAGES/contribs.po b/docs/source/locale/zh/LC_MESSAGES/contribs.po index cb11a0fd..004ca724 100644 --- a/docs/source/locale/zh/LC_MESSAGES/contribs.po +++ b/docs/source/locale/zh/LC_MESSAGES/contribs.po @@ -9,142 +9,222 @@ msgid "" msgstr "" "Project-Id-Version: tensorcircuit \n" "Report-Msgid-Bugs-To: \n" -"POT-Creation-Date: 2023-02-02 14:19+0800\n" +"POT-Creation-Date: 2023-07-14 15:43+0800\n" "PO-Revision-Date: YEAR-MO-DA HO:MI+ZONE\n" "Last-Translator: FULL NAME \n" "Language-Team: LANGUAGE \n" "MIME-Version: 1.0\n" "Content-Type: text/plain; charset=utf-8\n" "Content-Transfer-Encoding: 8bit\n" -"Generated-By: Babel 2.9.1\n" +"Generated-By: Babel 2.12.1\n" +#: ../../source/contribs/development_Mac.md:1 #: ../../source/contribs/development_MacARM.md:1 +#: ../../source/contribs/development_MacM2.md:1 msgid "Tensorcircuit Installation Guide on MacOS" msgstr "" -#: ../../source/contribs/development_MacARM.md:3 -msgid "Contributed by Mark (Zixuan) Song" +#: ../../source/contribs/development_Mac.md:3 +msgid "Contributed by [_Mark (Zixuan) Song_](https://marksong.tech)" msgstr "" -#: ../../source/contribs/development_MacARM.md:5 +#: ../../source/contribs/development_Mac.md:5 +msgid "" +"Apple has updated Tensorflow (for MacOS) so that installation on M-series" +" (until M2) and Intel-series Mac can follow the exact same procedure." +msgstr "" + +#: ../../source/contribs/development_Mac.md:7 +#: ../../source/contribs/development_MacARM.md:8 +#: ../../source/contribs/development_MacM2.md:10 msgid "Starting From Scratch" msgstr "" -#: ../../source/contribs/development_MacARM.md:7 -msgid "For completely new macos or macos without xcode and brew" +#: ../../source/contribs/development_Mac.md:9 +msgid "For completely new Macos or Macos without Xcode and Homebrew installed." msgstr "" -#: ../../source/contribs/development_MacARM.md:9 +#: ../../source/contribs/development_Mac.md:11 +#: ../../source/contribs/development_MacARM.md:12 +#: ../../source/contribs/development_MacM2.md:12 msgid "Install Xcode Command Line Tools" msgstr "" -#: ../../source/contribs/development_MacARM.md:11 +#: ../../source/contribs/development_Mac.md:13 +#: ../../source/contribs/development_MacARM.md:14 +#: ../../source/contribs/development_MacM2.md:14 msgid "Need graphical access to the machine." msgstr "" -#: ../../source/contribs/development_MacARM.md:13 +#: ../../source/contribs/development_Mac.md:15 +#: ../../source/contribs/development_MacARM.md:16 +#: ../../source/contribs/development_MacM2.md:16 msgid "Run `xcode-select --install` to install if on optimal internet." msgstr "" -#: ../../source/contribs/development_MacARM.md:15 +#: ../../source/contribs/development_Mac.md:17 msgid "" -"Or Download from [Apple](https://developer.apple.com/download/more/) " -"Command Line Tools installation image then install if internet connection" -" is weak." +"Or Download it from [Apple](https://developer.apple.com/download/more/) " +"Command Line Tools installation image then install it if the internet " +"connection is weak." msgstr "" -#: ../../source/contribs/development_MacARM.md:17 +#: ../../source/contribs/development_Mac.md:19 +#: ../../source/contribs/development_MacARM.md:20 +#: ../../source/contribs/development_MacM2.md:20 msgid "Install Miniconda" msgstr "" -#: ../../source/contribs/development_MacARM.md:19 +#: ../../source/contribs/development_Mac.md:21 msgid "" -"Due to the limitation of MacOS and packages, the lastest version of " -"python does not always function as desired, thus miniconda installation " -"is advised to solve the issues." +"Due to the limitation of MacOS and packages, the latest version of Python" +" does not always function as desired, thus miniconda installation is " +"advised to solve the issues." msgstr "" -#: ../../source/contribs/development_MacARM.md:28 -msgid "Install TC Prerequisites" -msgstr "" - -#: ../../source/contribs/development_MacARM.md:34 +#: ../../source/contribs/development_Mac.md:30 +#: ../../source/contribs/development_MacARM.md:37 msgid "Install TC Backends" msgstr "" -#: ../../source/contribs/development_MacARM.md:36 -msgid "There are four backends to choose from, Numpy, Tensorflow, Jax, Torch." +#: ../../source/contribs/development_Mac.md:32 +msgid "There are four backends to choose from, Numpy, Tensorflow, Jax, and Torch." msgstr "" -#: ../../source/contribs/development_MacARM.md:38 +#: ../../source/contribs/development_Mac.md:34 +#: ../../source/contribs/development_MacARM.md:41 msgid "Install Jax, Pytorch, Qiskit, Cirq (Optional)" msgstr "" -#: ../../source/contribs/development_MacARM.md:44 +#: ../../source/contribs/development_Mac.md:40 +#: ../../source/contribs/development_MacARM.md:47 msgid "Install Tensorflow (Optional)" msgstr "" -#: ../../source/contribs/development_MacARM.md:46 -msgid "Install Tensorflow (Recommended Approach)" +#: ../../source/contribs/development_Mac.md:42 +msgid "Installation" +msgstr "" + +#: ../../source/contribs/development_Mac.md:44 +msgid "For Tensorflow version 2.13 or later:" msgstr "" -#: ../../source/contribs/development_MacARM.md:48 +#: ../../source/contribs/development_Mac.md:50 +msgid "For Tensorflow version 2.12 or earlier:" +msgstr "" + +#: ../../source/contribs/development_Mac.md:56 +#: ../../source/contribs/development_MacARM.md:57 +#: ../../source/contribs/development_MacARM.md:89 +msgid "Verify Tensorflow Installation" +msgstr "" + +#: ../../source/contribs/development_Mac.md:74 +#: ../../source/contribs/development_MacARM.md:107 +msgid "Install Tensorcircuit" +msgstr "" + +#: ../../source/contribs/development_Mac.md:80 msgid "" -"❗️ Tensorflow with MacOS optimization would not function correctly in " -"version 2.11.0 and before. Do not use this version of tensorflow if you " -"intented to train any machine learning model." +"Until July 2023, this has been tested on Intel Macs running Ventura, M1 " +"Macs running Ventura, M2 Macs running Ventura, and M2 Macs running Sonoma" +" beta." +msgstr "" + +#: ../../source/contribs/development_MacARM.md:3 +msgid "Contributed by Mark (Zixuan) Song" +msgstr "" + +#: ../../source/contribs/development_MacARM.md:5 +#: ../../source/contribs/development_MacM2.md:5 +msgid "" +".. warning:: This page is deprecated. Please visit `the update " +"tutorial `_ for the latest information." +msgstr "" + +#: ../../source/contribs/development_MacARM.md:10 +msgid "For completely new macos or macos without xcode and brew" msgstr "" -#: ../../source/contribs/development_MacARM.md:50 +#: ../../source/contribs/development_MacARM.md:18 +#: ../../source/contribs/development_MacM2.md:18 msgid "" -"FYI: Error can occur when machine learning training or gpu related code " -"is involved." +"Or Download from [Apple](https://developer.apple.com/download/more/) " +"Command Line Tools installation image then install if internet connection" +" is weak." msgstr "" -#: ../../source/contribs/development_MacARM.md:52 +#: ../../source/contribs/development_MacARM.md:22 msgid "" -"⚠️ Tensorflow without macos optimization does not support Metal API and " -"utilizing GPU (both intel chips and M-series chips) until at least " -"tensorflow 2.11. Tensorflow-macos would fail when running " -"`tc.backend.to_dense()`" +"Due to the limitation of MacOS and packages, the lastest version of " +"python does not always function as desired, thus miniconda installation " +"is advised to solve the issues." msgstr "" -#: ../../source/contribs/development_MacARM.md:60 -msgid "Verify Tensorflow Installation" +#: ../../source/contribs/development_MacARM.md:31 +msgid "Install TC Prerequisites" msgstr "" -#: ../../source/contribs/development_MacARM.md:78 -msgid "Install Tensorcircuit" +#: ../../source/contribs/development_MacARM.md:39 +msgid "There are four backends to choose from, Numpy, Tensorflow, Jax, Torch." +msgstr "" + +#: ../../source/contribs/development_MacARM.md:49 +msgid "Install Tensorflow without MacOS optimization" +msgstr "" + +#: ../../source/contribs/development_MacARM.md:75 +msgid "Install Tensorflow with MacOS optimization (Recommended)" +msgstr "" + +#: ../../source/contribs/development_MacARM.md:77 +msgid "For tensorflow version 2.13 or later:" +msgstr "" + +#: ../../source/contribs/development_MacARM.md:83 +msgid "For tensorflow version 2.12 or earlier:" msgstr "" -#: ../../source/contribs/development_MacARM.md:84 -msgid "Testing Platform (Tested Feb 2023)" +#: ../../source/contribs/development_MacARM.md:113 +msgid "Testing Platform (Tested Jun 2023)" msgstr "" -#: ../../source/contribs/development_MacARM.md:86 +#: ../../source/contribs/development_MacARM.md:115 msgid "Platform 1:" msgstr "" -#: ../../source/contribs/development_MacARM.md:87 +#: ../../source/contribs/development_MacARM.md:116 msgid "MacOS Ventura 13.1 (Build version 22C65)" msgstr "" -#: ../../source/contribs/development_MacARM.md:88 +#: ../../source/contribs/development_MacARM.md:117 msgid "M1 Ultra" msgstr "" -#: ../../source/contribs/development_MacARM.md:89 +#: ../../source/contribs/development_MacARM.md:118 msgid "Platform 2:" msgstr "" -#: ../../source/contribs/development_MacARM.md:90 +#: ../../source/contribs/development_MacARM.md:119 msgid "MacOS Ventura 13.2 (Build version 22D49)" msgstr "" -#: ../../source/contribs/development_MacARM.md:91 +#: ../../source/contribs/development_MacARM.md:120 msgid "M1 Ultra (Virtual)" msgstr "" +#: ../../source/contribs/development_MacARM.md:121 +msgid "Platform 4:" +msgstr "" + +#: ../../source/contribs/development_MacARM.md:122 +msgid "MacOS Sonoma 14.0 Beta 2 (Build version 23A5276g)" +msgstr "" + +#: ../../source/contribs/development_MacARM.md:123 +msgid "M2 Max" +msgstr "" + #: ../../source/contribs/development_MacM1.rst:2 msgid "Run TensorCircuit on TensorlowBackend with Apple M1" msgstr "" @@ -156,7 +236,7 @@ msgstr "" #: ../../source/contribs/development_MacM1.rst:7 msgid "" "This page is deprecated. Please visit `the update tutorial " -"`_ for latest information." +"`_ for the latest information." msgstr "" #: ../../source/contribs/development_MacM1.rst:11 @@ -256,6 +336,146 @@ msgstr "" msgid "Then unpackage it, and cd into the folder with \"setup.py\". Conducting" msgstr "" +#: ../../source/contribs/development_MacM2.md:3 +msgid "Contributed by [Hong-Ye Hu](https://github.com/hongyehu)" +msgstr "" + +#: ../../source/contribs/development_MacM2.md:8 +msgid "" +"The key issue addressed in this document is **how to install both " +"TensorFlow and Jax on a M2 chip MacOS without conflict**." +msgstr "" + +#: ../../source/contribs/development_MacM2.md:22 +msgid "" +"Due to the limitation of MacOS and packages, the lastest version of " +"python does not always function as desired, thus miniconda installation " +"is advised to solve the issues. And use anaconda virtual environment is " +"always a good habit." +msgstr "" + +#: ../../source/contribs/development_MacM2.md:30 +msgid "Install Packages" +msgstr "" + +#: ../../source/contribs/development_MacM2.md:31 +msgid "" +"First, create a virtual environment, and make sure the python version is " +"3.8.5 by" +msgstr "" + +#: ../../source/contribs/development_MacM2.md:36 +msgid "" +"Then, install the TensorFlow from `.whl` file (file can be downloaded " +"from this " +"[URL](https://drive.google.com/drive/folders/1oSipZLnoeQB0Awz8U68KYeCPsULy_dQ7))." +" This will install TensorFlow version 2.4.1" +msgstr "" + +#: ../../source/contribs/development_MacM2.md:40 +msgid "Next, one need to install **Jax** and **Optax** by" +msgstr "" + +#: ../../source/contribs/development_MacM2.md:45 +msgid "" +"Now, hopefully, you should be able to use both Jax and TensorFlow in this" +" environment. But sometimes, it may give you an error \"ERROR: package " +"Chardet not found.\". If that is the case, you can install it by `conda " +"install chardet`. Lastly, install tensorcircuit" +msgstr "" + +#: ../../source/contribs/development_MacM2.md:51 +msgid "" +"This is the solution that seems to work for M2-chip MacOS. Please let me " +"know if there is a better solution!" +msgstr "" + +#: ../../source/contribs/development_Mac_cn.md:1 +msgid "MacOS Tensorcircuit 安装教程" +msgstr "" + +#: ../../source/contribs/development_Mac_cn.md:3 +msgid "[_Mark (Zixuan) Song_](https://marksong.tech) 撰写" +msgstr "" + +#: ../../source/contribs/development_Mac_cn.md:5 +msgid "由于苹果更新了Tensorflow，因此M系列（直到M2）和英特尔系列Mac上的安装可以遵循完全相同的过程。" +msgstr "" + +#: ../../source/contribs/development_Mac_cn.md:7 +msgid "从头开始" +msgstr "" + +#: ../../source/contribs/development_Mac_cn.md:9 +msgid "对于全新的Macos或未安装Xcode和Homebrew的Macos。" +msgstr "" + +#: ../../source/contribs/development_Mac_cn.md:11 +msgid "安装Xcode命令行工具" +msgstr "" + +#: ../../source/contribs/development_Mac_cn.md:13 +msgid "需要对机器的图形访问。" +msgstr "" + +#: ../../source/contribs/development_Mac_cn.md:15 +msgid "如果网络良好，请运行`xcode-select --install`进行安装。" +msgstr "" + +#: ../../source/contribs/development_Mac_cn.md:17 +msgid "或者，如果网络连接较弱，请从[苹果](https://developer.apple.com/download/more/)下载命令行工具安装映像，然后进行安装。" +msgstr "" + +#: ../../source/contribs/development_Mac_cn.md:19 +msgid "安装Miniconda" +msgstr "" + +#: ../../source/contribs/development_Mac_cn.md:21 +msgid "由于MacOS和软件包的限制，因此建议安装miniconda以解决问题。" +msgstr "" + +#: ../../source/contribs/development_Mac_cn.md:30 +msgid "安装TC后端" +msgstr "" + +#: ../../source/contribs/development_Mac_cn.md:32 +msgid "有四个后端可供选择，Numpy，Tensorflow，Jax和Torch。" +msgstr "" + +#: ../../source/contribs/development_Mac_cn.md:34 +msgid "安装Jax，Pytorch，Qiskit，Cirq（可选）" +msgstr "" + +#: ../../source/contribs/development_Mac_cn.md:40 +msgid "安装Tensorflow（可选）" +msgstr "" + +#: ../../source/contribs/development_Mac_cn.md:42 +msgid "安装步骤" +msgstr "" + +#: ../../source/contribs/development_Mac_cn.md:44 +msgid "Tensorflow版本2.13或之后：" +msgstr "" + +#: ../../source/contribs/development_Mac_cn.md:50 +msgid "Tensorflow版本2.12或之前：" +msgstr "" + +#: ../../source/contribs/development_Mac_cn.md:56 +msgid "验证Tensorflow安装" +msgstr "" + +#: ../../source/contribs/development_Mac_cn.md:74 +msgid "安装Tensorcircuit" +msgstr "" + +#: ../../source/contribs/development_Mac_cn.md:80 +msgid "" +"直到2023年7月，这已在运行Ventura的英特尔i9 Mac、运行Ventura的M1 Mac、运行Ventura的M2 " +"Mac、运行Sonoma测试版的M2 Mac上进行了测试。" +msgstr "" + #: ../../source/contribs/development_windows.rst:2 msgid "Run TensorCircuit on Windows Machine with Docker" msgstr "" @@ -666,3 +886,39 @@ msgstr "" #~ msgid "Testing Platform" #~ msgstr "" +#~ msgid "Install Tensorflow (Recommended Approach)" +#~ msgstr "" + +#~ msgid "" +#~ "❗️ Tensorflow with MacOS optimization " +#~ "would not function correctly in version" +#~ " 2.11.0 and before. Do not use " +#~ "this version of tensorflow if you " +#~ "intented to train any machine learning" +#~ " model." +#~ msgstr "" + +#~ msgid "" +#~ "FYI: Error can occur when machine " +#~ "learning training or gpu related code" +#~ " is involved." +#~ msgstr "" + +#~ msgid "" +#~ "⚠️ Tensorflow without macos optimization " +#~ "does not support Metal API and " +#~ "utilizing GPU (both intel chips and " +#~ "M-series chips) until at least " +#~ "tensorflow 2.11. Tensorflow-macos would " +#~ "fail when running `tc.backend.to_dense()`" +#~ msgstr "" + +#~ msgid "Testing Platform (Tested Feb 2023)" +#~ msgstr "" + +#~ msgid "" +#~ "This page is deprecated. Please visit" +#~ " `the update tutorial `_" +#~ " for latest information." +#~ msgstr "" + diff --git a/docs/source/locale/zh/LC_MESSAGES/index.po b/docs/source/locale/zh/LC_MESSAGES/index.po index 08959a7d..20ed436d 100644 --- a/docs/source/locale/zh/LC_MESSAGES/index.po +++ b/docs/source/locale/zh/LC_MESSAGES/index.po @@ -8,8 +8,8 @@ msgid "" msgstr "" "Project-Id-Version: tensorcircuit\n" "Report-Msgid-Bugs-To: \n" -"POT-Creation-Date: 2023-05-10 22:52+0800\n" -"PO-Revision-Date: 2023-05-10 22:54+0800\n" +"POT-Creation-Date: 2023-05-28 14:36+0800\n" +"PO-Revision-Date: 2023-05-28 14:39+0800\n" "Last-Translator: Xinghan Yang\n" "Language-Team: \n" "Language: cn\n" @@ -27,44 +27,48 @@ msgstr "参考文档" msgid "**Welcome and congratulations! You have found TensorCircuit.** 👏" msgstr "**祝贺你发现了 TensorCircuit！** 👏" -#: ../../source/index.rst:10 +#: ../../source/index.rst:11 +msgid "Introduction" +msgstr "介绍" + +#: ../../source/index.rst:13 msgid "" "TensorCircuit is an open-source high-performance quantum computing software " "framework in Python." msgstr "TensorCircuit 是基于 Python 的开源高性能量子计算软件框架。" -#: ../../source/index.rst:12 +#: ../../source/index.rst:15 msgid "It is built for humans. 👽" msgstr "适合人类。👽" -#: ../../source/index.rst:14 +#: ../../source/index.rst:17 msgid "It is designed for speed, flexibility and elegance. 🚀" msgstr "速度，灵活，优雅。🚀" -#: ../../source/index.rst:16 +#: ../../source/index.rst:19 msgid "It is empowered by advanced tensor network simulator engine. 🔋" msgstr "先进张量网络引擎赋能。🔋" -#: ../../source/index.rst:18 +#: ../../source/index.rst:21 msgid "" "It is ready for quantum hardware access with CPU/GPU/QPU (local/cloud) hybrid " "solutions. 🖥" msgstr "量子硬件支持，优雅 CPU/GPU/QPU 混合部署方案。 🖥" -#: ../../source/index.rst:20 +#: ../../source/index.rst:23 msgid "" "It is implemented with industry-standard machine learning frameworks: " "TensorFlow, JAX, and PyTorch. 🤖" msgstr "业界标准机器学习框架 TensorFlow，JAX，PyTorch 实现。🤖" -#: ../../source/index.rst:22 +#: ../../source/index.rst:25 msgid "" "It is compatible with machine learning engineering paradigms: automatic " "differentiation, just-in-time compilation, vectorized parallelism and GPU " "acceleration. 🛠" msgstr "与机器学习工程实践兼容：自动微分，即时编译，向量并行化和 GPU 加速。🛠" -#: ../../source/index.rst:24 +#: ../../source/index.rst:27 msgid "" "With the help of TensorCircuit, now get ready to efficiently and elegantly " "solve interesting and challenging quantum computing problems: from academic " @@ -73,11 +77,11 @@ msgstr "" "有了 TensorCircuit，你现在可以高效优雅地解决量子计算中的各种问题：从学术研究的原" "型开发到工业应用的部署。" -#: ../../source/index.rst:29 +#: ../../source/index.rst:33 msgid "Relevant Links" msgstr "相关链接" -#: ../../source/index.rst:31 +#: ../../source/index.rst:35 msgid "" "TensorCircuit is created and maintained by `Shi-Xin Zhang `_ and this version is released by `Tencent Quantum Lab `_ 创建和维" "护；此版本由 `腾讯量子实验室 `_ 发布。" -#: ../../source/index.rst:33 +#: ../../source/index.rst:37 msgid "" "The current core authors of TensorCircuit are `Shi-Xin Zhang `_ and `Yu-Qin Chen `_. We also " @@ -98,7 +102,7 @@ msgstr "" "区的 `贡献 `_。" -#: ../../source/index.rst:36 +#: ../../source/index.rst:40 msgid "" "If you have any further questions or collaboration ideas, please use the issue " "tracker or forum below, or send email to shixinzhang#tencent.com." @@ -106,93 +110,189 @@ msgstr "" "如果关于 TensorCircuit 有任何问题咨询或合作意向，请在 issue 或 discussion 提问，" "或发送邮件到 shixinzhang#tencent.com。" -#: ../../source/index.rst:39 -msgid "Source code: https://github.com/tencent-quantum-lab/tensorcircuit" -msgstr "源代码: https://github.com/tencent-quantum-lab/tensorcircuit" +#: ../../source/index.rst:45 +msgid "Source code" +msgstr "源代码" -#: ../../source/index.rst:41 -msgid "Documentation: https://tensorcircuit.readthedocs.io" -msgstr "文档: https://tensorcircuit.readthedocs.io" +#: ../../source/index.rst:49 +msgid "GitHub" +msgstr "" -#: ../../source/index.rst:43 -msgid "" -"Software Whitepaper (published in Quantum): https://quantum-journal.org/papers/" -"q-2023-02-02-912/" +#: ../../source/index.rst:52 +msgid "Documentation" +msgstr "参考文档" + +#: ../../source/index.rst:56 +msgid "Readthedocs" msgstr "" -"软件白皮书 (发表于 Quantum): https://quantum-journal.org/papers/" -"q-2023-02-02-912/" -#: ../../source/index.rst:45 -msgid "Issue Tracker: https://github.com/tencent-quantum-lab/tensorcircuit/issues" -msgstr "问题跟踪: https://github.com/tencent-quantum-lab/tensorcircuit/issues" +#: ../../source/index.rst:59 +msgid "Whitepaper" +msgstr "白皮书" + +#: ../../source/index.rst:63 +msgid "*Quantum* journal" +msgstr "Quantum 期刊" + +#: ../../source/index.rst:66 +msgid "Issue Tracker" +msgstr "问题跟踪" -#: ../../source/index.rst:47 -msgid "Forum: https://github.com/tencent-quantum-lab/tensorcircuit/discussions" +#: ../../source/index.rst:70 +msgid "GitHub Issues" msgstr "" -"论坛社区: https://github.com/tencent-quantum-lab/tensorcircuit/discussions" -#: ../../source/index.rst:49 -msgid "PyPI page: https://pypi.org/project/tensorcircuit" -msgstr "PyPI 页面: https://pypi.org/project/tensorcircuit" +#: ../../source/index.rst:73 +msgid "Forum" +msgstr "论坛" -#: ../../source/index.rst:51 -msgid "" -"DockerHub page: https://hub.docker.com/repository/docker/tensorcircuit/" -"tensorcircuit" +#: ../../source/index.rst:77 +msgid "GitHub Discussions" +msgstr "" + +#: ../../source/index.rst:80 +msgid "PyPI" msgstr "" -"DockerHub 页面: https://hub.docker.com/repository/docker/tensorcircuit/" -"tensorcircuit" -#: ../../source/index.rst:53 +#: ../../source/index.rst:84 +msgid "``pip install``" +msgstr "" + +#: ../../source/index.rst:87 +msgid "DockerHub" +msgstr "" + +#: ../../source/index.rst:91 +msgid "``docker pull``" +msgstr "" + +#: ../../source/index.rst:94 +msgid "Application" +msgstr "应用" + +#: ../../source/index.rst:98 +msgid "Research using TC" +msgstr "研究项目" + +#: ../../source/index.rst:101 +msgid "Cloud" +msgstr "量子云" + +#: ../../source/index.rst:104 +msgid "Tencent Quantum Cloud" +msgstr "腾讯量子云平台" + +#: ../../source/index.rst:131 +msgid "Unified Quantum Programming" +msgstr "统一量子编程" + +#: ../../source/index.rst:133 msgid "" -"Research and projects based on TensorCircuit: https://github.com/tencent-" -"quantum-lab/tensorcircuit#research-and-applications" +"TensorCircuit is unifying infrastructures and interfaces for quantum computing." +msgstr "TensorCircuit 尝试统一量子计算的基础设施和编程界面。" + +#: ../../source/index.rst:140 +msgid "Unified Backends" +msgstr "统一后端" + +#: ../../source/index.rst:144 +msgid "Jax/TensorFlow/PyTorch/Numpy/Cupy" +msgstr "" + +#: ../../source/index.rst:146 +msgid "Unified Devices" +msgstr "统一设备" + +#: ../../source/index.rst:150 +msgid "CPU/GPU/TPU" msgstr "" -"基于 TensorCircuit 的研究和项目: https://github.com/tencent-quantum-lab/" -"tensorcircuit#research-and-applications" -#: ../../source/index.rst:55 -msgid "Tencent Quantum Cloud Service: https://quantum.tencent.com/cloud/" -msgstr "腾讯量子云服务: https://quantum.tencent.com/cloud/" +#: ../../source/index.rst:152 +msgid "Unified Providers" +msgstr "统一平台" + +#: ../../source/index.rst:156 +msgid "QPUs from different vendors" +msgstr "不同供应商的 QPU" + +#: ../../source/index.rst:158 +msgid "Unified Resources" +msgstr "统一资源" + +#: ../../source/index.rst:162 +msgid "local/cloud/HPC" +msgstr "本地/云/集群" + +#: ../../source/index.rst:170 +msgid "Unified Interfaces" +msgstr "统一接口" + +#: ../../source/index.rst:174 +msgid "numerical sim/hardware exp" +msgstr "数值模拟/硬件实验" + +#: ../../source/index.rst:176 +msgid "Unified Engines" +msgstr "统一引擎" + +#: ../../source/index.rst:180 +msgid "ideal/noisy/approximate simulation" +msgstr "理想/含噪/近似模拟" + +#: ../../source/index.rst:182 +msgid "Unified Representations" +msgstr "统一表示" -#: ../../source/index.rst:61 +#: ../../source/index.rst:186 +msgid "from/to_IR/qiskit/openqasm/json" +msgstr "" + +#: ../../source/index.rst:188 +msgid "Unified Pipelines" +msgstr "统一流程" + +#: ../../source/index.rst:192 +msgid "stateless functional programming/stateful ML models" +msgstr "函数式编程/面向对象模型" + +#: ../../source/index.rst:198 msgid "Reference Documentation" msgstr "参考文档" -#: ../../source/index.rst:63 +#: ../../source/index.rst:200 msgid "" "The following documentation sections briefly introduce TensorCircuit to the " "users and developpers." msgstr "以下文档向用户和开发者简要介绍了 TensorCircuit 软件。" -#: ../../source/index.rst:76 +#: ../../source/index.rst:213 msgid "Tutorials" msgstr "教程" -#: ../../source/index.rst:78 +#: ../../source/index.rst:215 msgid "" "The following documentation sections include integrated examples in the form of " "Jupyter Notebook." msgstr "" "以下 Jupyter Notebook 格式的文档包括了一系列使用 TensorCircuit 的集成案例。" -#: ../../source/index.rst:92 +#: ../../source/index.rst:229 msgid "API References" msgstr "API 参考" -#: ../../source/index.rst:101 +#: ../../source/index.rst:238 msgid "Indices and Tables" msgstr "索引和表格" -#: ../../source/index.rst:103 +#: ../../source/index.rst:240 msgid ":ref:`genindex`" msgstr ":ref:`genindex`" -#: ../../source/index.rst:104 +#: ../../source/index.rst:241 msgid ":ref:`modindex`" msgstr ":ref:`modindex`" -#: ../../source/index.rst:105 +#: ../../source/index.rst:242 msgid ":ref:`search`" msgstr ":ref:`search`" @@ -213,3 +313,47 @@ msgstr ":ref:`search`" #~ msgid "Links" #~ msgstr "重要链接" + +#~ msgid "Source code: https://github.com/tencent-quantum-lab/tensorcircuit" +#~ msgstr "源代码: https://github.com/tencent-quantum-lab/tensorcircuit" + +#~ msgid "Documentation: https://tensorcircuit.readthedocs.io" +#~ msgstr "文档: https://tensorcircuit.readthedocs.io" + +#~ msgid "" +#~ "Software Whitepaper (published in Quantum): https://quantum-journal.org/" +#~ "papers/q-2023-02-02-912/" +#~ msgstr "" +#~ "软件白皮书 (发表于 Quantum): https://quantum-journal.org/papers/" +#~ "q-2023-02-02-912/" + +#~ msgid "" +#~ "Issue Tracker: https://github.com/tencent-quantum-lab/tensorcircuit/issues" +#~ msgstr "问题跟踪: https://github.com/tencent-quantum-lab/tensorcircuit/issues" + +#~ msgid "Forum: https://github.com/tencent-quantum-lab/tensorcircuit/discussions" +#~ msgstr "" +#~ "论坛社区: https://github.com/tencent-quantum-lab/tensorcircuit/discussions" + +#~ msgid "PyPI page: https://pypi.org/project/tensorcircuit" +#~ msgstr "PyPI 页面: https://pypi.org/project/tensorcircuit" + +#~ msgid "" +#~ "DockerHub page: https://hub.docker.com/repository/docker/tensorcircuit/" +#~ "tensorcircuit" +#~ msgstr "" +#~ "DockerHub 页面: https://hub.docker.com/repository/docker/tensorcircuit/" +#~ "tensorcircuit" + +#~ msgid "" +#~ "Research and projects based on TensorCircuit: https://github.com/tencent-" +#~ "quantum-lab/tensorcircuit#research-and-applications" +#~ msgstr "" +#~ "基于 TensorCircuit 的研究和项目: https://github.com/tencent-quantum-lab/" +#~ "tensorcircuit#research-and-applications" + +#~ msgid "Tencent Quantum Cloud Service: https://quantum.tencent.com/cloud/" +#~ msgstr "腾讯量子云服务: https://quantum.tencent.com/cloud/" + +#~ msgid "Research based on TC" +#~ msgstr "基于 TC 的研究项目" diff --git a/docs/source/locale/zh/LC_MESSAGES/infras.po b/docs/source/locale/zh/LC_MESSAGES/infras.po index a24e7660..b285ed77 100644 --- a/docs/source/locale/zh/LC_MESSAGES/infras.po +++ b/docs/source/locale/zh/LC_MESSAGES/infras.po @@ -8,7 +8,7 @@ msgid "" msgstr "" "Project-Id-Version: tensorcircuit\n" "Report-Msgid-Bugs-To: \n" -"POT-Creation-Date: 2023-05-07 10:47+0800\n" +"POT-Creation-Date: 2023-05-27 18:52+0800\n" "PO-Revision-Date: 2022-04-18 20:44+0800\n" "Last-Translator: Xinghan Yang\n" "Language: cn\n" @@ -403,6 +403,62 @@ msgstr "" "(``*``)、张量乘积（``|``）和偏迹（``.partial_trace(subsystems_to_trace_out)``）。要提取这些对象的矩阵信息，我们可以使用" " ``.eval()`` 或 ``.eval_matrix() ``，前者保留了张量网络的形状信息，而后者给出了形状秩为2的矩阵表示。" +#: ../../source/infras.rst:162 +msgid "Quantum Cloud SDK: Layerwise API design" +msgstr "" + +#: ../../source/infras.rst:164 +msgid "From lower level to higher level, a view of API layers invoking QPU calls" +msgstr "" + +#: ../../source/infras.rst:166 +msgid "" +"Vendor specific implementation of functional API in, e.g., " +":py:mod:`tensorcircuit.cloud.tencent`" +msgstr "" + +#: ../../source/infras.rst:168 +msgid "" +"Provider agnostic functional lower level API for task/device management " +"in :py:mod:`tensorcircuit.cloud.apis`" +msgstr "" + +#: ../../source/infras.rst:170 +msgid "" +"Object oriented abstraction for Provider/Device/Task in " +":py:mod:`tensorcircuit.cloud.abstraction`" +msgstr "" + +#: ../../source/infras.rst:172 +msgid "" +"Unified batch submission interface as standarized in " +":py:meth:`tensorcircuit.cloud.wrapper.batch_submit_template`" +msgstr "" + +#: ../../source/infras.rst:174 +msgid "" +"Numerical and experimental unified all-in-one interface as " +":py:meth:`tensorcircuit.cloud.wrapper.batch_expectation_ps`" +msgstr "" + +#: ../../source/infras.rst:176 +msgid "" +"Application level code with QPU calls built directly on " +"``batch_expectation_ps`` or more fancy algorithms can be built on " +"``batch_submit_func`` so that these algorithms can be reused as long as " +"one function ``batch_submit_func`` is defined for a given vendor (cheaper" +" than defining a new provider from lower level)." +msgstr "" + +#: ../../source/infras.rst:181 +msgid "" +"For compiler, error mitigation and results post-processing parts, they " +"can be carefully designed to decouple with the QPU calls, so they are " +"separately implemented in :py:mod:`tensorcircuit.compiler` and " +":py:mod:`tensorcircuit.results`, and they can be independently useful " +"even without tc's cloud access." +msgstr "" + #~ msgid "" #~ ":py:mod:`tensorcircuit.densitymatrix2`: Highly efficient" #~ " implementation of " diff --git a/docs/source/locale/zh/LC_MESSAGES/quickstart.po b/docs/source/locale/zh/LC_MESSAGES/quickstart.po index 75a6f3e5..b4275455 100644 --- a/docs/source/locale/zh/LC_MESSAGES/quickstart.po +++ b/docs/source/locale/zh/LC_MESSAGES/quickstart.po @@ -6,18 +6,17 @@ # msgid "" msgstr "" -"Project-Id-Version: tensorcircuit\n" +"Project-Id-Version: tensorcircuit\n" "Report-Msgid-Bugs-To: \n" -"POT-Creation-Date: 2023-05-07 10:47+0800\n" +"POT-Creation-Date: 2023-07-14 15:43+0800\n" "PO-Revision-Date: 2023-05-07 11:01+0800\n" "Last-Translator: Xinghan Yang\n" -"Language-Team: Xinghan Yang\n" "Language: cn\n" +"Language-Team: Xinghan Yang\n" "MIME-Version: 1.0\n" "Content-Type: text/plain; charset=utf-8\n" "Content-Transfer-Encoding: 8bit\n" -"Generated-By: Babel 2.9.1\n" -"X-Generator: Poedit 3.2.2\n" +"Generated-By: Babel 2.12.1\n" #: ../../source/quickstart.rst:3 msgid "Quick Start" @@ -28,22 +27,23 @@ msgid "Installation" msgstr "安装" #: ../../source/quickstart.rst:8 -msgid "For x86 Linux or Mac," -msgstr "" +msgid "For x86 Linux," +msgstr "x64 Linux" #: ../../source/quickstart.rst:10 msgid "``pip install tensorcircuit``" -msgstr "" +msgstr "``pip install tensorcircuit``" #: ../../source/quickstart.rst:12 msgid "" -"is in general enough. Either pip from conda or other python env managers is fine." +"is in general enough. Either pip from conda or other python env managers " +"is fine." msgstr "" #: ../../source/quickstart.rst:15 msgid "" -"Since there are many optional packages for various features, the users may need " -"to install more pip packages when required." +"Since there are many optional packages for various features, the users " +"may need to install more pip packages when required." msgstr "" #: ../../source/quickstart.rst:18 @@ -52,9 +52,10 @@ msgstr "" #: ../../source/quickstart.rst:19 msgid "" -"please refer to the GPU aware installation guide of corresponding machine " -"learning frameworks: `TensorFlow `_, " -"`Jax `_, or `PyTorch " +"please refer to the GPU aware installation guide of corresponding machine" +" learning frameworks: `TensorFlow " +"`_, `Jax " +"`_, or `PyTorch " "`_." msgstr "" @@ -64,46 +65,48 @@ msgstr "" #: ../../source/quickstart.rst:26 msgid "" -"``sudo docker run -it --network host --gpus all tensorcircuit/tensorcircuit``." +"``sudo docker run -it --network host --gpus all " +"tensorcircuit/tensorcircuit``." msgstr "" #: ../../source/quickstart.rst:28 msgid "" -"For more details on docker setup, please refer to `docker readme `_." +"For more details on docker setup, please refer to `docker readme " +"`_." msgstr "" #: ../../source/quickstart.rst:30 msgid "" -"For Windows, due to the lack of support for Jax, we recommend to use docker or " -"WSL, please refer to `TC via windows docker `_ or `TC via WSL `_." +"For Windows, due to the lack of support for Jax, we recommend to use " +"docker or WSL, please refer to `TC via windows docker " +"`_ or `TC via WSL " +"`_." msgstr "" #: ../../source/quickstart.rst:32 -msgid "" -"For Mac with M series chips (arm architecture), please refer to `TC on Mac M " -"series `_." -msgstr "" +msgid "For MacOS, please refer to `TC on Mac `_." +msgstr "For MacOS, please refer to `在Mac上安装TC `_." #: ../../source/quickstart.rst:34 msgid "" -"Overall, the installation of TensorCircuit is simple, since it is purely in " -"Python and hence very portable. As long as the users can take care of the " -"installation of ML frameworks on the corresponding system, TensorCircuit will " -"work as expected." +"Overall, the installation of TensorCircuit is simple, since it is purely " +"in Python and hence very portable. As long as the users can take care of " +"the installation of ML frameworks on the corresponding system, " +"TensorCircuit will work as expected." msgstr "" #: ../../source/quickstart.rst:37 msgid "" -"To debug the installation issue or report bugs, please check the environment " -"information by ``tc.about()``." +"To debug the installation issue or report bugs, please check the " +"environment information by ``tc.about()``." msgstr "" #: ../../source/quickstart.rst:40 msgid "" -"We also provide a nightly build of tensorcircuit via PyPI which can be accessed " -"by ``pip uninstall tensorcircuit``, then ``pip install tensorcircuit-nightly``" +"We also provide a nightly build of tensorcircuit via PyPI which can be " +"accessed by ``pip uninstall tensorcircuit``, then ``pip install " +"tensorcircuit-nightly``" msgstr "" #: ../../source/quickstart.rst:46 @@ -124,20 +127,18 @@ msgstr "**输入状态:**" #: ../../source/quickstart.rst:54 msgid "" -"The default input function for the circuit is :math:`\\vert 0^n \\rangle`. One " -"can change this to other wavefunctions by directly feeding the inputs state " -"vectors w: ``c=tc.Circuit(n, inputs=w)``." +"The default input function for the circuit is :math:`\\vert 0^n " +"\\rangle`. One can change this to other wavefunctions by directly feeding" +" the inputs state vectors w: ``c=tc.Circuit(n, inputs=w)``." msgstr "" -"电路的默认输入函数是 :math:`\\vert 0^n \\rangle` 。可以通过直接输入输入状态向量 " -"w 将其更改为其他波函数: ``c=tc.Circuit(n, inputs=w)``。" +"电路的默认输入函数是 :math:`\\vert 0^n \\rangle` 。可以通过直接输入输入状态向量 w 将其更改为其他波函数: " +"``c=tc.Circuit(n, inputs=w)``。" #: ../../source/quickstart.rst:56 msgid "" -"One can also feed matrix product states as input states for the circuit, but we " -"leave MPS/MPO usage for future sections." -msgstr "" -"也可以将矩阵乘积状态作为电路的输入状态，但我们将矩阵乘积状态/矩阵乘积算子的使用留" -"待后续讲解。" +"One can also feed matrix product states as input states for the circuit, " +"but we leave MPS/MPO usage for future sections." +msgstr "也可以将矩阵乘积状态作为电路的输入状态，但我们将矩阵乘积状态/矩阵乘积算子的使用留待后续讲解。" #: ../../source/quickstart.rst:58 msgid "**Quantum Gates:**" @@ -145,13 +146,12 @@ msgstr "**量子门:**" #: ../../source/quickstart.rst:60 msgid "" -"We can apply gates on circuit objects. For example, using ``c.H(1)`` or ``c." -"rx(2, theta=0.2)``, we can apply Hadamard gate on qubit 1 (0-based) or apply Rx " -"gate on qubit 2 as :math:`e^{-i\\theta/2 X}`." +"We can apply gates on circuit objects. For example, using ``c.H(1)`` or " +"``c.rx(2, theta=0.2)``, we can apply Hadamard gate on qubit 1 (0-based) " +"or apply Rx gate on qubit 2 as :math:`e^{-i\\theta/2 X}`." msgstr "" -"我们可以将门应用于电路对象。 例如，使用 ``c.H(1)`` 或 ``c.rx(2, theta=0.2)``，我" -"们可以将 Hadamard 门应用于量子比特1 （基于0）或将 Rx 门应用于量子比特2 :math:" -"`e^{-i\\theta/2 X}`。" +"我们可以将门应用于电路对象。 例如，使用 ``c.H(1)`` 或 ``c.rx(2, theta=0.2)``，我们可以将 Hadamard " +"门应用于量子比特1 （基于0）或将 Rx 门应用于量子比特2 :math:`e^{-i\\theta/2 X}`。" #: ../../source/quickstart.rst:62 msgid "The same rule also applies to multi-qubit gates, such as ``c.cnot(0, 1)``." @@ -163,16 +163,16 @@ msgstr "这些量子门也是高度可定制的，下面是两个例子" #: ../../source/quickstart.rst:66 msgid "" -"``c.exp1(0, 1, unitary=m, theta=0.2)`` which is for the exponential gate :math:" -"`e^{i\\theta m}` of any matrix m as long as :math:`m^2=1`." +"``c.exp1(0, 1, unitary=m, theta=0.2)`` which is for the exponential gate " +":math:`e^{i\\theta m}` of any matrix m as long as :math:`m^2=1`." msgstr "" -"``c.exp1(0, 1, unitary=m, theta=0.2)`` 用于任何矩阵 m 的指数门 :math:" -"`e^{i\\theta m}`，只要 m 满足 :math:`m^2=1`。" +"``c.exp1(0, 1, unitary=m, theta=0.2)`` 用于任何矩阵 m 的指数门 :math:`e^{i\\theta " +"m}`，只要 m 满足 :math:`m^2=1`。" #: ../../source/quickstart.rst:68 msgid "" -"``c.any(0, 1, unitary=m)`` which is for applying the unitary gate m on the " -"circuit." +"``c.any(0, 1, unitary=m)`` which is for applying the unitary gate m on " +"the circuit." msgstr "``c.any(0, 1, unitary=m)`` 在电路上作用任意的幺正量子门。" #: ../../source/quickstart.rst:70 @@ -185,36 +185,33 @@ msgstr "**测量与期望**" #: ../../source/quickstart.rst:74 msgid "" -"The most straightforward way to get the output from the circuit object is by " -"getting the output wavefunction in vector form as ``c.state()``." -msgstr "" -"从电路对象中获取输出的最直接的方法是通过 ``c.state()`` 以向量形式获取输出波函数。" +"The most straightforward way to get the output from the circuit object is" +" by getting the output wavefunction in vector form as ``c.state()``." +msgstr "从电路对象中获取输出的最直接的方法是通过 ``c.state()`` 以向量形式获取输出波函数。" #: ../../source/quickstart.rst:76 msgid "" -"For bitstring sampling, we have ``c.perfect_sampling()`` which returns the " -"bitstring and the corresponding probability amplitude." -msgstr "" -"对于位串采样，我们有 ``c.perfect_sampling()``，它返回位串和相应的概率幅度。" +"For bitstring sampling, we have ``c.perfect_sampling()`` which returns " +"the bitstring and the corresponding probability amplitude." +msgstr "对于位串采样，我们有 ``c.perfect_sampling()``，它返回位串和相应的概率幅度。" #: ../../source/quickstart.rst:78 msgid "" -"To measure part of the qubits, we can use ``c.measure(0, 1)``, if we want to " -"know the corresponding probability of the measurement output, try ``c.measure(0, " -"1, with_prob=True)``. The measure API is by default non-jittable, but we also " -"have a jittable version as ``c.measure_jit(0, 1)``." +"To measure part of the qubits, we can use ``c.measure(0, 1)``, if we want" +" to know the corresponding probability of the measurement output, try " +"``c.measure(0, 1, with_prob=True)``. The measure API is by default non-" +"jittable, but we also have a jittable version as ``c.measure_jit(0, 1)``." msgstr "" -"要测量部分量子比特，我们可以使用 ``c.measure(0, 1)``，如果我们想知道测量的结果的" -"对应概率，可以尝试 ``c.measure(0, 1, with_prob=True)``。 测量 API 在默认情况下是" -"不可即时编译的 ，但我们也有一个可即时编译的版本，如 ``c.measure_jit(0, 1)``。" +"要测量部分量子比特，我们可以使用 ``c.measure(0, 1)``，如果我们想知道测量的结果的对应概率，可以尝试 " +"``c.measure(0, 1, with_prob=True)``。 测量 API 在默认情况下是不可即时编译的 " +"，但我们也有一个可即时编译的版本，如 ``c.measure_jit(0, 1)``。" #: ../../source/quickstart.rst:80 msgid "" -"The measurement and sampling utilize advanced algorithms based on tensornetwork " -"and thus require no knowledge or space for the full wavefunction." -msgstr "" -"测量和采样使用了基于张量网络的高级算法，因此不需要任何相关知识或者空间来获取全波" -"函数。" +"The measurement and sampling utilize advanced algorithms based on " +"tensornetwork and thus require no knowledge or space for the full " +"wavefunction." +msgstr "测量和采样使用了基于张量网络的高级算法，因此不需要任何相关知识或者空间来获取全波函数。" #: ../../source/quickstart.rst:82 msgid "See the example below:" @@ -222,25 +219,26 @@ msgstr "请看下面的例子：" #: ../../source/quickstart.rst:100 msgid "" -"To compute expectation values for local observables, we have ``c.expectation([tc." -"gates.z(), [0]], [tc.gates.z(), [1]])`` for :math:`\\langle Z_0Z_1 \\rangle` or " -"``c.expectation([tc.gates.x(), [0]])`` for :math:`\\langle X_0 \\rangle`." +"To compute expectation values for local observables, we have " +"``c.expectation([tc.gates.z(), [0]], [tc.gates.z(), [1]])`` for " +":math:`\\langle Z_0Z_1 \\rangle` or ``c.expectation([tc.gates.x(), " +"[0]])`` for :math:`\\langle X_0 \\rangle`." msgstr "" -"为了计算局部可观察量的期望值，我们有 ``c.expectation([tc.gates.z(), [0]], [tc." -"gates.z(), [1]])`` 对应的期望为 :math:`\\langle Z_0Z_1 \\rangle` 时，或 ``c." -"expectation([tc.gates.x(), [0]])`` 对应的期望为 :math:`\\langle X_0 \\rangle`时." +"为了计算局部可观察量的期望值，我们有 ``c.expectation([tc.gates.z(), [0]], [tc.gates.z(), " +"[1]])`` 对应的期望为 :math:`\\langle Z_0Z_1 \\rangle` 时，或 " +"``c.expectation([tc.gates.x(), [0]])`` 对应的期望为 :math:`\\langle X_0 " +"\\rangle`时." #: ../../source/quickstart.rst:102 msgid "" -"This expectation API is rather flexible, as one can measure an m on several " -"qubits as ``c.expectation([m, [0, 1, 2]])``." -msgstr "" -"因为可以在几个量子比特上测量一个 m，这种计算期望值的 API 相当灵活：``c." -"expectation([m, [0, 1, 2]])``。" +"This expectation API is rather flexible, as one can measure an m on " +"several qubits as ``c.expectation([m, [0, 1, 2]])``." +msgstr "因为可以在几个量子比特上测量一个 m，这种计算期望值的 API 相当灵活：``c.expectation([m, [0, 1, 2]])``。" #: ../../source/quickstart.rst:104 msgid "" -"We can also extract the unitary matrix underlying the whole circuit as follows:" +"We can also extract the unitary matrix underlying the whole circuit as " +"follows:" msgstr "我们还可以提取整个电路下面的幺正矩阵，如下所示：" #: ../../source/quickstart.rst:117 @@ -251,22 +249,20 @@ msgstr "**电路可视化**" msgid "" "We currently support transform ``tc.Circuit`` from and to Qiskit " "``QuantumCircuit`` object." -msgstr "" -"我们目前支持 ``tc.Circuit`` 与 Qiskit ``QuantumCircuit`` 对象之间的互相转换。" +msgstr "我们目前支持 ``tc.Circuit`` 与 Qiskit ``QuantumCircuit`` 对象之间的互相转换。" #: ../../source/quickstart.rst:121 msgid "" -"Export to Qiskit (possible for further hardware experiment, compiling, and " -"visualization): ``c.to_qiskit()``." -msgstr "" -"导出到 Qiskit（可能用于进一步的硬件实验、编译和可视化）：``c.to_qiskit()``。" +"Export to Qiskit (possible for further hardware experiment, compiling, " +"and visualization): ``c.to_qiskit()``." +msgstr "导出到 Qiskit（可能用于进一步的硬件实验、编译和可视化）：``c.to_qiskit()``。" #: ../../source/quickstart.rst:123 msgid "" "Import from Qiskit: ``c = tc.Circuit.from_qiskit(QuantumCircuit, n)``. " -"Parameterized Qiskit circuit is supported by passing the parameters to the " -"``binding_parameters`` argument of the ``from_qiskit`` function, similar to the " -"``assign_parameters`` function in Qiskit." +"Parameterized Qiskit circuit is supported by passing the parameters to " +"the ``binding_parameters`` argument of the ``from_qiskit`` function, " +"similar to the ``assign_parameters`` function in Qiskit." msgstr "" #: ../../source/quickstart.rst:127 @@ -275,40 +271,41 @@ msgstr "**电路可视化**" #: ../../source/quickstart.rst:129 msgid "" -"``c.vis_tex()`` can generate tex code for circuit visualization based on LaTeX " -"`quantikz `__ package." +"``c.vis_tex()`` can generate tex code for circuit visualization based on " +"LaTeX `quantikz `__ package." msgstr "" "``c.vis_tex()`` 可以基于 `quantikz `__ " "package 生成用于电路可视化的 tex 代码。" #: ../../source/quickstart.rst:131 msgid "" -"There are also some automatic pipeline helper functions to directly generate " -"figures from tex code, but they require extra installations in the environment." -msgstr "" -"还有一些自动辅助函数可以直接从 tex 代码生成图形，但它们需要在环境中进行额外安装。" +"There are also some automatic pipeline helper functions to directly " +"generate figures from tex code, but they require extra installations in " +"the environment." +msgstr "还有一些自动辅助函数可以直接从 tex 代码生成图形，但它们需要在环境中进行额外安装。" #: ../../source/quickstart.rst:133 msgid "" -"``render_pdf(tex)`` function requires full installation of LaTeX locally. And in " -"the Jupyter environment, we may prefer ``render_pdf(tex, notebook=True)`` to " -"return jpg figures, which further require wand magicwand library installed, see " -"`here `__." +"``render_pdf(tex)`` function requires full installation of LaTeX locally." +" And in the Jupyter environment, we may prefer ``render_pdf(tex, " +"notebook=True)`` to return jpg figures, which further require wand " +"magicwand library installed, see `here `__." msgstr "" -"``render_pdf(tex)`` 函数需要在本地完全安装 LaTeX。 在 Jupyter 环境中，我们可能会" -"偏好 ``render_pdf(tex, notebook=True)`` 来返回 jpg 图形，这需要安装 wand " -"magicwand 库，请参阅 `这里 `__ 。" +"``render_pdf(tex)`` 函数需要在本地完全安装 LaTeX。 在 Jupyter 环境中，我们可能会偏好 " +"``render_pdf(tex, notebook=True)`` 来返回 jpg 图形，这需要安装 wand magicwand 库，请参阅 " +"`这里 `__ 。" #: ../../source/quickstart.rst:135 msgid "" -"Or since we can transform ``tc.Circuit`` into QuantumCircuit easily, we have a " -"simple pipeline to first transform ``tc.Circuit`` into Qiskit and then call the " -"visualization built in Qiskit. Namely, we have ``c.draw()`` API." +"Or since we can transform ``tc.Circuit`` into QuantumCircuit easily, we " +"have a simple pipeline to first transform ``tc.Circuit`` into Qiskit and " +"then call the visualization built in Qiskit. Namely, we have ``c.draw()``" +" API." msgstr "" -"从 Qiskit 导入：``c = tc.Circuit.from_qiskit(QuantumCircuit, n)`` 或者因为我们可" -"以轻松地将 ``tc.Circuit`` 转换为 QuantumCircuit，我们有一个简单的管道来首先转换 " -"``tc.Circuit`` 为 Qiskit，然后调用 Qiskit 中内置的可视化。 也就是说，我们有 ``c." -"draw()`` API。" +"从 Qiskit 导入：``c = tc.Circuit.from_qiskit(QuantumCircuit, n)`` " +"或者因为我们可以轻松地将 ``tc.Circuit`` 转换为 QuantumCircuit，我们有一个简单的管道来首先转换 " +"``tc.Circuit`` 为 Qiskit，然后调用 Qiskit 中内置的可视化。 也就是说，我们有 ``c.draw()`` API。" #: ../../source/quickstart.rst:137 msgid "**Circuit Intermediate Representation:**" @@ -316,21 +313,19 @@ msgstr "**电路中间表示:**" #: ../../source/quickstart.rst:139 msgid "" -"TensorCircuit provides its own circuit IR as a python list of dicts. This IR can " -"be further utilized to run compiling, generate serialization qasm, or render " -"circuit figures." -msgstr "" -"TensorCircuit 提供自己的中间表示是元素是字典的列表。此中间表示可进一步用于运行编" -"译、生成序列化 qasm 或渲染电路图。" +"TensorCircuit provides its own circuit IR as a python list of dicts. This" +" IR can be further utilized to run compiling, generate serialization " +"qasm, or render circuit figures." +msgstr "TensorCircuit 提供自己的中间表示是元素是字典的列表。此中间表示可进一步用于运行编译、生成序列化 qasm 或渲染电路图。" #: ../../source/quickstart.rst:141 msgid "" -"The IR is given as a list, each element is a dict containing information on one " -"gate that is applied to the circuit. Note gate attr in the dict is a python " -"function that returns the gate's node." +"The IR is given as a list, each element is a dict containing information " +"on one gate that is applied to the circuit. Note gate attr in the dict is" +" a python function that returns the gate's node." msgstr "" -"中间表示以列表形式给出，每个元素都是一个字典，其中包含应用于电路的一个量子门的信" -"息。 注意字典中的 gate atrr 实际上是一个返回此量子门的节点的 python 函数。" +"中间表示以列表形式给出，每个元素都是一个字典，其中包含应用于电路的一个量子门的信息。 注意字典中的 gate atrr " +"实际上是一个返回此量子门的节点的 python 函数。" #: ../../source/quickstart.rst:153 msgid "Programming Paradigm" @@ -338,38 +333,36 @@ msgstr "编程范式" #: ../../source/quickstart.rst:155 msgid "" -"The most common case and the most typical programming paradigm for TensorCircuit " -"are to evaluate the circuit output and the corresponding quantum gradients, " -"which is common in variational quantum algorithms." -msgstr "" -"TensorCircuit 最常见的情况和最典型的编程范式是评估电路的输出以及相应的量子梯度，" -"这在变分量子算法中很常见。" +"The most common case and the most typical programming paradigm for " +"TensorCircuit are to evaluate the circuit output and the corresponding " +"quantum gradients, which is common in variational quantum algorithms." +msgstr "TensorCircuit 最常见的情况和最典型的编程范式是评估电路的输出以及相应的量子梯度，这在变分量子算法中很常见。" #: ../../source/quickstart.rst:182 #, fuzzy msgid "" -"Also for a non-quantum example (linear regression) demonstrating the backend " -"agnostic feature, variables with pytree support, AD/jit/vmap usage, and " -"variational optimization loops. Please refer to the example script: `linear " -"regression example `_. This example might be more friendly to the " -"machine learning community since it is purely classical while also showcasing " -"the main features and paradigms of tensorcircuit." +"Also for a non-quantum example (linear regression) demonstrating the " +"backend agnostic feature, variables with pytree support, AD/jit/vmap " +"usage, and variational optimization loops. Please refer to the example " +"script: `linear regression example `_. This example " +"might be more friendly to the machine learning community since it is " +"purely classical while also showcasing the main features and paradigms of" +" tensorcircuit." msgstr "" -"同样对于演示后端不可知特性的非量子示例（线性回归），pytree 支持变量、自动微分/即" -"时编译/矢量并行化 用法和变分优化循环。请参考示例脚本: `线性回归示例 `_ 。 这" -"个例子可能对机器学习的用户更友好，因为它纯粹是经典的，同时也展示了 TensorCircuit " -"的主要特征和范式。" +"同样对于演示后端不可知特性的非量子示例（线性回归），pytree 支持变量、自动微分/即时编译/矢量并行化 用法和变分优化循环。请参考示例脚本: " +"`线性回归示例 `_ 。 " +"这个例子可能对机器学习的用户更友好，因为它纯粹是经典的，同时也展示了 TensorCircuit 的主要特征和范式。" #: ../../source/quickstart.rst:185 msgid "" -"If the user has no intention to maintain the application code in a backend " -"agnostic fashion, the API for ML frameworks can be more handily used and " -"interleaved with the TensorCircuit API." +"If the user has no intention to maintain the application code in a " +"backend agnostic fashion, the API for ML frameworks can be more handily " +"used and interleaved with the TensorCircuit API." msgstr "" -"如果用户无意以与后端无关的方式维护应用程序代码，则可以更方便地使用用于机器学习框" -"架的 API 并将其与 TensorCircuit API 交替使用。" +"如果用户无意以与后端无关的方式维护应用程序代码，则可以更方便地使用用于机器学习框架的 API 并将其与 TensorCircuit API " +"交替使用。" #: ../../source/quickstart.rst:220 msgid "Automatic Differentiation, JIT, and Vectorized Parallelism" @@ -377,22 +370,21 @@ msgstr "自动微分、即时编译和矢量化并行 " #: ../../source/quickstart.rst:222 msgid "" -"For concepts of AD, JIT and VMAP, please refer to `Jax documentation `__ ." +"For concepts of AD, JIT and VMAP, please refer to `Jax documentation " +"`__ ." msgstr "" -"关于自动微分、即时编译和向量并行化，请参考 `Jax 文档 `__ 。" +"关于自动微分、即时编译和向量并行化，请参考 `Jax 文档 " +"`__ 。" #: ../../source/quickstart.rst:224 msgid "" "The related API design in TensorCircuit closely follows the functional " -"programming design pattern in Jax with some slight differences. So we strongly " -"recommend users learn some basics about Jax no matter which ML backend they " -"intend to use." +"programming design pattern in Jax with some slight differences. So we " +"strongly recommend users learn some basics about Jax no matter which ML " +"backend they intend to use." msgstr "" -"TensorCircuit 中的相关 API 设计与 Jax 中的函数式编程的设计模式密切相关，但是略有" -"不同。因此，我们强烈建议用户学习一些有关 Jax 的基础知识，无论他们打算使用哪种机器" -"学习后端。" +"TensorCircuit 中的相关 API 设计与 Jax 中的函数式编程的设计模式密切相关，但是略有不同。因此，我们强烈建议用户学习一些有关 " +"Jax 的基础知识，无论他们打算使用哪种机器学习后端。" #: ../../source/quickstart.rst:226 msgid "**AD Support:**" @@ -400,11 +392,9 @@ msgstr "**自动微分支持**" #: ../../source/quickstart.rst:228 msgid "" -"Gradients, vjps, jvps, natural gradients, Jacobians, and Hessians. AD is the " -"base for all modern machine learning libraries." -msgstr "" -"梯度、矢量雅可比乘积、自然梯度、 Jacobian 矩阵和 Hessian 矩阵。自动微分是所有现代" -"机器学习库的基础。" +"Gradients, vjps, jvps, natural gradients, Jacobians, and Hessians. AD is " +"the base for all modern machine learning libraries." +msgstr "梯度、矢量雅可比乘积、自然梯度、 Jacobian 矩阵和 Hessian 矩阵。自动微分是所有现代机器学习库的基础。" #: ../../source/quickstart.rst:232 msgid "**JIT Support:**" @@ -412,19 +402,18 @@ msgstr "**自动微分支持**" #: ../../source/quickstart.rst:234 msgid "" -"Parameterized quantum circuits can run in a blink. Always use jit if the circuit " -"will get evaluations multiple times, it can greatly boost the simulation with " -"two or three order time reduction. But also be cautious, users need to be " -"familiar with jit, otherwise, the jitted function may return unexpected results " -"or recompile on every hit (wasting lots of time). To learn more about the jit " -"mechanism, one can refer to documentation or blogs on ``tf.function`` or ``jax." -"jit``, though these two still have subtle differences." +"Parameterized quantum circuits can run in a blink. Always use jit if the " +"circuit will get evaluations multiple times, it can greatly boost the " +"simulation with two or three order time reduction. But also be cautious, " +"users need to be familiar with jit, otherwise, the jitted function may " +"return unexpected results or recompile on every hit (wasting lots of " +"time). To learn more about the jit mechanism, one can refer to " +"documentation or blogs on ``tf.function`` or ``jax.jit``, though these " +"two still have subtle differences." msgstr "" -"参数化的量子电路可以在瞬间完成运行。如果电路将得到多次运行，请始终使用即时编译，" -"它可以大大提高仿真速度，减少两到三个数量级的运行时间。但也要小心，用户需要熟悉 即" -"时编译，否则，即时编译的函数可能会返回意外结果或每次在点击时都重新编译（浪费大量" -"时间）。要了解更多关于即时编译机制的信息，可以参考关于 ``tf.function`` 或 ``jax." -"jit`` 的文档或博客，即使这两者仍然存在细微差别。" +"参数化的量子电路可以在瞬间完成运行。如果电路将得到多次运行，请始终使用即时编译，它可以大大提高仿真速度，减少两到三个数量级的运行时间。但也要小心，用户需要熟悉" +" 即时编译，否则，即时编译的函数可能会返回意外结果或每次在点击时都重新编译（浪费大量时间）。要了解更多关于即时编译机制的信息，可以参考关于 " +"``tf.function`` 或 ``jax.jit`` 的文档或博客，即使这两者仍然存在细微差别。" #: ../../source/quickstart.rst:238 msgid "**VMAP Support:**" @@ -432,12 +421,13 @@ msgstr "**自动微分支持**" #: ../../source/quickstart.rst:240 msgid "" -"Inputs, parameters, measurements, circuit structures, and Monte Carlo noise can " -"all be evaluated in parallel. To learn more about vmap mechanism, one can refer " -"to documentation or blogs on ``tf.vectorized_map`` or ``jax.vmap``." +"Inputs, parameters, measurements, circuit structures, and Monte Carlo " +"noise can all be evaluated in parallel. To learn more about vmap " +"mechanism, one can refer to documentation or blogs on " +"``tf.vectorized_map`` or ``jax.vmap``." msgstr "" -"输入、参数、测量、电路结构、蒙特卡洛噪声都可以并行测算。 要了解有关矢量并行化机制" -"的更多信息，可以参考 ``tf.vectorized_map`` 或 ``jax.vmap`` 上的文档或博客。" +"输入、参数、测量、电路结构、蒙特卡洛噪声都可以并行测算。 要了解有关矢量并行化机制的更多信息，可以参考 ``tf.vectorized_map``" +" 或 ``jax.vmap`` 上的文档或博客。" #: ../../source/quickstart.rst:245 msgid "Backend Agnosticism" @@ -445,34 +435,36 @@ msgstr "后端无关特性" #: ../../source/quickstart.rst:247 msgid "" -"TensorCircuit supports TensorFlow, Jax, and PyTorch backends. We recommend using " -"TensorFlow or Jax backend since PyTorch lacks advanced jit and vmap features." +"TensorCircuit supports TensorFlow, Jax, and PyTorch backends. We " +"recommend using TensorFlow or Jax backend since PyTorch lacks advanced " +"jit and vmap features." msgstr "" -"TensorCircuit 支持 TensorFlow、Jax 和 PyTorch 后端。 我们建议使用 TensorFlow 或 " -"Jax 后端，因为 PyTorch 缺乏高级 jit 和 vmap 功能。" +"TensorCircuit 支持 TensorFlow、Jax 和 PyTorch 后端。 我们建议使用 TensorFlow 或 Jax " +"后端，因为 PyTorch 缺乏高级 jit 和 vmap 功能。" #: ../../source/quickstart.rst:249 msgid "" -"The backend can be set as ``K=tc.set_backend(\"jax\")`` and ``K`` is the backend " -"with a full set of APIs as a conventional ML framework, which can also be " -"accessed by ``tc.backend``." +"The backend can be set as ``K=tc.set_backend(\"jax\")`` and ``K`` is the " +"backend with a full set of APIs as a conventional ML framework, which can" +" also be accessed by ``tc.backend``." msgstr "" -"后端可以设置为 ``K=tc.set_backend(\"jax\")`` ，``K``作为常规机器学习框架的全套API" -"的后端，也可以通过``tc .backend`` 被访问。" +"后端可以设置为 ``K=tc.set_backend(\"jax\")`` ，``K``作为常规机器学习框架的全套API的后端，也可以通过``tc" +" .backend`` 被访问。" #: ../../source/quickstart.rst:272 #, fuzzy msgid "" -"The supported APIs in the backend come from two sources, one part is implemented " -"in `TensorNetwork package `__ and the other part is implemented " -"in `TensorCircuit package `__. To " -"see all the backend agnostic APIs, try:" +"The supported APIs in the backend come from two sources, one part is " +"implemented in `TensorNetwork package " +"`__" +" and the other part is implemented in `TensorCircuit package " +"`__. To see all the backend " +"agnostic APIs, try:" msgstr "" -"在后端支持的 APIs 有两个来源 , 一个来自 `TensorNetwork `__ " -"另一个来自 `TensorCircuit package `__。" +"在后端支持的 APIs 有两个来源 , 一个来自 `TensorNetwork " +"`__" +" 另一个来自 `TensorCircuit package `__。" #: ../../source/quickstart.rst:427 msgid "​" @@ -484,20 +476,19 @@ msgstr "转换 dtype" #: ../../source/quickstart.rst:432 msgid "" -"TensorCircuit supports simulation using 32/64 bit precession. The default dtype " -"is 32-bit as \"complex64\". Change this by ``tc.set_dtype(\"complex128\")``." +"TensorCircuit supports simulation using 32/64 bit precession. The default" +" dtype is 32-bit as \"complex64\". Change this by " +"``tc.set_dtype(\"complex128\")``." msgstr "" "TensorCircuit 支持使用 32/64 bit 精确度的模拟。默认的 dtype 是 32-bit 的 " -"\"complex64\"。可以通过 ``tc.set_dtype(\"complex128\")`` 把 dtype 改为 " -"\"complex 128\" 。" +"\"complex64\"。可以通过 ``tc.set_dtype(\"complex128\")`` 把 dtype 改为 \"complex" +" 128\" 。" #: ../../source/quickstart.rst:435 msgid "" -"``tc.dtypestr`` always returns the current dtype string: either \"complex64\" or " -"\"complex128\"." -msgstr "" -"``tc.dtypestr`` 总会返回当前的 dtype 字符串: 不是 \"complex64\" 就是 " -"\"complex128\"." +"``tc.dtypestr`` always returns the current dtype string: either " +"\"complex64\" or \"complex128\"." +msgstr "``tc.dtypestr`` 总会返回当前的 dtype 字符串: 不是 \"complex64\" 就是 \"complex128\"." #: ../../source/quickstart.rst:439 msgid "Setup the Contractor" @@ -505,29 +496,29 @@ msgstr "设置 contractor" #: ../../source/quickstart.rst:441 msgid "" -"TensorCircuit is a tensornetwork contraction-based quantum circuit simulator. A " -"contractor is for searching for the optimal contraction path of the circuit " -"tensornetwork." -msgstr "" -"TensorCircuit 是一个基于张量网络收缩的量子电路模拟器。 contractor 用于搜索电路张" -"量网络的最佳收缩路径。" +"TensorCircuit is a tensornetwork contraction-based quantum circuit " +"simulator. A contractor is for searching for the optimal contraction path" +" of the circuit tensornetwork." +msgstr "TensorCircuit 是一个基于张量网络收缩的量子电路模拟器。 contractor 用于搜索电路张量网络的最佳收缩路径。" #: ../../source/quickstart.rst:443 msgid "" -"There are various advanced contractors provided by third-party packages, such as " -"`opt-einsum `__ and `cotengra `__." +"There are various advanced contractors provided by third-party packages, " +"such as `opt-einsum `__ and " +"`cotengra `__." msgstr "" -"有各种第三方包提供的高级 contractor ，例如 `opt-einsum `__ 和 `cotengra `__ 。" +"有各种第三方包提供的高级 contractor ，例如 `opt-einsum " +"`__ 和 `cotengra " +"`__ 。" #: ../../source/quickstart.rst:445 msgid "" -"`opt-einsum` is shipped with TensorNetwork package. To use cotengra, one needs " -"to pip install it; kahypar is also recommended to install with cotengra." +"`opt-einsum` is shipped with TensorNetwork package. To use cotengra, one " +"needs to pip install it; kahypar is also recommended to install with " +"cotengra." msgstr "" -"`opt-einsum` 随 TensorNetwork 软件包一起。如要使用 cotengra，则需要 pip 安装它； " -"还建议安装 cotengra 随 kahypar 一起使用。" +"`opt-einsum` 随 TensorNetwork 软件包一起。如要使用 cotengra，则需要 pip 安装它； 还建议安装 " +"cotengra 随 kahypar 一起使用。" #: ../../source/quickstart.rst:447 msgid "Some setup cases:" @@ -536,15 +527,17 @@ msgstr "一些设置案例：" #: ../../source/quickstart.rst:473 #, fuzzy msgid "" -"For advanced configurations on cotengra contractors, please refer to cotengra " -"`doc `__ and more fancy " -"examples can be found at `contractor tutorial `__." +"For advanced configurations on cotengra contractors, please refer to " +"cotengra `doc " +"`__ and more " +"fancy examples can be found at `contractor tutorial `__." msgstr "" -"有关 cotengra contractor 的高级配置，请参阅 cotengra `doc `__ 更多精彩示例在 `contractor 教程 " -"`__." +"有关 cotengra contractor 的高级配置，请参阅 cotengra `doc " +"`__ 更多精彩示例在 " +"`contractor 教程 `__." #: ../../source/quickstart.rst:475 msgid "**Setup in Function or Context Level**" @@ -552,11 +545,9 @@ msgstr "**函数和上下文级别的设置**" #: ../../source/quickstart.rst:477 msgid "" -"Beside global level setup, we can also setup the backend, the dtype, and the " -"contractor at the function level or context manager level:" -msgstr "" -"除了全局级别设置，我们还可以在函数级别或上下文管理器级别设置后端、dtype 和" -"contractor：" +"Beside global level setup, we can also setup the backend, the dtype, and " +"the contractor at the function level or context manager level:" +msgstr "除了全局级别设置，我们还可以在函数级别或上下文管理器级别设置后端、dtype 和contractor：" #: ../../source/quickstart.rst:495 msgid "Noisy Circuit Simulation" @@ -568,12 +559,12 @@ msgstr "**蒙特卡洛态模拟器**" #: ../../source/quickstart.rst:499 msgid "" -"For the Monte Carlo trajectory noise simulator, the unitary Kraus channel can be " -"handled easily. TensorCircuit also supports fully jittable and differentiable " -"general Kraus channel Monte Carlo simulation, though." +"For the Monte Carlo trajectory noise simulator, the unitary Kraus channel" +" can be handled easily. TensorCircuit also supports fully jittable and " +"differentiable general Kraus channel Monte Carlo simulation, though." msgstr "" -"对于蒙特卡洛轨迹噪声模拟器，可以轻松处理幺正的 Kraus 通道。 不过，TensorCircuit " -"还支持完全可即时编译和可微分的通用 Kraus 通道蒙特卡罗模拟。" +"对于蒙特卡洛轨迹噪声模拟器，可以轻松处理幺正的 Kraus 通道。 不过，TensorCircuit 还支持完全可即时编译和可微分的通用 " +"Kraus 通道蒙特卡罗模拟。" #: ../../source/quickstart.rst:526 msgid "**Density Matrix Simulator:**" @@ -581,12 +572,10 @@ msgstr "**密度矩阵模拟器**" #: ../../source/quickstart.rst:528 msgid "" -"Density matrix simulator ``tc.DMCircuit`` simulates the noise in a full form, " -"but takes twice qubits to do noiseless simulation. The API is the same as ``tc." -"Circuit``." -msgstr "" -"密度矩阵模拟器``tc.DMCircuit`` 以完整形式模拟噪声，但需要两倍的量子比特。API 与 " -"``tc.Circuit`` 基本相同。" +"Density matrix simulator ``tc.DMCircuit`` simulates the noise in a full " +"form, but takes twice qubits to do noiseless simulation. The API is the " +"same as ``tc.Circuit``." +msgstr "密度矩阵模拟器``tc.DMCircuit`` 以完整形式模拟噪声，但需要两倍的量子比特。API 与 ``tc.Circuit`` 基本相同。" #: ../../source/quickstart.rst:547 msgid "**Experiment with quantum errors:**" @@ -602,8 +591,8 @@ msgstr "" #: ../../source/quickstart.rst:567 msgid "" -"Readout error can be added in experiments for sampling and expectation value " -"calculation." +"Readout error can be added in experiments for sampling and expectation " +"value calculation." msgstr "" #: ../../source/quickstart.rst:593 @@ -612,27 +601,27 @@ msgstr "矩阵乘积状态和矩阵乘积算子" #: ../../source/quickstart.rst:595 msgid "" -"TensorCircuit has its class for MPS and MPO originally defined in TensorNetwork " -"as ``tc.QuVector``, ``tc.QuOperator``." +"TensorCircuit has its class for MPS and MPO originally defined in " +"TensorNetwork as ``tc.QuVector``, ``tc.QuOperator``." msgstr "" -"TensorCircuit 有自己的 MPS 和 MPO 类，起初在 TensorNetwork 中定义为“tc.QuVector” " -"和 “tc.QuOperator”。" +"TensorCircuit 有自己的 MPS 和 MPO 类，起初在 TensorNetwork 中定义为“tc.QuVector” 和 " +"“tc.QuOperator”。" #: ../../source/quickstart.rst:597 msgid "" -"``tc.QuVector`` can be extracted from ``tc.Circuit`` as the tensor network form " -"for the output state (uncontracted) by ``c.quvector()``." +"``tc.QuVector`` can be extracted from ``tc.Circuit`` as the tensor " +"network form for the output state (uncontracted) by ``c.quvector()``." msgstr "" -"作为``c.quvector()`` 的输出状态（未收缩）的张量网络形式，``tc.QuVector`` 可以从" -"``tc.Circuit`` 中提取。" +"作为``c.quvector()`` 的输出状态（未收缩）的张量网络形式，``tc.QuVector`` 可以从``tc.Circuit`` " +"中提取。" #: ../../source/quickstart.rst:599 msgid "" -"The QuVector forms a wavefunction w, which can also be fed into Circuit as the " -"inputs state as ``c=tc.Circuit(n, mps_inputs=w)``." +"The QuVector forms a wavefunction w, which can also be fed into Circuit " +"as the inputs state as ``c=tc.Circuit(n, mps_inputs=w)``." msgstr "" -"QuVector 形成一个波函数 w，它也可以作为 ``c=tc.Circuit(n, mps_inputs=w)`` 的输入" -"状态输入到 Circuit 中。" +"QuVector 形成一个波函数 w，它也可以作为 ``c=tc.Circuit(n, mps_inputs=w)`` 的输入状态输入到 " +"Circuit 中。" #: ../../source/quickstart.rst:601 msgid "MPS as input state for circuit" @@ -640,8 +629,8 @@ msgstr "MPS 作为电路的输入状态" #: ../../source/quickstart.rst:603 msgid "" -"The MPS/QuVector representation of the input state has a more efficient and " -"compact form." +"The MPS/QuVector representation of the input state has a more efficient " +"and compact form." msgstr "输入状态的 MPS/QuVector 表示具有更高效和紧凑的形式。" #: ../../source/quickstart.rst:615 @@ -660,12 +649,14 @@ msgstr "MPO 作为电路上的门" #: ../../source/quickstart.rst:636 msgid "" -"Instead of a common quantum gate in matrix/node format, we can directly apply a " -"gate in MPO/QuOperator format." +"Instead of a common quantum gate in matrix/node format, we can directly " +"apply a gate in MPO/QuOperator format." msgstr "代替矩阵/节点格式的普通量子门，我们可以直接应用 MPO/QuOperator 格式的门。" #: ../../source/quickstart.rst:647 -msgid "The representative gate defined in MPO format is the ``multicontrol`` gate." +msgid "" +"The representative gate defined in MPO format is the ``multicontrol`` " +"gate." msgstr "以 MPO 格式定义的代表门是 ``multicontrol`` 门。" #: ../../source/quickstart.rst:649 @@ -674,8 +665,8 @@ msgstr "MPO作为电路期望估测算子" #: ../../source/quickstart.rst:651 msgid "" -"We can also measure operator expectation on the circuit output state where the " -"operator is in MPO/QuOperator format." +"We can also measure operator expectation on the circuit output state " +"where the operator is in MPO/QuOperator format." msgstr "我们还可以测量运算符对 MPO/QuOperator 格式的电路输出状态的期望。" #: ../../source/quickstart.rst:663 @@ -688,46 +679,47 @@ msgstr "**与 PyTorch 模块混合的 PyTorch 接口：**" #: ../../source/quickstart.rst:667 msgid "" -"As we have mentioned in the backend section, the PyTorch backend may lack " -"advanced features. This doesn't mean we cannot hybrid the advanced circuit " -"module with PyTorch neural module. We can run the quantum function on TensorFlow " -"or Jax backend while wrapping it with a Torch interface." +"As we have mentioned in the backend section, the PyTorch backend may lack" +" advanced features. This doesn't mean we cannot hybrid the advanced " +"circuit module with PyTorch neural module. We can run the quantum " +"function on TensorFlow or Jax backend while wrapping it with a Torch " +"interface." msgstr "" -"正如我们在后端部分提到的，PyTorch 后端可能缺少高级功能。 这并不意味着我们不能将高" -"级量子电路模块与 PyTorch 神经模块混合。 我们可以在 TensorFlow 或 Jax 后端运行量子" -"函数，同时使用 Torch 接口包装它。 " +"正如我们在后端部分提到的，PyTorch 后端可能缺少高级功能。 这并不意味着我们不能将高级量子电路模块与 PyTorch 神经模块混合。 " +"我们可以在 TensorFlow 或 Jax 后端运行量子函数，同时使用 Torch 接口包装它。 " #: ../../source/quickstart.rst:694 msgid "" -"For a GPU/CPU, torch/tensorflow, quantum/classical hybrid machine learning " -"pipeline enabled by tensorcircuit, see `example script `__." +"For a GPU/CPU, torch/tensorflow, quantum/classical hybrid machine " +"learning pipeline enabled by tensorcircuit, see `example script " +"`__." msgstr "" #: ../../source/quickstart.rst:696 msgid "" -"There is also a more flexible torch interface that support static non-tensor " -"inputs as keyword arguments, which can be utilized as below:" +"There is also a more flexible torch interface that support static non-" +"tensor inputs as keyword arguments, which can be utilized as below:" msgstr "" #: ../../source/quickstart.rst:710 msgid "" -"We also provider wrapper of quantum function for torch module as :py:meth:" -"`tensorcircuit.TorchLayer` alias to :py:meth:`tensorcircuit.torchnn.QuantumNet`." +"We also provider wrapper of quantum function for torch module as " +":py:meth:`tensorcircuit.TorchLayer` alias to " +":py:meth:`tensorcircuit.torchnn.QuantumNet`." msgstr "" #: ../../source/quickstart.rst:712 msgid "" -"For ``TorchLayer``, ``use_interface=True`` is by default, which natively allow " -"the quantum function defined on other tensorcircuit backends, such as jax or tf " -"for speed consideration." +"For ``TorchLayer``, ``use_interface=True`` is by default, which natively " +"allow the quantum function defined on other tensorcircuit backends, such " +"as jax or tf for speed consideration." msgstr "" #: ../../source/quickstart.rst:714 msgid "" -"``TorchLayer`` can process multiple input arguments as multiple function inputs, " -"following torch practice." +"``TorchLayer`` can process multiple input arguments as multiple function " +"inputs, following torch practice." msgstr "" #: ../../source/quickstart.rst:742 @@ -736,28 +728,29 @@ msgstr "" #: ../../source/quickstart.rst:744 msgid "" -"Similar rules apply similar as torch interface. The interface can even be used " -"within jit environment outside. See :py:meth:`tensorcircuit.interfaces." -"tensorflow.tensorflow_interface`." +"Similar rules apply similar as torch interface. The interface can even be" +" used within jit environment outside. See " +":py:meth:`tensorcircuit.interfaces.tensorflow.tensorflow_interface`." msgstr "" #: ../../source/quickstart.rst:747 msgid "" -"We also provider ``enable_dlpack=True`` option in torch and tf interfaces, which " -"allow the tensor transformation happen without memory transfer via dlpack, " -"higher version of tf or torch package required." +"We also provider ``enable_dlpack=True`` option in torch and tf " +"interfaces, which allow the tensor transformation happen without memory " +"transfer via dlpack, higher version of tf or torch package required." msgstr "" #: ../../source/quickstart.rst:750 msgid "" -"We also provider wrapper of quantum function for keras layer as :py:meth:" -"`tensorcircuit.KerasLayer` alias to :py:meth:`tensorcircuit.keras.KerasLayer`." +"We also provider wrapper of quantum function for keras layer as " +":py:meth:`tensorcircuit.KerasLayer` alias to " +":py:meth:`tensorcircuit.keras.KerasLayer`." msgstr "" #: ../../source/quickstart.rst:752 msgid "" -"``KerasLayer`` can process multiple input arguments with the input as a dict, " -"following the common keras practice, see example below." +"``KerasLayer`` can process multiple input arguments with the input as a " +"dict, following the common keras practice, see example below." msgstr "" #: ../../source/quickstart.rst:774 @@ -766,11 +759,9 @@ msgstr "**使用 scipy接口使用scipy优化器：**" #: ../../source/quickstart.rst:776 msgid "" -"Automatically transform quantum functions as scipy-compatible values and grad " -"functions as provided for scipy interface with ``jac=True``." -msgstr "" -"为带有 jac=True 的 scipy 接口自动将量子函数转换为与 scipy 兼容的 value 和 grad 函" -"数。" +"Automatically transform quantum functions as scipy-compatible values and " +"grad functions as provided for scipy interface with ``jac=True``." +msgstr "为带有 jac=True 的 scipy 接口自动将量子函数转换为与 scipy 兼容的 value 和 grad 函数。" #: ../../source/quickstart.rst:802 msgid "Templates as Shortcuts" @@ -785,18 +776,20 @@ msgid "Ising type Hamiltonian defined on a general graph" msgstr "在一般图上定义的伊辛型哈密顿量" #: ../../source/quickstart.rst:808 -msgid "See :py:meth:`tensorcircuit.templates.measurements.spin_glass_measurements`" -msgstr "" -"参考 :py:meth:`tensorcircuit.templates.measurements.spin_glass_measurements`" +msgid "" +"See " +":py:meth:`tensorcircuit.templates.measurements.spin_glass_measurements`" +msgstr "参考 :py:meth:`tensorcircuit.templates.measurements.spin_glass_measurements`" #: ../../source/quickstart.rst:810 msgid "Heisenberg Hamiltonian on a general graph with possible external fields" msgstr "具有可能存在的外场的一般图上的海森堡哈密顿量" #: ../../source/quickstart.rst:812 -msgid "See :py:meth:`tensorcircuit.templates.measurements.heisenberg_measurements`" -msgstr "" -"参考 :py:meth:`tensorcircuit.templates.measurements.heisenberg_measurements`" +msgid "" +"See " +":py:meth:`tensorcircuit.templates.measurements.heisenberg_measurements`" +msgstr "参考 :py:meth:`tensorcircuit.templates.measurements.heisenberg_measurements`" #: ../../source/quickstart.rst:814 msgid "**Circuit Blocks:**" @@ -812,45 +805,71 @@ msgstr "**电路块**" #~ msgstr "从GitHub安装" #~ msgid "" -#~ "For beta version usage, one needs to install tensorcircuit package from " -#~ "GitHub. For development and PR workflow, please refer to `contribution " +#~ "For beta version usage, one needs " +#~ "to install tensorcircuit package from " +#~ "GitHub. For development and PR workflow," +#~ " please refer to `contribution " #~ "`__ instead." #~ msgstr "" -#~ "如需使用测试版本，则需要从 GitHub 安装 tensorcircuit。对于开发和 PR 工作流程，" -#~ "请另外参考 `贡献 `__ 。" +#~ "如需使用测试版本，则需要从 GitHub 安装 tensorcircuit。对于开发和 PR" +#~ " 工作流程，请另外参考 `贡献 `__ 。" #~ msgid "" -#~ "For private tensorcircuit-dev repo, one needs to first configure the SSH key " -#~ "on GitHub and locally, please refer to `GitHub doc `__" +#~ "For private tensorcircuit-dev repo, one" +#~ " needs to first configure the SSH " +#~ "key on GitHub and locally, please " +#~ "refer to `GitHub doc " +#~ "`__" #~ msgstr "" -#~ "对于私有 tensorcircuit 开发库，首先需要在 GitHub 和本地配置 SSH 密钥, 请参考 " -#~ "`GitHub 文档 `__" +#~ "对于私有 tensorcircuit 开发库，首先需要在 GitHub 和本地配置 " +#~ "SSH 密钥, 请参考 `GitHub 文档 " +#~ "`__" #~ msgid "" -#~ "Then try ``pip3 install --force-reinstall git+ssh://git@github.com/quclub/" -#~ "tensorcircuit-dev.git`` in shell." +#~ "Then try ``pip3 install --force-" +#~ "reinstall git+ssh://git@github.com/quclub/tensorcircuit-" +#~ "dev.git`` in shell." #~ msgstr "" -#~ "然后尝试在命令行窗口中输入 ``pip3 install --force-reinstall git+ssh://" -#~ "git@github.com/quclub/tensorcircuit-dev.git`` 。" +#~ "然后尝试在命令行窗口中输入 ``pip3 install --force-reinstall" +#~ " git+ssh://git@github.com/quclub/tensorcircuit-dev.git`` " +#~ "。" #~ msgid "" -#~ "Depending on one's need, one may further pip install tensorflow (for " -#~ "TensorFlow backend) or jax and jaxlib (for jax backend) or `cotengra `__ (for more advanced tensornetwork contraction " -#~ "path solver)." +#~ "Depending on one's need, one may " +#~ "further pip install tensorflow (for " +#~ "TensorFlow backend) or jax and jaxlib" +#~ " (for jax backend) or `cotengra " +#~ "`__ (for more " +#~ "advanced tensornetwork contraction path " +#~ "solver)." #~ msgstr "" -#~ "基于个人情况，用户可能需要进一步安装 tensorflow, jax 或 jaxlib 或 `cotengra " -#~ "`_ 以满足后端要求。" +#~ "基于个人情况，用户可能需要进一步安装 tensorflow, jax 或 jaxlib" +#~ " 或 `cotengra `_" +#~ " 以满足后端要求。" #~ msgid "" -#~ "If one needs circuit visualization on JupyterLab, python package `wand " -#~ "`__ and its binary bindings, as well as " -#~ "LaTeX installation, are required." +#~ "If one needs circuit visualization on" +#~ " JupyterLab, python package `wand " +#~ "`__ and its " +#~ "binary bindings, as well as LaTeX " +#~ "installation, are required." #~ msgstr "" -#~ "如果需要在 JupyterLab 中进行电路可视化，则需要 python 库 `wand `__ 及其二进制绑定以及 LaTeX 的安装。" +#~ "如果需要在 JupyterLab 中进行电路可视化，则需要 python 库 " +#~ "`wand `__ " +#~ "及其二进制绑定以及 LaTeX 的安装。" #~ msgid "Import from Qiskit: ``c = tc.Circuit.from_qiskit(QuantumCircuit, n)``" #~ msgstr "从 Qiskit 导入：``c = tc.Circuit.from_qiskit(QuantumCircuit, n)``" + +#~ msgid "For x86 Linux or Mac," +#~ msgstr "" + +#~ msgid "" +#~ "For Mac with M series chips (arm" +#~ " architecture), please refer to `TC " +#~ "on Mac M series " +#~ "`_." +#~ msgstr "" + diff --git a/docs/source/modules.rst b/docs/source/modules.rst index 280c7584..0144a199 100644 --- a/docs/source/modules.rst +++ b/docs/source/modules.rst @@ -1,5 +1,5 @@ tensorcircuit -================================================== +================================================================================ .. toctree:: ./api/about.rst ./api/abstractcircuit.rst @@ -13,6 +13,7 @@ tensorcircuit ./api/cons.rst ./api/densitymatrix.rst ./api/experimental.rst + ./api/fgs.rst ./api/gates.rst ./api/interfaces.rst ./api/keras.rst @@ -21,6 +22,7 @@ tensorcircuit ./api/noisemodel.rst ./api/quantum.rst ./api/results.rst + ./api/shadows.rst ./api/simplify.rst ./api/templates.rst ./api/torchnn.rst diff --git a/docs/source/modules.rst.backup b/docs/source/modules.rst.backup index 28261e24..280c7584 100644 --- a/docs/source/modules.rst.backup +++ b/docs/source/modules.rst.backup @@ -1,200 +1,29 @@ -tensorcircuit API -===================== - +tensorcircuit +================================================== .. toctree:: - :maxdepth: 4 - - -tensorcircuit.backends module ------------------------------------- - -.. automodule:: tensorcircuit.backends - :members: - :undoc-members: - :show-inheritance: - -tensorcircuit.backends.backend_factory module -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - -.. automodule:: tensorcircuit.backends.backend_factory - :members: - :undoc-members: - :show-inheritance: - -tensorcircuit.backends.jax_backend module -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - -.. automodule:: tensorcircuit.backends.jax_backend - :members: - :undoc-members: - :show-inheritance: - -tensorcircuit.backends.numpy_backend module -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - -.. automodule:: tensorcircuit.backends.numpy_backend - :members: - :undoc-members: - :show-inheritance: - -tensorcircuit.backends.pytorch_backend module -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - -.. automodule:: tensorcircuit.backends.pytorch_backend - :members: - :undoc-members: - :show-inheritance: - -tensorcircuit.backends.tensorflow_backend module -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - -.. automodule:: tensorcircuit.backends.tensorflow_backend - :members: - :undoc-members: - :show-inheritance: - -tensorcircuit.channels module -------------------------------------- - -.. automodule:: tensorcircuit.channels - :members: - :undoc-members: - :show-inheritance: - -tensorcircuit.circuit module -------------------------------------- - -.. automodule:: tensorcircuit.circuit - :members: - :undoc-members: - :show-inheritance: - - -tensorcircuit.cons module -------------------------------------- - -.. automodule:: tensorcircuit.cons - :members: - :undoc-members: - :show-inheritance: - -tensorcircuit.densitymatrix module -------------------------------------- - -.. automodule:: tensorcircuit.densitymatrix - :members: - :undoc-members: - :show-inheritance: - -tensorcircuit.densitymatrix2 module -------------------------------------- - -.. automodule:: tensorcircuit.densitymatrix2 - :members: - :undoc-members: - :show-inheritance: - -tensorcircuit.experimental module -------------------------------------- - -.. automodule:: tensorcircuit.experimental - :members: - :undoc-members: - :show-inheritance: - - -tensorcircuit.gates module ---------------------------------- - -.. automodule:: tensorcircuit.gates - :members: - :undoc-members: - :show-inheritance: - -tensorcircuit.interfaces module ---------------------------------- - -.. automodule:: tensorcircuit.interfaces - :members: - :undoc-members: - :show-inheritance: - -tensorcircuit.keras module ---------------------------------- - -.. automodule:: tensorcircuit.keras - :members: - :undoc-members: - :show-inheritance: - -tensorcircuit.mpscircuit module ---------------------------------- - -.. automodule:: tensorcircuit.mpscircuit - :members: - :undoc-members: - :show-inheritance: - -tensorcircuit.quantum module ---------------------------------- - -.. automodule:: tensorcircuit.quantum - :members: - :undoc-members: - :show-inheritance: - -tensorcircuit.simplify module ---------------------------------- - -.. automodule:: tensorcircuit.simplify - :members: - :undoc-members: - :show-inheritance: - -tensorcircuit.templates module ------------------------------------- - -.. automodule:: tensorcircuit.templates - :members: - :undoc-members: - :show-inheritance: - -tensorcircuit.templates.blocks module -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - -.. automodule:: tensorcircuit.templates.blocks - :members: - :undoc-members: - :show-inheritance: - -tensorcircuit.templates.graphs module -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - -.. automodule:: tensorcircuit.templates.graphs - :members: - :undoc-members: - :show-inheritance: - -tensorcircuit.templates.measurements module -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - -.. automodule:: tensorcircuit.templates.measurements - :members: - :undoc-members: - :show-inheritance: - -tensorcircuit.utils module ---------------------------------- - -.. automodule:: tensorcircuit.utils - :members: - :undoc-members: - :show-inheritance: - -tensorcircuit.vis module ---------------------------------- - -.. automodule:: tensorcircuit.vis - :members: - :undoc-members: - :show-inheritance: \ No newline at end of file + ./api/about.rst + ./api/abstractcircuit.rst + ./api/applications.rst + ./api/backends.rst + ./api/basecircuit.rst + ./api/channels.rst + ./api/circuit.rst + ./api/cloud.rst + ./api/compiler.rst + ./api/cons.rst + ./api/densitymatrix.rst + ./api/experimental.rst + ./api/gates.rst + ./api/interfaces.rst + ./api/keras.rst + ./api/mps_base.rst + ./api/mpscircuit.rst + ./api/noisemodel.rst + ./api/quantum.rst + ./api/results.rst + ./api/simplify.rst + ./api/templates.rst + ./api/torchnn.rst + ./api/translation.rst + ./api/utils.rst + ./api/vis.rst \ No newline at end of file diff --git a/docs/source/quickstart.rst b/docs/source/quickstart.rst index 9767d08f..647066b6 100644 --- a/docs/source/quickstart.rst +++ b/docs/source/quickstart.rst @@ -5,7 +5,7 @@ Quick Start Installation -------------- -- For x86 Linux or Mac, +- For x86 Linux, ``pip install tensorcircuit`` @@ -29,7 +29,7 @@ For more details on docker setup, please refer to `docker readme `_ or `TC via WSL `_. -- For Mac with M series chips (arm architecture), please refer to `TC on Mac M series `_. +- For MacOS, please refer to `TC on Mac `_. Overall, the installation of TensorCircuit is simple, since it is purely in Python and hence very portable. As long as the users can take care of the installation of ML frameworks on the corresponding system, TensorCircuit will work as expected. @@ -148,6 +148,8 @@ The IR is given as a list, each element is a dict containing information on one >>> c.to_qir() [{'gate': cnot, 'index': (0, 1), 'name': 'cnot', 'split': None}, {'gate': crx, 'index': (1, 0), 'name': 'crx', 'split': None, 'parameters': {'theta': 0.2}}] +We can also create new copied circuit via ``c.copy()`` which internally utilize the ``qir``. + Programming Paradigm ------------------------- diff --git a/docs/source/statics/landscape.jpg b/docs/source/statics/landscape.jpg new file mode 100644 index 00000000..3ffd7902 Binary files /dev/null and b/docs/source/statics/landscape.jpg differ diff --git a/docs/source/statics/qd_alg.jpg b/docs/source/statics/qd_alg.jpg new file mode 100644 index 00000000..3300f074 Binary files /dev/null and b/docs/source/statics/qd_alg.jpg differ diff --git a/docs/source/statics/tianxuan_s1.png b/docs/source/statics/tianxuan_s1.png new file mode 100644 index 00000000..983ac187 Binary files /dev/null and b/docs/source/statics/tianxuan_s1.png differ diff --git a/docs/source/tutorial.rst b/docs/source/tutorial.rst index 2596f072..e5697960 100644 --- a/docs/source/tutorial.rst +++ b/docs/source/tutorial.rst @@ -6,6 +6,9 @@ Jupyter Tutorials tutorials/circuit_basics.ipynb tutorials/qaoa.ipynb + tutorials/qaoa_bo.ipynb + tutorials/qaoa_nae3sat.ipynb + tutorials/qaoa_quantum_dropout.ipynb tutorials/tfim_vqe.ipynb tutorials/mnist_qml.ipynb tutorials/torch_qml.ipynb @@ -20,4 +23,9 @@ Jupyter Tutorials tutorials/vqex_mbl.ipynb tutorials/dqas.ipynb tutorials/barren_plateaus.ipynb - tutorials/qaoa_portfolio_optimization.ipynb \ No newline at end of file + tutorials/qubo_problem.ipynb + tutorials/portfolio_optimization.ipynb + tutorials/imag_time_evo.ipynb + tutorials/classical_shadows.ipynb + tutorials/sklearn_svc.ipynb + tutorials/qcloud_sdk_demo.ipynb \ No newline at end of file diff --git a/docs/source/tutorial_cn.rst b/docs/source/tutorial_cn.rst index a6f4d03f..956d03b6 100644 --- a/docs/source/tutorial_cn.rst +++ b/docs/source/tutorial_cn.rst @@ -19,4 +19,5 @@ tutorials/optimization_and_expressibility_cn.ipynb tutorials/vqex_mbl_cn.ipynb tutorials/dqas_cn.ipynb - tutorials/barren_plateaus_cn.ipynb \ No newline at end of file + tutorials/barren_plateaus_cn.ipynb + tutorials/sklearn_svc_cn.ipynb \ No newline at end of file diff --git a/docs/source/tutorials/barren_plateaus_cn.ipynb b/docs/source/tutorials/barren_plateaus_cn.ipynb index 4288475f..6f5a8a49 100644 --- a/docs/source/tutorials/barren_plateaus_cn.ipynb +++ b/docs/source/tutorials/barren_plateaus_cn.ipynb @@ -158,7 +158,9 @@ " dtype=\"float32\",\n", ")\n", "\n", - "e, grad = op_expectation_vmap_vvag(params, seed, n, nlayers) # 不同随机电路的 ZZ 可观测量和梯度的期望\n", + "e, grad = op_expectation_vmap_vvag(\n", + " params, seed, n, nlayers\n", + ") # 不同随机电路的 ZZ 可观测量和梯度的期望\n", "\n", "grad_var = tf.math.reduce_std(tf.math.reduce_std(grad, axis=0), axis=0)[\n", " 0, 0\n", diff --git a/docs/source/tutorials/benchmark_circuits.ipynb b/docs/source/tutorials/benchmark_circuits.ipynb new file mode 100644 index 00000000..e2e5eb1d --- /dev/null +++ b/docs/source/tutorials/benchmark_circuits.ipynb @@ -0,0 +1,211 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Benchmark Chips" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Benchmark chips using mirror circuit" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "import networkx as nx\n", + "from tensorcircuit.results import qem\n", + "from tensorcircuit.results.qem import benchmark_circuits\n", + "import random\n", + "import numpy as np\n", + "\n", + "from tensorcircuit.cloud import apis\n", + "from tensorcircuit.results import counts\n", + "from tensorcircuit.compiler.qiskit_compiler import qiskit_compile\n", + "from matplotlib import cm\n", + "\n", + "%matplotlib inline\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0, 1], [6, 2], [4, 0], [0, 4], [8, 4], [1, 5], [3, 7], [0, 3], [2, 0], [5, 1], [3, 0], [7, 3], [0, 2], [2, 6], [4, 8], [1, 0]]\n" + ] + } + ], + "source": [ + "d = apis.get_device(\"tianxuan_s1\")\n", + "couple_list = d.topology()\n", + "print(couple_list)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "nq: [0, 1] depth: 1 success 4.1484000000000005\n", + "nq: [0, 1] depth: 2 success 3.7722999999999995\n", + "nq: [0, 1, 2] depth: 1 success 3.2711\n", + "nq: [0, 1, 2] depth: 2 success 3.2814\n", + "nq: [0, 1, 2, 3] depth: 1 success 3.1682000000000006\n", + "nq: [0, 1, 2, 3] depth: 2 success 2.5158\n", + "nq: [0, 1, 2, 3, 4] depth: 1 success 2.1039999999999996\n", + "nq: [0, 1, 2, 3, 4] depth: 2 success 1.4552999999999998\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "result_list = []\n", + "\n", + "\n", + "for nq in range(2, 6):\n", + " qlis = list(range(nq))\n", + " graph = []\n", + " for i in range(len(couple_list)):\n", + " if couple_list[i][0] in qlis and couple_list[i][1] in qlis:\n", + " graph.append(couple_list[i])\n", + "\n", + " G = nx.Graph()\n", + " G.add_edges_from(graph)\n", + " nx.draw(G, with_labels=True)\n", + "\n", + " for depth in range(1, 3):\n", + " A = 0\n", + " for numc in range(5):\n", + " c, ideal = benchmark_circuits.mirror_circuit(\n", + " depth=depth,\n", + " two_qubit_gate_prob=1,\n", + " connectivity_graph=G,\n", + " seed=random.randint(0, 100),\n", + " ) # includes np.sqrt(X)^{\\dagger} gate,identity gate\n", + "\n", + " c1, info = qiskit_compile(\n", + " c,\n", + " compiled_options={\n", + " \"basis_gates\": [\"h\", \"rz\", \"x\", \"y\", \"z\", \"cz\"],\n", + " \"optimization_level\": 2,\n", + " # \"coupling_map\": d.topology(),\n", + " },\n", + " )\n", + "\n", + " t = apis.submit_task(\n", + " circuit=c1,\n", + " shots=10000,\n", + " device=d,\n", + " enable_qos_qubit_mapping=False,\n", + " enable_qos_gate_decomposition=False,\n", + " )\n", + " raw_count = t.results(blocked=True) # position_counts=logical_counts\n", + " # print(\"raw\",raw_count[list(ideal.keys())[0]]/10000)\n", + "\n", + " A += raw_count[list(ideal.keys())[0]] / 10000\n", + " print(\"nq:\", qlis, \"depth:\", depth, \"success\", A)\n", + " result_list.append(A)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "result_list1 = [i / 5 for i in result_list]\n", + "result_list2 = np.reshape(result_list1, [4, 2])" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, 'Depth')" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "Z = np.transpose(result_list2)\n", + "X = list(range(2, 6))\n", + "Y = list(range(1, 3))\n", + "p = ax.pcolor(X, Y, Z, vmin=Z.min(), vmax=Z.max(), cmap=\"rainbow\")\n", + "cb = fig.colorbar(p, ax=ax)\n", + "plt.xlabel(\"Nqubit\")\n", + "plt.ylabel(\"Depth\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.8.13 ('tf')", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.13" + }, + "orig_nbformat": 4, + "vscode": { + "interpreter": { + "hash": "4d2770c334f3778740193ba4b3686745ae5c2e3ee10c8c0d673798cf1c2fcefe" + } + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/docs/source/tutorials/classical_shadows.ipynb b/docs/source/tutorials/classical_shadows.ipynb new file mode 100644 index 00000000..e6776482 --- /dev/null +++ b/docs/source/tutorials/classical_shadows.ipynb @@ -0,0 +1,795 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# Classical Shadows in Pauli Basis" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "## Overview" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "[Classical shadows](https://www.nature.com/articles/s41567-020-0932-7) formalism is an efficient method to estimate multiple observables. In this tutorial, we will show how to use the ``shadows`` module in ``TensorCircuit`` to implement classic shadows in Pauli basis." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "Let's first briefly review the classical shadows in Pauli basis. For an $n$-qubit quantum state $\\rho$, we randomly perform Pauli projection measurement on each qubit and obtain a snapshot like $\\{1,-1,-1,1,\\cdots,1,-1\\}$. This process is equivalent to apply a random unitary $U_i$ to $\\rho$ and measure in computational basis to obtain $|b_i\\rangle=|s_{i1}\\cdots s_{in}\\rangle,\\ s_{ij}\\in\\{0,1\\}$:\n", + "$$\n", + "\\rho\\rightarrow U_i\\rho U_i^{\\dagger}\\xrightarrow{measure}|b_i\\rangle\\langle b_i|,\n", + "$$\n", + "where $U_i=\\bigotimes_{j=1}^{n}u_{ij}$, $u_{ij}\\in\\{H, HS^{\\dagger}, \\mathbb{I}\\}$ correspond to the projection measurements of Pauli $X$, $Y$, $Z$ respectively. Then we reverse the operation to get the equivalent measurement result on $\\rho$:\n", + "$$\n", + "\\rho\\xrightarrow{measure}U_i^{\\dagger}|b_i\\rangle\\langle b_i| U_i.\n", + "$$\n", + "Moreover, we perform $N$ random measurements and view their average as a quantum channel:\n", + "$$\n", + "\\mathbb{E}\\left[U_i^{\\dagger}|b_i\\rangle\\langle b_i|U_i\\right]=\\mathcal{M}(\\rho),\n", + "$$\n", + "we can invert the channel to get the approximation of $\\rho$:\n", + "$$\n", + "\\rho=\\mathbb{E}\\left[\\mathcal{M}^{-1}(U_i^{\\dagger}|b_i\\rangle\\langle b_i|U_i)\\right].\n", + "$$\n", + "We call each $\\rho_i=\\mathcal{M}^{-1}(U_i^{\\dagger}|b_i\\rangle\\langle b_i|U_i)$ a shadow snapshot state and their ensemble $S(\\rho;N)=\\{\\rho_i|i=1,\\cdots,N\\}$ classical shadows." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "In Pauli basis, we have a simple expression of $\\mathcal{M}^{-1}$:\n", + "$$\n", + "\\begin{split}\n", + " \\rho_i&=\\mathcal{M}^{-1}(U_i^{\\dagger}|b_i\\rangle\\langle b_i|U_i)=\\bigotimes_{j=1}^{n}\\left(3u_{ij}^{\\dagger}|s_{ij}\\rangle\\langle s_{ij}|u_{ij}-\\mathbb{I}\\right),\\\\\n", + " \\rho&=\\frac{1}{N}\\sum_{i=1}^{N}\\rho_i\\ .\n", + "\\end{split}\n", + "$$\n", + "For an observable Pauli string $O=\\bigotimes_{j=1}^{n}P_j,\\ P_j\\in\\{\\mathbb{I}, X, Y, Z\\}$, we can directly use $\\rho$ to calculate $\\langle O\\rangle=\\text{Tr}(O\\rho)$. In practice, we will divide the classical shadows into $K$ parts to calculate the expectation values independently and take the median to avoid the influence of outliers:\n", + "$$\n", + "\\langle O\\rangle=\\text{median}\\{\\langle O_{(1)}\\rangle,\\cdots,\\langle O_{(K)}\\rangle\\},\n", + "$$\n", + "where\n", + "$$\n", + "\\begin{split}\n", + " \\langle O_{(k)}\\rangle&=\\frac{1}{\\lceil N/K\\rceil}\\sum_{i=(k-1)\\lceil N/K\\rceil+1}^{k\\lceil N/K\\rceil}\\text{Tr}\\left[\\bigotimes_{j=1}^{n}P_j(3u_{ij}^{\\dagger}|s_{ij}\\rangle\\langle s_{ij}|u_{ij}-\\mathbb{I})\\right]\\\\\n", + " &=\\frac{1}{\\lceil N/K\\rceil}\\sum_{i=(k-1)\\lceil N/K\\rceil+1}^{k\\lceil N/K\\rceil}\\prod_{j=1}^n\\text{Tr}\\left[3P_j u_{ij}^{\\dagger}|s_{ij}\\rangle\\langle s_{ij}|u_{ij}\\right].\n", + "\\end{split}\n", + "$$" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "## Setup" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 13, + "outputs": [ + { + "data": { + "text/plain": "('complex128', 'float64')" + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import tensorcircuit as tc\n", + "from tensorcircuit import shadows\n", + "import numpy as np\n", + "from functools import partial\n", + "import time\n", + "import matplotlib.pyplot as plt\n", + "\n", + "tc.set_backend(\"jax\")\n", + "tc.set_dtype(\"complex128\")" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-08-09T04:51:21.649753Z", + "start_time": "2023-08-09T04:51:21.598273400Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "## Construct the Classical Shadow Snapshots" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "We first set the number of qubits $n$ and the number of repeated measurements $r$ on each Pauli string. Then from the target observable Pauli strings $\\{O_i|i=1,\\cdots,M\\}$ (0, 1, 2, and 3 correspond to $\\mathbb{I}$, $X$, $Y$, and $Z$, respectively), the error $\\epsilon$ and the rate of failure $\\delta$, we can use ``shadow_bound`` function to get the total number of snapshots $N$ and the number of equal parts $K$ to split the shadow snapshot states to compute the median of means:\n", + "$$\n", + "\\begin{split}\n", + " K&=2\\log(2M/\\delta),\\\\\n", + " N&=K\\frac{34}{\\epsilon^2}\\max_{1\\le i\\le M}\\left\\|O_i-\\frac{\\text{Tr}(O_i)}{2^n}\\mathbb{I}\\right\\|^2_{\\text{shadow}}=K\\frac{34}{\\epsilon^2}3^{\\max_{1\\le i\\le M}k_i},\n", + "\\end{split}\n", + "$$\n", + "where $k_i$ is the number of nontrivial Pauli matrices in $O_i$. Please refer to the Theorem S1 and Lemma S3 in [Huang, Kueng and Preskill (2020)](https://www.nature.com/articles/s41567-020-0932-7) for the details of proof. It should be noted that ``shadow_bound`` has a certain degree of overestimation of $N$, and so many measurements are not really needed in practice. Moreover, ``shadow_bound`` is not jitable and no need to jit." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 14, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "N: 489600\tK: 16\tnumber of Pauli strings: 97920\n" + ] + } + ], + "source": [ + "n, r = 8, 5\n", + "ps = [\n", + " [1, 0, 0, 0, 0, 0, 0, 2],\n", + " [0, 3, 0, 0, 0, 0, 1, 0],\n", + " [0, 0, 2, 0, 0, 3, 0, 0],\n", + " [0, 0, 0, 1, 2, 0, 0, 0],\n", + " [0, 0, 0, 3, 1, 0, 0, 0],\n", + " [0, 0, 0, 0, 0, 3, 0, 0],\n", + " [0, 0, 0, 0, 0, 0, 2, 0],\n", + " [3, 0, 0, 0, 0, 0, 0, 1],\n", + " [0, 2, 0, 0, 0, 0, 3, 0],\n", + " [0, 0, 1, 0, 0, 2, 0, 0],\n", + "]\n", + "\n", + "epsilon, delta = 0.1, 0.01\n", + "N, K = shadows.shadow_bound(ps, epsilon, delta)\n", + "nps = N // r # number of random selected Pauli strings\n", + "print(f\"N: {N}\\tK: {K}\\tnumber of Pauli strings: {nps}\")" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-08-09T04:51:21.707924900Z", + "start_time": "2023-08-09T04:51:21.604342400Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "Then we use random quantum circuit to generate an entangled state." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 15, + "outputs": [], + "source": [ + "nlayers = 10\n", + "thetas = 2 * np.random.rand(nlayers, n) - 1\n", + "\n", + "c = tc.Circuit(n)\n", + "for i in range(n):\n", + " c.H(i)\n", + "for i in range(nlayers):\n", + " for j in range(n):\n", + " c.cnot(j, (j + 1) % n)\n", + " for j in range(n):\n", + " c.rz(j, theta=thetas[i, j] * np.pi)\n", + "\n", + "psi = c.state()" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-08-09T04:51:21.814604700Z", + "start_time": "2023-08-09T04:51:21.615066400Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "We randomly generate Pauli strings. Since the function after just-in-time (jit) compilation does not support random sampling, we need to generate all random states in advance, that is, variable ``status``." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 16, + "outputs": [], + "source": [ + "pauli_strings = tc.backend.convert_to_tensor(np.random.randint(1, 4, size=(nps, n)))\n", + "status = tc.backend.convert_to_tensor(np.random.rand(nps, r))" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-08-09T04:51:21.815119500Z", + "start_time": "2023-08-09T04:51:21.813574500Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "If ``measurement_only=True`` (default ``False``), the outputs of ``shadow_snapshots`` are snapshot bit strings $\\{b_i=s_{i1}\\cdots s_{in}\\ |i=1,\\cdots,N,\\ s_{ij}\\in\\{0,1\\}\\}$, otherwise the outputs are snapshot states $\\{u_{ij}^{\\dagger}|s_{ij}\\rangle\\langle s_{ij}| u_{ij}\\ |i=1,\\cdots,N,\\ j=1,\\cdots,n\\}$. If you only need to generate one batch of snapshots or generate multiple batches of snapshots with different ``nps`` or ``r``, jit cannot provide speedup. Jit will only accelerate when the same shape of snapshots are generated multiple times." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 17, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "shape of snapshot states: (97920, 5, 8, 2, 2)\n" + ] + } + ], + "source": [ + "@partial(tc.backend.jit, static_argnums=(3,))\n", + "def shadow_ss(psi, pauli_strings, status, measurement_only=False):\n", + " return shadows.shadow_snapshots(\n", + " psi, pauli_strings, status, measurement_only=measurement_only\n", + " )\n", + "\n", + "\n", + "ss_states = shadow_ss(psi, pauli_strings, status) # jit is not necessary here\n", + "print(\"shape of snapshot states:\", ss_states.shape)" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-08-09T04:51:24.715816800Z", + "start_time": "2023-08-09T04:51:21.883673400Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "## Estimate the Expectation Values of Observables" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "Since the operation of taking the median is not jitable, the outputs of ``expectation_ps_shadows`` have $K$ values, and we need to take the median of them." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 18, + "outputs": [], + "source": [ + "def shadow_expec(snapshots_states, ob):\n", + " return shadows.expectation_ps_shadow(snapshots_states, ps=ob, k=K)\n", + "\n", + "\n", + "sejit = tc.backend.jit(shadow_expec)" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-08-09T04:51:25.082792700Z", + "start_time": "2023-08-09T04:51:24.750909500Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "It can be seen from the running time that every time the number of Pauli strings changes, ``shadow_expec`` will be recompiled, but for the same number of Pauli strings but different observables, ``shadow_expec`` will only be compiled once. In the end, the absolute errors given by classical shadows are much smaller than the $\\epsilon=0.1$ we set, so ``shadow_bound`` gives a very loose upper bound." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 19, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "observable: No.0\tnumber of Pauli strings: 1000\ttime: 0.9454922676086426\n", + "observable: No.1\tnumber of Pauli strings: 1000\ttime: 0.001840353012084961\n", + "observable: No.2\tnumber of Pauli strings: 1000\ttime: 0.0014374256134033203\n", + "observable: No.3\tnumber of Pauli strings: 1000\ttime: 0.0013763904571533203\n", + "observable: No.4\tnumber of Pauli strings: 1000\ttime: 0.0013554096221923828\n", + "observable: No.5\tnumber of Pauli strings: 1000\ttime: 0.0013613700866699219\n", + "observable: No.6\tnumber of Pauli strings: 1000\ttime: 0.0013325214385986328\n", + "observable: No.7\tnumber of Pauli strings: 1000\ttime: 0.0013136863708496094\n", + "observable: No.8\tnumber of Pauli strings: 1000\ttime: 0.0013325214385986328\n", + "observable: No.9\tnumber of Pauli strings: 1000\ttime: 0.0013117790222167969\n", + "observable: No.0\tnumber of Pauli strings: 10000\ttime: 0.9969091415405273\n", + "observable: No.1\tnumber of Pauli strings: 10000\ttime: 0.012966394424438477\n", + "observable: No.2\tnumber of Pauli strings: 10000\ttime: 0.012765884399414062\n", + "observable: No.3\tnumber of Pauli strings: 10000\ttime: 0.012974739074707031\n", + "observable: No.4\tnumber of Pauli strings: 10000\ttime: 0.012665033340454102\n", + "observable: No.5\tnumber of Pauli strings: 10000\ttime: 0.012889623641967773\n", + "observable: No.6\tnumber of Pauli strings: 10000\ttime: 0.013180255889892578\n", + "observable: No.7\tnumber of Pauli strings: 10000\ttime: 0.012682914733886719\n", + "observable: No.8\tnumber of Pauli strings: 10000\ttime: 0.012678146362304688\n", + "observable: No.9\tnumber of Pauli strings: 10000\ttime: 0.012636423110961914\n", + "observable: No.0\tnumber of Pauli strings: 20000\ttime: 1.015674352645874\n", + "observable: No.1\tnumber of Pauli strings: 20000\ttime: 0.025749921798706055\n", + "observable: No.2\tnumber of Pauli strings: 20000\ttime: 0.02578139305114746\n", + "observable: No.3\tnumber of Pauli strings: 20000\ttime: 0.02524733543395996\n", + "observable: No.4\tnumber of Pauli strings: 20000\ttime: 0.025956153869628906\n", + "observable: No.5\tnumber of Pauli strings: 20000\ttime: 0.02669525146484375\n", + "observable: No.6\tnumber of Pauli strings: 20000\ttime: 0.026634931564331055\n", + "observable: No.7\tnumber of Pauli strings: 20000\ttime: 0.026463985443115234\n", + "observable: No.8\tnumber of Pauli strings: 20000\ttime: 0.0273745059967041\n", + "observable: No.9\tnumber of Pauli strings: 20000\ttime: 0.026821374893188477\n", + "observable: No.0\tnumber of Pauli strings: 30000\ttime: 1.0086262226104736\n", + "observable: No.1\tnumber of Pauli strings: 30000\ttime: 0.03922295570373535\n", + "observable: No.2\tnumber of Pauli strings: 30000\ttime: 0.038678884506225586\n", + "observable: No.3\tnumber of Pauli strings: 30000\ttime: 0.03868269920349121\n", + "observable: No.4\tnumber of Pauli strings: 30000\ttime: 0.04024958610534668\n", + "observable: No.5\tnumber of Pauli strings: 30000\ttime: 0.03927755355834961\n", + "observable: No.6\tnumber of Pauli strings: 30000\ttime: 0.039815664291381836\n", + "observable: No.7\tnumber of Pauli strings: 30000\ttime: 0.04002213478088379\n", + "observable: No.8\tnumber of Pauli strings: 30000\ttime: 0.03934764862060547\n", + "observable: No.9\tnumber of Pauli strings: 30000\ttime: 0.04060721397399902\n", + "observable: No.0\tnumber of Pauli strings: 40000\ttime: 1.2912404537200928\n", + "observable: No.1\tnumber of Pauli strings: 40000\ttime: 0.05326724052429199\n", + "observable: No.2\tnumber of Pauli strings: 40000\ttime: 0.05272030830383301\n", + "observable: No.3\tnumber of Pauli strings: 40000\ttime: 0.054486989974975586\n", + "observable: No.4\tnumber of Pauli strings: 40000\ttime: 0.0538792610168457\n", + "observable: No.5\tnumber of Pauli strings: 40000\ttime: 0.05555129051208496\n", + "observable: No.6\tnumber of Pauli strings: 40000\ttime: 0.05361533164978027\n", + "observable: No.7\tnumber of Pauli strings: 40000\ttime: 0.05325675010681152\n", + "observable: No.8\tnumber of Pauli strings: 40000\ttime: 0.05487465858459473\n", + "observable: No.9\tnumber of Pauli strings: 40000\ttime: 0.05441641807556152\n", + "observable: No.0\tnumber of Pauli strings: 50000\ttime: 0.999931812286377\n", + "observable: No.1\tnumber of Pauli strings: 50000\ttime: 0.06137228012084961\n", + "observable: No.2\tnumber of Pauli strings: 50000\ttime: 0.06159329414367676\n", + "observable: No.3\tnumber of Pauli strings: 50000\ttime: 0.06138134002685547\n", + "observable: No.4\tnumber of Pauli strings: 50000\ttime: 0.060491085052490234\n", + "observable: No.5\tnumber of Pauli strings: 50000\ttime: 0.06045842170715332\n", + "observable: No.6\tnumber of Pauli strings: 50000\ttime: 0.0629739761352539\n", + "observable: No.7\tnumber of Pauli strings: 50000\ttime: 0.06146860122680664\n", + "observable: No.8\tnumber of Pauli strings: 50000\ttime: 0.061437129974365234\n", + "observable: No.9\tnumber of Pauli strings: 50000\ttime: 0.061475515365600586\n", + "observable: No.0\tnumber of Pauli strings: 60000\ttime: 1.03033447265625\n", + "observable: No.1\tnumber of Pauli strings: 60000\ttime: 0.06811189651489258\n", + "observable: No.2\tnumber of Pauli strings: 60000\ttime: 0.06913161277770996\n", + "observable: No.3\tnumber of Pauli strings: 60000\ttime: 0.06945395469665527\n", + "observable: No.4\tnumber of Pauli strings: 60000\ttime: 0.06843304634094238\n", + "observable: No.5\tnumber of Pauli strings: 60000\ttime: 0.06950116157531738\n", + "observable: No.6\tnumber of Pauli strings: 60000\ttime: 0.07009696960449219\n", + "observable: No.7\tnumber of Pauli strings: 60000\ttime: 0.06856656074523926\n", + "observable: No.8\tnumber of Pauli strings: 60000\ttime: 0.06969141960144043\n", + "observable: No.9\tnumber of Pauli strings: 60000\ttime: 0.0678703784942627\n", + "observable: No.0\tnumber of Pauli strings: 70000\ttime: 1.0191996097564697\n", + "observable: No.1\tnumber of Pauli strings: 70000\ttime: 0.07705307006835938\n", + "observable: No.2\tnumber of Pauli strings: 70000\ttime: 0.07620859146118164\n", + "observable: No.3\tnumber of Pauli strings: 70000\ttime: 0.07670450210571289\n", + "observable: No.4\tnumber of Pauli strings: 70000\ttime: 0.0766746997833252\n", + "observable: No.5\tnumber of Pauli strings: 70000\ttime: 0.07552027702331543\n", + "observable: No.6\tnumber of Pauli strings: 70000\ttime: 0.07716488838195801\n", + "observable: No.7\tnumber of Pauli strings: 70000\ttime: 0.07647228240966797\n", + "observable: No.8\tnumber of Pauli strings: 70000\ttime: 0.07623863220214844\n", + "observable: No.9\tnumber of Pauli strings: 70000\ttime: 0.07545590400695801\n", + "observable: No.0\tnumber of Pauli strings: 80000\ttime: 1.0341267585754395\n", + "observable: No.1\tnumber of Pauli strings: 80000\ttime: 0.08658909797668457\n", + "observable: No.2\tnumber of Pauli strings: 80000\ttime: 0.08614206314086914\n", + "observable: No.3\tnumber of Pauli strings: 80000\ttime: 0.0857245922088623\n", + "observable: No.4\tnumber of Pauli strings: 80000\ttime: 0.08441877365112305\n", + "observable: No.5\tnumber of Pauli strings: 80000\ttime: 0.08495783805847168\n", + "observable: No.6\tnumber of Pauli strings: 80000\ttime: 0.08582544326782227\n", + "observable: No.7\tnumber of Pauli strings: 80000\ttime: 0.0861966609954834\n", + "observable: No.8\tnumber of Pauli strings: 80000\ttime: 0.08437252044677734\n", + "observable: No.9\tnumber of Pauli strings: 80000\ttime: 0.0852508544921875\n", + "observable: No.0\tnumber of Pauli strings: 90000\ttime: 1.031904697418213\n", + "observable: No.1\tnumber of Pauli strings: 90000\ttime: 0.09243512153625488\n", + "observable: No.2\tnumber of Pauli strings: 90000\ttime: 0.09180665016174316\n", + "observable: No.3\tnumber of Pauli strings: 90000\ttime: 0.09398865699768066\n", + "observable: No.4\tnumber of Pauli strings: 90000\ttime: 0.09126615524291992\n", + "observable: No.5\tnumber of Pauli strings: 90000\ttime: 0.09299516677856445\n", + "observable: No.6\tnumber of Pauli strings: 90000\ttime: 0.09152960777282715\n", + "observable: No.7\tnumber of Pauli strings: 90000\ttime: 0.09381914138793945\n", + "observable: No.8\tnumber of Pauli strings: 90000\ttime: 0.09076142311096191\n", + "observable: No.9\tnumber of Pauli strings: 90000\ttime: 0.08988714218139648\n", + "observable: No.0\tnumber of Pauli strings: 97920\ttime: 1.050750494003296\n", + "observable: No.1\tnumber of Pauli strings: 97920\ttime: 0.09993815422058105\n", + "observable: No.2\tnumber of Pauli strings: 97920\ttime: 0.10038924217224121\n", + "observable: No.3\tnumber of Pauli strings: 97920\ttime: 0.09895133972167969\n", + "observable: No.4\tnumber of Pauli strings: 97920\ttime: 0.09973955154418945\n", + "observable: No.5\tnumber of Pauli strings: 97920\ttime: 0.10170507431030273\n", + "observable: No.6\tnumber of Pauli strings: 97920\ttime: 0.09864187240600586\n", + "observable: No.7\tnumber of Pauli strings: 97920\ttime: 0.09945058822631836\n", + "observable: No.8\tnumber of Pauli strings: 97920\ttime: 0.09991574287414551\n", + "observable: No.9\tnumber of Pauli strings: 97920\ttime: 0.09802794456481934\n" + ] + }, + { + "data": { + "text/plain": "
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" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "bz = 1000\n", + "\n", + "exact = []\n", + "for ob in ps:\n", + " exact.append(tc.backend.real(c.expectation_ps(ps=ob)))\n", + "exact = np.asarray(exact)[:, None]\n", + "\n", + "bzs, res = [], []\n", + "for i in range(bz, nps + bz, bz):\n", + " res.append([])\n", + " ss_states_batch = ss_states[:i]\n", + " bzs.append(ss_states_batch.shape[0])\n", + " t0 = time.time()\n", + " for j, ob in enumerate(ps):\n", + " expcs = sejit(ss_states_batch, ob)\n", + " res[-1].append(np.median(expcs))\n", + " t = time.time()\n", + " if i == bz or i % (bz * 10) == 0 or i >= nps:\n", + " print(\n", + " f\"observable: No.{j}\\tnumber of Pauli strings: {bzs[-1]}\\ttime: {t - t0}\"\n", + " )\n", + " t0 = t\n", + "res = np.asarray(res).T\n", + "bzs = np.asarray(bzs) * r\n", + "\n", + "error = np.abs(res - exact)\n", + "plt.figure()\n", + "plt.xlabel(\"N\")\n", + "plt.ylabel(\"Error\")\n", + "for i, y in enumerate(error):\n", + " plt.plot(bzs, y, label=f\"No.{i}\")\n", + "plt.legend()\n", + "plt.show()" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-08-09T04:53:57.091936Z", + "start_time": "2023-08-09T04:51:25.071809100Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "## Estimate the Entanglement Entropy" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "We can also use classical shadows to calculate entanglement entropy. ``entropy_shadow`` first reconstructs the reduced density matrix, then solves the eigenvalues and finally calculates the entanglement entropy from non-negative eigenvalues. Since the time and space complexity of reconstructing the density matrix is exponential with respect to the system size, this method is only efficient when the reduced system size is constant. ``entropy_shadow`` is jitable, but it will only accelerate when the reduced sub systems have the same shape." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 20, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sub: [1, 4]\ttime: 0.1788625717163086\texact: 1.3222456063743848\tshadow entropy: 1.323659494989336\n", + "sub: [2, 7]\ttime: 0.03922629356384277\texact: 1.313932933107046\tshadow entropy: 1.315937416629094\n", + "sub: [3, 6]\ttime: 0.03881263732910156\texact: 1.342032043092265\tshadow entropy: 1.3427963599754822\n", + "sub: [0, 5]\ttime: 0.03893852233886719\texact: 1.3458706554536102\tshadow entropy: 1.346507278883028\n", + "sub: [7, 0]\ttime: 0.039243221282958984\texact: 1.3496695271830874\tshadow entropy: 1.3504498597279848\n", + "sub: [1, 4, 7]\ttime: 0.2567908763885498\texact: 1.8741003653918944\tshadow entropy: 1.8777698830270055\n", + "sub: [0, 3, 6]\ttime: 0.11173439025878906\texact: 1.8633273061204374\tshadow entropy: 1.8638162138941512\n", + "sub: [5, 4, 2]\ttime: 0.11144137382507324\texact: 1.908653965480665\tshadow entropy: 1.9084333256925539\n", + "sub: [7, 2, 5]\ttime: 0.1119997501373291\texact: 1.8916979397866593\tshadow entropy: 1.88828077605345\n", + "sub: [0, 1, 2]\ttime: 0.11184382438659668\texact: 1.8717789129825904\tshadow entropy: 1.8724197548909916\n" + ] + } + ], + "source": [ + "subs = [\n", + " [1, 4],\n", + " [2, 7],\n", + " [3, 6],\n", + " [0, 5],\n", + " [7, 0],\n", + " [1, 4, 7],\n", + " [0, 3, 6],\n", + " [5, 4, 2],\n", + " [7, 2, 5],\n", + " [0, 1, 2],\n", + "]\n", + "\n", + "\n", + "@tc.backend.jit\n", + "def shadow_ent(snapshots_states, sub, alpha=2):\n", + " return shadows.entropy_shadow(snapshots_states, sub=sub, alpha=alpha)\n", + "\n", + "\n", + "for sub in subs:\n", + " exact_rdm = tc.quantum.reduced_density_matrix(\n", + " psi, cut=[i for i in range(n) if i not in sub]\n", + " )\n", + " exact_ent = tc.quantum.renyi_entropy(exact_rdm, k=2)\n", + "\n", + " t0 = time.time()\n", + " ent = shadow_ent(ss_states, sub)\n", + " t = time.time()\n", + " print(f\"sub: {sub}\\ttime: {t - t0}\\texact: {exact_ent}\\tshadow entropy: {ent}\")" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-08-09T04:53:58.139584Z", + "start_time": "2023-08-09T04:53:57.091936Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "On the other hand, for the second order Renyi entropy, we have another method to calculate it in polynomial time by random measurements:\n", + "$$\n", + "\\begin{split}\n", + " R_A^2&=-\\log\\left(\\text{Tr}(\\rho_A^2)\\right),\\\\\n", + " \\text{Tr}(\\rho_A^2)&=2^k\\sum_{b,b'\\in\\{0,1\\}^k}(-2)^{-H(b,b')}\\overline{P(b)P(b')},\n", + "\\end{split}\n", + "$$\n", + "where $A$ is the $k$-d reduced system, $H(b,b')$ is the Hamming distance between $b$ and $b'$, $P(b)$ is the probability for measuring $\\rho_A$ and obtaining the outcomes $b$ thus we need a larger $r$ to obtain a good enough priori probability, and the overline means the average on all random selected Pauli strings. Please refer to [Brydges, et al. (2019)](https://www.science.org/doi/full/10.1126/science.aau4963) for more details. We can use ``renyi_entropy_2`` to implement this method, but it is not jitable because we need to build the dictionary based on the bit strings obtained by measurements, which is a dynamical process. Compared with ``entropy_shadow``, it cannot filter out non-negative eigenvalues, so the accuracy is slightly worse." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 21, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "sub: [1, 4]\ttime: 3.794407606124878\tshadow entropy 2: 1.2866729353788704\n", + "sub: [2, 7]\ttime: 3.796651840209961\tshadow entropy 2: 1.2875279355654872\n", + "sub: [3, 6]\ttime: 3.760688066482544\tshadow entropy 2: 1.314993963087972\n", + "sub: [0, 5]\ttime: 3.765700101852417\tshadow entropy 2: 1.317198599992926\n", + "sub: [7, 0]\ttime: 3.784120559692383\tshadow entropy 2: 1.3218300427352758\n", + "sub: [1, 4, 7]\ttime: 3.859661817550659\tshadow entropy 2: 1.7701671972428563\n", + "sub: [0, 3, 6]\ttime: 3.874009132385254\tshadow entropy 2: 1.7684695179560657\n", + "sub: [5, 4, 2]\ttime: 3.831859827041626\tshadow entropy 2: 1.8037352454314826\n", + "sub: [7, 2, 5]\ttime: 3.824885368347168\tshadow entropy 2: 1.8006117836020135\n", + "sub: [0, 1, 2]\ttime: 3.8377578258514404\tshadow entropy 2: 1.782393800345501\n" + ] + } + ], + "source": [ + "nps, r = 1000, 500\n", + "\n", + "pauli_strings = tc.backend.convert_to_tensor(np.random.randint(1, 4, size=(nps, n)))\n", + "status = tc.backend.convert_to_tensor(np.random.rand(nps, r))\n", + "\n", + "snapshots = shadows.shadow_snapshots(psi, pauli_strings, status, measurement_only=True)\n", + "\n", + "t0 = time.time()\n", + "for sub in subs:\n", + " ent2 = shadows.renyi_entropy_2(snapshots, sub)\n", + "\n", + " t = time.time()\n", + " print(f\"sub: {sub}\\ttime: {t - t0}\\tshadow entropy 2: {ent2}\")\n", + " t0 = t" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-08-09T04:54:36.511330700Z", + "start_time": "2023-08-09T04:53:58.139683500Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "## Reconstruct the Density Matrix" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "We can use ``global_shadow_state``, ``global_shadow_state1`` or ``global_shadow_state2`` to reconstruct the density matrix. These three functions use different methods, but the results are exactly the same. All functions are jitable, but since we only use each of them once here, they are not wrapped. In terms of implementation details, ``global_shadow_state`` uses ``kron`` and is recommended, the other two use ``einsum``." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 22, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "exact:\n", + " [[0.5+0.j 0. +0.j 0. +0.j 0.5+0.j]\n", + " [0. +0.j 0. +0.j 0. +0.j 0. +0.j]\n", + " [0. +0.j 0. +0.j 0. +0.j 0. +0.j]\n", + " [0.5+0.j 0. +0.j 0. +0.j 0.5+0.j]]\n", + "\n", + "shadow state: error: 0.02441655995426051\n", + " [[ 0.49141+0.j 0.00159+0.00219j 0.00378+0.00306j 0.5004 +0.0081j ]\n", + " [ 0.00159-0.00219j 0.0019 +0.j -0.00855+0.00297j -0.00567-0.00126j]\n", + " [ 0.00378-0.00306j -0.00855-0.00297j 0.00805+0.j -0.00273-0.00249j]\n", + " [ 0.5004 -0.0081j -0.00567+0.00126j -0.00273+0.00249j 0.49864+0.j ]]\n", + "\n", + "shadow state 1: error: 0.02441655995426051\n", + " [[ 0.49141+0.j 0.00159+0.00219j 0.00378+0.00306j 0.5004 +0.0081j ]\n", + " [ 0.00159-0.00219j 0.0019 +0.j -0.00855+0.00297j -0.00567-0.00126j]\n", + " [ 0.00378-0.00306j -0.00855-0.00297j 0.00805+0.j -0.00273-0.00249j]\n", + " [ 0.5004 -0.0081j -0.00567+0.00126j -0.00273+0.00249j 0.49864+0.j ]]\n", + "\n", + "shadow state 2: error: 0.02441655995426051\n", + " [[ 0.49141+0.j 0.00159+0.00219j 0.00378+0.00306j 0.5004 +0.0081j ]\n", + " [ 0.00159-0.00219j 0.0019 +0.j -0.00855+0.00297j -0.00567-0.00126j]\n", + " [ 0.00378-0.00306j -0.00855-0.00297j 0.00805+0.j -0.00273-0.00249j]\n", + " [ 0.5004 -0.0081j -0.00567+0.00126j -0.00273+0.00249j 0.49864+0.j ]]\n" + ] + } + ], + "source": [ + "n, nps, r = 2, 10000, 5\n", + "\n", + "c = tc.Circuit(n)\n", + "c.H(0)\n", + "c.cnot(0, 1)\n", + "\n", + "psi = c.state()\n", + "bell_state = psi[:, None] @ psi[None, :]\n", + "\n", + "pauli_strings = tc.backend.convert_to_tensor(np.random.randint(1, 4, size=(nps, n)))\n", + "status = tc.backend.convert_to_tensor(np.random.rand(nps, r))\n", + "lss_states = shadows.shadow_snapshots(psi, pauli_strings, status)\n", + "sdw_state = shadows.global_shadow_state(lss_states)\n", + "sdw_state1 = shadows.global_shadow_state1(lss_states)\n", + "sdw_state2 = shadows.global_shadow_state2(lss_states)\n", + "\n", + "print(\"exact:\\n\", bell_state)\n", + "print(f\"\\nshadow state: error: {np.linalg.norm(bell_state - sdw_state)}\\n\", sdw_state)\n", + "print(\n", + " f\"\\nshadow state 1: error: {np.linalg.norm(bell_state - sdw_state)}\\n\", sdw_state1\n", + ")\n", + "print(\n", + " f\"\\nshadow state 2: error: {np.linalg.norm(bell_state - sdw_state)}\\n\", sdw_state2\n", + ")" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-08-09T04:54:36.634162200Z", + "start_time": "2023-08-09T04:54:36.517005400Z" + } + } + }, + { + "cell_type": "code", + "execution_count": 23, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "OS info: Linux-5.4.119-1-tlinux4-0010.2-x86_64-with-glibc2.28\n", + "Python version: 3.10.11\n", + "Numpy version: 1.23.5\n", + "Scipy version: 1.11.0\n", + "Pandas version: 2.0.2\n", + "TensorNetwork version: 0.4.6\n", + "Cotengra version: 0.2.1.dev15+g120379e\n", + "TensorFlow version: 2.12.0\n", + "TensorFlow GPU: []\n", + "TensorFlow CUDA infos: {'cpu_compiler': '/dt9/usr/bin/gcc', 'cuda_compute_capabilities': ['sm_35', 'sm_50', 'sm_60', 'sm_70', 'sm_75', 'compute_80'], 'cuda_version': '11.8', 'cudnn_version': '8', 'is_cuda_build': True, 'is_rocm_build': False, 'is_tensorrt_build': True}\n", + "Jax version: 0.4.13\n", + "Jax installation doesn't support GPU\n", + "JaxLib version: 0.4.13\n", + "PyTorch version: 2.0.1\n", + "PyTorch GPU support: False\n", + "PyTorch GPUs: []\n", + "Cupy is not installed\n", + "Qiskit version: 0.24.1\n", + "Cirq version: 1.1.0\n", + "TensorCircuit version 0.10.0\n" + ] + } + ], + "source": [ + "tc.about()" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-08-09T04:54:36.638744200Z", + "start_time": "2023-08-09T04:54:36.634714500Z" + } + } + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/docs/source/tutorials/error_mitigation.ipynb b/docs/source/tutorials/error_mitigation.ipynb new file mode 100644 index 00000000..abb35992 --- /dev/null +++ b/docs/source/tutorials/error_mitigation.ipynb @@ -0,0 +1,613 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# QEM Applications" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "import tensorcircuit as tc\n", + "from tensorcircuit.results import qem\n", + "from tensorcircuit.results.qem import qem_methods, benchmark_circuits\n", + "from tensorcircuit.results.qem import (\n", + " zne_option,\n", + " apply_zne,\n", + " dd_option,\n", + " apply_dd,\n", + " apply_rc,\n", + ")\n", + "\n", + "from tensorcircuit.cloud import apis\n", + "from tensorcircuit.results import counts\n", + "from tensorcircuit.results.readout_mitigation import ReadoutMit\n", + "from tensorcircuit.compiler.qiskit_compiler import qiskit_compile\n", + "\n", + "from functools import partial\n", + "import numpy as np\n", + "import networkx as nx" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## ZNE" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0, 1], [6, 2], [4, 0], [0, 4], [8, 4], [1, 5], [3, 7], [0, 3], [2, 0], [5, 1], [3, 0], [7, 3], [0, 2], [2, 6], [4, 8], [1, 0]]\n" + ] + } + ], + "source": [ + "d = apis.get_device(\"tianxuan_s1\")\n", + "couple_list = d.topology()\n", + "print(couple_list)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "mit = tc.results.rem.ReadoutMit(\n", + " \"tianxuan_s1?o=0\"\n", + ") # set ?o=0 for readout mitigation initialization\n", + "mit.cals_from_system(qubits=9, shots=4096)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "graph = [(2, 0), (3, 7), (0, 3), (1, 5), (2, 6)]\n", + "weight = [1] * len(graph)\n", + "params = np.array([[1, 1], [1, 1]])\n", + "optimization_level = 2\n", + "\n", + "\n", + "c = benchmark_circuits.QAOA_circuit(graph, weight, params)\n", + "c.to_qiskit().draw(\"mpl\")" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [], + "source": [ + "c1, info = qiskit_compile(\n", + " c,\n", + " compiled_options={\n", + " \"basis_gates\": [\"h\", \"rz\", \"x\", \"y\", \"z\", \"cz\"],\n", + " \"optimization_level\": optimization_level,\n", + " # \"coupling_map\": d.topology(),\n", + " },\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ideal 0.9400000000000001\n", + "raw 0.37379999999999997\n", + "read 0.4909275773352902\n" + ] + } + ], + "source": [ + "t = apis.submit_task(circuit=c, shots=10000, device=\"simulator:aer\")\n", + "raw_count = t.results(blocked=True)\n", + "ideal = sum(\n", + " [\n", + " -counts.expectation(raw_count, z=[graph[e][0], graph[e][1]]) * weight[e]\n", + " for e in range(len(graph))\n", + " ]\n", + ")\n", + "print(\"ideal\", ideal)\n", + "\n", + "t = apis.submit_task(\n", + " circuit=c1,\n", + " shots=10000,\n", + " device=d,\n", + " enable_qos_qubit_mapping=False,\n", + " enable_qos_gate_decomposition=False,\n", + ")\n", + "raw_count = t.results(blocked=True)\n", + "raw = sum(\n", + " [\n", + " -counts.expectation(raw_count, z=[graph[e][0], graph[e][1]]) * weight[e]\n", + " for e in range(len(graph))\n", + " ]\n", + ")\n", + "print(\"raw\", raw)\n", + "read = sum(\n", + " [\n", + " -mit.expectation(raw_count, z=[graph[e][0], graph[e][1]], **info) * weight[e]\n", + " for e in range(len(graph))\n", + " ]\n", + ")\n", + "print(\"read\", read)" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "zne 0.6603988839789069\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def execute(circuit):\n", + " t = apis.submit_task(\n", + " circuit=circuit,\n", + " shots=10000,\n", + " device=d,\n", + " enable_qos_qubit_mapping=False,\n", + " enable_qos_gate_decomposition=False,\n", + " )\n", + " count = t.results(blocked=True)\n", + " a = sum(\n", + " [\n", + " -mit.expectation(count, z=[graph[e][0], graph[e][1]], **info) * weight[e]\n", + " for e in range(len(graph))\n", + " ]\n", + " )\n", + " # a = sum([-counts.expectation(raw_count, z=[graph[e][0], graph[e][1]])*w[e] for e in range(len(graph))])\n", + " return a\n", + "\n", + "\n", + "random_state = np.random.RandomState(0)\n", + "noise_scaling_function = partial(\n", + " zne_option.scaling.fold_gates_at_random,\n", + " fidelities={\"single\": 1.0},\n", + " random_state=random_state,\n", + ")\n", + "factory = zne_option.inference.PolyFactory(scale_factors=[1, 3, 5], order=1)\n", + "# factory = zne_option.inference.ExpFactory(scale_factors=[1,1.5,2],asymptote=0.)\n", + "# factory = zne_option.inference.RichardsonFactory(scale_factors=[1,1.5,2])\n", + "# factory = zne_option.inference.AdaExpFactory(steps=5, asymptote=0.)\n", + "\n", + "result = apply_zne(\n", + " circuit=c1,\n", + " executor=execute,\n", + " factory=factory,\n", + " scale_noise=noise_scaling_function,\n", + " num_to_average=1,\n", + ")\n", + "_ = factory.plot_fit()\n", + "print(\"zne\", result)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## DD" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[18, 17], [7, 17], [3, 4], [14, 4], [4, 3], [5, 4], [16, 17], [12, 13], [14, 13], [3, 13], [8, 9], [10, 0], [9, 8], [19, 9], [1, 0], [19, 18], [17, 18], [8, 18], [13, 14], [15, 5], [6, 5], [15, 14], [18, 19], [4, 5], [5, 6], [18, 8], [4, 14], [14, 15], [0, 1], [11, 1], [5, 15], [1, 2], [10, 11], [2, 1], [11, 10], [0, 10], [1, 11], [9, 19], [16, 6], [6, 7], [15, 16], [7, 6], [16, 15], [12, 2], [6, 16], [3, 2], [12, 11], [17, 7], [8, 7], [17, 16], [2, 3], [11, 12], [13, 3], [2, 12], [13, 12], [7, 8]]\n" + ] + } + ], + "source": [ + "d = apis.get_device(\"tianshu_s1\")\n", + "couple_list = d.topology()\n", + "print(couple_list)" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c, ideal = benchmark_circuits.ghz_circuit(8)\n", + "c.to_qiskit().draw(\"mpl\") # logical circuit" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'logical_physical_mapping': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7}, 'positional_logical_mapping': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7}}\n" + ] + } + ], + "source": [ + "c1, info = qiskit_compile(\n", + " c,\n", + " compiled_options={\n", + " \"basis_gates\": [\"h\", \"rz\", \"x\", \"y\", \"z\", \"cz\"],\n", + " \"optimization_level\": 2,\n", + " # \"coupling_map\": d.topology(),\n", + " },\n", + ")\n", + "\n", + "print(info)" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ideal 1.0\n", + "raw 0.156\n" + ] + } + ], + "source": [ + "zpauli = [0, 6] # logical\n", + "\n", + "t = apis.submit_task(circuit=c, shots=10000, device=\"simulator:aer\")\n", + "raw_count = t.results(blocked=True)\n", + "ideal = counts.expectation(raw_count, z=zpauli)\n", + "print(\"ideal\", ideal)\n", + "\n", + "\n", + "t = apis.submit_task(\n", + " circuit=c1,\n", + " shots=10000,\n", + " device=d,\n", + " enable_qos_qubit_mapping=False,\n", + " enable_qos_gate_decomposition=False,\n", + ")\n", + "raw_count = t.results(blocked=True) # position_counts=logical_counts\n", + "raw = counts.expectation(raw_count, z=zpauli)\n", + "print(\"raw\", raw)" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "mit 0.1734\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 45, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def execute(circuit):\n", + " t = apis.submit_task(\n", + " circuit=circuit,\n", + " shots=10000,\n", + " device=d,\n", + " enable_qos_qubit_mapping=False,\n", + " enable_qos_gate_decomposition=False,\n", + " )\n", + " count = t.results(blocked=True) # physical_counts\n", + "\n", + " n = len(info[\"logical_physical_mapping\"])\n", + " physical_qubits = [info[\"logical_physical_mapping\"][i] for i in range(n)]\n", + " count = counts.marginal_count(count, physical_qubits)\n", + "\n", + " # a = mit.expectation(count, z=zpauli,**info)\n", + " a = counts.expectation(count, z=zpauli)\n", + " return a\n", + "\n", + "\n", + "mitigated_result = apply_dd(\n", + " circuit=c1,\n", + " executor=execute,\n", + " rule=dd_option.rules.yy,\n", + " rule_args={\"spacing\": -1},\n", + " full_output=True,\n", + " ignore_idle_qubit=True,\n", + " fulldd=False,\n", + ")\n", + "\n", + "print(\"mit\", mitigated_result[0])\n", + "mitigated_result[1].to_qiskit().draw(\"mpl\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## RC" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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3Bjxu5z43GRkzQx9ILig9PZ2tW7cGNdaxRdbZ2QlAV1dXr9PLy8txu92kpKQwceLEsGZxuVw0NjaG9XfIl9I6jgU99nDrEdwDYVklDGVImJ7amnoFvPKq/78h1NTcBN3HQ/qcwco7GdzBLis2Xq9VAzm2yNLT02ltbaWmpobCwp4Hspubm1m1ahUAeXl5YT+hIz1d5/VGUuKQwPcp2baNZVlckhTH0LFjw5AqwDzx8XwR7RABunzM5QNmiyzW1/sH2As5eayFsQNg+Q9GF/M+6dgimz9/PrW1tZSVlbFgwQJyc3MBqK6uZunSpbjdbiAyF0IHu7kswTl2An7yIpwI4EO5ZVlMGAWf1m4LX7AAhPI6skip21M3YK4jq3PB//lj4ONuvWECv1zeEPpAElaOPdmjtLSUtLQ0Dh48yLRp05gxYwY5OTnMnj2brKws5s2bB/Q8PibOkBQPs4LYW3x9buizSHTkXAaXBnhpqAVcmx2WOBJmji2yjIwMqqqqWLRoEQkJCdTX1zNy5EjWr19PRUUFdXX+c61VZM40b6r/jg39lTEC8seFL49ElmXBLTMDG1OYDaNSLjyfDDwDYz9AmEyZMoVNmzad83hHRwf19fXExMQwffr0KCSTcBudAn95Ezz9FnSf7Hve9EvgL4tgSGwkkkmk5GXCnQXw4tYL3yg4LxPu1GWjxnJ0kZ3Pzp07sW2b3NxckpKSzpn+/PPPA7Br164ef54wYQIFBQWRCyoXJetSeOBP4D8/8l/o6jvr3SxhCMzOgpvz/LsjB4uYry4g5qsLoh0jIm6Y7N/Kev1j2NfL2TMjk/3z3DgZwnDljUTIoCyyHTt2AOffrXjXXXf1+uf77ruP5557LqzZJLTSL4Fv3eC/eez2z/x3fIiNgbRhMHM8DB2Ur4DBZcrl/p/GVtjV6L+3YnwcZI6EKWNUYE4wKF/GFyoyB38hwKB1SdLAu8O9RNbYEf4fcZ5B+VnkQkUmIiLmGJRbZKfuwygiIuYblFtkIiLiHCoyERExmopMRESMpiITERGjqchERMRoKjIRETGaikxERIymIhMREaOpyERExGgqMhERMZqKTEREjGbZutW7yIBj2zbHfN5oxwhIUkwslmVFO4YMQioyERExmnYtioiI0VRkIiJiNBWZiIgYTUUmIiJGU5GJiIjRVGQiImI0FZmIiBhNRSYiIkZTkYmIiNFUZCIiYjQVmYiIGE1FJiIiRlORiYiI0VRkIiJiNBWZiIgYTUUmIiJGU5GJiIjRVGQiImK0uGgHkN7ZNpzwRjtF/8XHgmVFO4VzmLb8QeuARI+KbIA64YUHy6Odov/K7oahWptCxrTlD1oHJHq0a1FERIymIhMREaOpyERExGgqMhERMZqKTEREjKYiExERo6nIRETEaCoyERExmopMRESMpiITERGjqchERMRoKjIRETGaikxERIw2KIrM7XZTWlpKdnY2CQkJZGZmsmLFCjo7O1m2bBmWZbFu3bpoxwyLhl1v8cQSi20Va847zxNLLH6/5pYIpoos24a9h+A3W+CXb8Oz78DGD+Dzo9FOFn5a/n4eL9TUw//dDM+8Bf/2LlTugo7uaCeTUHD8ly5s376dhQsX4nK5SE5OZurUqTQ1NbF27Vr27t1LS0sLADNnzoxuUAmL2ib4fQ24jpw7rXIXTE6Hr8+G0SmRzybhZ9vwzm54Yye0n1VaHxyAVz6EgolwxywYOiQ6GeXiOXqLzO12s3jxYlwuFytXrqS5uZmamhpcLhdlZWVUVFRQXV2NZVnk5eVFO66E2LZ6/6fv3krslN0u+Mc/QFNrpFJJpNg2vLgNXtp2bomd4vHB+3th3RvQdSKy+SR0HF1ky5cvp6GhgZKSEtasWUNKypcfu0tLS8nPz8fj8TBhwgRSU1OjmFRC7YAb/uM98NkXnrfzODz9lt7InObdOqja3b95D7bAv28Obx4JH8cWWW1tLeXl5YwaNYrVq1f3Os+sWbMAyM/PP/3Y888/z5133sn48eNJSkriiiuu4KGHHqKjoyMiucPFc+IYXe3uXn+cqLIWvL7+z992DKr3hy9PtA225e/1+XcnBmJXEzS0hCePhJdjj5Ft2LABn89HcXExw4YN63WexMREoGeRrVmzhnHjxvHTn/6UjIwMtm/fzqOPPsrbb7/NO++8Q0yMmd3//guP8P4Lj0Q7RkQcOQY7DgY+7t06uCEXLCv0maJtMC1/gI8b4EhX4OM274G7rwl9HgkvxxZZZWUlAEVFReedp6GhAehZZC+//DKjR48+/ecbb7yR0aNHU1xczLvvvsvcuXPDlDi8phd9h5xr7up12ks/WxDhNOG129W/XYpn+/wotHRCWu+fe4w2mJY/+E/yieQ4iS7HFtmBAwcAGD9+fK/TPR4Pmzf7d4qfWWRnltgpBQUFADQ2NgaVpaCgAJfLFdCY2CGJ3PF3e4L6fb0Znp7DuOnzQ/Z8Z8vNycF7MoiPwGEw6do/58rb/ndQY+cWfZUjzbtCnChwpi1/GFjrwDXF/0Rm3uKAx33R2kFGxhVhSCQXkp6eztatW4Ma69gi6+zsBKCrq/cXVnl5OW63m5SUFCZOnNjnc7355psATJkyJagsLpcr4BKMG5oU1O+KlqbmJjzHj0U7BgCXHAruAwdA48F9HLmI8aFi2vKHgbUOtLcdDmrcia72oD+wSvQ4tsjS09NpbW2lpqaGwsLCHtOam5tZtWoVAHl5eVh9HBRpbGzk4Ycf5uabbw76WrP09PSAx8QOSQzqd0XL5WMuHzCfxu0O/9a4bdt9Ltuzdbd/QcpQL8PGjg1XtH4zbfnDwFoHug/XBTXuSONHjB0Ay38wCuZ98hTHFtn8+fOpra2lrKyMBQsWkJubC0B1dTVLly7F7fafrdVXOXV0dHDbbbcRHx/Ps88+G3SWYDaXj3vgwfKgf2XE1e3Zw9ABtDatfQ32fRHYWRuL54zmnw8MjFMXTVv+MLDWge6T8MiL/n/HQDxa8idM+WlDeEJJ2Jh5Cl4/lJaWkpaWxsGDB5k2bRozZswgJyeH2bNnk5WVxbx584Cex8fO1NXVxeLFi9m/fz+vvfYaY8aMiWR8uUg3BniYIy4WCrPDk0UiL2EIXDMpsDGXpcJkvcyN5Ngiy8jIoKqqikWLFpGQkEB9fT0jR45k/fr1VFRUUFfn3/XQW5GdPHmSr3/962zdupVXX32VqVOnRjq+XKT8cVDUz0OaFrD0WhjpwLMVB7PFV8KkS/s3b/JQWHYjxDjw0ovBwLJtO4gTlc3W0dFBamoqlmXR3t5OUtKXB9Z9Ph/33HMPGzdu5JVXXjm95RZppu1aKrubAbNb6RTbhtd3wh92nP/i6OSh8M1CmDbADouYtvxhYK4DJzyw4X3/fRXPJ/0S+PZcuFQ39zHWAFvtImPnzp3Ytk1ubm6PEgO4//77+e1vf8sPf/hDkpKSeP/9909PmzRpUq+n58vAZFnw1elwbTb89z7YWt/znopLrvVvuQ2JjVpECbP4OLjverg5D/5rD+xqhC/av5z+V1+BnMuceRH8YOLYXYt92bFjB9D7bsVXX30VgJ/97GcUFhb2+KmoqIhoTgmNYQkwbyqUfs2/GxH8/y2YqBIbLC5L9d/h/qFbe64DuekqMScYlFtkfRVZfX19hNOIiMjF0BaZiIgYbVBukZ26D6OIiJhvUG6RiYiIc6jIRETEaCoyERExmopMRESMpiITERGjqchERMRoKjIRETGaikxERIymIhMREaOpyERExGgqMhERMdqgvNeiCeJj/V9UaIp4fR1KSJm2/EHrgESPimyAsqyB9227Ejla/iL9p12LIiJiNBWZiIgYTUUmIiJGU5GJiIjRVGQiImI0FZmIiBhNRSYiIkZTkYmIiNFUZCIiYjQVmYiIGE1FJiIiRlORiYiI0VRkIiJiNBWZiIgYTUUmIiJGU5GJiIjRVGQiImI0FZmIiBhNRSYiIkZTkYmIiNFUZCIiYjQVmYiIGE1FJiIiRlORiYiI0VRkIiJiNBWZiIgYTUUmIiJGU5GJiIjRVGQiImI0FZmIiBhNRSYiIkZTkYmIiNEGRZG53W5KS0vJzs4mISGBzMxMVqxYQWdnJ8uWLcOyLNatWxftmBJGPhsOuMH+nz/bfc4tTnTCA3tcg3cdsG1oaoWdDfBxAzS0+B9zgrhoBwi37du3s3DhQlwuF8nJyUydOpWmpibWrl3L3r17aWlpAWDmzJnRDSph0X0S3vsUNu8Bd3vPaWtfg+ty4crxEGNFJ5+EX0sHVNXBlr1w7ETPac9VwdzJkHVpdLJFgscL1fv9r4GGlp7TxgyH63Ng9iQYEhuVeCFh2bZTOvlcbrebK6+8koaGBlauXMkjjzxCSkoKAI899hgPPvggcXFxeL1e2traSE1NjXJiCaXWTlj/JriO9D1ffiYsuc7sF7L07tND8Mu3/R9o+nLLTJg/LSKRIqrrBDz7Duw51Pd8E0fBX9wEyUMjEivkHF1k3/zmN9mwYQMlJSU8+eST50yfOXMmH374IRMnTmTfvn1RSCjhcuw4PPEaHDrav/mvHA9Lr9OWmZM0tMCTr8NxT//mv7MAbpgc3kyR5PH6P8hdqMROmTgK/mq+mR/oHHuMrLa2lvLyckaNGsXq1at7nWfWrFkA5Ofnn36sqqqK+fPnM2bMGIYOHUpGRgZ33303tbW1EcktofHWJ/0vMYAPDviPn4hzvLSt/yUG8PsPoPN4+PJEWs2B/pcYwH63f/eriRxbZBs2bMDn81FcXMywYcN6nScxMRHoWWStra3MmDGDtWvX8tprr1FWVsbOnTspLCykoaEhItnl4ni8/uNigXq3LvRZJDqa22Dv54GN8Xjhvx20YyaY9XlznZkngDj2ZI/KykoAioqKzjvPqWI6s8huvfVWbr311h7zXX311UyePJkXXniBFStWhCGthNLuZmjvDnzcx43+T+SmHieQL1UHWUjV+6BoSmizRMOhI/DZ4cDHNR/x75LNTAt9pnBybJEdOHAAgPHjx/c63ePxsHnzZqBnkfUmLc2/VOPigvvnKigowOXSfqtIyZqzlKvu6H13cl9sG66+9iscPbQ7DKkkkmb/2TrGzbw94HH1TW1kZEwPfaAIuzTnBub+xYagxt75Z8to2vWHECe6sPT0dLZu3RrUWMcWWWdnJwBdXV29Ti8vL8ftdpOSksLEiRPPme71evH5fBw4cIC/+Zu/IT09nW984xtBZXG5XDQ2NgY1VgI3sq0t6LGHDrlo0bIyXtexY0GN8/l8jnitxgz/Iuixhw+7jfs3cGyRpaen09raSk1NDYWFhT2mNTc3s2rVKgDy8vKwrHNPVbvxxhtPb7FlZ2dTWVnJ6NGjg84ikRNPZ1DjfF4PqYkWiWPHhjiRRNyJtqCGdR91MdYByz8pzn/BnG3bvb6/9ebUvImxx6Pyb3Ax75OOPf1++fLlPPnkk2RmZvLGG2+Qm5sLQHV1NUuXLmXfvn2cPHmS+++/v9e7euzevZu2tjb279/Pz3/+cz7//HM2b97MuHHjIv1XkQB5ffDoS3A0wONkeZnw7bnhySSR5ToCP9sU+LjbZ8FNV4Q+TzQ8/gf/3WwCcflwWPU16Gf3DRiOPWuxtLSUtLQ0Dh48yLRp05gxYwY5OTnMnj2brKws5s2bB5z/+NjkyZO55ppruOeee/jjH/9Ie3s7jz32WCT/ChKk2BgozAl83PW5oc8i0ZF+CeRcFtiYIbEw+9yjDMa6PojXwHW55pUYOLjIMjIyqKqqYtGiRSQkJFBfX8/IkSNZv349FRUV1NX5z0290IkeAMOHDyc7O5tPPw3inG6JipuugDGX9H/+WRMCf+OTge2OWTA0gIMnt8+CJAedsXrVBJg8pv/zT7oUrskKW5ywcuyuxb50dHSQmpqKZVm0t7eTlJTU5/yff/45kyZN4t577+Wpp56KUEq5WEeO+e9s0NTW93xXjofiQogz8I4G0rd9n/tvUXX2PRbPdttVzjjt/mzdJ+Ff34HdFzhpetKlsGyuuUU+KItsy5YtzJkzh8mTJ/PJJ5/0mLZkyRKys7OZOXMmw4cPZ8+ePTz++OM0NzdTXV1NdnZ2lFJLMI6fhC37/BeHfn7WnT5yLvPvSsnL1K2pnKztmH/5v/8pdJxx547YGJg5zn9bqgmjopcv3Lw+2Fbvv9j5wFnXlmWM9O9SL5hg9gc5x5612JcdO3YAve9WnDNnDr/61a944okn6O7uJjMzk6KiIn70ox+d95o0GbiGDvHf3fyGXGhohfYuiImBtGEwOiXa6SQShif5bwp88wz/RcJdJyA+zn/n92EJ0U4XfrExMDvL/3P2STArbzbzmNjZVGRnKSkpoaSkJNKRJMwsCzJHRjuFRFNcrLO/rqU/0i8BC/93sVk4o8TAwSd79KWvIhMREbMMyi2yU/dhFBER8w3KLTIREXEOFZmIiBhNRSYiIkZTkYmIiNFUZCIiYjQVmYiIGE1FJiIiRlORiYiI0VRkIiJiNBWZiIgYTUUmIiJGU5GJiIjRVGQiImI0FZmIiBhNRSYiIkZTkYmIiNFUZCIiYjQVmYiIGE1FJiIiRlORiYiI0VRkIiJiNBWZiIgYTUUmIiJGU5GJiIjRVGQiImI0FZmIiBhNRSYiIkZTkYmIiNFUZCIiYjQVmYiIGC0u2gGkd7YNJ7zRTtF/8bFgWdFOISKDkYpsgDrhhQfLo52i/8ruhqFam0QkCrRrUUREjKYiExERo6nIRETEaCoyERExmopMRESMpiITERGjqchERMRoKjIRETGaikxERIymIhMREaOpyERExGgqMhERMZqKTEREjKYiExERozm+yNxuN6WlpWRnZ5OQkEBmZiYrVqygs7OTZcuWYVkW69ati3bMsGnY9RZPLLHYVrHmvPM8scTi92tuiWAqEYmkrhNQtRvWvAr2/zxmA2/VwrHj0UwWGo7+Bqnt27ezcOFCXC4XycnJTJ06laamJtauXcvevXtpaWkBYObMmdENKiISJlv2wgtb4YTn3Gm/q4GKD+G2q+D63MhnCxXHbpG53W4WL16My+Vi5cqVNDc3U1NTg8vloqysjIqKCqqrq7Esi7y8vGjHFREJuardsOH93kvslJNeeL4a/rgzcrlCzbFFtnz5choaGigpKWHNmjWkpKScnlZaWkp+fj4ej4cJEyaQmpoaxaQiIqH32WF4cWv/5395O+z9PGxxwsqRRVZbW0t5eTmjRo1i9erVvc4za9YsAPLz88/7PAsXLsSyLH7yk5+EI2ZEeU4co6vd3euPiDhPVd2Xx8P6653dYYkSdo48RrZhwwZ8Ph/FxcUMGzas13kSExOB8xfZb37zG7Zv3x6uiBH3/guP8P4Lj0Q7hohEQOdx+KA+8HE7DsKRY3BJUsgjhZUji6yyshKAoqKi887T0NAA9F5kR48e5YEHHmDNmjUsWbLkovMUFBTgcrkCGhM7JJE7/m7PRf/uU6YXfYeca+7qddpLP1tw0c+fm5OD92TXRT+PiFy8UROv4abvvRDwOJ8NX1m8FNfuN8OQqm/p6els3RrAvtAzOLLIDhw4AMD48eN7ne7xeNi8eTPQe5E99NBD5ObmUlxcHJIic7lcNDY2BjQmbmhoPxINT89h3PT5IX3OMzU1N+E5fixszy8i/ReX1hn02CPtXQG/X0WbI4uss9O/ELu6et9CKC8vx+12k5KSwsSJE3tM27p1K8888wzbtm0LWZ709PSAx8QOSQzZ74+Ey8dcri0ykQEiNTk+6LEpSXGMHTs2hGn6J5j3yVMcWWTp6em0trZSU1NDYWFhj2nNzc2sWrUKgLy8PCzLOj3N6/Xy3e9+l5KSEqZNmxayPMFsLh/3wIPlIYsQdnV79jDUkWuTiHk8XvjJ76CjO7BxCUPgvTd+bdxr2ZFnLc6f79+FVlZWRl1d3enHq6urKSoqwu32n6l39oXQ69at49ChQ444S1FEBq+4WCicFPi42VkYV2Lg0CIrLS0lLS2NgwcPMm3aNGbMmEFOTg6zZ88mKyuLefPmAT2Pj7ndbh5++GF+/OMf4/F4aGtro62tDYDu7m7a2trw+XzR+OuIiATsulxICmAPY8IQmDs5fHnCyZFFlpGRQVVVFYsWLSIhIYH6+npGjhzJ+vXrqaioOL2VdmaRNTQ00N7ezne/+11GjBhx+gf8W3YjRozgs88+i8rfR0QkUMOT4C9v6t8W1pBY+PZcGJVy4XkHIsu27UCvmTNaR0cHqampWJZFe3s7SUlJpx/v7VhWUVER9913H9/61reYM2cOCQkJEclp2jGysrvN3CUh4nRNrf57LZ7vrh0TR8Mds2BcWmRzhdKge+vZuXMntm2Tm5t7usQAhg0bxk033dTrmAkTJpx3mojIQHb5CPj+Amhug+p90HoMbNu/xXZ1FowdEe2EF2/QFdmOHTuAvm9NJSLiNGOGw61XRTtFeKjILmCQ7XkVETGOI0/26Iu2yEREnGXQbZGdug+jiIg4w6DbIhMREWdRkYmIiNFUZCIiYjQVmYiIGE1FJiIiRlORiYiI0VRkIiJiNBWZiIgYTUUmIiJGU5GJiIjRBt33kZnCtuGEN9op+i8+Fiwr2ilEZDBSkYmIiNG0a1FERIymIhMREaOpyERExGgqMhERMZqKTEREjKYiExERo6nIRETEaCoyERExmopMRESMpiITERGjqchERMRoKjIRETGaikxERIymIhMREaOpyERExGgqMhERMZqKTEREjKYiExERo6nIRETEaCoyERExmopMRESMpiITERGjqchERMRoKjIRETGaikxERIz2/wHX/E5Spy81bwAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "execution_count": 48, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c = tc.Circuit(5)\n", + "c.x(0)\n", + "c.h(2)\n", + "c.cz(0, 1)\n", + "c.cz(2, 3)\n", + "c.y(1)\n", + "c.h(2)\n", + "c.cz(0, 1)\n", + "c.cz(2, 3)\n", + "c.h(4)\n", + "c.cz(3, 4)\n", + "\n", + "c.to_qiskit().draw(\"mpl\")" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 50, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "circuit = qem.rc_circuit(c)\n", + "circuit = qem.washcircuit(circuit, qlist=list(range(circuit.circuit_param[\"nqubits\"])))\n", + "circuit.to_qiskit().draw(\"mpl\")" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'logical_physical_mapping': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4}, 'positional_logical_mapping': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4}}\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 54, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c1, info = qiskit_compile(\n", + " c,\n", + " compiled_options={\n", + " \"basis_gates\": [\"h\", \"rz\", \"x\", \"y\", \"z\", \"cz\"],\n", + " \"optimization_level\": 2,\n", + " # \"coupling_map\": d.topology(),\n", + " },\n", + ")\n", + "\n", + "print(info)\n", + "c1.to_qiskit().draw(\"mpl\")" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ideal -1.0\n", + "raw -0.3894\n" + ] + } + ], + "source": [ + "zpauli = [1, 2] # logical\n", + "\n", + "t = apis.submit_task(circuit=c, shots=10000, device=\"simulator:aer\")\n", + "raw_count = t.results(blocked=True)\n", + "ideal = counts.expectation(raw_count, z=zpauli)\n", + "print(\"ideal\", ideal)\n", + "\n", + "\n", + "t = apis.submit_task(\n", + " circuit=c1,\n", + " shots=10000,\n", + " device=d,\n", + " enable_qos_qubit_mapping=False,\n", + " enable_qos_gate_decomposition=False,\n", + ")\n", + "raw_count = t.results(blocked=True) # position_counts=logical_counts\n", + "raw = counts.expectation(raw_count, z=zpauli)\n", + "print(\"raw\", raw)" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "mit -0.39233333333333337\n", + "mit -0.4132\n" + ] + } + ], + "source": [ + "def execute(circuit):\n", + " t = apis.submit_task(\n", + " circuit=circuit,\n", + " shots=10000,\n", + " device=d,\n", + " enable_qos_qubit_mapping=False,\n", + " enable_qos_gate_decomposition=False,\n", + " )\n", + " count = t.results(blocked=True) # physical_counts\n", + "\n", + " n = len(info[\"logical_physical_mapping\"])\n", + " physical_qubits = [info[\"logical_physical_mapping\"][i] for i in range(n)]\n", + " count = counts.marginal_count(count, physical_qubits)\n", + "\n", + " # a = mit.expectation(count, z=zpauli,**info)\n", + " a = counts.expectation(count, z=zpauli)\n", + " return a\n", + "\n", + "\n", + "mitigated_result = apply_rc(\n", + " circuit=c1, executor=execute, num_to_average=6, simplify=True\n", + ")\n", + "\n", + "print(\"mit\", mitigated_result[0])\n", + "\n", + "\n", + "mitigated_result = apply_rc(\n", + " circuit=c1, executor=execute, num_to_average=6, simplify=False\n", + ")\n", + "\n", + "print(\"mit\", mitigated_result[0])" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.8.13 ('tf')", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.13" + }, + "orig_nbformat": 4, + "vscode": { + "interpreter": { + "hash": "4d2770c334f3778740193ba4b3686745ae5c2e3ee10c8c0d673798cf1c2fcefe" + } + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/docs/source/tutorials/imag_time_evo.ipynb b/docs/source/tutorials/imag_time_evo.ipynb new file mode 100644 index 00000000..f698e793 --- /dev/null +++ b/docs/source/tutorials/imag_time_evo.ipynb @@ -0,0 +1,1301 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "dc0db886", + "metadata": {}, + "source": [ + "# Solving the Ground State of Hamiltonian by Imaginary-time Evolution" + ] + }, + { + "cell_type": "markdown", + "id": "aecf6615", + "metadata": {}, + "source": [ + "## Overview" + ] + }, + { + "cell_type": "markdown", + "id": "b533d43e", + "metadata": {}, + "source": [ + "Imaginary-time evolution (IME) is a method to solve the ground state of the Hamiltonian, which is more efficient than naive gradient descent and will not fall into a local minimum.\n", + "\n", + "However, exact imaginary-time evolution takes exponentially more space and time to execute on a classical computer. On the other hand, it is non-unitary and also cannot be implemented on a quantum computer. Therefore, we consider the approximate imaginary-time evolution, also known as the quantum natural gradient (QNG), that is, at each step we adjust the parameters in the quantum circuit to realize the imaginary-time evolution in a very short time $\\tau$. Let the parameters in the circuit be $\\boldsymbol{\\theta}$ and the output of the circuit is $|\\psi\\rangle$, define\n", + "$$\n", + "\\begin{split}\n", + " |\\psi_\\tau\\rangle&=e^{-\\tau\\hat{H}}|\\psi\\rangle\\approx|\\psi\\rangle-\\tau\\hat{H}|\\psi\\rangle,\\\\\n", + " |\\psi'\\rangle&=|\\psi(\\boldsymbol{\\theta}-\\tau\\boldsymbol{\\delta})\\rangle\\approx|\\psi\\rangle-\\tau\\sum_j\\boldsymbol{\\delta}_j|\\partial_{\\boldsymbol{\\theta}_{j}}\\psi\\rangle,\n", + "\\end{split}\n", + "$$\n", + "and the overlap is\n", + "$$\n", + "O=\\sqrt{\\frac{\\langle\\psi_\\tau\\rangle|\\psi'\\rangle\\langle\\psi'|\\psi_\\tau\\rangle}{\\langle\\psi_\\tau\\rangle|\\psi_\\tau\\rangle\\langle\\psi'|\\psi'\\rangle}}.\n", + "$$\n", + "Let $\\partial|O|^2/\\partial\\boldsymbol{\\delta}=0$, we can get $\\boldsymbol{A\\delta=C}$, then the update method is as follows\n", + "$$\n", + "\\boldsymbol{\\theta}^{n+1}=\\boldsymbol{\\theta}^{n}-\\tau\\boldsymbol{\\delta}=\\boldsymbol{\\theta}^{n}-\\tau\\boldsymbol{A}^{-1}\\boldsymbol{C},\n", + "$$\n", + "where $\\boldsymbol{A}$ is the quantum Fisher information matrix and the matrix element\n", + "$$\n", + "\\boldsymbol{A}_{ij}=\\Re\\left[\\frac{\\langle\\partial_{\\boldsymbol{\\theta}_{i}}\\psi|\\partial_{\\boldsymbol{\\theta}_{j}}\\psi\\rangle}{\\langle\\psi|\\psi\\rangle}-\\frac{\\langle\\partial_{\\boldsymbol{\\theta}_{i}}\\psi|\\psi\\rangle}{\\langle\\psi|\\psi\\rangle}\\frac{\\langle\\psi|\\partial_{\\boldsymbol{\\theta}_{j}}\\psi\\rangle}{\\langle\\psi|\\psi\\rangle}\\right];\n", + "$$\n", + "$\\boldsymbol{C}$ is the gradient vector of energy versus parameters and the vector element\n", + "$$\n", + "\\boldsymbol{C}_j=\\Re\\left[\\frac{\\langle\\psi|\\hat{H}|\\partial_{\\boldsymbol{\\theta}_{j}}\\psi\\rangle}{\\langle\\psi|\\psi\\rangle}-\\frac{\\langle\\psi|\\hat{H}|\\psi\\rangle}{\\langle\\psi|\\psi\\rangle}\\frac{\\langle\\psi|\\partial_{\\boldsymbol{\\theta}_{j}}\\psi\\rangle}{\\langle\\psi|\\psi\\rangle}\\right].\n", + "$$\n", + "Since $|\\psi\\rangle$ is represented by quantum circuit and naturally normalized, the second term of $\\boldsymbol{C}$ vanishes. And because the global phase is not important, we can add a $U(1)$ gauge to make the second term of $\\boldsymbol{A}$ vanishes. Related theoretical work can refer to [Yuan, Endo, Zhao, Li and Benjamin](https://doi.org/10.22331/q-2019-10-07-191) and [Stokes, Izaac, Killoran and Carleo](https://doi.org/10.22331/q-2020-05-25-269), which will also show how to measure $\\boldsymbol{A}$ and $\\boldsymbol{C}$ in circuit." + ] + }, + { + "cell_type": "markdown", + "source": [ + "In fields other than quantum computation, equivalent forms of imaginary-time evolution are stochastic reconfiguration in variational Monte Carlo method and natural gradient method and Gauss-Newton method in classical optimization. In stochastic reconfiguration, $|\\psi\\rangle$ is not normalized, so $\\boldsymbol{A}$ and $\\boldsymbol{C}$ are the form shown above. In classical optimization, the second terms of $\\boldsymbol{A}$ and $\\boldsymbol{C}$ vanish automatically when the output is the classical probability distribution. Therefore, when $|\\psi\\rangle$ is similar to the classical probability distribution, that is, when there is no sign structure and phase information, the second term of $\\boldsymbol{A}$ will automatically vanish." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "In this tutorial, we solve a classical Hamiltonian and a quantum Hamiltonian by the approximate imaginary-time evolution and demonstrate various forms of code implementation." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "## Setup" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b0def04d", + "metadata": {}, + "outputs": [], + "source": [ + "import tensorcircuit as tc\n", + "from tensorcircuit import experimental\n", + "import optax\n", + "import jax.numpy as jnp\n", + "import tensorflow as tf\n", + "import networkx as nx\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import cotengra as ctg\n", + "import time\n", + "from functools import partial\n", + "from IPython.display import clear_output\n", + "\n", + "K = tc.set_backend(\"jax\")\n", + "tc.set_dtype(\"complex128\")\n", + "\n", + "# cotengra package to speed up the calculation\n", + "opt_ctg = ctg.ReusableHyperOptimizer(\n", + " methods=[\"greedy\", \"kahypar\"],\n", + " parallel=True,\n", + " minimize=\"combo\",\n", + " max_time=20,\n", + " max_repeats=128,\n", + " progbar=True,\n", + ")\n", + "\n", + "tc.set_contractor(\"custom\", optimizer=opt_ctg, preprocessing=True)" + ] + }, + { + "cell_type": "markdown", + "source": [ + "## Classical Hamiltonian" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "The classical Hamiltonian is the Hamiltonian of NAE3SAT, which can be solved by QAOA. Please refer to the tutorial of [QAOA for NAE3SAT](qaoa_nae3sat.ipynb) for details.\n", + "\n", + "Let the set of clauses in the NAE3SAT be $\\mathcal{C}$. In each clause, there are three literals and each literal is represented by a spin. Spins up ($s=1$, $\\text{bit}=0$) and down ($s=-1$, $\\text{bit}=1$) represent false and true respectively. For the clause $(s_i,\\ s_j,\\ s_k)\\in\\mathcal{C}$, $s_i,\\ s_j,\\ s_k$ cannot be 1 or -1 at the same time. The Hamiltonian of the NAE3SAT is as follows\n", + "$$\n", + "\\begin{split}\n", + " \\hat{H}_C&=\\sum_{(i,j,k)\\in\\mathcal{C}}\\left[(s_i+s_j+s_k)^2-1\\right]/2\\\\\n", + " &=\\sum_{(i,j,k)\\in\\mathcal{C}}(s_i s_j+s_j s_k+s_k s_i)+|\\mathcal{C}|,\n", + "\\end{split}\n", + "$$\n", + "where $|\\mathcal{C}|$ is the number of clauses in $\\mathcal{C}$. When all clauses are true, $\\hat{H}_C$ takes the minimum value 0, and the corresponding bit string is the solution of the NAE3SAT." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "id": "6e407437", + "metadata": {}, + "source": [ + "### Define the Hamiltonian" + ] + }, + { + "cell_type": "markdown", + "source": [ + "We select the hard problem in the tutorial of [QAOA for NAE3SAT](qaoa_nae3sat.ipynb). We first construct the graph by the clauses." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "f1532831", + "metadata": { + "ExecuteTime": { + "end_time": "2023-07-13T02:33:37.851074700Z", + "start_time": "2023-07-13T02:33:37.537921300Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": "
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" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# a classical Hamiltonian instance\n", + "clauses = [\n", + " [4, 1, 7],\n", + " [5, 11, 8],\n", + " [4, 1, 8],\n", + " [4, 11, 8],\n", + " [4, 1, 10],\n", + " [5, 11, 8],\n", + " [4, 1, 8],\n", + " [1, 11, 8],\n", + " [4, 1, 7],\n", + " [0, 11, 8],\n", + " [4, 1, 10],\n", + " [4, 11, 8],\n", + " [5, 0, 10],\n", + " [0, 6, 7],\n", + " [5, 0, 11],\n", + " [0, 6, 7],\n", + " [5, 0, 9],\n", + " [3, 6, 7],\n", + " [5, 0, 8],\n", + " [5, 6, 7],\n", + " [5, 0, 10],\n", + " [3, 6, 7],\n", + " [5, 0, 10],\n", + " [1, 6, 7],\n", + " [2, 4, 6],\n", + " [1, 8, 11],\n", + " [2, 4, 6],\n", + " [2, 8, 11],\n", + " [2, 4, 9],\n", + " [5, 8, 11],\n", + " [2, 4, 10],\n", + " [2, 8, 11],\n", + " [2, 4, 10],\n", + " [4, 8, 11],\n", + " [2, 4, 8],\n", + " [4, 8, 11],\n", + " [3, 0, 9],\n", + " [5, 11, 7],\n", + " [3, 0, 10],\n", + " [2, 11, 7],\n", + " [3, 0, 9],\n", + " [0, 11, 7],\n", + " [3, 0, 9],\n", + " [5, 11, 7],\n", + " [3, 0, 10],\n", + " [3, 11, 7],\n", + " [3, 0, 7],\n", + " [4, 11, 7],\n", + " [5, 0, 10],\n", + " [4, 0, 10],\n", + " [2, 5, 6],\n", + " [2, 11, 10],\n", + " [2, 6, 10],\n", + " [2, 4, 9],\n", + " [0, 9, 10],\n", + " [3, 0, 7],\n", + " [2, 5, 6],\n", + " [1, 10, 9],\n", + " [1, 4, 11],\n", + " [5, 10, 11],\n", + " [0, 4, 8],\n", + " [0, 9, 8],\n", + " [2, 11, 10],\n", + " [2, 8, 6],\n", + " [3, 6, 7],\n", + " [0, 8, 10],\n", + " [4, 0, 9],\n", + " [3, 5, 8],\n", + " [5, 11, 10],\n", + " [2, 11, 10],\n", + " [4, 11, 8],\n", + " [1, 3, 11],\n", + "]\n", + "factor = 1 / len(clauses) / 4\n", + "\n", + "# convert to a NetworkX graph\n", + "graph = nx.Graph()\n", + "for i, j, k in clauses:\n", + " graph.add_edge(i, j, weight=0)\n", + " graph.add_edge(j, k, weight=0)\n", + " graph.add_edge(k, i, weight=0)\n", + "for i, j, k in clauses:\n", + " graph[i][j][\"weight\"] += 1\n", + " graph[j][k][\"weight\"] += 1\n", + " graph[k][i][\"weight\"] += 1\n", + "pos = nx.spring_layout(graph)\n", + "nx.draw_networkx(graph, with_labels=True, pos=pos)\n", + "ax = plt.gca()\n", + "ax.set_facecolor(\"w\")" + ] + }, + { + "cell_type": "markdown", + "source": [ + "Then we construct the Hamiltonian from the graph." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": null, + "outputs": [], + "source": [ + "def b2s(bit):\n", + " return 1 - 2 * int(bit)\n", + "\n", + "\n", + "def energy(cfg):\n", + " E = 0.25\n", + " for a, b in graph.edges:\n", + " E += cfg[a] * cfg[b] * graph[a][b][\"weight\"] * factor\n", + " return E\n", + "\n", + "\n", + "def construct_Ham():\n", + " num_nodes = graph.number_of_nodes()\n", + " Es = []\n", + " for i in range(2**num_nodes):\n", + " case = f\"{bin(i)[2:]:0>{num_nodes}}\"\n", + " Es.append(energy(list(map(b2s, case))))\n", + " return jnp.asarray(Es)\n", + "\n", + "\n", + "Hv = construct_Ham()" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "Here we calculate $e^{-\\tau\\hat{H}}$ in advance to perform exact imaginary-time evolution for comparison with approximate imaginary-time evolution." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 5, + "outputs": [], + "source": [ + "tau_c = 0.025\n", + "exp_tauHv = K.exp(-tau_c * Hv)" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-13T02:33:37.999586200Z", + "start_time": "2023-07-13T02:33:37.923540200Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "### Variational wave function" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "Here we choose regular QAOA ansatz as the parameterized quantum circuit ([PQC](https://tensorcircuit.readthedocs.io/en/latest/textbook/chap5.html?highlight=变分))." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 6, + "outputs": [], + "source": [ + "nlayers = 20 # the number of layers\n", + "\n", + "\n", + "@partial(K.jit, static_argnums=(1, 2))\n", + "def wfn_classical(params, each=1, return_loss=False):\n", + " n = graph.number_of_nodes() # the number of nodes\n", + "\n", + " # PQC loop\n", + " def pqc_loop(s_, params_):\n", + " c_ = tc.Circuit(n, inputs=s_)\n", + " for j in range(each):\n", + " # driving layer\n", + " for a, b in graph.edges:\n", + " c_.RZZ(a, b, theta=graph[a][b][\"weight\"] * params_[2 * j] * factor)\n", + " # mixing layer\n", + " for i in range(n):\n", + " c_.RX(i, theta=params_[2 * j + 1])\n", + " s_ = c_.state()\n", + " return s_\n", + "\n", + " c0 = tc.Circuit(n)\n", + " for i in range(n):\n", + " c0.H(i)\n", + " s0 = c0.state()\n", + " s = K.scan(pqc_loop, K.reshape(params, [nlayers // each, 2 * each]), s0)\n", + " c = tc.Circuit(n, inputs=s)\n", + "\n", + " if return_loss:\n", + " loss = 0.25\n", + " for a, b in graph.edges:\n", + " loss += c.expectation_ps(z=[a, b]) * graph[a][b][\"weight\"] * factor\n", + " return K.real(loss)\n", + " else:\n", + " return c.state()" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-13T02:33:38.001837Z", + "start_time": "2023-07-13T02:33:37.969064900Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "### Optimization" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "We use two methods to calculate $\\boldsymbol{\\delta}$, one is to calculate directly according to the expressions of $\\boldsymbol{A}$ and $\\boldsymbol{C}$, and the other is to call the existing API to calculate $\\boldsymbol{A}$ and $\\boldsymbol{C}$. The former only needs to calculate the $|\\partial_{\\boldsymbol{\\theta}_{j}}\\psi\\rangle$ once, while the latter needs to calculate that twice, but the code of the latter is more concise. In each method, we set the parameter ``fixed_global_phase`` to decide whether to fix the global phase, that is, whether the second term of $\\boldsymbol{A}$ vanishes.\n", + "\n", + "Then we choose the existing optimizer, SGD, to implement the update step. Since compared with naive gradient descent, the approximate imaginary-time evolution has been corrected on the update step size, the adaptive optimizer improved for the naive gradient descent such as Adam is not suitable for the approximate imaginary-time evolution. When update by the adaptive optimizer, the loss function fluctuates greatly. On the other hand, the update method of SGD without momentum is naive update, which is convenient for comparison with the exact imaginary-time evolution." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 7, + "outputs": [], + "source": [ + "@partial(K.jit, static_argnums=(3,))\n", + "def d_params(params, psi, eps=1e-6, fixed_global_phase=False):\n", + " psi = psi[:, None]\n", + " psiHT = K.conj(K.transpose(psi))\n", + " par_psi = K.jacfwd(wfn_classical, argnums=0)\n", + " jac = par_psi(params)\n", + " jacHT = K.conj(K.transpose(jac))\n", + "\n", + " A = K.real(jacHT @ jac)\n", + " if not fixed_global_phase:\n", + " A -= K.real(jacHT @ psi @ psiHT @ jac)\n", + " # protection\n", + " A += eps * K.eye(params.shape[-1], dtype=A.dtype)\n", + "\n", + " C = K.real((psiHT * Hv) @ jac)[0]\n", + "\n", + " return K.solve(A, C, assume_a=\"sym\")\n", + "\n", + "\n", + "@partial(K.jit, static_argnums=(2,))\n", + "def d_params_api(params, eps=1e-6, fixed_global_phase=False):\n", + " if fixed_global_phase:\n", + " qng = experimental.qng(\n", + " wfn_classical, kernel=\"dynamics\", postprocess=None, mode=\"fwd\"\n", + " )\n", + " else:\n", + " qng = experimental.qng(\n", + " wfn_classical, kernel=\"qng\", postprocess=None, mode=\"fwd\"\n", + " )\n", + " A = K.real(qng(params))\n", + " # protection\n", + " A += eps * K.eye(params.shape[-1], dtype=A.dtype)\n", + "\n", + " vag = K.value_and_grad(partial(wfn_classical, return_loss=True), argnums=0)\n", + " loss, C2 = vag(params)\n", + "\n", + " return loss, K.solve(A, C2 / 2, assume_a=\"sym\")\n", + "\n", + "\n", + "if K.name == \"jax\":\n", + " opt = K.optimizer(optax.sgd(tau_c))\n", + "else:\n", + " opt = K.optimizer(tf.keras.optimizers.SGD(tau_c))" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-13T02:33:38.002380500Z", + "start_time": "2023-07-13T02:33:37.969607700Z" + } + } + }, + { + "cell_type": "code", + "execution_count": 8, + "outputs": [ + { + "data": { + "text/plain": "
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" + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 1999: 6.1109702587127686\tTotal: 12327.309196949005\n" + ] + } + ], + "source": [ + "steps_classical = 2000\n", + "\n", + "# initial parameters\n", + "params = K.implicit_randn(shape=(2 * nlayers,), stddev=0.1)\n", + "params_fgp = K.copy(params)\n", + "params_api = K.copy(params)\n", + "params_fgp_api = K.copy(params)\n", + "psi_exact = wfn_classical(params)\n", + "\n", + "losses, losses_fgp, losses_exact = [], [], []\n", + "losses_api, losses_fgp_api = [], []\n", + "\n", + "eps = 1e-6\n", + "t0 = ts = time.time()\n", + "\n", + "for i in range(steps_classical):\n", + " psi = wfn_classical(params)\n", + " loss = K.real(K.tensordot(K.conj(psi) * Hv, psi, 1))\n", + " delta = d_params(params, psi, eps)\n", + " params = opt.update(delta, params)\n", + " losses.append(K.numpy(loss))\n", + "\n", + " psi_fgp = wfn_classical(params_fgp)\n", + " loss_fgp = K.real(K.tensordot(K.conj(psi_fgp) * Hv, psi_fgp, 1))\n", + " delta_fgp = d_params(params_fgp, psi_fgp, eps, fixed_global_phase=True)\n", + " params_fgp = opt.update(delta_fgp, params_fgp)\n", + " losses_fgp.append(K.numpy(loss_fgp))\n", + "\n", + " loss_api, delta_api = d_params_api(params_api, eps)\n", + " params_api = opt.update(delta_api, params_api)\n", + " losses_api.append(K.numpy(loss_api))\n", + "\n", + " loss_fgp_api, delta_fgp_api = d_params_api(\n", + " params_fgp_api, eps, fixed_global_phase=True\n", + " )\n", + " params_fgp_api = opt.update(delta_fgp_api, params_fgp_api)\n", + " losses_fgp_api.append(K.numpy(loss_fgp_api))\n", + "\n", + " loss_exact = K.real(K.tensordot(K.conj(psi_exact) * Hv, psi_exact, 1))\n", + " psi_exact *= exp_tauHv\n", + " psi_exact /= K.norm(psi_exact)\n", + " losses_exact.append(K.numpy(loss_exact))\n", + "\n", + " eps *= 0.999\n", + "\n", + " # visualise the progress\n", + " clear_output(wait=True)\n", + " plt.xlabel(\"Iteration\")\n", + " plt.ylabel(\"Cost\")\n", + " plt.plot(range(i + 1), losses_exact, c=\"r\", label=\"exact\")\n", + " plt.plot(range(i + 1), losses, c=\"b\", label=\"unfixed GP\")\n", + " plt.plot(range(i + 1), losses_fgp, c=\"g\", label=\"fixed GP\")\n", + " plt.plot(range(i + 1), losses_api, c=\"m\", label=\"unfixed GP (API)\")\n", + " plt.plot(range(i + 1), losses_fgp_api, c=\"y\", label=\"fixed GP (API)\")\n", + " plt.legend()\n", + " plt.show()\n", + "\n", + " te = time.time()\n", + " print(f\"Epoch {i}: {te - ts}\\tTotal: {te - t0}\")\n", + " ts = te" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "id": "98a6b152", + "metadata": {}, + "source": [ + "### Results" + ] + }, + { + "cell_type": "markdown", + "source": [ + "We first show the overlap between the final states obtained by different methods. The final states obtained by different methods but with the same parameter of ``fixed_global_phase`` are almost the same, which are also close to the exact final state. And the final states obtained by the same method but with the different parameter of ``fixed_global_phase`` has a global phase difference." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 9, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "overlap between psi_fgp and psi\n", + "|overlap|: 0.9184369993048669\n", + "overlap: (-0.4580633040968157+0.7960556080651879j)\n", + "\n", + "overlap between psi_fgp_api and psi_api\n", + "|overlap|: 0.9184279183739732\n", + "overlap: (-0.4588479071459403+0.7955931368209131j)\n", + "\n", + "overlap between psi_api and psi\n", + "|overlap|: 0.999999996801054\n", + "overlap: (0.999999545918014-0.0009496135391365943j)\n", + "\n", + "overlap between psi_fgp_api and psi_fgp\n", + "|overlap|: 0.9999999922593946\n", + "overlap: (0.9999999907968652+5.408381530766986e-05j)\n", + "\n", + "overlap between psi_exact and psi\n", + "|overlap|: 0.8876639929202528\n", + "overlap: (-0.45130602703961775+0.7643757153944926j)\n", + "\n", + "overlap between psi_exact and psi_fgp\n", + "|overlap|: 0.9290015132797724\n", + "overlap: (0.9278995939751679-0.04523444679473629j)\n", + "\n", + "overlap between psi_exact and psi_api\n", + "|overlap|: 0.8876569548840061\n", + "overlap: (-0.45202998890392976+0.7639396302624046j)\n", + "\n", + "overlap between psi_exact and psi_fgp_api\n", + "|overlap|: 0.9290084278770248\n", + "overlap: (0.9279048483224752-0.04526865942553761j)\n" + ] + } + ], + "source": [ + "psi = wfn_classical(params)\n", + "psi_fgp = wfn_classical(params_fgp)\n", + "psi_api = wfn_classical(params_api)\n", + "psi_fgp_api = wfn_classical(params_fgp_api)\n", + "\n", + "overlap = K.tensordot(K.conj(psi_fgp), psi, 1)\n", + "print(\n", + " f\"overlap between psi_fgp and psi\\n|overlap|: {K.abs(overlap)}\\noverlap: {overlap}\\n\"\n", + ")\n", + "overlap = K.tensordot(K.conj(psi_fgp_api), psi_api, 1)\n", + "print(\n", + " f\"overlap between psi_fgp_api and psi_api\\n|overlap|: {K.abs(overlap)}\\noverlap: {overlap}\\n\"\n", + ")\n", + "overlap = K.tensordot(K.conj(psi_api), psi, 1)\n", + "print(\n", + " f\"overlap between psi_api and psi\\n|overlap|: {K.abs(overlap)}\\noverlap: {overlap}\\n\"\n", + ")\n", + "overlap = K.tensordot(K.conj(psi_fgp_api), psi_fgp, 1)\n", + "print(\n", + " f\"overlap between psi_fgp_api and psi_fgp\\n|overlap|: {K.abs(overlap)}\\noverlap: {overlap}\\n\"\n", + ")\n", + "overlap = K.tensordot(K.conj(psi_exact), psi, 1)\n", + "print(\n", + " f\"overlap between psi_exact and psi\\n|overlap|: {K.abs(overlap)}\\noverlap: {overlap}\\n\"\n", + ")\n", + "overlap = K.tensordot(K.conj(psi_exact), psi_fgp, 1)\n", + "print(\n", + " f\"overlap between psi_exact and psi_fgp\\n|overlap|: {K.abs(overlap)}\\noverlap: {overlap}\\n\"\n", + ")\n", + "overlap = K.tensordot(K.conj(psi_exact), psi_api, 1)\n", + "print(\n", + " f\"overlap between psi_exact and psi_api\\n|overlap|: {K.abs(overlap)}\\noverlap: {overlap}\\n\"\n", + ")\n", + "overlap = K.tensordot(K.conj(psi_exact), psi_fgp_api, 1)\n", + "print(\n", + " f\"overlap between psi_exact and psi_fgp_api\\n|overlap|: {K.abs(overlap)}\\noverlap: {overlap}\"\n", + ")" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-13T05:59:13.932343300Z", + "start_time": "2023-07-13T05:59:13.843507900Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "Then we show the exact solution by the brutal force method." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 10, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "min cost: 0.0\n", + "exact solution: ['000000111111', '111111000000']\n" + ] + }, + { + "data": { + "text/plain": "
", + "image/png": 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" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "idx = [f\"{bin(i)[2:]:0>{graph.number_of_nodes()}}\" for i in np.where(Hv < 1e-6)[0]]\n", + "print(f\"min cost: {0.}\\nexact solution: {idx}\")\n", + "\n", + "# plot NetworkX graph\n", + "colors = [\"r\" if idx[0][i] == \"0\" else \"c\" for i in graph.nodes]\n", + "nx.draw_networkx(graph, with_labels=True, node_color=colors, pos=pos)\n", + "ax = plt.gca()\n", + "ax.set_facecolor(\"w\")" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-13T05:59:14.080058300Z", + "start_time": "2023-07-13T05:59:13.925677800Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "Then we use the bit string with the maximum probability as the approximate solution since we know all information of the probability distribution of the output quantum state, but which is not feasible in the experiment. For the hard problem with rough energy landscape, approximate imaginary-time evolution with 20-layer ansatz gives mediocre results, similar to those obtained by the Adam optimizer with 30-layer ansatz, which can be found in the tutorial of [QAOA for NAE3SAT](qaoa_nae3sat.ipynb). However, this does not mean that approximate imaginary-time evolution is more practical than Adam optimizer because under the same ansatz, the former consumes much more time for each step update than the latter. In contrast, the exact imaginary-time evolution gives excellent results but takes exponential time to compute on a classical computer." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 11, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "cost by exact IME: 0.01636900218695893\n", + "cost: 0.03377396891545763\t0.02951298530564577 (fgp)\n", + "cost (API): 0.033775089880425574\t0.0295121140061756 (fgp)\n", + "\n", + "max prob by exact IME: 0.13847431901217763\n", + "max prob: 0.03930045644879558\t0.05100224184204695 (fgp)\n", + "max prob (API): 0.03929777441862845\t0.05100594691342963 (fgp)\n", + "\n", + "bit strings by exact IME: ['111111000000']\n", + "bit strings: ['111111000000']\t['000000111111'] (fgp)\n", + "bit strings (API): ['000000111111']\t['111111000000'] (fgp)\n" + ] + } + ], + "source": [ + "loss = K.real(K.tensordot(K.conj(psi) * Hv, psi, 1))\n", + "loss_fgp = K.real(K.tensordot(K.conj(psi_fgp) * Hv, psi_fgp, 1))\n", + "loss_api = K.real(K.tensordot(K.conj(psi_api) * Hv, psi_api, 1))\n", + "loss_fgp_api = K.real(K.tensordot(K.conj(psi_fgp_api) * Hv, psi_fgp_api, 1))\n", + "loss_exact = K.real(K.tensordot(K.conj(psi_exact) * Hv, psi_exact, 1))\n", + "print(f\"cost by exact IME: {K.numpy(loss_exact)}\")\n", + "print(f\"cost: {K.numpy(loss)}\\t{K.numpy(loss_fgp)} (fgp)\")\n", + "print(f\"cost (API): {K.numpy(loss_api)}\\t{K.numpy(loss_fgp_api)} (fgp)\\n\")\n", + "\n", + "\n", + "# find the states with max probabilities\n", + "def find_max(psi):\n", + " probs = K.numpy(K.real(K.conj(psi) * psi))\n", + " max_prob = max(probs)\n", + " index = np.where(probs == max_prob)[0]\n", + " states = []\n", + " for i in index:\n", + " states.append(f\"{bin(i)[2:]:0>{graph.number_of_nodes()}}\")\n", + " return max_prob, states\n", + "\n", + "\n", + "prob, states = find_max(psi)\n", + "prob_fpg, states_fpg = find_max(psi_fgp)\n", + "prob_api, states_api = find_max(psi_api)\n", + "prob_fpg_api, states_fpg_api = find_max(psi_fgp_api)\n", + "prob_exact, states_exact = find_max(psi_exact)\n", + "print(f\"max prob by exact IME: {prob_exact}\")\n", + "print(f\"max prob: {prob}\\t{prob_fpg} (fgp)\")\n", + "print(f\"max prob (API): {prob_api}\\t{prob_fpg_api} (fgp)\\n\")\n", + "print(f\"bit strings by exact IME: {states_exact}\")\n", + "print(f\"bit strings: {states}\\t{states_fpg} (fgp)\")\n", + "print(f\"bit strings (API): {states_api}\\t{states_fpg_api} (fgp)\")" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-13T05:59:14.197783300Z", + "start_time": "2023-07-13T05:59:14.080058300Z" + } + } + }, + { + "cell_type": "markdown", + "id": "4ae99ab9", + "metadata": {}, + "source": [ + "## Quantum Hamiltonian" + ] + }, + { + "cell_type": "markdown", + "id": "720dd1a4", + "metadata": {}, + "source": [ + "The quantum Hamiltonian is the Hamiltonian of the transverse and longitudinal field Ising model." + ] + }, + { + "cell_type": "markdown", + "source": [ + "### Define the Hamiltonian" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "Here we also calculate $e^{-\\tau\\hat{H}}$ in advance to perform exact imaginary-time evolution for comparison with approximate imaginary-time evolution." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "2115bb6d", + "metadata": { + "ExecuteTime": { + "end_time": "2023-07-13T06:54:56.088379500Z", + "start_time": "2023-07-13T06:54:55.808504500Z" + } + }, + "outputs": [], + "source": [ + "N = 10\n", + "g = tc.templates.graphs.Line1D(N, pbc=False)\n", + "h = tc.quantum.heisenberg_hamiltonian(\n", + " g, hzz=1, hyy=0, hxx=0, hz=0.5, hx=1, hy=0, sparse=True\n", + ")\n", + "H = tc.array_to_tensor(h.todense())\n", + "\n", + "tau_q = 0.001\n", + "exp_tauH = K.expm(-tau_q * H)" + ] + }, + { + "cell_type": "markdown", + "source": [ + "### Variational wave function" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "Compared with the regular QAOA ansatz in the classic example, this ansatz has a higher parameter density and the initial state is $|0\\rangle$ instead of $|+\\rangle$." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 14, + "outputs": [], + "source": [ + "l = 10 # the number of layers\n", + "\n", + "\n", + "@partial(K.jit, static_argnums=(1,))\n", + "def wfn_quantum(theta, each=1):\n", + " # PQC loop\n", + " def pqc_loop(s_, theta_):\n", + " c_ = tc.Circuit(N, inputs=s_)\n", + " for i in range(each):\n", + " for j in range(N):\n", + " c_.RZZ(j, (j + 1) % N, theta=theta_[i, j, 0])\n", + " for j in range(N):\n", + " c_.RX(j, theta=theta_[i, j, 1])\n", + " s_ = c_.state()\n", + " return s_\n", + "\n", + " c0 = tc.Circuit(N)\n", + " s0 = c0.state()\n", + " s = K.scan(pqc_loop, K.reshape(theta, [l // each, each, N, 2]), s0)\n", + " c = tc.Circuit(N, inputs=s)\n", + "\n", + " return c.state()" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-13T06:54:58.940024800Z", + "start_time": "2023-07-13T06:54:58.920216200Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "### Optimization" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "We also use two methods to calculate $\\boldsymbol{\\delta}$, but make some changes in the method of directly calling the API and the update method. When calculating $\\boldsymbol{A}$, we call ``qng2`` instead of ``qng``, and when calculating $\\boldsymbol{C}$, we call ``dynamics_rhs`` instead of calculating the energy gradient by ``value_and_grad``. For the update method, we do not call the existing optimizer but directly adopt the naive update method." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 15, + "outputs": [], + "source": [ + "@partial(K.jit, static_argnums=(3,))\n", + "def d_theta(theta, psi, eps=1e-6, fixed_global_phase=False):\n", + " psi = psi[:, None]\n", + " psiHT = K.conj(K.transpose(psi))\n", + " par_psi = K.jacfwd(wfn_quantum, argnums=0)\n", + " jac = par_psi(theta)\n", + " jacHT = K.conj(K.transpose(jac))\n", + "\n", + " A = K.real(jacHT @ jac)\n", + " if not fixed_global_phase:\n", + " A -= K.real(jacHT @ psi @ psiHT @ jac)\n", + " # protection\n", + " A += eps * K.eye(theta.shape[-1], dtype=A.dtype)\n", + "\n", + " C = K.real(psiHT @ K.sparse_dense_matmul(h, jac))[0]\n", + "\n", + " return K.solve(A, C, assume_a=\"sym\")\n", + "\n", + "\n", + "@partial(K.jit, static_argnums=(2,))\n", + "def d_theta_api(theta, eps=1e-6, fixed_global_phase=False):\n", + " if fixed_global_phase:\n", + " qng = experimental.qng2(\n", + " wfn_quantum, kernel=\"dynamics\", postprocess=None, mode=\"fwd\"\n", + " )\n", + " else:\n", + " qng = experimental.qng2(wfn_quantum, kernel=\"qng\", postprocess=None, mode=\"fwd\")\n", + " A = K.real(qng(theta))\n", + " # protection\n", + " A += eps * K.eye(theta.shape[-1], dtype=A.dtype)\n", + "\n", + " vag = experimental.dynamics_rhs(wfn_quantum, h)\n", + " C = vag(theta)\n", + "\n", + " return K.solve(A, C, assume_a=\"sym\")\n", + "\n", + "\n", + "@K.jit\n", + "def update(theta, delta, tau):\n", + " return theta - K.cast(tau * delta, dtype=theta.dtype)" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-13T06:55:01.610891800Z", + "start_time": "2023-07-13T06:55:01.549133100Z" + } + } + }, + { + "cell_type": "code", + "execution_count": 16, + "outputs": [ + { + "data": { + "text/plain": "
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" + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 1999: 0.9534459114074707\tTotal: 1922.968999862671\n" + ] + } + ], + "source": [ + "steps_quantum = 2000\n", + "\n", + "# initial parameters\n", + "theta = K.implicit_randn(shape=(2 * l * N,), stddev=0.1)\n", + "theta_fgp = K.copy(theta)\n", + "theta_api = K.copy(theta)\n", + "theta_fgp_api = K.copy(theta)\n", + "psi_exact = wfn_quantum(theta)[:, None]\n", + "\n", + "losses, losses_fgp, losses_exact = [], [], []\n", + "losses_api, losses_fgp_api = [], []\n", + "\n", + "eps = 1e-6\n", + "t0 = ts = time.time()\n", + "\n", + "for i in range(steps_quantum):\n", + " psi = wfn_quantum(theta)\n", + " loss = K.real(K.conj(psi)[None, :] @ K.sparse_dense_matmul(h, psi[:, None]))[0, 0]\n", + " delta = d_theta(theta, psi, eps)\n", + " theta = update(theta, delta, tau_q)\n", + " losses.append(loss)\n", + "\n", + " psi_fgp = wfn_quantum(theta_fgp)\n", + " loss_fgp = K.real(\n", + " K.conj(psi_fgp)[None, :] @ K.sparse_dense_matmul(h, psi_fgp[:, None])\n", + " )[0, 0]\n", + " delta_fgp = d_theta(theta_fgp, psi_fgp, eps, fixed_global_phase=True)\n", + " theta_fgp = update(theta_fgp, delta_fgp, tau_q)\n", + " losses_fgp.append(loss_fgp)\n", + "\n", + " psi_api = wfn_quantum(theta_api)\n", + " loss_api = K.real(\n", + " K.conj(psi_api)[None, :] @ K.sparse_dense_matmul(h, psi_api[:, None])\n", + " )[0, 0]\n", + " delta_api = d_theta_api(theta_api, eps)\n", + " theta_api = update(theta_api, delta_api, tau_q)\n", + " losses_api.append(loss_api)\n", + "\n", + " psi_fgp_api = wfn_quantum(theta_fgp_api)\n", + " loss_fgp_api = K.real(\n", + " K.conj(psi_fgp_api)[None, :] @ K.sparse_dense_matmul(h, psi_fgp_api[:, None])\n", + " )[0, 0]\n", + " delta_fgp_api = d_theta_api(theta_fgp_api, eps, fixed_global_phase=True)\n", + " theta_fgp_api = update(theta_fgp_api, delta_fgp_api, tau_q)\n", + " losses_fgp_api.append(loss_fgp_api)\n", + "\n", + " loss_exact = K.real(\n", + " K.transpose(K.conj(psi_exact)) @ K.sparse_dense_matmul(h, psi_exact)\n", + " )[0, 0]\n", + " psi_exact = exp_tauH @ psi_exact\n", + " psi_exact /= K.norm(psi_exact)\n", + " losses_exact.append(K.numpy(loss_exact))\n", + "\n", + " eps *= 0.999\n", + "\n", + " # visualise the progress\n", + " clear_output(wait=True)\n", + " plt.xlabel(\"Iteration\")\n", + " plt.ylabel(\"Energy\")\n", + " plt.plot(range(i + 1), losses_exact, c=\"r\", label=\"exact\")\n", + " plt.plot(range(i + 1), losses, c=\"b\", label=\"unfixed GP\")\n", + " plt.plot(range(i + 1), losses_fgp, c=\"g\", label=\"fixed GP\")\n", + " plt.plot(range(i + 1), losses_api, c=\"m\", label=\"unfixed GP (API)\")\n", + " plt.plot(range(i + 1), losses_fgp_api, c=\"y\", label=\"fixed GP (API)\")\n", + " plt.legend()\n", + " plt.show()\n", + "\n", + " te = time.time()\n", + " print(f\"Epoch {i}: {te - ts}\\tTotal: {te - t0}\")\n", + " ts = te" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "### Results" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "We first show the overlap between the final states obtained by different methods. Similar to the classical example, all final states obtained by approximate imaginary-time evolution are close to the exact final state. However, the final states obtained by the same method but with fixed and unfixed global phases are closer and have only one global phase difference." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 17, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "overlap between psi_fgp and psi\n", + "|overlap|: 0.9946308905819007\n", + "overlap: (-0.740140807928335-0.6644412637238422j)\n", + "\n", + "overlap between psi_fgp_api and psi_api\n", + "|overlap|: 0.9989073073947322\n", + "overlap: (0.027072660263567746+0.9985403746633621j)\n", + "\n", + "overlap between psi_api and psi\n", + "|overlap|: 0.9986726114097008\n", + "overlap: (-0.7188677460240553+0.6932359976993155j)\n", + "\n", + "overlap between psi_fgp_api and psi_fgp\n", + "|overlap|: 0.9997543606572588\n", + "overlap: (0.9987177429478946+0.04551539930910164j)\n", + "\n", + "overlap between psi_exact and psi\n", + "|overlap|: 0.8722054344579724\n", + "overlap: (-0.6784167782997877-0.5481724134059986j)\n", + "\n", + "overlap between psi_exact and psi_fgp\n", + "|overlap|: 0.8783189735765569\n", + "overlap: (0.8783163699487184-0.002138603442025992j)\n", + "\n", + "overlap between psi_exact and psi_api\n", + "|overlap|: 0.8763977936851081\n", + "overlap: (0.08830490967227977+0.8719376902645599j)\n", + "\n", + "overlap between psi_exact and psi_fgp_api\n", + "|overlap|: 0.8776241084735666\n", + "overlap: (0.876306874146697-0.048065976503842395j)\n" + ] + } + ], + "source": [ + "psi = wfn_quantum(theta)\n", + "psi_fgp = wfn_quantum(theta_fgp)\n", + "psi_api = wfn_quantum(theta_api)\n", + "psi_fgp_api = wfn_quantum(theta_fgp_api)\n", + "\n", + "overlap = K.tensordot(K.conj(psi_fgp), psi, 1)\n", + "print(\n", + " f\"overlap between psi_fgp and psi\\n|overlap|: {K.abs(overlap)}\\noverlap: {overlap}\\n\"\n", + ")\n", + "overlap = K.tensordot(K.conj(psi_fgp_api), psi_api, 1)\n", + "print(\n", + " f\"overlap between psi_fgp_api and psi_api\\n|overlap|: {K.abs(overlap)}\\noverlap: {overlap}\\n\"\n", + ")\n", + "overlap = K.tensordot(K.conj(psi_api), psi, 1)\n", + "print(\n", + " f\"overlap between psi_api and psi\\n|overlap|: {K.abs(overlap)}\\noverlap: {overlap}\\n\"\n", + ")\n", + "overlap = K.tensordot(K.conj(psi_fgp_api), psi_fgp, 1)\n", + "print(\n", + " f\"overlap between psi_fgp_api and psi_fgp\\n|overlap|: {K.abs(overlap)}\\noverlap: {overlap}\\n\"\n", + ")\n", + "overlap = K.tensordot(K.conj(psi_exact[:, 0]), psi, 1)\n", + "print(\n", + " f\"overlap between psi_exact and psi\\n|overlap|: {K.abs(overlap)}\\noverlap: {overlap}\\n\"\n", + ")\n", + "overlap = K.tensordot(K.conj(psi_exact[:, 0]), psi_fgp, 1)\n", + "print(\n", + " f\"overlap between psi_exact and psi_fgp\\n|overlap|: {K.abs(overlap)}\\noverlap: {overlap}\\n\"\n", + ")\n", + "overlap = K.tensordot(K.conj(psi_exact[:, 0]), psi_api, 1)\n", + "print(\n", + " f\"overlap between psi_exact and psi_api\\n|overlap|: {K.abs(overlap)}\\noverlap: {overlap}\\n\"\n", + ")\n", + "overlap = K.tensordot(K.conj(psi_exact[:, 0]), psi_fgp_api, 1)\n", + "print(\n", + " f\"overlap between psi_exact and psi_fgp_api\\n|overlap|: {K.abs(overlap)}\\noverlap: {overlap}\"\n", + ")" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-13T07:30:17.637583800Z", + "start_time": "2023-07-13T07:30:17.598679600Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "Then we compare the approximate ground state energy with the exact result. The differences are very small, but the result obtained by exact imaginary-time evolution is indeed the closest to the real ground state energy." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 18, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "exact ground state energy: -12.669360644773814\n", + "\n", + "ground state energy by exact IME: -12.635107323414964\n", + "ground state energy: -12.455023327986686\t-12.457418138786805 (fgp)\n", + "ground state energy (API): -12.454034180766776\t-12.456395342061295 (fgp)\n" + ] + } + ], + "source": [ + "E = K.eigvalsh(H)[0]\n", + "print(f\"exact ground state energy: {E}\\n\")\n", + "loss_exact = K.real(\n", + " K.transpose(K.conj(psi_exact)) @ K.sparse_dense_matmul(h, psi_exact)\n", + ")[0, 0]\n", + "print(f\"ground state energy by exact IME: {K.numpy(loss_exact)}\")\n", + "loss = K.real(K.conj(psi)[None, :] @ K.sparse_dense_matmul(h, psi[:, None]))[0, 0]\n", + "loss_fgp = K.real(\n", + " K.conj(psi_fgp)[None, :] @ K.sparse_dense_matmul(h, psi_fgp[:, None])\n", + ")[0, 0]\n", + "print(f\"ground state energy: {K.numpy(loss)}\\t{K.numpy(loss_fgp)} (fgp)\")\n", + "loss_api = K.real(\n", + " K.conj(psi_api)[None, :] @ K.sparse_dense_matmul(h, psi_api[:, None])\n", + ")[0, 0]\n", + "loss_fgp_api = K.real(\n", + " K.conj(psi_fgp_api)[None, :] @ K.sparse_dense_matmul(h, psi_fgp_api[:, None])\n", + ")[0, 0]\n", + "print(f\"ground state energy (API): {K.numpy(loss_api)}\\t{K.numpy(loss_fgp_api)} (fgp)\")" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-13T07:30:28.049137Z", + "start_time": "2023-07-13T07:30:27.749665300Z" + } + } + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "89ed16e3", + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + }, + "ExecuteTime": { + "end_time": "2023-07-13T06:54:06.262972100Z", + "start_time": "2023-07-13T06:54:06.180740100Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "OS info: Linux-5.4.119-1-tlinux4-0010.2-x86_64-with-glibc2.28\n", + "Python version: 3.10.11\n", + "Numpy version: 1.23.5\n", + "Scipy version: 1.11.0\n", + "Pandas version: 2.0.2\n", + "TensorNetwork version: 0.4.6\n", + "Cotengra version: 0.2.1.dev15+g120379e\n", + "TensorFlow version: 2.12.0\n", + "TensorFlow GPU: []\n", + "TensorFlow CUDA infos: {'cpu_compiler': '/dt9/usr/bin/gcc', 'cuda_compute_capabilities': ['sm_35', 'sm_50', 'sm_60', 'sm_70', 'sm_75', 'compute_80'], 'cuda_version': '11.8', 'cudnn_version': '8', 'is_cuda_build': True, 'is_rocm_build': False, 'is_tensorrt_build': True}\n", + "Jax version: 0.4.13\n", + "Jax installation doesn't support GPU\n", + "JaxLib version: 0.4.13\n", + "PyTorch version: 2.0.1\n", + "PyTorch GPU support: False\n", + "PyTorch GPUs: []\n", + "Cupy is not installed\n", + "Qiskit version: 0.24.1\n", + "Cirq version: 1.1.0\n", + "TensorCircuit version 0.10.0\n" + ] + } + ], + "source": [ + "tc.about()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.9" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/source/tutorials/nnvqe.ipynb b/docs/source/tutorials/nnvqe.ipynb new file mode 100644 index 00000000..ba48f3f3 --- /dev/null +++ b/docs/source/tutorials/nnvqe.ipynb @@ -0,0 +1,4015 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "id": "64ba95d6", + "metadata": {}, + "source": [ + "#
Neural Network encoded Variational Quantum Eigensolver (NN-VQE)" + ] + }, + { + "cell_type": "markdown", + "id": "b65f64bf", + "metadata": {}, + "source": [ + "## Overview\n", + "\n", + "In this tutorial, we'll show you a general framework called neural network encoded variational quantum algorithms (NN-VQAs) with TensorCircuit. NN-VQA feeds input (such as parameters of a Hamiltonian) from a given problem to a neural network and uses its outputs to parameterize an ansatz circuit for the standard VQA. Here, we take NN-variational quantum eigensolver (VQE) to illustrate concretely." + ] + }, + { + "cell_type": "markdown", + "id": "831930ae", + "metadata": {}, + "source": [ + "## Setup" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "4e1651b9", + "metadata": { + "scrolled": false + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import tensorflow as tf\n", + "import tensorcircuit as tc\n", + "import cotengra\n", + "import quimb\n", + "from tqdm.notebook import tqdm\n", + "from functools import partial\n", + "\n", + "optc = cotengra.ReusableHyperOptimizer(\n", + " methods=[\"greedy\"],\n", + " parallel=\"ray\",\n", + " minimize=\"combo\",\n", + " max_time=30,\n", + " max_repeats=1024,\n", + " progbar=True,\n", + ")\n", + "tc.set_contractor(\"custom\", optimizer=optc, preprocessing=True)\n", + "\n", + "K = tc.set_backend(\"tensorflow\")\n", + "tc.set_dtype(\"complex128\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "d78b480b", + "metadata": {}, + "source": [ + "## Energy\n", + "\n", + "The Hamiltonian used in this tutorial is a 1D XXZ model with periodic boundary conditions, with the transverse field strength $\\lambda$ and the anisotropy parameter $\\Delta$. The Hamiltonian energy expectation function is chosen as loss.\n", + "\n", + "$$ \\hat{H}_{XXZ}=\\sum_{i}{ \\left( X_{i}X_{i+1}+Y_{i}Y_{i+1}+\\Delta Z_{i}Z_{i+1} \\right) } + \\lambda \\sum_{i}{Z_{i}} $$" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "fff67346", + "metadata": {}, + "outputs": [], + "source": [ + "def energy(c: tc.Circuit, lamb: float = 1.0, delta: float = 1.0):\n", + " e = 0.0\n", + " n = c._nqubits\n", + " for i in range(n):\n", + " e += lamb * c.expectation((tc.gates.z(), [i])) # \n", + " for i in range(n):\n", + " e += c.expectation(\n", + " (tc.gates.x(), [i]), (tc.gates.x(), [(i + 1) % n])\n", + " ) # \n", + " e += c.expectation(\n", + " (tc.gates.y(), [i]), (tc.gates.y(), [(i + 1) % n])\n", + " ) # \n", + " e += delta * c.expectation(\n", + " (tc.gates.z(), [i]), (tc.gates.z(), [(i + 1) % n])\n", + " ) # \n", + " return K.real(e)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "0ad6a7a6", + "metadata": {}, + "source": [ + "## Ansatz circuit\n", + "\n", + "Now we design the circuit. We choose multi-scale entangled renormalization ansatz (MERA) as the ansatz here, $d$ is the circuit depth. (see [MERA tutorial](https://tensorcircuit.readthedocs.io/en/latest/tutorials/mera.html))" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "445b7c86", + "metadata": {}, + "outputs": [], + "source": [ + "def MERA(\n", + " inp, n, d=1, lamb=1.0, energy_flag=False\n", + "): # for single-parameter 1D XXZ model, we fix lamb\n", + " params = K.cast(inp[\"params\"], \"complex128\")\n", + " delta = K.cast(inp[\"delta\"], \"complex128\")\n", + " c = tc.Circuit(n)\n", + "\n", + " idx = 0\n", + "\n", + " for i in range(n):\n", + " c.rx(i, theta=params[3 * i])\n", + " c.rz(i, theta=params[3 * i + 1])\n", + " c.rx(i, theta=params[3 * i + 2])\n", + " idx += 3 * n\n", + "\n", + " for n_layer in range(1, int(np.log2(n)) + 1):\n", + " n_qubit = 2**n_layer # number of qubits involving\n", + " step = int(n / n_qubit)\n", + "\n", + " for _ in range(d): # circuit depth\n", + " # even\n", + " for i in range(step, n - step, 2 * step):\n", + " c.rxx(i, i + step, theta=params[idx])\n", + " c.rzz(i, i + step, theta=params[idx + 1])\n", + " idx += 2\n", + "\n", + " # odd\n", + " for i in range(0, n, 2 * step):\n", + " c.rxx(i, i + step, theta=params[idx])\n", + " c.rzz(i, i + step, theta=params[idx + 1])\n", + " idx += 2\n", + "\n", + " # single qubit\n", + " for i in range(0, n, step):\n", + " c.rx(i, theta=params[idx])\n", + " c.rz(i, theta=params[idx + 1])\n", + " idx += 2\n", + "\n", + " if energy_flag:\n", + " return energy(c, lamb, delta) # return Hamiltonian energy expectation\n", + " else:\n", + " return c, idx # return the circuit & number of circuit parameters" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "6daa2f64", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The number of parameters is 74\n" + ] + }, + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " 2023-08-06T16:31:47.918946\n", + " image/svg+xml\n", + " \n", + " \n", + " Matplotlib 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" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# circuit visulization\n", + "n = 8\n", + "d = 1\n", + "cirq, idx = MERA({\"params\": np.zeros(3000), \"delta\": 0.0}, n, d, 1.0)\n", + "print(\"The number of parameters is\", idx)\n", + "cirq.draw()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "bfe2fbee", + "metadata": {}, + "source": [ + "## NN-VQE\n", + "\n", + "Design the NN-VQE. We use a neural network to transform the Hamiltonian parameters to the optimized parameters in the parameterized quantum circuit (PQC) for VQE." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "1ac050a8", + "metadata": {}, + "outputs": [], + "source": [ + "def NN_MERA(n, d, lamb, NN_shape, stddev):\n", + " input = tf.keras.layers.Input(shape=[1]) # input layer\n", + "\n", + " x = tf.keras.layers.Dense(\n", + " units=NN_shape,\n", + " kernel_initializer=tf.keras.initializers.RandomNormal(stddev=stddev),\n", + " activation=\"ReLU\",\n", + " )(\n", + " input\n", + " ) # hidden layer\n", + "\n", + " x = tf.keras.layers.Dropout(0.05)(x) # dropout layer\n", + "\n", + " _, idx = MERA(\n", + " {\"params\": np.zeros(3000), \"delta\": 0.0}, n, d, 1.0, energy_flag=False\n", + " )\n", + " params = tf.keras.layers.Dense(\n", + " units=idx,\n", + " kernel_initializer=tf.keras.initializers.RandomNormal(stddev=stddev),\n", + " activation=\"sigmoid\",\n", + " )(\n", + " x\n", + " ) # output layer\n", + "\n", + " qlayer = tc.KerasLayer(partial(MERA, n=n, d=d, lamb=lamb, energy_flag=True)) # PQC\n", + "\n", + " output = qlayer({\"params\": 6.3 * params, \"delta\": input}) # NN-VQE output\n", + "\n", + " m = tf.keras.Model(inputs=input, outputs=output)\n", + "\n", + " return m" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "e9afb1a5", + "metadata": {}, + "source": [ + "## Train\n", + "\n", + "Now we can train the NN-VQE with TensorFlow." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "873ebd5e", + "metadata": { + "scrolled": false + }, + "outputs": [], + "source": [ + "def train(n, d, lamb, delta, NN_shape, maxiter=10000, lr=0.005, stddev=1.0):\n", + " exp_lr = tf.keras.optimizers.schedules.ExponentialDecay(\n", + " initial_learning_rate=lr, decay_steps=1000, decay_rate=0.7\n", + " )\n", + " opt = tf.keras.optimizers.Adam(exp_lr) # optimizer\n", + "\n", + " m = NN_MERA(n, d, lamb, NN_shape, stddev)\n", + " for i in range(maxiter):\n", + " with tf.GradientTape() as tape:\n", + " e = tf.zeros([1], dtype=tf.float64)\n", + " for de in delta:\n", + " e += m(K.reshape(de, [1])) # sum up energies of all training points\n", + " grads = tape.gradient(e, m.variables)\n", + " opt.apply_gradients(zip(grads, m.variables))\n", + " if i % 500 == 0:\n", + " print(\"epoch\", i, \":\", e)\n", + "\n", + " m.save_weights(\"NN-VQE.weights.h5\") # save the trained model" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "e8df3d67", + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "epoch 0 : tf.Tensor([[117.53523392]], shape=(1, 1), dtype=float64)\n", + "epoch 500 : tf.Tensor([[-361.85937039]], shape=(1, 1), dtype=float64)\n", + "epoch 1000 : tf.Tensor([[-365.35288984]], shape=(1, 1), dtype=float64)\n", + "epoch 1500 : tf.Tensor([[-366.65891358]], shape=(1, 1), dtype=float64)\n", + "epoch 2000 : tf.Tensor([[-366.94258369]], shape=(1, 1), dtype=float64)\n" + ] + } + ], + "source": [ + "n = 8 # number of qubits\n", + "d = 2 # circuit depth\n", + "lamb = 0.75 # fixed\n", + "delta = np.linspace(-3.0, 3.0, 20, dtype=\"complex128\") # training set\n", + "NN_shape = 20 # node number of the hidden layer\n", + "maxiter = 2500 # maximum iteration for the optimization\n", + "lr = 0.009 # learning rate\n", + "stddev = 0.1 # the initial standard deviation of the NN\n", + "\n", + "with tf.device(\"/cpu:0\"):\n", + " train(n, d, lamb, delta, NN_shape=NN_shape, maxiter=maxiter, lr=lr, stddev=stddev)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "c5a7cdb0", + "metadata": {}, + "source": [ + "## Test\n", + "\n", + "We use a test set beyond the training set to test the accuracy and generalization capability of NN-VQE." + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "id": "f15f4f68", + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "4a3ceb8bdf90463f88050b771fde6925", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "0it [00:00, ?it/s]" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "test_delta = np.linspace(-4.0, 4.0, 201) # test set\n", + "test_energies = tf.zeros_like(test_delta).numpy()\n", + "m = NN_MERA(n, d, lamb, NN_shape, stddev)\n", + "m.load_weights(\"NN-VQE.weights.h5\")\n", + "for i, de in tqdm(enumerate(test_delta)):\n", + " test_energies[i] = m(K.reshape(de, [1]))" + ] + }, + { + "cell_type": "markdown", + "id": "924027f8", + "metadata": {}, + "source": [ + "## Compare\n", + "\n", + "We compare the results of NN-VQE with the analytical ones to calculate the ground-state energy relative error. From the figure, we can see that NN-VQE is able to estimate the ground-state energies of parameterized Hamiltonians with high precision without fine-tuning and has a favorable generalization capability." + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "id": "c8668a13", + "metadata": {}, + "outputs": [], + "source": [ + "analytical_energies = [] # analytical result\n", + "for i in test_delta:\n", + " h = quimb.tensor.tensor_builder.MPO_ham_XXZ(\n", + " n, i * 4, jxy=4.0, bz=2.0 * 0.75, S=0.5, cyclic=True\n", + " )\n", + " h = h.to_dense()\n", + " analytical_energies.append(np.min(quimb.eigvalsh(h)))" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "id": "42799e3e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " 2023-08-06T23:44:26.082098\n", + " image/svg+xml\n", + " \n", + " \n", + " Matplotlib v3.5.3, https://matplotlib.org/\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "\n" + ], + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# relative error\n", + "plt.plot(\n", + " test_delta,\n", + " (test_energies - analytical_energies) / np.abs(analytical_energies),\n", + " \"-\",\n", + " color=\"b\",\n", + ")\n", + "plt.xlabel(\"Delta\", fontsize=14)\n", + "plt.ylabel(\"GS Relative Error\", fontsize=14)\n", + "plt.axvspan(-3.0, 3.0, color=\"darkgrey\", alpha=0.5) # training set span\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "5f9bda8a", + "metadata": {}, + "source": [ + "To get more detailed information or further study, please refer to our [paper](https://arxiv.org/abs/2308.01068) and [GitHub](https://github.com/JachyMeow/NN-VQA)." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.12" + }, + "vscode": { + "interpreter": { + "hash": "18d2a9923f839b0d86cf68fd09770e726264cf9d62311eaf57b1fff0ca4bed8e" + } + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/source/tutorials/nnvqe_cn.ipynb b/docs/source/tutorials/nnvqe_cn.ipynb new file mode 100644 index 00000000..056990bb --- /dev/null +++ b/docs/source/tutorials/nnvqe_cn.ipynb @@ -0,0 +1,4015 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "id": "64ba95d6", + "metadata": {}, + "source": [ + "#
神经网络编码的变分量子本征值求解器（NN-VQE）" + ] + }, + { + "cell_type": "markdown", + "id": "b65f64bf", + "metadata": {}, + "source": [ + "## 概述\n", + "\n", + "在本教程中，我们将使用TensorCircuit展示一个量子计算通用框架——神经网络编码的变分量子算法（neural network encoded variational quantum algorithms，NN-VQAs）。NN-VQA将一个给定问题的参量（如哈密顿量的参数）作为神经网络的输入，并使用其输出来参数化标准的变分量子算法（variational quantum algorithms，VQAs）的线路拟设（ansatz circuit）。在本文中，我们以神经网络编码的变分量子本征值求解器（NN-variational quantum eigensolver，NN-VQE）来具体说明。" + ] + }, + { + "cell_type": "markdown", + "id": "831930ae", + "metadata": {}, + "source": [ + "## 设置" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "4e1651b9", + "metadata": { + "scrolled": false + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import tensorflow as tf\n", + "import tensorcircuit as tc\n", + "import cotengra\n", + "import quimb\n", + "from tqdm.notebook import tqdm\n", + "from functools import partial\n", + "\n", + "optc = cotengra.ReusableHyperOptimizer(\n", + " methods=[\"greedy\"],\n", + " parallel=\"ray\",\n", + " minimize=\"combo\",\n", + " max_time=30,\n", + " max_repeats=1024,\n", + " progbar=True,\n", + ")\n", + "tc.set_contractor(\"custom\", optimizer=optc, preprocessing=True)\n", + "\n", + "K = tc.set_backend(\"tensorflow\")\n", + "tc.set_dtype(\"complex128\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "d78b480b", + "metadata": {}, + "source": [ + "## 能量\n", + "\n", + "本教程所使用的哈密顿量是具有周期性边界条件的一维XXZ伊辛模型。它具有横向场强$\\lambda$和各向异性参数$\\Delta$。我们选择哈密顿量的能量期望函数作为损失函数。\n", + "\n", + "$$ \\hat{H}_{XXZ}=\\sum_{i}{ \\left( X_{i}X_{i+1}+Y_{i}Y_{i+1}+\\Delta Z_{i}Z_{i+1} \\right) } + \\lambda \\sum_{i}{Z_{i}} $$" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "fff67346", + "metadata": {}, + "outputs": [], + "source": [ + "def energy(c: tc.Circuit, lamb: float = 1.0, delta: float = 1.0):\n", + " e = 0.0\n", + " n = c._nqubits\n", + " for i in range(n):\n", + " e += lamb * c.expectation((tc.gates.z(), [i])) # \n", + " for i in range(n):\n", + " e += c.expectation(\n", + " (tc.gates.x(), [i]), (tc.gates.x(), [(i + 1) % n])\n", + " ) # \n", + " e += c.expectation(\n", + " (tc.gates.y(), [i]), (tc.gates.y(), [(i + 1) % n])\n", + " ) # \n", + " e += delta * c.expectation(\n", + " (tc.gates.z(), [i]), (tc.gates.z(), [(i + 1) % n])\n", + " ) # \n", + " return K.real(e)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "0ad6a7a6", + "metadata": {}, + "source": [ + "## 线路拟设\n", + "\n", + "现在我们来设计线路。我们选择多尺度纠缠重整化拟设（multi-scale entangled renormalization ansatz，MERA）作为线路拟设，其中$d$为线路深度。（详见[MERA教程](https://tensorcircuit.readthedocs.io/zh/latest/tutorials/mera_cn.html)）" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "445b7c86", + "metadata": {}, + "outputs": [], + "source": [ + "def MERA(\n", + " inp, n, d=1, lamb=1.0, energy_flag=False\n", + "): # 对于单变量一维XXZ模型，我们固定lamb\n", + " params = K.cast(inp[\"params\"], \"complex128\")\n", + " delta = K.cast(inp[\"delta\"], \"complex128\")\n", + " c = tc.Circuit(n)\n", + "\n", + " idx = 0\n", + "\n", + " for i in range(n):\n", + " c.rx(i, theta=params[3 * i])\n", + " c.rz(i, theta=params[3 * i + 1])\n", + " c.rx(i, theta=params[3 * i + 2])\n", + " idx += 3 * n\n", + "\n", + " for n_layer in range(1, int(np.log2(n)) + 1):\n", + " n_qubit = 2**n_layer # 涉及的量子比特数\n", + " step = int(n / n_qubit)\n", + "\n", + " for _ in range(d): # 线路深度\n", + " # 偶数层\n", + " for i in range(step, n - step, 2 * step):\n", + " c.rxx(i, i + step, theta=params[idx])\n", + " c.rzz(i, i + step, theta=params[idx + 1])\n", + " idx += 2\n", + "\n", + " # 奇数层\n", + " for i in range(0, n, 2 * step):\n", + " c.rxx(i, i + step, theta=params[idx])\n", + " c.rzz(i, i + step, theta=params[idx + 1])\n", + " idx += 2\n", + "\n", + " # 单比特门\n", + " for i in range(0, n, step):\n", + " c.rx(i, theta=params[idx])\n", + " c.rz(i, theta=params[idx + 1])\n", + " idx += 2\n", + "\n", + " if energy_flag:\n", + " return energy(c, lamb, delta) # 返回哈密顿量的能量期望\n", + " else:\n", + " return c, idx # 返回线路&线路参量数" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "6daa2f64", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The number of parameters is 74\n" + ] + }, + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " 2023-08-06T16:31:47.918946\n", + " image/svg+xml\n", + " \n", + " \n", + " Matplotlib v3.5.3, https://matplotlib.org/\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", 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" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# 线路可视化\n", + "n = 8\n", + "d = 1\n", + "cirq, idx = MERA({\"params\": np.zeros(3000), \"delta\": 0.0}, n, d, 1.0)\n", + "print(\"The number of parameters is\", idx)\n", + "cirq.draw()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "bfe2fbee", + "metadata": {}, + "source": [ + "## NN-VQE\n", + "\n", + "设计NN-VQE。我们使用神经网络将哈密顿量参数转换为VQE的变分量子线路（parameterized quantum ciecuit，PQC）的优化参数。" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "1ac050a8", + "metadata": {}, + "outputs": [], + "source": [ + "def NN_MERA(n, d, lamb, NN_shape, stddev):\n", + " input = tf.keras.layers.Input(shape=[1]) # 输入层\n", + "\n", + " x = tf.keras.layers.Dense(\n", + " units=NN_shape,\n", + " kernel_initializer=tf.keras.initializers.RandomNormal(stddev=stddev),\n", + " activation=\"ReLU\",\n", + " )(\n", + " input\n", + " ) # 隐层\n", + "\n", + " x = tf.keras.layers.Dropout(0.05)(x) # dropout层\n", + "\n", + " _, idx = MERA(\n", + " {\"params\": np.zeros(3000), \"delta\": 0.0}, n, d, 1.0, energy_flag=False\n", + " )\n", + " params = tf.keras.layers.Dense(\n", + " units=idx,\n", + " kernel_initializer=tf.keras.initializers.RandomNormal(stddev=stddev),\n", + " activation=\"sigmoid\",\n", + " )(\n", + " x\n", + " ) # 输出层\n", + "\n", + " qlayer = tc.KerasLayer(partial(MERA, n=n, d=d, lamb=lamb, energy_flag=True)) # PQC\n", + "\n", + " output = qlayer({\"params\": 6.3 * params, \"delta\": input}) # NN-VQE输出\n", + "\n", + " m = tf.keras.Model(inputs=input, outputs=output)\n", + "\n", + " return m" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "e9afb1a5", + "metadata": {}, + "source": [ + "## 训练\n", + "\n", + "现在我们用TensorFlow来训练NN-VQE。" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "873ebd5e", + "metadata": { + "scrolled": false + }, + "outputs": [], + "source": [ + "def train(n, d, lamb, delta, NN_shape, maxiter=10000, lr=0.005, stddev=1.0):\n", + " exp_lr = tf.keras.optimizers.schedules.ExponentialDecay(\n", + " initial_learning_rate=lr, decay_steps=1000, decay_rate=0.7\n", + " )\n", + " opt = tf.keras.optimizers.Adam(exp_lr) # 优化器\n", + "\n", + " m = NN_MERA(n, d, lamb, NN_shape, stddev)\n", + " for i in range(maxiter):\n", + " with tf.GradientTape() as tape:\n", + " e = tf.zeros([1], dtype=tf.float64)\n", + " for de in delta:\n", + " e += m(K.reshape(de, [1])) # 将所有训练点的能量相加\n", + " grads = tape.gradient(e, m.variables)\n", + " opt.apply_gradients(zip(grads, m.variables))\n", + " if i % 500 == 0:\n", + " print(\"epoch\", i, \":\", e)\n", + "\n", + " m.save_weights(\"NN-VQE.weights.h5\") # 保存已训练的模型" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "e8df3d67", + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "epoch 0 : tf.Tensor([[117.53523392]], shape=(1, 1), dtype=float64)\n", + "epoch 500 : tf.Tensor([[-361.85937039]], shape=(1, 1), dtype=float64)\n", + "epoch 1000 : tf.Tensor([[-365.35288984]], shape=(1, 1), dtype=float64)\n", + "epoch 1500 : tf.Tensor([[-366.65891358]], shape=(1, 1), dtype=float64)\n", + "epoch 2000 : tf.Tensor([[-366.94258369]], shape=(1, 1), dtype=float64)\n" + ] + } + ], + "source": [ + "n = 8 # 量子比特数\n", + "d = 2 # 线路深度\n", + "lamb = 0.75 # 固定参数\n", + "delta = np.linspace(-3.0, 3.0, 20, dtype=\"complex128\") # 训练集\n", + "NN_shape = 20 # 隐层节点数\n", + "maxiter = 2500 # 最大迭代轮数\n", + "lr = 0.009 # 学习率\n", + "stddev = 0.1 # 神经网络参数初始值的标准差\n", + "\n", + "with tf.device(\"/cpu:0\"):\n", + " train(n, d, lamb, delta, NN_shape=NN_shape, maxiter=maxiter, lr=lr, stddev=stddev)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "c5a7cdb0", + "metadata": {}, + "source": [ + "## 测试\n", + "\n", + "我们使用较训练集更大的测试集来测试NN-VQE的准确性和泛化能力。" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "id": "f15f4f68", + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "4a3ceb8bdf90463f88050b771fde6925", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "0it [00:00, ?it/s]" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "test_delta = np.linspace(-4.0, 4.0, 201) # 测试集\n", + "test_energies = tf.zeros_like(test_delta).numpy()\n", + "m = NN_MERA(n, d, lamb, NN_shape, stddev)\n", + "m.load_weights(\"NN-VQE.weights.h5\")\n", + "for i, de in tqdm(enumerate(test_delta)):\n", + " test_energies[i] = m(K.reshape(de, [1]))" + ] + }, + { + "cell_type": "markdown", + "id": "924027f8", + "metadata": {}, + "source": [ + "## 对比\n", + "\n", + "我们将NN-VQE的结果与解析解相比，计算基态能量相对误差。从图中可以看出，NN-VQE能够在无微调（fine-tuning）的情况下准确估计参数化哈密顿量的基态能量，且具有良好的泛化能力。" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "id": "c8668a13", + "metadata": {}, + "outputs": [], + "source": [ + "analytical_energies = [] # 解析解\n", + "for i in test_delta:\n", + " h = quimb.tensor.tensor_builder.MPO_ham_XXZ(\n", + " n, i * 4, jxy=4.0, bz=2.0 * 0.75, S=0.5, cyclic=True\n", + " )\n", + " h = h.to_dense()\n", + " analytical_energies.append(np.min(quimb.eigvalsh(h)))" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "id": "42799e3e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " 2023-08-06T23:44:26.082098\n", + " image/svg+xml\n", + " \n", + " \n", + " Matplotlib v3.5.3, https://matplotlib.org/\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "\n" + ], + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# 基态能量相对误差\n", + "plt.plot(\n", + " test_delta,\n", + " (test_energies - analytical_energies) / np.abs(analytical_energies),\n", + " \"-\",\n", + " color=\"b\",\n", + ")\n", + "plt.xlabel(\"Delta\", fontsize=14)\n", + "plt.ylabel(\"GS Relative Error\", fontsize=14)\n", + "plt.axvspan(-3.0, 3.0, color=\"darkgrey\", alpha=0.5) # 训练集区间\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "5f9bda8a", + "metadata": {}, + "source": [ + "想要获得更详细的信息或进一步的研究，请参考我们的[论文](https://arxiv.org/abs/2308.01068)和[GitHub](https://github.com/JachyMeow/NN-VQA)." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.12" + }, + "vscode": { + "interpreter": { + "hash": "18d2a9923f839b0d86cf68fd09770e726264cf9d62311eaf57b1fff0ca4bed8e" + } + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/source/tutorials/optimization_and_expressibility_cn.ipynb b/docs/source/tutorials/optimization_and_expressibility_cn.ipynb index 3fdaa7a8..e09df93c 100644 --- a/docs/source/tutorials/optimization_and_expressibility_cn.ipynb +++ b/docs/source/tutorials/optimization_and_expressibility_cn.ipynb @@ -276,7 +276,9 @@ "@tf.function\n", "def entropy(v):\n", " ψ = get_state(v)\n", - " ρ_reduced = tc.quantum.reduced_density_matrix(ψ, NA) # 部分描绘出子系统A得到的降密度矩阵\n", + " ρ_reduced = tc.quantum.reduced_density_matrix(\n", + " ψ, NA\n", + " ) # 部分描绘出子系统A得到的降密度矩阵\n", " S = tc.quantum.renyi_entropy(ρ_reduced) # Renyi 纠缠熵\n", " return S" ] diff --git a/docs/source/tutorials/portfolio_optimization.ipynb b/docs/source/tutorials/portfolio_optimization.ipynb new file mode 100644 index 00000000..7ec25888 --- /dev/null +++ b/docs/source/tutorials/portfolio_optimization.ipynb @@ -0,0 +1,499 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "id": "6ddb8a88-779a-43f7-ae14-115463bd87f5", + "metadata": {}, + "source": [ + "# Portfolio Optimization\n", + "\n", + "In this tutorial, we demonstrate the transformation of financial portfolio optimization into a quadratic unconstrained binary optimization (QUBO) problem. Subsequently, we employ the Quantum Approximate Optimization Algorithm (QAOA) to solve it. We will conduct a comparative analysis between the outcomes obtained through QAOA and those derived from classical brute force searching. Additionally, we explore the potential for enhancing results by customizing the QAOA 'mixer' component.\n", + "\n", + "## Introduction\n", + "\n", + "Consider the following scenario: Xiaoming, an astute individual, possesses a sum of money represented by $B$ and is contemplating investing it in the stock market. The market contains $n$ shares, each having an identical price. Xiaoming's objective is to maximize returns while minimizing risk, taking into account the varying levels of risk tolerance among individuals. Xiaoming's personal risk tolerance is represented by $q$. In light of these considerations, the question arises: Which shares should Xiaoming choose to construct an optimal portfolio?\n", + "\n", + "Xiaoming's predicament falls under the purview of portfolio optimization problems. These problems are classified as Quadratic Unconstrained Binary Optimization (QUBO) problems, wherein binary numbers are utilized to represent decisions. In this case, \"1\" signifies selection, while \"0\" denotes the opposite. To address the challenge of portfolio optimization, the Quantum Approximate Optimization Algorithm (QAOA) is employed.\n", + "\n", + "## Solving portfolio optimization problems with QAOA\n", + "\n", + "In a simple boolean Markowitz portfolio optimization problem, we wish to solve \n", + "\n", + "$$\n", + "\\min_{x\\in\\{0,1\\}^n}\\quad q x^T \\Sigma x - \\mu^T x\n", + "$$\n", + "\n", + "subject to a constraint\n", + "\n", + "$$\n", + "1^T x = B\n", + "$$\n", + "\n", + "where \n", + "* $n$: number of assets under consideration\n", + "* $q > 0 $: risk-appetite\n", + "* $\\Sigma \\in \\mathbb{R}^{n\\times n}$: covariance matrix of the assets\n", + "* $\\mu\\in\\mathbb{R}^n$: mean return of the assets\n", + "* $B$: budget (i.e., the total number of assets out of $n$ that can be selected)\n", + "\n", + "Our first step is to convert this constrained quadratic programming problem into a QUBO. We do this by adding a penalty factor $t$ and considering the alternative problem:\n", + "\n", + "$$\n", + "\\min_{x\\in\\{0,1\\}^n}\\quad q x^T \\Sigma x - \\mu^Tx + t(1^Tx-B)^2\n", + "$$\n", + "\n", + "The linear terms $\\mu^Tx = \\mu_1 x_1 + \\mu_2 x_2+\\ldots$ can all be transformed into squared forms, exploiting the properties of boolean variables where $0^2=0$ and $1^2=1$. The same trick is applied to the middle term of $t(1^Tx-B)^2$. Then the function is written as\n", + "\n", + "$$\n", + "\\min_{x\\in\\{0,1\\}^n}\\quad q x^T \\Sigma x - \\sum_{i=1}^n\\mu_i x_i^2 + t(1^Tx-B)^2\n", + "$$\n", + "\n", + "which is a QUBO problem\n", + "\n", + "$$\n", + "\\min_{x\\in\\{0,1\\}^n}\\quad x^T Q x + tB^2\n", + "$$\n", + "\n", + "where matrix $Q$ is\n", + "\n", + "$$\n", + "Q = q\\Sigma -\\mu\\begin{pmatrix}1 & \\\\ & 1\\\\ & & \\ddots\\end{pmatrix} + t\\begin{pmatrix}1 -2B & 1 & \\ldots & 1 \\\\\n", + "1 & 1-2B & 1 & \\ldots \\\\1 & 1 & 1-2B \\\\\n", + "\\vdots\\end{pmatrix}\n", + "$$\n", + "\n", + "and we ignore the constant term $t B^2$. We can now solve this by QAOA.\n", + "\n", + "## Set up" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "4f4feab6", + "metadata": {}, + "outputs": [], + "source": [ + "import tensorcircuit as tc\n", + "import numpy as np\n", + "import tensorflow as tf\n", + "import matplotlib.pyplot as plt\n", + "\n", + "from tensorcircuit.templates.ansatz import QAOA_ansatz_for_Ising\n", + "from tensorcircuit.templates.conversions import QUBO_to_Ising\n", + "from tensorcircuit.applications.optimization import QUBO_QAOA, QAOA_loss\n", + "from tensorcircuit.applications.finance.portfolio import StockData, QUBO_from_portfolio\n", + "\n", + "K = tc.set_backend(\"tensorflow\")\n", + "tf.compat.v1.logging.set_verbosity(tf.compat.v1.logging.ERROR)" + ] + }, + { + "cell_type": "markdown", + "id": "55659298", + "metadata": {}, + "source": [ + "## Import data\n", + "\n", + "To optimize a portfolio, it is essential to utilize historical data from various stocks within the same time frame. Websites such as [Nasdaq](Nasdaq.com) and [Yahoo Finance](https://finance.yahoo.com/) provide access to such data. The next step involves transforming this data into an annualized return ($\\mu$) and covariance matrix ($\\sigma$), which can be recognized by the Quantum Approximate Optimization Algorithm (QAOA). To simplify this process, we can utilize the `StockData` class. This class performs the necessary calculations for annualized return and covariance, as outlined in this [paper](https://doi.org/10.1007/s11128-022-03766-5). They are:\n", + "\n", + "$$\n", + "\\mu = \\left[\\prod ^m_{k=1}\\left(1+r_k^{(i)}\\right)\\right]^{\\frac{252}{m}}\\\\\n", + "\\sigma_{ij}=\\frac{252}{m}\\sum^m_{k=1}\\left(r_k^{(i)}-\\overline{r^{(i)}}\\right)\\left(r_k^{(j)}-\\overline{r^{(j)}}\\right)\n", + "$$\n", + "\n", + "Here is a demonstration of how to use this class:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "62bf0673", + "metadata": {}, + "outputs": [], + "source": [ + "import random\n", + "\n", + "# randomly generate historical data of 6 stocks in 1000 days\n", + "data = [[random.random() for i in range(1000)] for j in range(6)]\n", + "stock_data = StockData(data) # Create an instance\n", + "\n", + "# calculate the annualized return and covariance matrix\n", + "mu = stock_data.get_return()\n", + "sigma = stock_data.get_covariance()\n", + "\n", + "# some other information can also be obtained from this class\n", + "n_stocks = stock_data.n_stocks # number of stocks\n", + "n_days = stock_data.n_days # length of the time span\n", + "daily_change = stock_data.daily_change # relative change of each day" + ] + }, + { + "cell_type": "markdown", + "id": "0fb1d227", + "metadata": {}, + "source": [ + "In this analysis, we have carefully chosen six prominent stocks: Apple Inc. (AAPL), Microsoft Corporation (MSFT), NVIDIA Corporation (NVDA), Pfizer Inc. (PFE), Levi Strauss & Co. (LEVI), and Cisco Systems, Inc. (CSCO). We acquired their historical data spanning from 09/07/2022 to 09/07/2023 from Yahoo Finance. Here are the return and covariance associated with this dataset" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "a7eb3a74", + "metadata": {}, + "outputs": [], + "source": [ + "# real-world stock data, calculated using the class above\n", + "# stock name: aapl, msft, nvda, pfe, levi, csco\n", + "# from 09/07/2022 to 09/07/2023\n", + "mu = [1.21141, 1.15325, 2.06457, 0.63539, 0.63827, 1.12224]\n", + "\n", + "sigma = np.array(\n", + " [\n", + " [0.08488, 0.06738, 0.09963, 0.02124, 0.05516, 0.04059],\n", + " [0.06738, 0.10196, 0.11912, 0.02163, 0.0498, 0.04049],\n", + " [0.09963, 0.11912, 0.31026, 0.01977, 0.10415, 0.06179],\n", + " [0.02124, 0.02163, 0.01977, 0.05175, 0.01792, 0.02137],\n", + " [0.05516, 0.0498, 0.10415, 0.01792, 0.19366, 0.0432],\n", + " [0.04059, 0.04049, 0.06179, 0.02137, 0.0432, 0.05052],\n", + " ]\n", + ")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "f6dc53d4-7ed0-436d-aa1f-8674c56e756e", + "metadata": {}, + "source": [ + "Using this mean and covariance data, we can now define our portfolio optimization problem, convert it to a QUBO matrix, and then extract the Pauli terms and weights, which is similar to what we do in the [QUBO tutorial](https://tensorcircuit.readthedocs.io/en/latest/tutorials/qubo_problem.html)." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "3f6edcd5-3c10-49fc-86ea-160fc6d3187e", + "metadata": {}, + "outputs": [], + "source": [ + "q = 0.5 # the risk preference of investor\n", + "budget = 4 # Note that in this example, there are 6 assets, but a budget of only 4\n", + "penalty = 1.2\n", + "\n", + "Q = QUBO_from_portfolio(sigma, mu, q, budget, penalty)\n", + "portfolio_pauli_terms, portfolio_weights, portfolio_offset = QUBO_to_Ising(Q)" + ] + }, + { + "cell_type": "markdown", + "id": "730da712", + "metadata": {}, + "source": [ + "## Classical method\n", + "\n", + "We first use brute force to calculate the cost of each combination, which is the expectation value $x^TQx$ for each $x\\in\\{0, 1\\}^n$ ($n$ is the number of stocks). It will give us a clue about the performance of QAOA." + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "id": "168f7c36", + "metadata": {}, + "outputs": [], + "source": [ + "def print_Q_cost(Q, wrap=False, reverse=False):\n", + " n_stocks = len(Q)\n", + " states = []\n", + " for i in range(2**n_stocks):\n", + " a = f\"{bin(i)[2:]:0>{n_stocks}}\"\n", + " n_ones = 0\n", + " for j in a:\n", + " if j == \"1\":\n", + " n_ones += 1\n", + " states.append(a)\n", + "\n", + " cost_dict = {}\n", + " for selection in states:\n", + " x = np.array([int(bit) for bit in selection])\n", + " cost_dict[selection] = np.dot(x, np.dot(Q, x))\n", + " cost_sorted = dict(sorted(cost_dict.items(), key=lambda item: item[1]))\n", + " if reverse == True:\n", + " cost_sorted = dict(\n", + " sorted(cost_dict.items(), key=lambda item: item[1], reverse=True)\n", + " )\n", + " num = 0\n", + " print(\"\\n-------------------------------------\")\n", + " print(\" selection\\t |\\t cost\")\n", + " print(\"-------------------------------------\")\n", + " for k, v in cost_sorted.items():\n", + " print(\"%10s\\t |\\t%.4f\" % (k, v))\n", + " num += 1\n", + " if (num >= 8) & (wrap == True):\n", + " break\n", + " print(\" ...\\t |\\t ...\")\n", + " print(\"-------------------------------------\")" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "6a9d41c9", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "-------------------------------------\n", + " selection\t |\t cost\n", + "-------------------------------------\n", + " 111001\t |\t-24.0487\n", + " 101101\t |\t-23.7205\n", + " 111100\t |\t-23.6414\n", + " 011101\t |\t-23.6340\n", + " 101011\t |\t-23.5123\n", + " 011011\t |\t-23.4316\n", + " 111010\t |\t-23.4269\n", + " 111101\t |\t-23.3742\n", + " ...\t |\t ...\n", + "-------------------------------------\n" + ] + } + ], + "source": [ + "print_Q_cost(Q, wrap=True)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "c34f3398", + "metadata": {}, + "source": [ + "### Use QAOA\n", + "\n", + "Here, a standard QAOA ansatz with 12 layers is used. This circuit will be trained for 1000 iterations." + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "id": "9249ea96", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "iterations = 1000\n", + "nlayers = 12\n", + "loss_list = []\n", + "\n", + "\n", + "# define a callback function to recode the loss\n", + "def record_loss(loss, params):\n", + " loss_list.append(loss)\n", + "\n", + "\n", + "# apply QAOA on this portfolio optimization problem\n", + "final_params = QUBO_QAOA(Q, nlayers, iterations, callback=record_loss)\n", + "\n", + "p = plt.plot(loss_list)" + ] + }, + { + "cell_type": "markdown", + "id": "9126333d", + "metadata": {}, + "source": [ + "Create a function to visualize the results, listing all combinations in descending order of probability." + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "4a2c60e4", + "metadata": {}, + "outputs": [], + "source": [ + "def print_result_prob(c, wrap=False, reverse=False):\n", + " states = []\n", + " n_qubits = c._nqubits\n", + " for i in range(2**n_qubits):\n", + " a = f\"{bin(i)[2:]:0>{n_qubits}}\"\n", + " states.append(a)\n", + " # Generate all possible binary states for the given number of qubits\n", + "\n", + " probs = K.numpy(c.probability()).round(decimals=4)\n", + " # Calculate the probabilities of each state using the circuit's probability method\n", + "\n", + " sorted_indices = np.argsort(probs)[::-1]\n", + " if reverse == True:\n", + " sorted_indices = sorted_indices[::-1]\n", + " state_sorted = np.array(states)[sorted_indices]\n", + " prob_sorted = np.array(probs)[sorted_indices]\n", + " # Sort the states and probabilities in descending order based on the probabilities\n", + "\n", + " print(\"\\n-------------------------------------\")\n", + " print(\" selection\\t |\\tprobability\")\n", + " print(\"-------------------------------------\")\n", + " if wrap == False:\n", + " for i in range(len(states)):\n", + " print(\"%10s\\t |\\t %.4f\" % (state_sorted[i], prob_sorted[i]))\n", + " # Print the sorted states and their corresponding probabilities\n", + " elif wrap == True:\n", + " for i in range(4):\n", + " print(\"%10s\\t |\\t %.4f\" % (state_sorted[i], prob_sorted[i]))\n", + " print(\" ... ...\")\n", + " for i in range(-5, -1):\n", + " print(\"%10s\\t |\\t %.4f\" % (state_sorted[i], prob_sorted[i]))\n", + " print(\"-------------------------------------\")" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "id": "680f52d2", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "-------------------------------------\n", + " selection\t |\tprobability\n", + "-------------------------------------\n", + " 111001\t |\t 0.1169\n", + " 101101\t |\t 0.0872\n", + " 111100\t |\t 0.0823\n", + " 101011\t |\t 0.0809\n", + " ... ...\n", + " 000100\t |\t 0.0000\n", + " 010000\t |\t 0.0000\n", + " 000010\t |\t 0.0000\n", + " 000001\t |\t 0.0000\n", + "-------------------------------------\n" + ] + } + ], + "source": [ + "c_final = QAOA_ansatz_for_Ising(\n", + " final_params, nlayers, portfolio_pauli_terms, portfolio_weights\n", + ")\n", + "print_result_prob(c_final, wrap=True)" + ] + }, + { + "cell_type": "markdown", + "id": "71c7a0e0", + "metadata": {}, + "source": [ + "The highest probability corresponds to the best combination, which is consistent with what we found with classical brute force search.\n", + "\n", + "## Use XY mixer to improve the performance\n", + "\n", + "In the context of QAOA, XY mixers serve as a specific type of quantum gate to augment the optimization process. XY mixers, which are quantum gates introducing qubit interactions through controlled rotations, enable modification of the quantum system's state. The utilization of XY mixers in QAOA provides several advantages. They facilitate more efficient exploration of the solution space, thereby potentially improving the algorithm's overall performance. Moreover, XY mixers can amplify gradients of the objective function during optimization and enhance quantum circuit depth. Notably, in scenarios like portfolio optimization (covered in another tutorial), where constraints exist, XY mixers preserve the constraints associated with individual combinations while allowing for smooth transitions between them.\n", + "\n", + "It is crucial to consider that the choice of mixers relies on the specific problem under consideration, its unique characteristics, and the quantum hardware available." + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "id": "3d558b9f", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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XBgDAaoSXGGDSLgAA8UN4iQHu9QIAQPwQXmKAkRcAAOKH8BIDkUcEEF4AALAc4SUGOG0EAED8EF5ioPsRAZw2AgDAeoSXGIjMeWHkBQAAyxFeYoD7vAAAED+Elxg4GV4YeQEAwGqElxjwt3XNeeG0EQAAlrM0vGRmZmrDhg1qamqS1+vVunXrlJ6e3uc2v/jFL7R//361traqrq5Ov/vd7zRz5kwryxw0Rl4AAIgfS8PLxo0bNWvWLBUXF2vZsmVatGiR1qxZ0+c2ZWVluv3223X++edr6dKlcjgc2rp1q5zOoTtI1B1ekpnzAgBAXBgrWn5+vjHGmPnz50eWLV261IRCIZObm9vvz5k9e7YxxpipU6f2q7/H4zHGGOPxeCz5Xr21JV/8nFm1t9TctGJ53PZJo9FoNNpwatH8fls2nFFUVCSv16uysrLIsm3btikcDmvBggX9+oy0tDTdfvvtqqys1OHDh3vtk5ycLI/H06PFG48HAAAgfiwLLzk5Oaqrq+uxLBQKqaGhQTk5OX1u++Uvf1nNzc1qaWnRVVddpeLiYgUCgV77Ll++XD6fL9Kqqqpi9h36qzu8JDFhFwAAy0UdXlauXCljTJ9tsBNsN27cqI997GNatGiR3n33Xf36179WymmCwcqVK5WRkRFpeXl5g9r3QDDnBQCA+EmKdoNVq1Zp/fr1ffaprKxUTU2NJkyY0GO5y+VSVlaWampq+ty+exRl//792rVrl7xerz7zmc9o06ZNH+nr9/vl9/uj/RoxxdVGAADET9Thpb6+XvX19WfsV1paqszMTBUUFKi8vFyStHjxYjmdTu3evbvf+3M4HHI4HKcdeRkKuM8LAADxY9mcl4qKCm3ZskVr165VYWGhFi5cqNWrV2vTpk2qrq6WJE2cOFH79u1TYWGhJGnKlCn61re+pYKCAk2aNElFRUX67//+b7W1tWnz5s1WlTpoQUZeAACIG0tvnlJSUqKKigpt375dmzdv1s6dO3XnnXdG1rvdbuXn5ystLU2S1N7erk984hPavHmz9u/fr1/96ldqbm7WwoULdezYMStLHRSuNgIAIH6iPm0UDa/Xq5KSktOuP3TokBwOR+R9dXW1Pv3pT1tZkiUic144bQQAgOWG7m1rE4i/vWvOCyMvAABYjvASA5HTRoy8AABgOcJLDJx62sgxhJ/BBADAcMAvbQx0j7xIkjsl2cZKAAAY/ggvMdA98iJx6ggAAKsRXmLAhMMKdt3l180jAgAAsBThJUa41wsAAPFBeIkR7vUCAEB8EF5ihHu9AAAQH4SXGOk+bZTMnBcAACxFeImR7tNGSZw2AgDAUoSXGAnwZGkAAOKC8BIjgTYm7AIAEA+ElxjpHnlhzgsAANYivMQIp40AAIgPwkuMBNq6LpXmtBEAAJYivMQIIy8AAMQH4SVGeDwAAADxQXiJER4PAABAfBBeYqSjtU2SlJKWZnMlAAAMb4SXGGlvaZEkpaQTXgAAsBLhJUY6TnSGl1Hp6TZXAgDA8EZ4iZH2rvCSMpqRFwAArER4iZHu00aMvAAAYC3CS4x0j7yMGk14AQDASoSXGOmITNglvAAAYCXCS4xE5rykpcrpctlcDQAAwxfhJUY6Wlojr7lcGgAA6xBeYiQUDEYeEcCkXQAArEN4iaHIjeqYtAsAgGUILzHUzo3qAACwHOElhiL3euFGdQAAWIbwEkM8IgAAAOsRXmKIOS8AAFiP8BJDzHkBAMB6hJcY6r7XyyjPaJsrAQBg+CK8xFBLY5MkKX3sGJsrAQBg+CK8xFCL1ytJSs8ca28hAAAMY5aGl8zMTG3YsEFNTU3yer1at26d0qOYD7J582YZY3TttddaWGXstHg7R15GE14AALCMpeFl48aNmjVrloqLi7Vs2TItWrRIa9as6de29957r4wxVpYXcye8jZIYeQEAwGrGipafn2+MMWb+/PmRZUuXLjWhUMjk5ub2ue3cuXPN4cOHTXZ2tjHGmGuvvbbf+/V4PMYYYzwejyXfq6+WO2O6WbW31Kz40wtx3zeNRqPRaIncovn9tmzkpaioSF6vV2VlZZFl27ZtUzgc1oIFC067XWpqqp555hndfffdqq2tPeN+kpOT5fF4ejS7dE/YTRuTIYfDYVsdAAAMZ5aFl5ycHNXV1fVYFgqF1NDQoJycnNNu9+ijj+q1117Tc88916/9LF++XD6fL9KqqqoGVfdgtHSdNnIlJWmUjSEKAIDhLOrwsnLlShlj+mwzZ84cUDFXX321Fi9erHvvvTeqejIyMiItLy9vQPuOhVAgELlR3eissbbVAQDAcJYU7QarVq3S+vXr++xTWVmpmpoaTZgwocdyl8ulrKws1dTU9Lrd4sWLNW3aNDU2NvZY/uyzz+rPf/6zrrjiio9s4/f75ff7o/oOVjrh9WrU6HSljx2rY/rA7nIAABh2og4v9fX1qq+vP2O/0tJSZWZmqqCgQOXl5ZI6w4nT6dTu3bt73eaRRx7RunXreix766239PWvf13PP/98tKXaoqWhUeMmnc3ICwAAFok6vPRXRUWFtmzZorVr1+quu+6S2+3W6tWrtWnTJlVXV0uSJk6cqO3bt+vWW2/V66+/rtra2l4n6X7wwQc6ePCgVaXGVOQuu1wuDQCAJSy9z0tJSYkqKiq0fft2bd68WTt37tSdd94ZWe92u5Wfn6+0tDQry4gr37HOUamM8eNsrgQAgOHJspEXSfJ6vSopKTnt+kOHDp3xkuJEu+SY8AIAgLV4tlGMNXWFlzGEFwAALEF4iTFfXdfIywTCCwAAViC8xJjv2DFJnDYCAMAqhJcYa+oaefGclSWny2VzNQAADD+Elxg70eBVKBiU0+XS6KxMu8sBAGDYIbzEmAmH1Xy8QRKnjgAAsALhxQLdk3bHZI+3uRIAAIYfwosFmLQLAIB1CC8W6J60O2YCIy8AAMQa4cUCTXWMvAAAYBXCiwUijwjgRnUAAMQc4cUCkQm7jLwAABBzhBcLNPFwRgAALEN4sYCva87L6KxMudxum6sBAGB4IbxYoLXJp0BHhyQpY/xZNlcDAMDwQnixiO/YcUmcOgIAINYILxZp8TZKktLHjrW1DgAAhhvCi0VaGhslSemZY+wtBACAYYbwYpEWb5MkRl4AAIg1wotFGHkBAMAahBeLMPICAIA1CC8WYeQFAABrEF4swtVGAABYg/BikZbG7tNGjLwAABBLhBeLRMJL5lh7CwEAYJghvFike85LaoZHDieHGQCAWOFX1SKtTT5JktPpVNqYDJurAQBg+CC8WCQcDKnN1yxJhBcAAGKI8GKhVl/n6AvhBQCA2CG8WKi1a+QlNcNjcyUAAAwfhBcLcdoIAIDYI7xYqHvSbhojLwAAxAzhxUJtkdNGjLwAABArhBcLnRx5IbwAABArhBcLtXVdbcSEXQAAYofwYqHIyAsTdgEAiBnCi4W6L5Vmwi4AALFDeLFQ98hLKiMvAADEjKXhJTMzUxs2bFBTU5O8Xq/WrVun9PT0Prd5+eWXZYzp0X7+859bWaZl2hh5AQAg5pKs/PCNGzcqNzdXxcXFcrvdevLJJ7VmzRqVlJT0ud2aNWv0b//2b5H3ra2tVpZpmcjIC+EFAICYsSy85Ofn66qrrtJFF12ksrIySdJXv/pVbd68Wffdd5+qq6tPu21ra6tqa2utKi1uukde3Ckpco9KUaC9w+aKAABIfJadNioqKpLX640EF0natm2bwuGwFixY0Oe2JSUlOnbsmPbu3auHH35YqampVpVpqY7WVoUCQUncqA4AgFixbOQlJydHdXV1PZaFQiE1NDQoJyfntNs988wzOnTokI4ePao5c+boe9/7nmbOnKnrr7++1/7JyclKSUmJvPd4htYpmlafT56zspQ2JkO+umN2lwMAQMKLOrysXLlS3/rWt/rsk5+fP+CC1q5dG3n91ltvqbq6Wn/84x81depUVVZWfqT/8uXLtWLFigHvz2ptvubO8MK8FwAAYiLq8LJq1SqtX7++zz6VlZWqqanRhAkTeix3uVzKyspSTU1Nv/e3e/duSdL06dN7DS8rV67UD3/4w8h7j8ejqqqqfn++1Vp93KgOAIBYijq81NfXq76+/oz9SktLlZmZqYKCApWXl0uSFi9eLKfTGQkk/TFv3jxJOu0EX7/fL7/f3+/Pi7eTD2dk5AUAgFiwbMJuRUWFtmzZorVr16qwsFALFy7U6tWrtWnTpkgQmThxovbt26fCwkJJ0tSpU/Wd73xHBQUFmjx5sq6++mo99dRTeuWVV7R3716rSrUUD2cEACC2LL1JXUlJiSoqKrR9+3Zt3rxZO3fu1J133hlZ73a7lZ+fr7S0NEmdoyj/8A//oK1bt6qiokKrVq3Ss88+q6uvvtrKMi0VGXkZw8gLAACxYOlN6rxeb583pDt06JAcDkfk/ZEjR3T55ZdbWVLcMfICAEBs8Wwji/FwRgAAYovwYrGTjwhg5AUAgFggvFgs8nBGLpUGACAmCC8W4+GMAADEFuHFYq1NTZKk9LFjbK4EAIDhgfBisebjXkmdp41cbrfN1QAAkPgILxZr8/kU6OiQJGWMO8vmagAASHyElzhorm+QJHnGE14AABgswksc+LqeBTVm/DibKwEAIPERXuLAd+y4JCmD8AIAwKARXuKgub4zvHDaCACAwSO8xIHvWOdpo4xxjLwAADBYhJc4OHnaiJEXAAAGi/ASB75jxyRJYyaMt7kSAAASH+ElDuoPV0mSxp0zSQ6Hw+ZqAABIbISXODh+uEqBjg4lp45SZl6u3eUAAJDQCC9xYMJh1R04JEnKmTbV5moAAEhshJc4qX3/gCQpZ/oUmysBACCxEV7ipGZ/Z3jJnkZ4AQBgMAgvcVL93vuSpLz8GTZXAgBAYiO8xMmRtyskSdlTz1Vy6iibqwEAIHERXuLEd6xeTbXH5HS5lHf+TLvLAQAgYRFe4ujw39+WJE268HybKwEAIHERXuLog7f2SZLOmUV4AQBgoAgvcXS4K7ycTXgBAGDACC9xdPjvnZN2x0+epNQMj83VAACQmAgvcdTm86nhaLUkKWc6d9oFAGAgCC9xVvNepSQp97xpNlcCAEBiIrzEWffN6ggvAAAMDOElzmr2E14AABgMwkucdY+8MOcFAICBIbzEWV3lIYUCQaVmeDQ2e4Ld5QAAkHAIL3EWCgZVd/CQJClnBqeOAACIFuHFBjVM2gUAYMAILzao5nJpAAAGjPBiA644AgBg4AgvNuh+TEDO9Kk8JgAAgCgRXmzgO1avmvcPyOly6fxPFNldDgAACYXwYpO/vbRdkrTki7cpJT3N5moAAEgcloWXzMxMbdiwQU1NTfJ6vVq3bp3S09PPuN0ll1yi7du368SJE2pqatIrr7yiUaNGWVWmbV7d9Kya6o4pZ9oUlTzyoBwOh90lAQCQECwLLxs3btSsWbNUXFysZcuWadGiRVqzZk2f21xyySV68cUXtXXrVl188cUqLCzU6tWrFQ6HrSrTNi3eRj15zwMKtHdo1uUf14WLF9ldEgAACcPEuuXn5xtjjJk/f35k2dKlS00oFDK5ubmn3a60tNQ89NBDg9q3x+Mxxhjj8Xhi/r2saFd+9U6zam+p+ZdnnzYOh8P2emg0Go1Gs6NF8/ttychLUVGRvF6vysrKIsu2bdumcDisBQsW9LrN+PHjdckll6iurk6vvvqqampq9Kc//UmXXnppn/tKTk6Wx+Pp0RLJK7/cpPYTLZo4Y7pmFF1sdzkAAAx5loSXnJwc1dXV9VgWCoXU0NCgnJycXreZOrXzQYUrVqzQ2rVrdeWVV6q8vFzbt2/X9OnTT7uv5cuXy+fzRVpVVVXsvkgctPl82v3b5yVJi/75n2yuBgCAoS+q8LJy5UoZY/psM2fOHFghzs5SHn/8ca1fv1579uzRN77xDb3zzjv6/Oc/32dNGRkZkZaXlzeg/dtp5zP/rXA4rPyPX6LsqefaXQ4AAENaUjSdV61apfXr1/fZp7KyUjU1NZowoecTk10ul7KyslRTU9PrdtXV1ZKkt99+u8fyffv26Zxzzjnt/vx+v/x+fz+qH7oajhzVW9tf0ZziK7T4jlv1X//rIbtLAgBgyIoqvNTX16u+vv6M/UpLS5WZmamCggKVl5dLkhYvXiyn06ndu3f3us3BgwdVVVX1kZGbGTNmaMuWLdGUmZC2rV2vOcVXqOBTn9S2Net17OAHdpcEAMCQZcms4c2bN5uysjJTWFhoFi5caN555x2zcePGyPqJEyeaffv2mcLCwsiyr33ta6axsdFcf/31Ztq0aeahhx4yra2tZurUqZbMVh5q7faffM+s2ltqPvsf/2Z7LTQajUajxbNF+fttTRGZmZlm48aNxufzmcbGRvPEE0+Y9PT0yPrJkycbY4y57LLLemz3wAMPmA8++MCcOHHCvPrqq+bSSy+18ssPqXb2Bflm1d5S873yHSZj/Djb66HRaDQaLV4tmt9vR9eLYcPj8cjn8ykjI0PNzc12lxO1u9f/XFPnz9MfHn9SL67u+6Z+AAAMF9H8fvNsoyFmx4ZfSZKKbrxOKWk88wgAgA8jvAwxf3/5zzp26LBGZ2Vq2TfutrscAACGHMLLEBMOhfTs//6BJGnhzf+oq+/7Kg9tBADgFISXIei9Xa/ruR/8RJJ0+edu0ecf+4FSMxLrsQcAAFiF8DJEvfLUf2nDA/+uQHuHLrjsUt37X/+p3BnT7C4LAADbEV6GsL9u3qrH/vlOHT9yVOPOOVv3bFingmVL7S4LAABbEV6GuKqKd/Wjf7pdFTt3KTl1lEpWrtA/fvs+udxuu0sDAMAWhJcE0Nrk07q7/0Vbf/6EJOnSf7peX3tmnSbOPM/mygAAiD/CS4Iw4bBe+tk6rf3y19XibVRe/gzd+1//qaV3f1GupKgeUQUAQEIjvCSYip279P3P3KK/bf2jXO4kffKuz+vrv16vsy/It7s0AADigscDJLA5xVfoH799nzxnZSkUDOpP65/R1p8/oaDfb3dpAABEhccDjBBv/uFl/eC6W/TXzVvlSkrSkjtu1dd/vV7nzJlld2kAAFiGkZdh4sLFi3T9v96vjHFnKRwKacfTv9KW1WsU7OiwuzQAAM6IkZcR6K0/7tD3r71Fbzy3RU6XS5ffdou++X83aEbRxXaXBgBATDHyMgydv+hS3fBv92ts9gRJUvnmrXru+z9W8/EGmysDAKB3jLyMcPt2vKrvX/NZ7Xj6VwqHQir41Cd1/3P/pUtuvI6HPAIAEh4jL8Pc2RfM1A3//i1N6rqU+uCevfrvh76nmvfet7kyAABOiub3m/AyAjhdLl36T9fryq/eqVHp6QoFg3p107Pa9viTamlssrs8AAAIL4SX3o3JHq/rHvi65hRfIUlq8zVr+7pf6s/P/IarkgAAtiK8EF76dN4lhbr6G/9TeefPkCT56o9rx9ObVPrr36r9RIvN1QEARiLCC+HljBwOhwqWXakr/+cXlTUxV5LUfqJFZb9/UX/57fM68vY7NlcIABhJCC+El35zJrn0sas+qcWf/x/KmT41svzou/u1d9uf9NYfd+joO+/ZWCEAYCQgvBBeouZwODT94vm6+B+v1uwll8mdkhJZ562u0f6/lKvyjb/q/bI9On74iI2VAgCGI8IL4WVQUjM8uuCyj+vCxYuUf+klSk4d1WP9iQavjr67X0cr3tPRd95TzfuVOn64ivkyAIABI7wQXmLGPSpFUz42V9Mu+pimXfQxTZp9gZLc7l77tngbVf/BER0/UqWGozXyHas/2erq5as/rlAgEOdvAABIBIQXwotlklJSlDNtivLyz9PEmecpd+Z0TTh3sjxnZfVr+xZvo5qPN6jN16zWJp9afc1q8zWrzedTq6/rfVOz2lta5G9rk7+tXR2tbZ2vW9sUDoUs/oYAADsQXggvcZeSlqazJuXprEl5GnfO2RqbPUGecWdpzITxXX/HKSk5edD7Cfr96mhtU6C9XUF/QMFAQKGuv8GAX6FAUEF/L3+DnX/DwZCMCSscCssYIxMOKxwOy4TDMmGjcDgkE/7QcmMUDoUi/U0ofMpndG/X/Rnd2535M8Kmu1/o9Ps+dfmH9xl53b1fE3ndvU8ASBTR/H4nxakmDHMdra06+s57fV6ZlJqRoTETxml0VqZSMzxKy/AobUyGUjMyuv56In9TUlOVkpam5NRRSk5LlSup8/+qScnJXSFoTJy+WWILhz4afHoGoFMC1YeDVyjUGfoCAYUDQQWDAYUCQYUCgc4WDCkU6AqQXcuDgYDCwaCCp/QL+gOdo2etrepoa+/82zWa1nHK63CQUTUA/UN4Qdy0+Xxq8/kGtK3L7VZyaqpS0lI7A01qqpLcbrncSUpKTpbL7VZSsrvn367mSu56neyWw+mS0+WUw+GUw+mQ0+WSw+GQw+WU0+GUw9ndHHI6T7539ljuksPpkMPhPPlZrq513a9PXXfqfnp8Vncfx8n9Orr6fvjzT9mv0+Xq93FzulxS/7vbqntUraO1Vf7WNrX5mnXC26gWb6NaGpvU4m3UCW+jmmrr5D1ao8aaWoWCQbvLBmADwgsSQigQUFsgMODwM9xEAo/DIYfLJWdX2OkRnPoIQH0Fsu4g50xyyZWUJJc7SS63u+u1W0nd7yPLkiJh0ZXkOrnOnSRXUpLcKSkng2daauR1SlqaUtLS5HL3HFVLH9u/UbVwOCzfsXp5j9bo+OEqVb+7X0ff3a/qd/er+XiDlYcfgM0IL0ACMsbIdE9eTvDRB1dSkpLT0roCTaqS09I0Kj1NqRkepY8dq/SssUofO0ajM8dqdFamxuZkKzM3R+5RKRqbPUFjsydoysfm9PhM37F6Hfjrm6os26MD5X/T0Xf3y4TDNn1DALHGhF0ACWn0WZnKzM1VVl6uxp97jibOmK7c86Zp3ORJcjqdPfq2NZ/Qwb/t1YGyv6myfI8Ov7VPQb/fpsoB9IarjQgvwIjlHpWisy/I19SCeZoyf66mzJujUaPTe/QJ+v06/NY+Hfjr33T47xWq2veuGqqOcoUWYCPCC+EFQBeH06mJM6ZrSsEcTSmYp6kFc5UxftxH+rU1n9DRd99T1b53dfSdzr+17x9gUjAQJ4QXwguAPpw16WxNnT9X586drbzzZyj3vGm93ocoGAio5r1K1eyvVG3lAdXsP6Da9w+o4Wg1c2iAGCO8EF4ARMGZ5NKEKecqL3+G8s6f0fl35nlKzfD02t/f1q66A4dOBpquvw1Hqjj1BAwQ4YXwAiAGsvJyNXHmDGVPO1c506Yoe9oUTZgyucdT10/V0drWGWTeq1T1/vdV8977qn6vUs31x+NcOZB4CC+EFwAWcTidysqbqJzpU5Q9dUpXsJmq7Knnyj2q91DT4m1U9f5KHd77tg7seVMH9+xVi7cxvoUDQ9yQCS+ZmZl67LHHdPXVVyscDuvZZ5/V1772NbW0tPTaf/LkyTp48GCv62688Ub95je/OeM+CS8A7OBwOnXWpDzlnjdNudOnKue8aZ2Xbp9zdq93RT528AO9t/sNvb3jNe3/yxsKtHfYUDUwdAyZ8LJ582bl5ubqS1/6ktxut5588km9/vrrKikp6bW/0+nU+PHjeyy788479c1vflO5ubmnDT2nIrwAGEqSUlKUPWWyJuafp8lzL9SUeXOUM31qjz6Bjg6989pulb+wVW+/spMggxFpSISX/Px87du3TxdddJHKysokSUuXLtXmzZt19tlnq7q6ul+fU15ervLyct1xxx396k94ATDUpWZ4NOVjc5X/8Ut0/qKFypqYG1nX3tKivdte0RvPbdb7r5czARgjxpAIL7fffrtWrVqlrKysyDKXy6X29nbdeOON+t3vfnfGzygoKFBZWZkWLlyo0tLSXvskJycr5ZTJcx6PR1VVVYQXAAkjd8Y0zbuyWAWf+qSy8k4GmYaj1Sp7/kW9/v826/jhIzZWCFgvmvBi2bONcnJyVFdX12NZKBRSQ0ODcnJy+vUZX/jCF/T222+fNrhI0vLly7VixYrBlAoAtqp+931Vv/u+tvzkFzp33hzNv/pKfezKf1DWxFwVf+l2FX/pdlWW7dHr/2+z/rZ1uzpaWu0uGbCV88xdelq5cmXnQ+H6aDNnzhx0YaNGjdItt9yiJ5544oz1ZGRkRFpeXt6g9w0Adjm45009+93va8UVy/T0fd/Rvp2lCodCmjp/nm5+6H9pxcsv6J//z//Wwpv/UTnnTZPD4bC7ZCDuoh55WbVqldavX99nn8rKStXU1GjChAk9lrtcLmVlZammpuaM+7nhhhuUlpamp556qs9+fr9ffh6wBmCYCfr92vPSdu15absyxo/T/GVLddG1n1bOtCmat3SJ5i1dIumj95apO3BIDUeOqqGqmodPYtiyfMLu/PnzVV5eLkkqLi7Wiy++2K8Juy+//LLq6+t14403RrVfJuwCGM4mzTpf+Z8o0tSCuZo8d7ZS0lJ77RcOh+WrO6bjXUHmRINXJxq8avF61dzgVUtDo9pOnJC/tU0dra3yt7XzyAPYakhM2JU6L5XOzs7WXXfdFblU+o033ohcKj1x4kRt375dt956q15//fXIdtOmTdO7776rT33qU3rppZei2ifhBcBI4XS5dNakPOVMnxq5t8y4c87WWZPyNCo9/cwf8CH+tvauINOmQHuHQoGggoGAQoFA5G/n66CCfr9CgeDJdf6AgsFAZFkoEFQoGDz5NxhUONj5eeHgR9eFAoGTy3pbHgwpFAgQsIaxITFhV5JKSkq0evVqbd++PXKTunvuuSey3u12Kz8/X2lpaT22+/znP68jR45o69atVpYHAAktHArp2MEPdOzgB9q77U891qWPHaOzJuXprLPzlDkxR+mZYzU6M1OjszKVnjVWnqxMpaSlKTktVa6kzp+C5NRRSk4dZcM36b9wOHz68POhwNQzLIV6BqfThKdwIKhgIBjpd+r2J4PUh/cTUjgckgkbmXBI4VBY4XBYJhTq/Bvufh9WuGu9OWV5OBTqfB06pS8hrU88HgAARrik5GSlpKUqOS1VKWlpSklPU5LbraTkZLncbrncSV3v3V3vT1nm/tCy5GS5kpLkcid1/k1K6lwXed3519m1vSspSc4kl5Lcbjk/1MfldsvpjPq6kmEj3B1+QuFTQlAo8j4cCskYc9rw03P7znB16vYnw5XpEap6+9zu7bqXN9c3aPu6X8b0+w6ZkRcAwNAX9PsV9PvV0thkdykf4XA6PxJ8IoHInSRnUpKSuv66kpJ6D0GnBii3S66kU7d1y5Xkirzuc9vThS+XSw6nUw6nQ06XS06nUw6ns2u5Q06nq+u9s+u1o9dHRnyY0+Xq7OeOw4GOUt2BQzEPL9EgvAAAhiwTDkfC1XDjcDo7g47LJafTEQk8ncuccjhOCTyuzr5Ol0sOh6Nrm871DufJkNT5/mS/7vXOru177rNre4ez6/P7t73D5VRro8/WY0d4AQDABiYcVigcloJBu0tJOCP3ZCIAAEhIhBcAAJBQCC8AACChEF4AAEBCIbwAAICEQngBAAAJhfACAAASCuEFAAAkFMILAABIKIQXAACQUAgvAAAgoRBeAABAQiG8AACAhDJsnyrt8XjsLgEAAPRTNL/bwy68dH/5qqoqmysBAADR8ng8am5u7rOPQ5KJTznxM3HixDN+8YHweDyqqqpSXl6eJZ+PThzn+OA4xw/HOj44zvFh5XH2eDw6evToGfsNu5EXSf364oPR3NzMfxhxwHGOD45z/HCs44PjHB9WHOf+fh4TdgEAQEIhvAAAgIRCeIlCR0eHVqxYoY6ODrtLGdY4zvHBcY4fjnV8cJzjYygc52E5YRcAAAxfjLwAAICEQngBAAAJhfACAAASCuEFAAAkFMJLP33lK1/RgQMH1NbWpl27dqmwsNDukhLKt771Lf3lL3+Rz+dTbW2tfvvb32rGjBk9+qSkpGj16tWqr69Xc3OzfvOb32jChAk9+kyaNEm///3v1dLSotraWn3/+9+Xy+WK51dJKA888ICMMXr00UcjyzjOsTNx4kQ9/fTTqq+vV2trq958803Nnz+/R58HH3xQR48eVWtrq/7whz9o+vTpPdZnZmZqw4YNampqktfr1bp165Senh7PrzGkOZ1OPfTQQ6qsrFRra6v279+v73znOx/px3GOzic+8Qk999xzqqqqkjFG11577Uf6xOKYzp49Wzt27FBbW5s++OADffOb34zZdzC0vttNN91k2tvbzW233WbOP/988/jjj5uGhgYzfvx422tLlLZlyxbzuc99zlxwwQVmzpw55ve//705ePCgSUtLi/T52c9+Zg4dOmSuuOIKU1BQYF577TWzc+fOyHqn02nefPNNs3XrVjN37lxz5ZVXmrq6OvMf//Eftn+/odguuugiU1lZafbs2WMeffRRjnOM29ixY82BAwfMf/7nf5rCwkJz7rnnmuLiYjN16tRIn/vvv994vV5zzTXXmNmzZ5vf/e535v333zcpKSmRPps3bzZ//etfzcUXX2wuvfRS8+6775qNGzfa/v2GSlu+fLk5duyY+dSnPmUmT55srr/+euPz+cxXv/pVjvMg2pVXXmm++93vmuuuu84YY8y1117bY30sjqnH4zHV1dXm6aefNhdccIG5+eabTUtLi/niF78Yi+9g/0Ec6m3Xrl3msccei7x3OBzmyJEj5oEHHrC9tkRt48aNM8YY84lPfMJIMhkZGaajo8Ncf/31kT4zZ840xhizYMECI3X+xxYMBs2ECRMifb70pS+ZxsZG43a7bf9OQ6mlp6ebd955xyxZssS8/PLLkfDCcY5dW7lypdmxY0effY4ePWr+5V/+JfI+IyPDtLW1mZtvvtlIMvn5+cYYY+bPnx/ps3TpUhMKhUxubq7t33EotOeff96sW7eux7Lf/OY35umnn+Y4x6j1Fl5icUzvuusuc/z48R7/bqxcudLs27dv0DVz2ugM3G635s+fr23btkWWGWO0bds2FRUV2VhZYhszZowkqaGhQZI0f/58JScn9zjO77zzjg4dOhQ5zkVFRdq7d6/q6uoifV566SWNGTNGs2bNimP1Q99Pf/pTvfDCC9q+fXuP5Rzn2Lnmmmv0xhtv6Ne//rVqa2tVXl6uO+64I7J+ypQpys3N7XGsfT6fdu/e3eNYe71elZWVRfps27ZN4XBYCxYsiN+XGcJee+01LVmyROedd54kac6cOfr4xz+uLVu2SOI4WyFWx7SoqEg7duxQIBCI9HnppZeUn5+vsWPHDqrGYflgxlgaN26ckpKSVFtb22N5bW2t8vPzbaoqsTkcDv3oRz/Szp079fe//12SlJOTo46ODjU1NfXoW1tbq5ycnEif3v536F6HTjfffLMKCgp6nZfFcY6dqVOn6stf/rJ++MMf6uGHH1ZhYaF+8pOfyO/366mnnoocq96O5anH+tSQKEmhUEgNDQ0c6y6PPPKIMjIyVFFRoVAoJJfLpW9/+9t65plnJInjbIFYHdOcnBwdOHDgI5/Rva6xsXHANRJeEHc//elPdeGFF+rjH/+43aUMO2effbZ+/OMfq7i4mFukW8zpdOqNN97Qt7/9bUnSnj17dOGFF+quu+7SU089ZXN1w8dNN92kkpIS3XLLLfr73/+uefPm6Uc/+pGOHj3KcR7BOG10BvX19QoGg8rOzu6xPDs7WzU1NTZVlbgee+wxLVu2TFdccYWqqqoiy2tqapSSkhI5ndTt1ONcU1PT6/8O3evQeVooOztb5eXlCgQCCgQCuvzyy3XPPfcoEAiotraW4xwj1dXVevvtt3ss27dvn8455xxJJ49VX/921NTUfORKL5fLpaysLI51lx/84Ad65JFH9Ktf/UpvvfWWNmzYoEcffVTLly+XxHG2QqyOqZX/lhBeziAQCKisrExLliyJLHM4HFqyZIlKS0ttrCzxPPbYY/rMZz6jxYsX6+DBgz3WlZWVye/39zjOM2bM0OTJkyPHubS0VLNnz9b48eMjfYqLi9XU1PSRH5GRavv27brwwgs1b968SHv99de1ceNGzZs3T2+88QbHOUZeffVVzZw5s8eyGTNm6NChQ5KkAwcOqLq6usex9ng8WrBgQY9jnZmZqYKCgkifxYsXy+l0avfu3XH4FkNfWlqawuFwj2WhUEhOZ+fPF8c59mJ1TEtLS7Vo0SIlJZ08yVNcXKyKiopBnTLqZvtM56HebrrpJtPW1mZuvfVWk5+fb37xi1+YhoaGHldj0PpuP/3pT43X6zWLFi0y2dnZkTZq1KhIn5/97Gfm4MGD5vLLLzcFBQXm1VdfNa+++mpkffclvC+++KKZM2eO+eQnP2lqa2u5hPcM7dSrjTjOsWsXXXSR8fv9Zvny5WbatGnms5/9rDlx4oS55ZZbIn3uv/9+09DQYK6++mpz4YUXmt/+9re9Xm5aVlZmCgsLzcKFC80777wzoi/h/XB78sknzeHDhyOXSl933XWmrq7OPPLIIxznQbT09HQzd+5cM3fuXGOMMffee6+ZO3eumTRpUsyOaUZGhqmurja//OUvzQUXXGBuuukmc+LECS6Vjme7++67zcGDB017e7vZtWuXufjii22vKZHa6Xzuc5+L9ElJSTGrV682x48fNydOnDDPPvusyc7O7vE555xzjnnhhRdMS0uLqaurMz/4wQ+My+Wy/fsN5fbh8MJxjl379Kc/bd58803T1tZm3n77bXPHHXd8pM+DDz5oqqurTVtbm/nDH/5gzjvvvB7rMzMzzcaNG43P5zONjY3miSeeMOnp6bZ/t6HSRo8ebR599FFz8OBB09raavbv32+++93vfuSyfY5zdO2yyy7r9d/kJ598MqbHdPbs2WbHjh2mra3NHD582Nx///0xqd/R9QIAACAhMOcFAAAkFMILAABIKIQXAACQUAgvAAAgoRBeAABAQiG8AACAhEJ4AQAACYXwAgAAEgrhBQAAJBTCCwAASCiEFwAAkFAILwAAIKH8f9rNGcxO0L85AAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "loss_list = []\n", + "final_params = QUBO_QAOA(Q, nlayers, iterations, mixer=\"XY\", callback=record_loss)\n", + "\n", + "p = plt.plot(loss_list)" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "id": "d83fc94c", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "-------------------------------------\n", + " selection\t |\tprobability\n", + "-------------------------------------\n", + " 111001\t |\t 0.1553\n", + " 001001\t |\t 0.1260\n", + " 101001\t |\t 0.1180\n", + " 111000\t |\t 0.0934\n", + " ... ...\n", + " 100110\t |\t 0.0000\n", + " 000111\t |\t 0.0000\n", + " 000101\t |\t 0.0000\n", + " 000100\t |\t 0.0000\n", + "-------------------------------------\n" + ] + } + ], + "source": [ + "c_final = QAOA_ansatz_for_Ising(\n", + " final_params, nlayers, portfolio_pauli_terms, portfolio_weights, mixer=\"XY\"\n", + ")\n", + "print_result_prob(c_final, wrap=True)" + ] + }, + { + "cell_type": "markdown", + "id": "917c9415", + "metadata": {}, + "source": [ + "Compared with the standard X mixer, the XY mixer gives a higher probability of measuring the best result." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "tc_dev", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/source/tutorials/qaoa.ipynb b/docs/source/tutorials/qaoa.ipynb index 647818e9..2e1f44ee 100644 --- a/docs/source/tutorials/qaoa.ipynb +++ b/docs/source/tutorials/qaoa.ipynb @@ -1,6 +1,7 @@ { "cells": [ { + "attachments": {}, "cell_type": "markdown", "id": "dc0db886", "metadata": {}, @@ -9,6 +10,7 @@ ] }, { + "attachments": {}, "cell_type": "markdown", "id": "aecf6615", "metadata": {}, @@ -17,28 +19,147 @@ ] }, { + "attachments": {}, "cell_type": "markdown", - "id": "ddada0ca", + "id": "eaf8cd3f", "metadata": {}, "source": [ - "QAOA is a hybrid classical-quantum algorithm that combines quantum circuits, and classical optimization of those circuits. In this tutorial, we utilize QAOA to solve the maximum cut (MAX CUT) combinatorial optimization problem: Given a graph $G=(V, E)$ with nodes $V$ and edges $E$, find a subset $S \\in V$ such that the number of edges between $S$ and $S \\backslash V$ is maximized. And this problem can be reduced to that of finding the ground state of an antiferromagnetic Ising model whose Hamiltonian reads:\n", + "QAOA is a hybrid classical-quantum algorithm that combines quantum circuits, and classical optimization of those circuits. In this tutorial, we utilize QAOA to solve the maximum cut (Max-Cut) combinatorial optimization problem, as proposed by [Farhi, Goldstone, and Gutmann (2014)](https://arxiv.org/abs/1411.4028)." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "16ad937f", + "metadata": {}, + "source": [ + "## Max-Cut Problem" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "197d6df4", + "metadata": {}, + "source": [ + "In graph theory, a graph is composed of $n$ nodes, also known as vertices, and $m$ edges that connect the nodes. Note that there is not necessarily a link between any pair of nodes. Those $n$ nodes are divided into two sets. The number of edges that are cut by a partition/partitions of the nodes is what is going to be maximized." + ] + }, + { + "attachments": { + "16c7f2fb-b981-4798-8346-da54e3bcbaeb.png": { + "image/png": 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VjdFoQ13deLMrBAAAAJyEHThgLUJwAAAqwmuv7WiOtcZiLc2xluPHO4q5ZOX7lxWaTaLRxprqiNkVAgAAAE7CDhywD0Jw6+Xz+Xw+LyK5XK7wVNM0EVEUxe12i4jL5XK5XCJSeAoAQJFim/r23LFYa3d3Ytj3ezzuaLQxurKhKdoYjTYEAv4SFAkApbdfy+zXMiLSnEmISFde255NiUi1S13sCYhIveqdqXpFJOoNW1opAKDMsAMH7EnRdd3qGiqUpmnpdDqXyxUi72IUYnGv1+vxeBRFMbU8AEA5ymSysVhLod8kFmvpTWeGvSQUCjSdGi8YXdmoqq4S1AkAltiRTT2VOtmcSRQi72JUu9Qmb3iNv/qj/uoqRTW1PABAOWIHDpQFQvBSy2azmUwmm82O8U9eVVWfz+f1eknDAaDCJRI9zbGW/p13Mf9/GTeuOrqysXCm/IoVS0pQJABY6Be9Xf/R27U+3dWVL7b7ZEiLPYEbAuNuDI4jDQeACscOHCg7hOClk8vlUqlUYeaJURRF8fv9Pp+PKBwAKsqJE539e+5XN28v5pLJkyf095s0LLvY7AoBwA5imcT98cOFmSdGqXapt4Ym3hqaSBQOABWFHThQ1gjBSyGfzyeTSWPj74EURQkGg16v16T7AwDs4L33jvX3m2zd+mYxl8ysn1o4VKcp2rhw4VyzKwQA+9ivZT7Xud/Y+Hugapf6YNW0GwLjTLo/AMAO2IEDjkEIbi5d13t6ejKZ4QdCjZ3L5QoGgx6PpwRrAQBKo739YCzW2hxriW1qeeON3cVcMm/ezL5+k5UN8+bNNLtCALCbbl27q+vgU6mTJVirXvV+q2raVf7qEqwFACgNduCAIxGCm0jTtEQikc/nS7loIBDw+zlKGADK2Ntvt/f3m+zevb+YSy5ZOO9Uv0lDff1UsysEANvakU1d37F3v1aKHpR+90Qm3x2eXMoVAQDGYgcOOB4huFmy2WwymbTkj9fr9QaDQaaEA0AZ2bHj7dim1sLO+8CBw8Vc0tBwcdOpA+UnT55gdoUAYH+/6O36bNf+MZ5+OTo3BMZ9q3oaU8IBoIywAwcqCiG4KdLpdE9Pj4UFqKoaiUTIwQHAzlpa2vr7TY4ePVHMJZevWFroN4lGG8bV8ul7ADjtb5PHvtJ90MICFnsCG8bPJQcHADtjBw5ULEJw4yWTydIMAT8/RVEikYiqsgsHABt56eUtfRMGYy2dnfFh36+qrsKhOtGVDdFoYygUKEGRAFB2Pte5vzRDwM+v2qVuGDd3kYfv1QBgI+zAAQghuOFskoAXkIMDgOVyOS0Wa2mOtRR23qlU77CXBAL+vk9ZRhujKxs8HncJ6gSA8mWTBLyAHBwALMcOHMDZCMGN1Nvbm0qlrK7iDC6Xq6qqirkoAFBKyZ5U7NSeOxZr0bThT0iuqYlEo41NKxuj0Yb3v39ZCYoEAGd4IHH4/nhRg1xLpl71vjxxPnNRAKCU2IEDOD9CcMNks9lEImF1FUNQVbWqqsrqKgDA4To6uvv7TV5+ZWsxl9TVjW/qGy/Y+L7GhWZXCADO84verus79lpdxRAWewKbJsy3ugoAcDh24ACKRwhuDE3T4vG4bf8wvV5vKBSyugoAcJrDR47HYq2FnXdr6xvFXDJjxuTCRyyboo2LFl1odoUA4GA7sqnVJ3d15TWrCxnaDYFxT9TUW10FADgNO3AAo0MIbgBd17u7u/P54T9rY6FgMOjz+ayuAgDK3v797/X1m2xqff31d4q55IIL6ptOjRecP3+22RUCQCXo1rXLj+3cr9nlMJ4hPVg17QuhiVZXAQBljx04gLEjBDeArQ7DPI/q6mqXy2V1FQBQft7Zta+/3+Sdd/YVc8nFF18QXdkYjTY0RRtnzZpmdoUAUGlsdRjmebTVXVyveq2uAgDKDztwAMYiBB+rXC4Xj8etrqIoHo8nHA5bXQUAlIe2tl2xWEvzptZYrGXfvkPFXLJ06YL+fpOpU+vMrhAAKlYsk1h9YpfVVRRljb/6X2vpQASAorADB2Aet9UFlL1UKmV1CcXKZrO5XM7t5l86AAxty5Y3mk/1mxw+fLyYSy5bvjga7es3GT++xuwKAQAicn/8sNUlFGt9b1csk4h66UQBgKGxAwdQGnSCj0kZtYEXuN3uSCRidRUAYCOvvLIttqmlsPM+ebJr2PcrihKNNjZFGwqftYxEOHYYAEqqjNrAC5q84efHz7W6CgCwEXbgAEqPpuAxSSaTVpcwMrlcjmZwABUun8/HYq3NsZZYrKU51ppM9gx7id/njUYbC/0m0Wijz+spQZ0AgCF9tnO/1SWMTHMmQTM4gArHDhyA5QhDRy+TyeTzeaurGLFkMlldXW11FQBQUqlUOrapb88di7Vks7lhL6mqChc+Yhld2RCNNpagSADAsJ5KndyvlcGJ9IN8tnN/W93FVlcBACXFDhyArRCCj14mU377bxHJ5/OapqmqanUhAGCurq54f7/Jppe2FHPJxAm1/c0myy9dZHaFAICRWt87/KfmbWi/ltmRTS3yBKwuBADMxQ4cgG0Rgo9eNpu1uoRRyuVyhOCAsTRN03Vd13VN0wpPC58Ucblchb9uhTFELpfL5XJZW6qzHT12MhZrKey8f/e714u5ZNq0SdFoQ9PKxmi0YcmSi8yuEAAwFmUagotIcyZBCA4YbNc2SXRKolPe2Soi8l67HG4XEZk8S6bMEhFZtqrv6eSZ1lRYGdiBAygLhOCjZFICns3m3n67fdv2t99998iCi2YvXjy/vn6yoijGrpJOp30+n7H3BCpTNpvNZDK5XK744Uiqqrrdbp/Px++ijPLuu4f7+02273i7mEvmzJ7e12+ysnHBgjlmVwgAMMQvTErAc1r+nYPajnb94HHX/OmuS2a7ZkwQo3fgT6VOfiE00dh7AhUq9pz89lnZsrEv8i7GvKWybJWsvknmLjGxsErCDhxA2VF0Xbe6hrKUTCYNH4eyZ++7n/jEne37Dg18cc1VV/z9E/cGAn5j16qpqTE8WwcqRyaTyWQyY/xlmKIoHo/H5/NxVu0o7N5zoL/fZOfOvcVcctFFcwp77qZow5w5M8yuEABguM917n8qddLYe+bbj/T+jwfy+48OfNH94Uv9j31BAgZ3jRycvKhK4VfgwGht+IE0J2ytqQAAIABJREFUPyvNz47pJuEaaVorH7lJll5hUFkVhB04gLJGCD5KXV1dxp6KuX3H22s+emsiMcQRycuWLXjuZ4+Gw0EDlwuFQl6v18AbAhUik8mkUilj//q73e5AIEAUPqw339wTi7U0x1pim1r37n23mEuWLJ7f328yffoksysEAJhq4dE3jD0VM/96e+oTX9cTvWd/ybXkgsDTf6GEjexEeaKm/obAOANvCFSKDT+Q760bQd93MZatklvWEYUPix04AMcgcxmN/mm/Bvrrb/x9IQH/QFPjd75zV/2MKVu3vnXDjV85drxjy5Y3n37ml39yyx8buFw2myUEB0Ykl8ulUqlcbvgzzUdx53g87vF4gsEgE8MH2brtrf5+k0OHjg5/gcilly4qnCbfFG2YOJGsAQAcYkc2ZWwCLiLpB58pJODqyoW+Bz/jmj5B276395aH9OPd+W27cz9t9nz69w1crjmdIAQHRmbri/K9dbJlo/F33rJRbl8lTWvli48wMXwQduAAHIlO8NEoJFYG3nDXrv3LV3xSRKZOrXt5079EIqHC621tu5qu+LSIXHDBjFdf/pGB6Zjb7Y5EIkbdDXC2fD6fTCbNiL/P5vV6g8FghU8r2rx5RyzW0rypJRZrPX68o5hLoisbCs0m0WhDdTXf3ADAgWKZxOoTuwy8YX73ez1XfFlElCnjgr/5thLpO7Uy/+b+nt//qoi45kwJbnxIXIb9T7nJG35+/Fyj7gY43OF9cv9NpsTfZ1t9k3zpEQlVl2Itu2IHDsDx6AQfDcOzsJ/++68LD2769NX9CbiILFw49/IVS15+Zdvu3QdaW9983/sWGrWipmlG3QpwNk3T4vF4yX5fmMlkNE0Lh8OV1hLeHGuJxVoLn7WMx5PDvt/r9fTvuZuijX4/h/0CgMM1ZxLG3jD33EuFB54bP9SfgIuIa0G9etlF2qtv5fe8p23drTYYFltvz6WMuhXgcLu2ye2rJNFZouU2fF92bZX7n620lnB24AAqCiG4LbS39x2GufrD0UFfuvrqD778yjYR2X/gPQNDcD4BABQjk8kkk8NvB42laVp3d3ckElFVJ5+dlU5nYpv69tyxWGs6Pfwn3MPhYNOp8YLRaEOl/Z4AAGCs/L6+z/i7/6Bx0Jfcay7TXn1LRPQDx8S4ELwrTxsKUIQNP5D7byr1ou9slZuXymMbZe6SUi9dQuzAAVQyQvDRMHwg+MGDRwoPZs6cOuhLM2ZMLjw4cviEsYsCOL+enp50Om3J0rqud3d3O+8A23g8ObDfpJhLxo+vKYwXjEYbVlzm5J9JAADnZ3iCrB/q210rM+oGfUmZNqHvPUeLmgkAwDCP3SnPPGLN0olOuXmp3PN9Wf1pawowBztwACggBB8Nw2eJvPtuXwgeDgcHfWlcbVXhweEjx41dNJfLud38BwAMQdf1ZDKZzWatLaMwiDwYHPxtobwcP9EZi7XEYi3NsdbNm7cXc8mUKROj0camlQ3RaOOyZQvMrhAAUBa2Zw2eJaIf7NtdK2H/oC8ptX3DbfWjBk9jiGUSUW/Y2HsCDpHskm/cJM3PWlzG/TfJrq1y+8MWlzE27MAB4GxkoLZw/ESniEycUHv2lwLBvk15V5fBYxABnEtPT4/lCXhBOp1WVdXnK7Nxe4cOHS3suWOxlq3b3irmklkzp0Wjff0mCy/m0DAAgOn0k90iokyoOvtLSqDvk1h6V09JawIq2XfvsD4BL3jmEZk8S675ktV1jAw7cAA4P0JwW5g2rW7nzvZjQx3B3HGyq/Cgrm5caYsCKlRvb28mM/x0vJLp6elxuVwej8fqQoaxt/1gf7/Jm2/uLuaSCy+c1d9vMnduvdkVAgAwkDJ1vP72Qf1499lf0jv6uk+UidWlLQqoVE9+TTZ83+oiBnj0DpkyS6JXW13HMNiBA0DxCMFtYdq0STt3totIPJ6MREIDv1RoEheRSZPGl76wgv/8VSwcCtbUVtXWVNXURILBgFWVAGbLZDKplMGfth67ZDJpz3Myd+7cG4u1NsdaYptadu8+UMwliy65MBptKBytU18/xewKAQA4F2XKeHn7oIjo8ZQSOWN/q5/oS8aVuhoLKhMRke7X9qoBrxr2qWG/Gva5/Hb/dTgweht+IN9bZ3URZ/nGTfY8J5MdOACMDiG4LUydOrHw4J139jU0XDzwS2+80ffrXMND8OKPdX7ssad+8fyL/U99Pm9NTaSmpqqmpqq270Gktraq8KCmpi8rr6mpqqmtqq2JMHkc5ULTtJ4eO37qWdf1RCJRVVWlKIrVtcj2HW/395u8++7hYi5pbFxYOFqnKdowadIEsysEAKAYrqnjCuf85HcfUpdeMPBL+bf6ciVlksEheL1a7JHXx37W2v3q6b5OxaOqYb/7VCY+6J/usE+NnPGKoha71QcstmubPHqH1UUMJdEpd6+V72+VkPWfCGEHDgBjRzo5Gh6PJ5fLGXjDBfPnFB6s/8VvB4bguq4//cx/Fh5fOG+mgSvKSELwzs4zPiWaTmeOHDlx5MiJIi+PhEM1taey8pozs/LaQWF6VXU1JwXBGrqux+NxXdetLmRo+Xw+Ho9XVQ0xt7QEfve712Ox1uZNLbFYy9GjJ4u55P2XLy2MF4yubKyttaZsAICTNPnCzRkjz8hxXTi98EDb8NoZIbiuZ3/a3PeeC6YauKKMJATXEr0Dn+pZLdeRzHUki7zcFfCekZhHBibmZ8XooTI7fQTOkeyS21dJwuATaA1zuF1uXyXf22LJ4uzAAcBYhOC2cM21f/gXf/WoiPzTP//0lps/Nn36pMLrP3v2vw8dOioil69YcuGFs6wqr6MzPpbL44lkPJE8cKCo31e7XK7TWXntmX3lhay89ozQPBBgyw5j9PT02DYBL9A0LZPJeL3F/vA8Rpte2hKLtRQ+a9nVNfw3AbdbjUYb+/tNmJsEALA59x9H01/7FxHJ/uBXnv/5e8q0vk7J3M9f0d87KSLqZRe55k2zqjwtkR7L5flUJpPKyLHitvEu5VRiPjgfHyIxD/tdPn6KhEG+e4d9E/CCd7bKhh/I6k+XZjV24ABgHrYvo2H4RIIJ42tuuGHNU0+tTyR6PvbxL/2fr98+a+bUV17d9r+//O3CGz77p9cYu+KIhgvPmjm1ujrc2dnd2Rnv6Oju7R3Tjvz88vn8yZNdJ08dBzosv993xgyW2oGh+YDG81Ov23CqMuwgn8/b6jDMc0mlUh6Px6ShKNlsLhZriW1qbY61xGItqdTwf9ODwUBT4UD5lQ3RaKPbzd8vAIBZqhWD/y+jjK/yXL8q+28b9URv6pMPeP/qBtfMOm3zzvRX/7nwBs8tf2jsios9I8invJOr1JBPS/RqiV4tkc5njPwc6mB5Pdfdm+vuHf6dIiLi8rrPTsYHJ+aR05G64rJ+nhvs6PA+ex2GeS7fWycfWGvSUBR24ABQMorNOx/tKZfLxeNjao4+2+HDx6+57sttbbvO/tINN6x5+G/uMvb/bW63OxKJjO7a3t50R2d3Z2e8s6O7s7O7ozPe2dndH5H3PTj1Smdnt6blDax8jKqqwqdC875e8nMNNK+trRp0SCkcLJFIZLNZq6soSiAQ8Pv9Rt0tmUwVNtyFfpN8fvi/rbW1VdGVjdFoQzTa+P7LlxpVCQAA5xfLJFafGGKrPBb6kY7UjQ/m39x/9pc816/yffNPxNAdeJM3/Pz4uaO7Np/JaYl0IRDv+2e8V0v05ga9mOjVEulcolfyNvopTw16ByfmkXPON1eDJfrQG6x3z8ek+VmriyjOLevk5vuMuhk7cACwBCH4aOTz+a6uYluVixePJ2+97Rvrf/HiwBfv/upn/uzLNxne+Onz+YLBoLH3PJfu7sTprLzjzNC8s7uz44zQPB4vdtBhCaiq2j+AZfBA89qzTgGtqfL72bKXJTN+rWUeRVGqq6vH8j3h5Mmu2KbWWKylOdbyyivbirlk0qQJ/f0mjY0LR700AACjtl/LLDz6huG31eOp9J1P5H752sAXvX92jfdLa8XoHfitoYnfrCrRfBWtJ63FB+fj50rM8z02+jyc4nINnGB++uTPc5wIqnj5cHN52vqi3L7K6iKKFq6Rn7SPpRmcHTgAWI4QfJS6u7s1TTPjzul05o03dh8+cmLuBTPmzJmhmnOweyQScbvtuF/M5bRCRH4qNI93dnZ3nGoqP7sDPZ220ZY9EPD3ZeVnReT901oGNqG7+GSoPcTjcWOPujXbKH6Jdfjw8f5+k9YtRSUI9fVTTvWbNCy65MJRVQoAgJFWHt+5PZsy5dbpbP6t/fkjna45U1yzJ4s5O/AN4+dGvXY8BF7X8oPbzE8n5v1d56df1LOm/Bw0Oi6f+7yJ+emjQQvTWgz/3QZG6YtXypaNVhcxEtfeIbc/PKIr2IEDgK0Qgo9Sb29vKmXOFtx8iqLU1NRYXYUxenp6Bw9g6TgrNB/QgW6r/+CrqyNnDS4fMKTl1OmghQfhcIk69yuNpmnd3d1WVzFiNTU1RTaDP7/ht3d95aEhRy2dbe7c+mi0sWllQzTaaOFhvAAADOmBxOH740WdtW5D1S713UmLrK7CGPl09oy4/KyW80ExuthoAy5qyDcwH3efnmA+xHxzV4APeppj1za5uQxnevyys8hmcHbgAGBDhOCjVKbBWYHH4wmH7diEUgJ9mfiZEXlHx6msfMCI846OeDLZY3W9p3k87gGDy09l5bWnM/RBp4B6vR6rSy4PPT096bSJZ72aJBwOezxF/Svujieray49zxsWXjw3euqDlrNmlegz2gAAjML2bGrl8Z1WVzFKa/zV/1o72+oqrDHcSJa+qSyFlvN8r42OaVFUV6GLfIiTPwcn5n417FM8HFFYnMfulGcesbqIkXvgWYleXcwb2YEDgA3ZcSBGWVBV1eVyFXOEhQ15vZXb0VBTE6mpKfZE0Gw21z+1/Iy+8s7ujo7BoXlnRzxj5smK2Wzu2LGTx46dLPL9wWBgyIHmQ09rqa0yr3KbK69BKP0ymUyRIXhVJLR8+aLNm3cMfHHZsgX9/SZTpkw0p0YAAAy22BOoV737NRtNwyveGv/opwmXOzXsU8O+It+s5/KDk/HBx4Ge8bqeM3E2i67lc109ua5iO2Ncfs+gXvIzRrL0T2s51XhuXuV2V16DUPr9ttgQnB04ANgQIfjoud3uTKYst+BFZmfweNx1E8fVTRxX5PuTyVTHqUB8cGh+5ijzQje6qcX39KR6elIHDx0t8v2nG8xrzzoFtKaqpvaM0DwUCphafMnk83kzhvufONG1Zcube/a+W1MTWbpk/gUX1Bs+3D87kt+4RKONmzfvWHHZkv5+k/HjHTIQCQBQaZq84adSxfYE2MoaX+WG4COiuF3umqC7pthJgPnebF9iHh9iJMvZveemFp/vzeZ7s9njiSLff86TPyNDvO7yO+WHuMP75J2txt92xoXywWtl3lLpOCovrZfXfi05o1uUmp8VebLI97IDBwC7YRzK6JXpRBSv1xsKhayuAqLr+qDTPgeH5qea0AvBek9Pr9Uln+b1egYNLj/zFNDBYbrHY9Pft6XT6Z4eI4fe9PamH/zW97776L8Mev2rX/nMXX9+s4ELiUhVVZWqFvWR2xd/+1pjw0LGygMAHKBMJ6LcEBj3RE291VVARJcBPebnmWPe13KeT9tpNotbPd1mftYQczXsHzStRXGbcr6rAX78XXn0DiNvGKmVhzbIxZcNfr31BfnSB41cSESe3CpzlxTzRnbgAGA3hOBjkkwmy64ZvLq62uWy634I55ZOZ8512uegqSyF0Dxn5idDRyocDtacmmPeP9C8tnboU0Crq4udVzN2iURiRC3V59fZGb/hxq+8/Mq2Ib/6pS/eeN+9nzdqLRHx+XzBILtqAEDF+Vzn/rJrBm+ru7herdyBhOVLz2pDzzGPn3Hy5+nZLJqNpmW6Ap5BI8vPPvnz9MTzULHzagxwz8ek+VnD7jZ5lnx/m4TOMd3xjVflsysMW0tErr1Dbn/YyBsCAEqFEHxM8vl8V1eX1VWMAKlZ5YjHk+cJzfsbzAuheXd3sZ/ZLAFFUfoHsJxxCmhNpPasEec1tVXBwOjHKXZ0dBhVdi6n/Y8b7/qv/3ql/5Wbb1q7e/eB3za39L/y/Pq/W7FisVErut3uSKR0vzAAAMAm9muZhUffsLqKEbg1NPGbVRx8VxHyqUwuPvjMz3PON0/a6Wx2RRl6MEvYr0aGmG/u8o3hg55NimFle3zys3elesLpV/a9KeMmS6T29Ct/8wV59u8MW3HZKnn0BcPuBgAoIZvOKCgXLpfL5/Ol03bavpyboiiBgENGOWNYkUgoEgnNmDG5mDfn8/mO857/eTo074x3dnSnek38b17X9ZMdXSc7iv31ks/n7cvKa/tC8x899ZB55Z3Lhl/G+hPwtWs/+O0H/2z8+GoRaWvb1XTFpwuvt7S2GRiC8ytMAEBlqle9t4Ym/t/kMasLKUq1S707XNR+DA7gCni9Aa/UFdemkNeHSMbPTszjfWF6PmPmce66rsV7tXhvkR9zVjzq6cQ84lPD/ll/8VETyzuXP/na6QT86AG54/fkwNsiIld8XP76J32vr1htZAie6DTsVgCA0qITfKx0Xe/q6iqLP8ZAIOD3V/AR5DBOb2+649T5n4NO++zoGBia972ulfCToddf/5F/LS4EN3asv67rX/8/T3z30X9ZterSf/vRt73e0ycX/dHVt8U2bRGRNVdd8cMf3G/UiiJSW1s7/JsAAHCcrry28NgbXXkbDX87l3sikwnBYYh8JjfozM8zp7IM/qeeL92PqLUfXFBsCL5rm9y81LCFXS75u5fk4suk+6R8YqakBny8dUOHhGtERE68J2unGraiiDSXwc/+AICz0Qk+Voqi+P3+VCpldSHDUBTF5yvhoDc4mt/vmzJ54pTJE4t8f3d3ov/8z8Gh+VlhejyeHEtttTXnGAh4FmN/d6Uoyn33fn7BgjmrPxwdmICLyLx5Mwsh+IkTdI4AAGCAapd6a2ji/fHDVhcyjGqX+oVgsfsl4PxcXrdrnNszLlTk+7Vk+nwN5me+nu8Z00lXarjonzSN7aTO5+WzK+TLfys//MYZCbiInHivLwT3F/snBgBwNkJwA/j9/lwuZ+DxeoZTFCUSiSiKccPXgJGoqgpXVYVn1hf15lxOG26U+Rlhejp9xpa9pugQ3AzXXvOHg145ebLrxz/5VeHx0mUXGbtcPp/nnFsAQGW6Ozx5eza1vte+x/NUu9Tnx82tdqlWF4IKpYZ8asgnk4raG+tafqjEfNBUltON53r2jM9hqGFLP3D8N18Y/Mr0uVJ/auN9aLfByx3eJ5NnGnxPAID5CMGNEQqF4vG4ptn0I5nBYFBV2X+jPLjd6oQJtRMmFDvoo6end2AjeaDoczJzOTPnKvYtod355W8lEj2Fp5/+1B8Ze39CcABAJXuiuv4j2q7tWZt+IvPBqmmLPZzHg/KgqC53dcBdXex/sfl0ti8fj6e1RK/i8wx/TcGWjaOrcAQ8PnnsRenvAPvHvzT4/ofbCcEBoBwRghtDUZRwONzd3W3D4eCBQMDr9VpdBWCWYNAfDPqnTq2zupDB8vn8nV/+1n/8x8bC01u/8MkLL5xlZUEAADhLtUv919rZ7z++04bDwe+JTL4hMM7qKgCzuHwel8/jGR+2upCzuFT54Q6ZcGoI+M4Wefl5SwsCANgFLYSGcblckUhx54CXkNfr5TBMoPR0Xb/7nkeeemp94ekf/P7777v389aWBACA89Sr3ufHzbW6isFuCIzjMEzAAi6XPLlFps/re9pxVD6/0tKCAAA2QghuJFVVQyEbHbuhqmowGLS6CsCmzJsRlEr1fvZzX//Hf/pp4en8+bP+8R/Wud2MJAIAwHiLPYEnaoo7eKQkFnsCD1ZNs7oKwK7mLTXrztXj5ek9MmdR39NsWv6kQbJps5YDAJQbQnCDeb3ecDhshyMovV4vh2EC52HS347Dh4+v+aPbfvLTvsMwL7hgxk+eeTgSMeXXY243I60AAJAbAuP+tXa2HY6gvCEwjsMwgfMJ15hy23lL5ScDzqvMZuTWD8ixg6astfQKU24LADAZIbjxPB5PJBKx9rQ6v98fCoVIwIES27Z95xWrbtqy5c3C08tXLPnVL/9h2jTbzSsHAMBh1virnx83t1618iCcu8OTn6ipJwEHSu33Pin/1CL+U00nyW65cYG8udnSmgAAtkMIbgpVVauqqswbtnAeiqKEQqFAgJPogWEY3kb93HO/ufKDtxw73lF4+scf+71//+kjtbVVxq7Sz9rftAEAYDeLPYGXJsxf7LFgG1ztUp+oqb8nwhxwYDiGt1Hf/h2570fSvzE+sl8+Xi+H9hi8Sr/Js8y6MwDAZIqu61bX4GTJZDKTyZRsOUVRIpGIJeE7UI46OjqMutXBg0cXLfnYwFcuuGCG263mcpqIaDlNRDLZ3K//8x+mTJloyIput9uGh/ECAGC5z3Xufyp1smTLVbvU58fNtSR8B8pSk3GfV16wXP7h1TNeyWZEdBFFREQ59c/PrpCdLcasuGyVPPqCMbcCAJQW82TNFQqFfD5fT0+PpmmmLqQois/n8/v9jEABiqeqqlF/Nwth90C7dx84+229acN+K0YnOAAAQ3qipv6G4Livdh/cnk2ZulC1S/1CcOKtoYmMQAFGYN5SeWerMbfynDUB6exXRCQQNmY5oRMcAMoYGYrp3G53VVVVKBQyL7Hyer1VVVWBQIAEHBgRAyeiuFxF/e1zKYZ9H/B6rRx7CgCAnTV5w5smzH+ipt68KeE3BMa9NGH+PZHJJODAyCxbZdit8sW1sxT5tmJ8YK1htwIAlBbjUEoqlUql02kD/8zdbrep8TrgbJqmdXd3W13FKNXU1PB7LwAAhnV//PDf9hzrMi4Fa/KGTY3XAYd7Z6vcsszqIkZrQ4eEa6wuAgAwGoTgFshms5lMJpfL5fP50d3BcwrxNzBGnZ2d5fht0OPxhMPGfa4TAACnW9/btb63qzmT2K+NcjTZVf7qJm/4o/5q4m9grFbXSqLT6iJGrmmt3P8zq4sAAIwSM8EtUMivRUTTtFwul8lkNE0bNoZTVVVVVa/X63a7af8EjOLxeEp5eq1RCt9DAABAkdb4q9f4q0VkezbVnEms7+3akUsN2x6+2BNY5A6s8Vc3ecOMPQEM07RWNnzf6iJGzsBBLgCAkqMT3F5yuZyI6Lqez+dVVRURl8tFuzdgnmw2m0gkrK5ixKqrq/nOAACAIZozCRHpymv7tMxiT0BEZqpe2r0BE8Wek7vLcLj2j/dyMCYAlC86we3FwGP6ABTD7Xa7XK5RzyayRKFmq6sAAMAhmrxMGANKa+kVMnmWHG63uo6RWLaKBBwAyhoxCoCKpihKIBCwuoqRKbuCAQAAgNPCNXLLOquLGKGb77O6AgDAmBCCA6h0Xq+3jBqrCwcDWF0FAAAAMAarP11OjdWrb2IgOACUu7LJfTB2qVSv1SUANhUMBq0uoVi0gQMAUEbYgQPn9MWHra6gaLfQBg4AZY8QvFKs/8XGRUuu/sEPn7W6EMCOPB5PWbRX+3y+MmpaBwCgwrEDB86naW15tFdfe0c5Na0DAM5B0XXd6hpgujv/9zcf+e4PRaSmJrJj28+nT59kdUWA7eRyuXg8bnUV56MoSnV1taIoVhcCAACGxw4cGN6WjfLFK60u4rzCNfLjvRKusboOAMBY0VHofK1b3ijsv0WkszN+x50PWFsPYE9utzsUClldxfmEw2EScAAAygI7cKAoy1bJPU9aXcR53f8zEnAAcAZ13bp1VtcAc02ZMjEUCvz6v14qPH3zzd2TJo2/9H2XWFsVYEOqqubzeU3TrC5kCKFQyOPxWF0FAAAoCjtwoFjzlsrhfbJrq9V1DOWeJ6VprdVFAACMwTiUSrH6I3/6y/+MFR57vZ4d25+7cN4sSysCbCoej+dyOaurOIPX67V5lzoAADgbO3CgWF+8UrZstLqIM62+ye5d6gCAkWAcSqV4+Dt3ezx95/5lMtk77vymtfUAthUOh1VVtbqK0+w/pwUAAAyJHThQrPt/JvOWWl3EAPaf0wIAGCHGoVSKCRNqx42rfn7DbwtPd+3aF4mE3n+5nfYZgD0oiuJ2uzOZjNWFiIioqhqJRBgFDgBAOWIHDhTL65eLV8h/Py2ZXqtLEZm3VB7aIF6/1XUAAIzEOJTK8sef+OLPfvZf/U+3tv77kiUXWVgPYFv5fD6RSFg7H9zj8YRCIRJwAADKGjtwoFiH2+Wej8k7ls4Hb1or9zzJYZgA4DyE4JVl//73Fi25urs7UXi66opLX/jND6wtCbAtXdeTyWQ2m7VkdZ/PFwwGLVkaAAAYiB04MAKJTrn/Zml+1prVr/mSfPERa5YGAJiMcSiVpbo6MnnyhOd+/pvC0/Z9h9xu9QMfeJ+1VQH2pCiK1+vVdb30/eChUMjv5wOYAAA4ATtwYAS8fvnQ9ZLolDdeLfXS9zwpN3611IsCAEqFTvBKdOOn7nrqR+v7n74U+9HljCYEzi2TyfT09JTmu6XL5bLbyZwAAGDs2IEDI7Ph+/LonZLoLMVak2fZ7mROAIDRCMEr0fHjHYuWXH348PHC0+WXLnr1laetLQmwOV3XU6lUOp02bwlFUXw+n9/vZwg4AADOww4cGLFEp3xvnfz4uyYuEa6Ra74k197BEHAAcDzGoVSiYDAwY/rkn/z0V4WnBw8dzWQyH/rQ5dZWBdiZoigej8fn85k0HcXv94fDYY/HQwIOAIAjsQMHRszrl8s+LB+5SRKdsmub8fe/+T752r/JZR8WL3MIAcD5CMEr1CWXzDt06Ghr6xuFp7FYa1O0cc6c6dZWBdhcYUq4x+PRdT2fzxt1w3A47PV6ib8BAHA2duDAaIRrpGmtLFsl8U7Zv9P2PE+zAAAgAElEQVSYG37oOnngWWlaS/wNAJWDcSiVK5lMLV66ds+eA4Wnl1wyb8e256wtCSgjuq7ncrlMJpPNZkf6jdTlcnlOMak8AABgQ+zAgTFJdMqWjdL8rDQ/N+Jx4ZNnSdPVsmyVNK01pzgAgK0Rgle0//iPF/5o7a39T7/0xU898vDdFtYDlClN0zKZTP+klHw+P7BPXFXVQpe32+0uxN8ul8uyWgEAgKXYgQPGeGerND8riU55Z6uIyOF9crj99FfnLZVQtYjIslUSrpEPrJXJs6yoEgBgF4Tgle6OOx/47qP/r//pz5/724+uWWVdOQAAAIDDsQMHAAAoMULwSqfr+uIla19ve6fwdM6cGTu2PRcMMhkNAAAAMAU7cAAAgBLjI/mVTlGUhx/+av/TPXsO3HHnAxbWAwAAADgbO3AAAIASU9etW2d1DbDYnDkz0ulMbFNr4Wlr6xsLFsy5ZOE8a6sCAAAAnIodOAAAQCkxDgV9Lltx3ebXdhQeT548Ycf2n08YX2NtSQAAAICDsQMHAAAoDcahoM/D3zn9kczDh4/zkUwAAADAVOzAAQAASoNxKOgzY8YUVXW9sHFz4emOHW/Pmjl16dIF1lYFAAAAOBU7cAAAgNKgExyn/dVffv6KKy7tf3rHnQ8cOPCehfUApbdz597LV37yP38Vs7oQAABQEdiBA70HTr59+790v7bX6kIAAE5GCI4zPPKdu/sfd3Un7rjzmxYWA5TefV97/JVXtn149Z9+6n9+ZffuA1aXAwAAnI8dOCrc4R/Ekm8c2v3VH+97YH36UKfV5QAAnIlxKDjD5MkTIpHgr379UuHpm2/tqasbd+mli6ytCiiNXzz/4l/8xSOFx9t3vL10yUXLlvF5ZAAAYC524Khk3a/sPvTPzYXHqT3HAnPrgnMnWVsSAMCRFF3Xra4BtvORqz674Zd9GxGPx71j23Pz58+2tiSgBC5dfs3vWtoKj69ctfw3//19S8sBAAAVhB04KtPOz/+w5+3DhcfhpfXz/uZ6a+sBADgV41AwhEcevtvr9RQeZ7M5zqlHJfj/7d15nNV1vT/wMzPMDDMM+w4yKosLJCq5g0uWuWTuljtWWl0hA6yEFjloKd26DLmU6fV28dJN/V0FUjH3FHAHZREFlU2UUZQdBmaYOb8/TvcL1xRZ5sznnO95Pv/6vHvYzMtHmZ9efr6fz+9u/q+oAU8kEsnk0IBhAIB8YwdOHlr5wMyoAU8kEl0HDwwYBoB4cx0Kn6J9+zYdOrR9eOoz6fHtd5ZVVJQfc8yhYVNB5qxatfacc3+weXNterzyivOGDrk4bCQAIK/YgZNv6tdvXjR6Uqq2Pj22/9rBHc8aEDYSADHmOhQ+03nn//D+Bx6Pxlmv3O9+ZOLq6h/+6pZb/5xeN29e+s5bj3br1ilsJAAgD9mBkz+W3/rEykmz0uuCkmb9Jn63uH1F2EgAxJjrUPhMVVWj2rRpGY3DRvgkk3h6+eW5UQOeSCSSo4dowAGAIOzAyROb3lwRNeCJRKLr4IEacAAyynUofKbWrSq6dOk4ZcqT6XHp0vcLCwuOP/7wsKmg0V35vevefntZet2vX+//nvibsHkAgLxlB06eWPZvj255b3V63XyfDvv87Oth8wAQe06CsyOXDz7r0kvOiMbRyVtnPPdqwDzQ6P5yz8OPPDItGsd4DxMACMoOnNhb/dQb615aFI1dBw8KGAaAPOFOcD7Hxx+v6X/wWe+v+DA9HnbYF15+8b6wkaAR7X/AqQvfWppen3nmiZMfuDVsHgAAO3Dibf7gO7cs/8cx8NYD+/S8/uyweQDIB06C8znat29TVTUyGl95Zd7IUeMC5oFGdMMv/xA14IlEYsxox8ABgPDswImx6onPRQ14IpHoOnhgwDAA5A93gvP5+vXrvaJ65cyZr6fHGTNmDRo4oGfPHmFTwR5asuS9c869Ovoa5poRl1926ZlhIwEApNmBE0u11WsXXTc5Gjudf3i7r34hYB4A8ofrUNgpNTWbDzr4rHfe+cfjgX379p47e0phYUHYVLAnLv/WqAl3T0mvO3Vq985bj1VUlIeNBAAQsQMnfpb+euqqx+al183alPeb+L3CsuKwkQDIE65DYaeUlTUfv90nmfPnvz18xE0B88AeeuLJ56MGPJFIjBk9VAMOAGQVO3BiZv2spVEDnkgkul4+SAMOQJNxHQo7a7/99lm7dv0LL85Ojy++NGfAoQfuv/++YVPB7rns8pHvvludXh9z9CF/+P3osHkAAP6ZHThxsnTsw3Ufrk+vW/Tr3mPYV8PmASCvOAnOLqgaN/Kgg/aLxmHDb9q4cVPAPLB7/njHvTNmvBqNyaT3MAGALGUHTjx89OBrG+e9F43ewwSgiSnB2TXjx237JHPxkveGDR8bMAzsho0ba0Ynb4vGSy8946SvHBMwDwDAjtmBk+saNtetmDAjGtud1K/lF/cJFweAfOQ6FHbNvvvuVVdXN236zPQ469X5Bxyw7xe+0CdsKth5P/v5+Mcffy69LihITLr/lrZtW4WNBACwA3bg5Lr375q2fuaSaOx5/TlFLZuHiwNAPipIpVKhM5B7jjrmghdfnJNed+7cfu7sKR07tgsbCXbGnDkLDj707Ggckxx63S+uCpgHAGAn2YGTo2oWrXzzyj9FY9fLB3W51IeYADQ116GwO6rGjYrWH3zwsU8yyRWjx2y7CKV370oNOACQK+zAyVErJkyP1qXd22rAAQjCdSjsjh57dSkuLnrq6RfT49x5Cysrux566IFhU8GOPTDp8euv/3003vK7n23/zBQAQDazAycXrZm2sPru56Kxxw++UtazY8A8AOQt16Gw+0788uVP//2l9LplyxZzZ0/Ze+9uQRPBjvQ/+Ky58xam16ecPOiRqXeEzQMAsKtOtAMnp7x5xZ9qFq9Mr1sdvm+vseeHzQNA3nIdCruvqmrbJ5nr128cNuKmgGFgx37zm7uiBjyRSCSTQwOGAQDYPXbg5JAP7n0pasATiUTXywcFDANAnnMdCruvS+cOrVpVPPbYjPT45puLO3Roe8QRB4VNBf9sxYqVZ5979datW9Pj0CEXXXmFQygAQO6xAydX1K3auHj0pFR9Q3rseNaA9l87OGwkAPKZ61DYU1/7+r9MnfpMel1UVDR3zpQDD+gZNhJ8wve+n7zjzvvS69atK95567H27duEjQQAsNvswMl+71Y9+tFDs9ProhalfSd+t1mrsrCRAMhnrkNhT40fN7J585L0ur6+fthwn2SSXaZPnxk14IlEIjl6qAYcAMhpduBkuQ1zl0cNeCKR6Dp4oAYcgLBch8Keat++TYcObR9++B9HUd55590W5c0HDhwQNhVEvvWdny9evDy9HjCg75/u+lXYPAAAe8gOnCy37DeP1FavTa/L+3Su/MlpYfMAgJPgNILvf++b5513cjT+ZOS/zZo1P2AeiPznhElPPfVCNI7xHiYAEAt24GStVY/OW//q0mjs4j1MALKAEpzGMX7cyLZtW0ejTzLJBvX19cnkbdH4jfNPOf1rJ4SLAwDQmOzAyUKp+oYVE6ZHY9sTDmh9VK+AeQAgzXUoNI5WrSq6du04efKT6XHZshUFBYkTjj8ibCry3HWjb33woaej8X/+3/gOHdoGzAMA0IjswMlC1f85fe3z70TjvqPPbNa6PGAeAEhzEpxGc9mlZ1526ZnRmBxz2/TpMwPmIc8tWLD4VzfeHo0/HfXdAw7oGTAPAECjswMnq2x5d1X1n5+Pxs4XHdW8sn3APAAQKUilUqEzEB+rV6896OCz3nvvg/T4xQH9Xnn5/4WNRN668KIf3XPv1PS6R48u77z1WHFxs7CRAAAanR042WPJLx9c/fQb6XVJp5Z9/+t7Bc0cvAMgK/gbEo2pbdvW48eNjMaZs16/duS/BcxD3np46jNRA55IJMaMHqoBBwBiyQ6cLLHuxUVRA55IJLoMHqQBByB7+HsSjey8807+/ve+GY3/+pu7Hnt8RsA85KfkmG3vYX7phCO+9a1zAoYBAMgoO3CywfbvYVYcUtn+lIMChgGAT1CC0/iqxo3q02fvaBw2/Kb6+vqAecg3N98y8ZVX5kVjMjk0YBgAgCZgB05YKx+YuWlBdTR2HTwwYBgA+GdKcBpf8+YlVdt9kvnGG4uGDR8bMA95ZdXqtaOTt0bjFVecd9yxhwXMAwDQBOzACah+/eYVE7Z9fND+tP4V/XsEzAMA/6womUyGzkAM7ddnn/XrNzz/wuz0+NLLcw855IADDugZNhX54NqR45599uX0unnzkkn339KyZYuwkQAAmoAdOKG8f+czG+a8m14XlDTref3ZReUlYSMBwCcUpFKp0BmIrUMOPXv2nAXp9d57d5s7e4o6kox6+eW5Rxy17ULMsTeNuPYnVwTMAwDQxOzAaWKbFqxYcNV/RWO3K4/vfMGRAfMAwKdyHQoZVFU1KlovXfr+sBE+ySSztn8Ps1+/3hpwACDf2IHTxLa/CKX5Ph004ABkJ9ehkEH77tN969at06bNTI+vvvrGfvvtc9BB+4VNRVz95Z6pY399ZzT+4bbr+vbtFTAPAEDTswOnKa1+6o0P/vJiNPb44UnN9+4QMA8AfBbXoZBxRw+88IX/vZqwY8d2c+dM6dypfdhIxNL+B562cOGS9PrMM06cPOnWHf7hAACxZQdO05g/+N+3LF+VXrce2Kfn9WeHzQMAn8V1KGTc+HHbPslcuXLV8OE3BQxDXP3yV7dHDXgikUgmh4bLAgAQmB04TaB64nNRA55IJLoOHhgwDADsmOtQyLi99upcUlL81FMvpMd5897qsVeXAQP6hk1FnCxZ+t7Z51wdfddyzYjLL7v0zLCRAAACsgMn02qr1y4aPTnxvx+Wdzr/8HZf/ULQRACwI65DoYl8+aRvR7vwioryubOn7LNP97CRiI3Lv/XTCXdPTq87dWr3zluPVVSUh40EABCcHTiZs/TXU1c9Ni+9btamvN/E7xaWlYSNBAA74DoUmsj4cSOj9YYNm4b5JJNG8uSTL0QNeCKRSI4eqgEHAEjYgZMx62ctjRrwRCLRdfAgDTgAWc51KDSRzp3bt2nT8tFHp6fHBQsWt2/f+sgj+odNRQxcdvnId99dkV4fc/Qhf/j96LB5AACyhB04GbJ07MN1H65Pr1v0695j2FfD5gGAz+UkOE1n2A8vO/1rJ2wbh4+dP/+dcHGIgz/ecd+MGbOi0XuYAADbswOn0X300Gsb570Xjd7DBCAnKMFpUlVVI8vKmqfXDQ0NPslkT2zaVJMcc2s0XnrJGSd95ZiAeQAAspAdOI2oYXNd9YQZ0djupH4tv7hPuDgAsLNch0KTateudccObR96+O/pcdGid8vKSgcNHBA0FLnqZz//3WOPbduCT37glrZtWwXMAwCQhezAaUTv3zVt/StLorHn9ecUtWweLg4A7KyCVCoVOgN555sXjLjv//0tGl9+8b7DDvtCwDzkojlzFhx86NnROCY59LpfXBUwDwBANrMDZ8/VLFr55pV/isaulw/qcqkPMQHIDa5DIYCqcSPbt28TjcNGjA0YhhyVHHNbtO7du1IDDgCwA3bg7LnqCdOjdWn3thpwAHKIEpwAunXrVDVuZDTOmDFrdPLWHfzx8AmTJj0xafIT0ThmtPcwAQB2xA6cPbRm+sI109+KRu9hApBblOCEceklZwwefFY0Xn/D75+d9krAPOSW0du9h3nKyYMuuuj0gGEAAHKCHTh7Yvv3MFsdvm/bL/cNGAYAdpUSnGDGjxvVY68u0eidenbSb377H3PnLozGZNIxcACAnWIHzu758N6XahatjMYugwcFDAMAu0EJTjBt2rSsqtr2Searr77x42t/GzAPOWFF9crkdsfAhwy56Mgj+gfMAwCQQ+zA2Q11qzau2O428I5nDWhxYNeAeQBgNxQlk8nQGchffQ/s9eGHH7/yyrz0+Nxzrx511MG9e1eGTUU2+9GPf/PCC7PT69atKybdf0t5efOwkQAAcogdOLvq/duf3vjGivS6qEXpvtefXVhaHDYSAOyqglQqFToDea22tu6gg89cuHBJejxg/33nzJ5SXNwsaCiy1PTps449/pJorBo3ctgPLwuYBwAgF9mBs/M2zF3+1rD/jsa9rjqx47mHBcwDALvHdSgEVlJSPH7cqGh8c8Hi4SPGBsxDNtv+IpQBA/pqwAEAdoMdODtv+/cwy/t01oADkKOU4IR36qnHXjPi8mi87ff/PWnSE+HikKX+c8LkJ596IRrHjPYeJgDAbrIDZ2esenTe+leXRqP3MAHIXa5DIVsc+sVzXnvtzfS6srLr3NlTWrWqCBuJ7FFfX9+rz8lLl76fHr9x/in33jMubCQAgFxnB84OpBpS8y/5Y+0H69Jj2xMO2OcXZ4SNBAC7zUlwssX2n2QuW7Zi2PCbAoYh2yTH3BY14IlEIpl0DBwAYE/ZgbMD1ROmRw14IpHoMnhgwDAAsIeKkslk6AyQSCQS++zTvaGh4dlnX0mPr732Zp8+e/c/aL+wqcgGCxYu+cY3h0fjT0d995vfODVgHgCAeLAD57NseXfV4uv/Go2dLzqq7ZcODJgHAPaQ61DILgMHXfzc86+m1x06tJ07e0qXLh3CRiK4Cy/60T33Tk2ve/To8s5bjxUXNwsbCQAgNuzA+WdLfvng6qffSK9LOrbsO/F7Bc18Rw5ADvO3MbJLVdXIaP3RR6t9ksnUqc9GDXgikUiOHqoBBwBoRHbgfMK6FxdFDXgikehy+SANOAC5znUoZJfu3TuXlpY8+dQL6fH119/u3r3TFwf0C5uKgC6+5Mfvv/9hev2lE44YXzVqx388AAC7xA6cT1hy44N1H29IrysOqdxryJfD5gGAPecf55J1Ro288itfPjoahw0fu2jRuwHzENDNt0x8+ZV50Zgc7T1MAIDGZwdOZOWkmZsWVEdjV+9hAhALSnCyUdW4kQUFBen1pk01w0aMDZuHIFavXpscc2s0XvGd84477rCAeQAAYswOnEQiUb9+84oJM6Kx/Wn9K/r3CJgHABqL61DIRp06tW/TptXfHp2eHhcuXNK2baujjjw4bCqa2MhR45555uX0urS0ZNIDt7Rq2SJsJACAuLIDJ5FIvH/nMxtm/+MjgIKSop5jzikqLwkbCQAaRUEqlQqdAT7dGWcNefDBp6Nx7pwpX+jXJ2AemtLLr8w74shvROPYm0Zc+5MrAuYBAMgHduD5bNOC6gVX3R2N3a48vvMFRwbMAwCNyHUoZK/x40aWl5dF4/DhPsnMI8nktotQ+vXrrQEHAGgCduD5bMWE6dG6+T4dNOAAxIkSnOzVs2eP8VUjo/GJJ58f++s7A+ahydxzz9Spjzwbjd7DBABoGnbgeWv102+se3FRNHoPE4CYcR0K2e6CC6+5975HovHFF+494vCDAuahCex/4GkLFy5Jr88848TJk27d4R8OAEBjsgPPQ/MH//uW5avS69bH9O55wzlh8wBA43ISnGw3vmpUhw5to3H48JsChqEJ/PJXt0cNeMIxcACAJmcHnm+qJz4fNeCJRKLr4EEBwwBAJhQlk8nQGWBHKirKu3fr9MCkJ9Lju8urGxoavvQl99PF05Kl759z7g+iL1RGjLh88GVnho0EAJBv7MDzSu0HaxePnpT430/EO51/eLuvfiFoIgBofE6CkwMuvvjr37r87Gi84Zd/eOaZlwPmIXOSY26tr29Irzt1bDfGMXAAgBDswPPHigkzUg3/qMCbtSl3GzgAsaQEJzdUVY2qrOwajcNG+CQzhp586oUJEyZHYzI5tKKiPGAeAIB8ZgeeD9bPWrrq0XnR2HXwwMKykoB5ACBDlODkhtatKsaPGxWNr7325o9+/JuAeciEZHLbA5hHH33Iv3z/goBhAADynB14PqieMCNat+jXvcMZhwYMAwCZowQnZ5x99leGXHVRNP7buD898rdpAfPQuO64477pM2ZFo4tQAACCswOPt48emr1h3vJodBEKADFWED1AB9mvrm5r/4PPfHPB4vS43377zJ09paSkOGwq9tymTTW9+pxcXf1Rerz0kjPunjA2bCQAABJ24PHVsLlu/qV31K3amB7bndRv75FfCxsJADLHSXBySXFxs6qqbZ9kLly4ZNhwVxPGQXLMbVEDnkgkko6BAwBkBzvwuFpx94yoAU8kEl0cAwcg1oqSyWToDLALeveu3Lix5rnnX02Pr7wy76CD+vQ9sFfYVOyJOXMXXnrZtdE4Jjn0rLO+HDAPAADbswOPn5pFK5fe9HA0dh08qM2gPgHzAECmuQ6FnPTFw86b9er89HqvvbrMnT2lTZuWYSOx28457+pJk55Ir3v3rnxrwd/C5gEA4J/ZgcfJ4tGT10xfmF6Xdm/b9+4rw+YBgExzHQo5qapqZLRevrx62AifZOaqSZOeiBrwhItQAACylR14bKyZvjBqwBPewwQgP7gOhZy0997dUqnUM8++nB5nz36zV68eB/ffP2wqdsMFF4744MOP0+tTTh7067HXhM0DAMCnsgOPjSU3/HXr6k3pdavD9+323ROCxgGApuA6FHLYoOMumTFjVnrdvl2bObMnd+vWKWwkdslvfvsfP7n2t9H4wnP3HHlk/4B5AADYMTvwXPfhfS+998e/R+N+t17S4sBu4eIAQBNxHQo5bPy4bZ9kfrxqzfARYwOGYVdVV3+UHHNrNA656iINOABAlrMDz2l1qzau+M8Z0djxrAEacADyhOtQyGHdunUqKyt94snn0+Pr89/u1rXjF7/YL2wqdtKPfvyvL7wwO71u1api0v03l5eXhY0EAMCO2YHntPdv//vGN95Pr4talO475uzC5sVhIwFA03AdCjnvq6dc8fjjz6XXZWWlc2ZP6d2rMmwkPtf0GbOOPe6SaKwaN3LYDy8LmAcAgJ1nB56LNs5bvvCH/x2N3a86sdO5hwXMAwBNyXUo5Lzx40YWFv7jv8k1NVuGD/dJZg7Y/iKUAQP6asABAHKIHXguWjFh20Uo5X06a8AByCtKcHJe3769x1dtu5rwoYf/Pv53dwfMw+eaMGHyk0++EI3J0UMDhgEAYFfZgeecVY/OWz9raTR2GTwoYBgAaHquQyEmzjp76JS/PhWNc16bfNBB+wXMw2epr6/v3efkJUv/cRfhN84/5d57xoWNBADAbrADzxWphtT8S+6o/WBtemxzwgH7/uKMsJEAoIk5CU5MVFWNqqgoj8ZhI24KGIYdSI65LWrAE4lEcvSQgGEAANhtduC5onrC9KgBTyQSXQcPDBgGAIIoSiaToTNAI2jbplWnTu0efPDp9Lh48XslJcXHHvvFsKn4hIULl3zjm8OjcdSo717wzdMC5gEAYLfZgeeELe+uWnz9X6Ox80VHtf3SgQHzAEAQrkMhVi66+Ed/uWdqNL7w3D1HHtk/YB4+Yfv/gHrs1eXttx4tKSkOGwkAgD1hB57llvzqwdVPvZFel3Rs2XfidwuaFYWNBABNz3UoxErVuFGdOrWLRp9kZpWpjzy7/f9BSiaHasABAHKdHXg2W/fioqgBTyQSXQYP0oADkJ9ch0KsVFSUd+/e+YEHHk+Py5d/sHXr1hNPPCpsKtIuvvTH77//YXp9wglH/K5qVNg8AADsOTvwbLbkxofqPt6QXlccUrnXkC+HzQMAoTgJTtxcdOHXvv3tc6PxVzf+8em/vxQwD2m33DLx5ZfnReOY0UMDhgEAoBHZgWenlZNmblqwIhq9hwlAPnMnODG0fv3Ggw4+c+nS99Nj//77z351UthIeW716nW9+py8evU/nqS/4jvn3XnH9WEjAQDQiOzAs039+s2vX3pH/frN6bH9af0rrzklbCQACMhJcGKoZcsW47e7amPOnAXX/OjXAfOQHHNr1ICXlpYkRw8JmwcAgMZlB55tVtw9I2rAC4qLug4eFDYPAISlBCeezjrzy0OHXByN46omPDz1mYB58tnLr8y7+ZaJ0TgmObR7984B8wAAkAl24Nlj04LqlQ/MjMaugwcVd6gImAcAgnMdCrFVX19/0MFnvfHGO+mxT++958ye3Lx5adhUeehrX//+1KnPptf9+vWeN+evYfMAAJAhduBZ4p2f/s+6Fxel18336XDgXd8OmwcAgnMSnNgqKioaP25kNL719tLhI8YGzJOf7rl3atSAJxKJpPcwAQDiyw48G6x++o2oAU94DxMAEolEIlGUTCZDZ4BM6dWrsqZm84znXk2Pr8x8/Qv9evft2ztsqrxy3jeGffzxmvT6zDNOvH7MD8LmAQAgo+zAg1s8Zkr9upr0uvUxvbt+69iweQAgG7gOhfg77IjzZ858Pb3u3r3znNmT27VtHTZSnvjlr27/xXU3R+OrM+8/5JADA+YBAKBp2IGHUj3x+RV/mhaNB/zx8rLenQLmAYAs4ToU4m/7TzLfe++D4cN9ktkUli59PznmtmgcMfxyDTgAQJ6wAw+i9oN11ROmR2On8w/XgANAmutQiL/Kym4FBYm/P/Nyepw9Z0HPnnsdfPABYVPF3vARN7366hvpdceO7Sbdf3NpaUnYSAAANA078CCW//7Jmrc/TK+btSnvOebsguKisJEAIEu4DoV8cdzxl06bPjO9btu21dzZU7p37xw2Uow9+dQLXzlp2xv0v7/tun/5/gUB8wAA0PTswJvS+llL3/7xvdHY44cndTjj0IB5ACCruA6FfFFVte2TzNWr1w3zTn0mbX8RytFHH6IBBwDIQ3bgTan67hnRukXfbhpwANie61DIF926diovb/7EE8+nx/nz3+nSpcNhh30hbKpYuuPO+37/+79E413/fkOvXpUB8wAAEIQdeJP56KHZH015NRr3/tGppd3aBMwDANnGdSjkl5NPvfKxx/5xRKK0tGTu7Cl9+uwdNlLMbNq0uXefk1dUr0yPl5N+RsMAAB4ASURBVF5yxt0THPkBAMhfduCZ1rClbv4ld9St2pge253Ub++RXwsbCQCyjetQyC/jx41q1uwfj8Ns2VI7bMRNYfPET3LMrVEDnkgkkqOHBAwDAEBwduCZVj1hRtSAJxKJLoMHBgwDANnJdSjkl44d27Zr1/qRR6alx7feWtqqVcXRRx8SNlVszJ278NLLro3G5OihZ5/1lYB5AAAIzg48o2oWrVx608PR2HXwwDaD9guYBwCyk+tQyEdnn/uDyZOfjMbXXp10cP/9A+aJjXPP++EDkx5Pr3v3qnxr4d/C5gEAIEvYgWfI4uTkNdMWptel3dr2/a8rw+YBgOzkOhTy0fhxo1q2bBGNw4f7JLMRTJr8RNSAJxKJZHJowDAAAGQVO/BMWDP9ragBT7gIBQA+m+tQyEdt2rTs3LnDX//6VHpcsuS94mZFxx13WNhUue6CC6/54IOP0+uTTx70r2OvCZsHAIDsYQeeCUtu+OvW1ZvS61aH79v9uycEjQMA2ctJcPLUt791zkUXnh6NP7/u5udfeC1gnlz329/+x5w5C6LRe5gAAHyCHXjj+vC+l2oWbXuR3jFwANgBd4KTv1auXHXQwWdGh5ePPKL/C8/fEzZSjqqu/qhXn5M3bapJj0OuuujWW34eNhIAAFnIDryx1K3aOP/SOxo216XHjmceutfVJ4WNBADZzElw8lfHju3GjxsVjS++NOdnPx8fME/uSo65NWrAW7WqcAwcAIBPZQfeWKonzIga8KIWpV0GDwqbBwCynBKcvHbBBadd8Z3zovHGm+546qkXAubJRdNnzPrjHfdFY3L00A4d2gbMAwBANrMD33Mb5y3/6KFtN8l0GTywWeuygHkAIPu5DoV8t2HDpv6HnLV48fL0eNBB+815bXLYSLnlpK9+54knn0+vBwzoO/Pl/wmbBwCALGcHvofe/vG962ctTa/L+3Te//bBYfMAQPZzEpx8V1FRXjVuZDTOnbtw+IixAfPklgl3T44a8IT3MAEA2Al24Hti1WPzogY84T1MANg5RclkMnQGCOyA/fddvXrtiy/NSY8vvDj7sC/222+/fYKGygH19Q3nnHf1mjXr0+M3zj/lZz/9fthIAADkBDvw3ZNqSC0ePbl+w5b02Ob4A7pccnTYSACQE1yHAolEItHQ0ND/4LNen/92euzVq3Lu7MllZc3Dpspyv7ju5l/+6vZonD/vwQMP7BUwDwAAOcQOfDes+NP06onPReOB//Gd5nu3D5gHAHKF61AgkUgkCgsLq6q2fZL5zjvLhg33SeaOLFy4ZPsGfNTI72rAAQDYeXbgu2rL8lXbN+CdLzpKAw4AO8l1KPAPvXr22Lx5y4wZs9LjzFmv9+3bq1+/3mFTZa0fXP2refPeSq977NXlgftvLioqChsJAIDcYge+S5bf8sTmxR+l18UdW/a8/uyCQsfaAGCnuA4F/o/Dj/zGK6/MS6+7du04d/aU9u3bhI2UhaY+8uzXTt92/fddd97w7W+fGzAPAAC5yw58Z6x7cdE7P/2faKz80SntT+0fMA8A5Bb/3Bj+j/HbvVO/YsXKYd6p/zTJMbdF6xNOOEIDDgDAbrMD3xkr7p4RrSsOqdSAA8AucR0K/B+VlV0LCwv+/veX0uOcOQv22af7IYccEDZVVrnl1ol33XV/NP7nn27cZ+/uAfMAAJDT7MA/18pJMz+eOica9/7JaSVdWgfMAwA5x3Uo8CmO/9Jlzz77Snrdpk3LOa9N6dGjS9hIWWL16nW99zt51aq16fGK75x35x3Xh40EAEAM2IF/lvr1m1+/9I769ZvTY/vT+ldec0rYSACQc1yHAp9i/LhR0XrNmvXDR9wUMExWSY65LWrAS0tLkqOHhM0DAEA82IF/lhV3z4ga8ILioq6DB4bNAwC5yHUo8Cm6du1YUVH++OPPpcc33ljUuVO7ww8/KGyq4F55Zd4VV/4iGn95w9WnnXpcwDwAAMSGHfin2rSgetlv/xaN3b59XKsjewbMAwA5ynUo8JlOPe27f3t0enpdUlI8Z/aU/ffbJ2iiwE7/+r88PPWZ9Lpf397z5v41bB4AAGLGDvwT3vnp/etefCe9br5PhwPv+nbYPACQo1yHAp9pfNWo4uJm6XVtbd3w4Xn9SeY9906NGvBEIuEiFAAAGp0d+PZWP/1G1IAnEgkXoQDAbnMdCnymDh3atm/XZuojz6bHt99e1rJl+TFHHxo2VSjnfWPYxx+vSa/POOPEG66/OmweAADixw58e0vGTNm6ria9bn1M767fOjZsHgDIXU6Cw45cddWF55x9UjT+6Me/ee21NwLmCeVXN96+YMHiaHQMHACADLEDT6v+8/Ob310VjY6BA8CeUILD56iqGtm6dUU0DhsxNmCYIJYufT855rZoHDH88kMPOTBgHgAA4s0OvPaDddUTZkRjp/MOL+vdOWAeAMh1rkOBz9G6dcvOnTtM+etT6XHp0veLigqPP+7wsKma0vARY2e9Oj+97tix3aT7by4tLQkbCQCAGLMDX/77J2ve+iC9btamfN8xZxcWF4WNBAA5zUlw+Hzfuvzsiy/+ejReN/qW5557NWCepvTkUy/854RJ0ZgcPaRlyxYB8wAAkA/yeQe+/tWlqx6dF41dBw8sKncGBQD2SEEqlQqdAXLARx+t7n/wWSuqV6bHww8/6KUX7g0bqWkcd/yl06bPTK+PPuqQ52b8d9g8AADkibzdgb817L83zF2eXrfo222/Wy4JmwcAYsBJcNgpHTq0raoaGY0vvzx31E+rAuZpGnfceV/UgCe8hwkAQBPKzx34Rw/NjhrwRCLRdfCggGEAIDaU4LCzvvmNU6+84vxoHPvrO5948vmAeTJt06bN27+HecklZ3z1q56kBwCg6eTbDrxhS1313dvew2x3Ur+Wh+0TLg4AxIcSHHbB+KqRPXv2iMbhw8fG+EKh5PW3rVixctvoGDgAAE0ur3bg1RNm1H28IRq7XOYMCgA0DiU47ILy8rLx232SOe/1t4aNGBswT+bMnbvwN7+5KxqTo4f02u7/ewAAQNPInx14zaKVH9z7UjR2HTywtFubgHkAIE6Kkslk6AyQS/bfb981a9a9+OKc9Pjii3MGDOi7//77hk3V6K4acv0bby5Kr3v3qrz/f24OmwcAgLyVJzvw5b97fPOyj9Pr0m5t9h1zdtg8ABAnToLDLhtfNeoLX+gTjcNH3LRxY03API1u0uQnHpj0eDSOdhEKAABBxX4Hvmb6W2umLYzGLt7DBIBGpQSH3TF+3KhovWjR8uEjbgoYptFt/x7myV8ddMnFXw8YBgAAEnHfgVdPmB6tWx2+b7uv9A0YBgDix3UosDt69tyrtrZ2+vRZ6XHWrPkHHtBz+8Mpueu3//YfEyc+GI0T7/71Xnt1CZgHAAASsd6Bf3jfS6uemB+Ne486vaRjy4B5ACB+CmL8sjZk2pFHffOll+em1126dJgze0rHDm3DRtpD1dUf9d7v5Ojb0iFXXXjrLb8IGwkAACLx24HXrdo4/9I7GjbXpccOZx7a4+qTwkYCgPhxHQrsvqqqbZ9kVld/NHx4zn+SmRxzW9SAt2pVkRw9NGweAADYXvx24NV3z4ga8KLy0q5uAweADHAdCuy+Hj26NGtW9PTTL6bHuXMX7l3Z9dBDDwybarfNmDFryNAbovGmG4d/+cSjAuYBAIBPiNkOfOO899793bYX6btdcXzLAXsHzAMAceU6FNhTXzpx8N+feTm9btWqYu7syZWV3cJG2j0nffU7Tzz5fHo94NC+M1/5n7B5AADgU8VmB/72j+9dP2tpel3ep/P+tw8OmwcA4sp1KLCntv8kc926DcOGjw0YZrdNuHty1IAnEonk6CEBwwAAwA7EYwe+6rF5UQOeSCS6DB4YMAwAxJvrUGBPdenSoWXLFo89PiM9vvnmoo4d2x5x+EFhU+2S+vqGc867es2a9enx/PNP/vnPvh82EgAAfJYY7MATDalFoyfXb9iSntocv3+XS44JmwgAYsx1KNA4Tjv9+4888mx63axZs7mzJx9wQM+wkXbedaNvueGXf4jG1+c+2Ldvr4B5AADgc+X0DnzFn6ZXT3wuGg/8j+8037t9wDwAEG+uQ4HGMX7cyNKS4vR669atw0bkzCeZCxcu2b4BHzXySg04AADZL3d34FuWr9q+Ae984VEacADIKNehQONo375N+w5tH576THp8551lLVqUDTzm0LCpdsYPrv7VvHlvpdd77dVl0v23FBUVhY0EAACfK3d34MtveWLz4o/S6+KOLXuOObugyAE1AMggf6OFRvMv37/g3HO/Go0/ufa3s2bND5hnZ0x95Nm/3PNwNCZHDyn539M0AACQ5XJxB77uxUWrn3ojGrsOHlhQ7AwKAGSWEhwa0/hxI9u0aRWNw7P+k8wxY26L1iccf8R3vn1uwDAAALCrcm4HvuLuGdG64uDK9qf2DxgGAPKEEhwa0157dRlfNTIan532ypjrfx8wz47dcuvEl16eG43J0UMChgEAgN2QWzvwlZNmbXpzRTR2HTwwYBgAyB8FqVQqdAaIm8sGj/yviX+NxmnPThw0cEDAPJ9q9ep1vfc7edWqtenxO98599/vuCFsJAAA2D05sQOv37D59UvuqF+/OT22P61/5TWnhI0EAHnCSXBofOOrRnbr1ikahw+/KWCYz5K8/raoAS8tLUleNzRsHgAA2G05sQNfMWFG1IAXFBd1vcwxcABoIkpwaHzt2rUZP27bJ5mvzHx95KhxAfP8s9dmv/nAA49HY3L0kL326hwwDwAA7Ins34HXvPPhmmkLo7Hr4IHFHVsGzAMAeaUomUyGzgAx1K9f7+rqlTNnvp4eZ8yYNfCYQ3v16hE2VaRLlw5Dh1xUX98wffrMvn17/+XPvw2dCAAA9kiW78CL27XoeNaAVENq49zlzffusM/Pvx46EQDkEXeCQ6bU1Gzpf8iZb7+9LD327dtrzmtTioqy6/OL+W+88/rrb59/3smhgwAAwJ7KiR345qUfb17yUZvj9w8dBADySHbtBiBOyspKq8aNSq+PO+6wiXf/a7btvxOJRN8De2nAAQCIh5zYgTffu70GHACamJPgkFnDrxnbtk2r635xVeggAACQF+zAAYBPUIIDAAAAABBbWfdpGAAAAAAANBYlOAAAAAAAsaUEBwAAAAAgtpqFDgDslK1btyYSiVQqVV9fH/2LBQUFRUVFiUSisLCwsNA/0wIAgEYzvXZDIpFY21A/Z2tN9C+2LijqX1yWSCQqi0oqi0qChQMAdoUSHLJUKpXaunVrbW1tXV3dTj5gW1RU1KxZs9LS0nQzDgAA7Lx1qfppWzY8uHntQ1vWrm2o//x/QyLRv7js2JKKi8vaHVRclul4AMBuK9jJcg1oGg0NDXV1dbW1temj37unoKCguLi4pKSkuLi4EbMBAED8LKuvfWjz2oc2r51Wu2G3f0jrwqLTS1t/vXnrrzVv3YjZAIBGoQSHbJFKpWpqarZs2dKIP7OwsLCsrKykxHeaAADwSetS9Teur75t48pG/JmVRSU/bdnl4rJ2jfgzAYA9pASH8FKp1JYtWzZv3pyhvx6LiorKy8ubNXP9EQAAJBKJxLpU/W0bV962ceVOXnuyq/oXl/26VfdBJRWZ+OEAwK5SgkNgtbW1mzZtaoK/Eps1a1ZeXu66cAAA8tyfa1Zdu+69DNXf2zu2pOLXrbq7LhwAglOCQzCpVGrjxo11dXVN+UtbtGjhdhQAAPLTulT999Yse2jz2qb8pbe3qXQ7CgCEpQSHMBoaGjZs2FBfn/HjJ/+stLS0vLy86X8vAAAEtKy+9sLVi+fU1TT9rx7SouPYVt2b/vcCAGlKcAigvr5+/fr1Af/qKy4ubtGiRUFBQagAAADQlObW1Zy66u0muALls5zevPUf21S2KnA5IQAEoASHplZbW7tx48bQKRJFRUUVFRWFhYWhgwAAQGb9uWbV99csC50i0b+47C9t960scjkhADQ1JTg0qSxpwNMKCwtbtWrlPDgAADGWJQ14WmVRyfMd93ceHACamBIcmk59ff26detCp/g/ioqKWrVqFToFAABkxNy6mmM+WhA6xf/Rv7hsRof9Q6cAgPziJgRoIg0NDevXrw+d4pPq6+uz52Q6AAA0omX1taeuejt0ik+aU1eTPSfTASBPKMGhKaRSqQ0bNmTnhxe1tbVbtmwJnQIAABrTulT9hasXB3wJcwf+XLPq9xtXhk4BAHlECQ5NYePGjfX12bj/Ttu0aVNdXV3oFAAA0Gi+t2bZnLqa0Ck+07Xr3nt489rQKQAgXyjBIeNqa2uzv2LeuHFjdh5UBwCAXfXnmlUPZX3F/L21y9alsvegDADEiRIcMiuVSm3atCl0is+XSqVqarL3pAwAAOykdan6a9e9FzrF51vbUH/j+urQKQAgLyjBIbO2bNmSKyest2zZ0tDQEDoFAADskds2rszOq8D/2W0bVy6rrw2dAgDiTwkOGZRKpTZv3hw6xS5wGBwAgJy2LlV/W069OekwOAA0ASU4ZFBNTU2uHANPq62tzeYHPAEAYMduXF+dK8fA0/5cs2puFj/gCQDxoASHTGloaNiyZUvoFLssJ24wBwCAf7asvja3joGn5cQN5gCQ05TgkCl1dXWhI+yOrVu35tbpdQAASHto89rQEXbHtNoN61K5dHodAHKOEhwypbY2V5+4ydH6HgCAPJejJXgikXgwZ5MDQE5oFjoAxFMqldq6dWuj/9gPP/x41ap16XWLFmU9enRp9F+RSCTq6upKSkoy8ZMBACBD1qXqp9VuaPQfm1q5JrX6Hz+2oLx5wV4dGv1XJBKJaVs2XFzWLhM/GQBIKMEhQzJ0mPrfxk2489/vT68HDTz0r1NuzcRvcRIcAICck6HD1LU3T67702PpddHRfcv+388z8Vse2uIkOABkkOtQICNyukfO0DF2AADInGlbGv8YeJNZ21A/PQPH2AGANCU4ZESGSvArrzhv4n+NzcRP/oTcvdAcAID8lKHD1MWXn9z8rmsy8ZM/IXcvNAeA7Oc6FGh8qVQqlUpl4if37l3ZtWvHTPzkT6iv9zw9AAA5Y12qfm1DRnawhb26FnRpm4mf/Alz6mqa4LcAQH5yEhwanwYZAACakgYZANgBJTjwKRoaGkJHAACAPLK03oWEAJApSnBofDFokGPwpwAAQP6IQYO8LPf/FAAgaynBofFpkAEAoClpkAGAHVCCA5/OzeYAANCU5rrZHAAyQwkOfLpUKhU6AgAA5JG1KcdQACAjlODApyss9L8PAADQdCqLSkJHAIB4UnIBn04JDgAATUkJDgAZouSCxtesWbPQEQAAII8cW1IROgIAkL2U4MCnKCoqCh0BAADySP/istARACC2lODQ+AoKCkJH2FMx+FMAACB/tCrI+TMcrXP/TwEAspYSHBqfY9QAANCUHKMGAHZACQ4ZkblXJaMz2hl9uLKkxJs8AADkkgy+Khl9JVmYwc8lT2/eOnM/HADyXEEqlQqdAWJo06ZNW7ZsCZ1i97Vu3TqjJTsAADSukeveu23jytApdt/rnfpmsMcHgPym5IKMyOmT1IWFhRpwAAByS06fpK4sKtGAA0Dm6LkgI5o1a5a7b0sWFxeHjgAAALtmUElF68JcfZvn67nc4ANA9lOCQ6bkbpWc08fYAQDIW6eX5mqVnNPH2AEg+ynBIVNytAQvKCho1qxZ6BQAALDLji2tCB1hd7QuLBpUkpPJASBXKMEhU4qLi3PxZu3mzZuHjgAAALvj9NLWuXiz9pAWHUNHAICYy72GDnJFQUFBWVlZ6BS7pqCgoLS0NHQKAADYHa0Li37askvoFLumdWHRVeVKcADILCU4ZFBJSUluHQZv3rx57r7nCQAAF5e1y63D4ENadMzd9zwBIFfkUj0Huai8vDx0hJ1VWFjoLhQAAHLdr1t1Dx1hZ1UWlYyqyLGj6wCQi5TgkFnFxcW58s5kzl3eAgAA/+z05q2PzZF3JnPu8hYAyFFKcMi4nCiXi4qKSkpy6btRAAD4LKNyoVzuX1x2cVm70CkAIC8owSHjmjVr1qJFi9ApdqSgoKBly5ahUwAAQOM4tqTi9jaVoVPsSOvCoqnteodOAQD5QgkOTaGkpCSbz1m3bNnSe5gAAMTJxWXtsvmc9dR2vb2HCQBNRgkOTaRFixbZeTl4ixYtiorsvwEAiJvb21Rm5+Xgt7ep7F+cA1cmAkBsKMGh6VRUVGRb3VxaWprNR9QBAGBP/KXtvtlWNw9p0TGbj6gDQCwpwaHpFBQUtGjRInsuHikpKSkvLw+dAgAAMqV1YdEfWldmz8UjF5e1G9uqe+gUAJB3lODQpIqKilq1apUN58FLS0uz/LlOAADYc/2Ly57rsH82nAe/qkXHLH+uEwDiqiCVSoXOAHknlUpt2rSptrY2VIAWLVq4BQUAgPyxtqH+2nXv/blmVagAt7epdAsKAISiBIdgampqNm/e3MS/tKCgoGXLltlwFB0AAJrYjeurb9pQ3cS/tHVh0dR2vbPhKDoA5C0lOIRUW1u7adOmJvvLsKioqKKiorDQPUgAAOSpP9esunbde2sb6pvm1/UvLvtL230ri3yFCQAhKcEhsIaGhpqamkxfjVJYWFhWVuYKFAAAWFZfe+P66kxfjVJZVPLTll1cgQIA2UAJDlmhoaFh06ZNdXV1jf6TCwoKSktLmzdvXlBQ0Og/HAAActSy+tpr17330Oa1jf6TWxcWXVXecUiLjq0LXUIIAFlBCQ5ZZOvWrTU1NVu3bm2Un6b+BgCAHZtWu+Gm9dXTajc0yk9TfwNAdlKCQ9ZpaGjYunVrbW3t7h0MLywsLP5fjZ4NAADiZ1l97bTaDQ9uXvvwbh0MrywqOb1562NLKk5v3rrRswEAe04JDlmtrq6utra2oaEhkUh81gnxwsLC9FuXJSUlzZo1Kypy6gQAAHbTQ5vXPrR57dL62kQiMf0zTohXFpWk37pMd9/9i8uaNCIAsIuU4JBjUqlUfX19IpEoKCjQdwMAQKatbaifs7UmkUi0LijSdwNALlKCAwAAAAAQW4WhAwAAAAAAQKYowQEAAAAAiC0lOAAAAAAAsaUEBwAAAAAgtpTgAAAAAADElhIcAAAAAIDYUoIDAAAAABBbSnAAAAAAAGJLCQ4AAAAAQGwpwQEAAAAAiC0lOAAAAAAAsaUEBwAAAAAgtpTgAAAAAADElhIcAAAAAIDYUoIDAAAAABBbSnAAAAAAAGJLCQ4AAAAAQGwpwQEAAAAAiC0lOAAAAAAAsaUEBwAAAAAgtpTgAAAAAADElhIcAAAAAIDYUoIDAAAAABBbSnAAAAAAAGJLCQ4AAAAAQGwpwQEAAAAAiC0lOAAAAAAAsaUEBwAAAAAgtpTgAAAAAADElhIcAAAAAIDYUoIDAAAAABBbSnAAAAAAAGJLCQ4AAAAAQGwpwQEAAAAAiC0lOAAAAAAAsaUEBwAAAAAgtpTgAAAAAADElhIcAAAAAIDYUoIDAAAAABBbSnAAAAAAAGJLCQ4AAAAAQGwpwQEAAAAAiC0lOAAAAAAAsaUEBwAAAAAgtpTgAAAAAADElhIcAAAAAIDYUoIDAAAAABBbSnAAAAAAAGJLCQ4AAAAAQGwpwQEAAAAAiC0lOAAAAAAAsaUEBwAAAAAgtpTgAAAAAADElhIcAAAAAIDYUoIDAAAAABBbSnAAAAAAAGJLCQ4AAAAAQGwpwQEAAAAAiC0lOAAAAAAAsaUEBwAAAAAgtpTgAAAAAADElhIcAAAAAIDYUoIDAAAAABBbSnAAAAAAAGJLCQ4AAAAAQGwpwQEAAAAAiC0lOAAAAAAAsaUEBwAAAAAgtpTgAAAAAADElhIcAAAAAIDYUoIDAAAAABBbSnAAAAAAAGJLCQ4AAAAAQGwpwQEAAAAAiC0lOAAAAAAAsaUEBwAAAAAgtpT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+ } + }, + "cell_type": "markdown", + "id": "10c267f3", + "metadata": {}, + "source": [ + "As illustrated in the graph on the left below, a graph consists of 4 nodes (or vertices) represented by grey circles, and 4 edges, which are black lines that connect the nodes. Max-Cut problem is to find the maximum number of cut when nodes are divided into two set. \n", + "\n", + "For instance, in the right graph, nodes 0 and 1 are in set 0 (light blue), and nodes 2 and 3 are in set 1 (red). If we partition the nodes between these two sets, it will cut two edges (colored pink). Therefore, the number of cut edges in this case is 2. Basically, to find the maximum cut, we need to find the maximum number of edges where the corresponding nodes belong to different sets.\n", + "\n", + "If we write down the set numbers that follow the node sequence (from 0 to 3), we can represent this instance as a bit string \"0011\". Since switching the names of the sets doesn't influence the results, the bit string \"1100\" gives the same number of edge cut. In general, we can use a binary string of length $n$ to represent a partition of $n$ nodes into two disjoint sets. This representation is commonly used in graph theory and combinatorial optimization, and it enables us to apply various computational techniques, including classical and quantum algorithms, to solve problems such as Max-Cut.\n", + "\n", + "![network1.png](attachment:16c7f2fb-b981-4798-8346-da54e3bcbaeb.png)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "2908c43d", + "metadata": {}, + "source": [ + "The Max-Cut problem is a NP-complete problem. Classically, one way to approach this problem is to brutally test every possible bit string, which takes an exponential amount of time as the number of nodes, denoted by $n$, grows. Specifically, for $n$ nodes, there are $2^n$ combinations to test. However, QAOA offers a more efficient way to solve this problem, where $n$ qubits are used to represent $n$ nodes. Nodes are divided according to the energy level of the qubits." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "4d28f719", + "metadata": {}, + "source": [ + "A cost (objective) function of the $\\alpha$-th edge (which connects $j$-th and $k$-th nodes) is defined\n", + "\n", + "$$\n", + "C_\\alpha=\\frac12(1-\\sigma_z^j\\sigma_z^k)\n", + "$$\n", + "\n", + "When $C_\\alpha = 1$, the $\\alpha$-th is accounted a cut edge. It will happen if and only if $j$-th and $k$-th nodes are in different set. The total number of edge cut is written as\n", "\n", - "$$H_C = \\frac{1}{2} \\sum_{i,j\\in E} C_{ij} \\sigma^{z}_{i} \\sigma^{z}_{j},$$\n", + "$$ \n", + "C(z)=\\sum_\\alpha^mC_\\alpha(z)\n", + "$$\n", + "\n", + "where $z = z_1z_2 . . . z_n$ is the bit string. Max-Cut asks for a string $z$ for which $C(z)$ is maximized. This problem is equivlant to finding the ground state of a cost Hamiltonian\n", "\n", - "where $\\sigma^{z}_{i}$ is the Pauli-z matrix on $i$th qubit and $C_{ij}$ is the weight of the edge between nodes $i$ and $j$. We set $C_{ij}=1$ for simplicity. If $\\sigma^{z}_{i}=\\sigma^{z}_{j}$, $i,j\\in S$ or $i,j\\in S \\backslash V$; if $\\sigma^{z}_{i}= -\\sigma^{z}_{j}$, $i\\in S, j\\in S \\backslash V$ or $i\\in S \\backslash V, j \\in S$. Obviously, the number of edges between $S$ and $S \\backslash V$ is maximized with the graph structure decoded from the ground state." + "$$\n", + "H_C = \\frac{1}{2} \\sum_{i,j} \\sigma^{j}_{z} \\sigma^{k}_{z}\n", + "$$" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "871bff2e", + "metadata": {}, + "source": [ + "## QAOA for Max-Cut" ] }, { + "attachments": {}, + "cell_type": "markdown", + "id": "598dc69e", + "metadata": {}, + "source": [ + "The Quantum Approximate Optimization Algorithm (QAOA) utilizes a parameterized quantum circuit ([PQC](https://tensorcircuit.readthedocs.io/en/latest/textbook/chap5.html?highlight=变分)) to generate a quantum state that represents a potential solution to the Max Cut problem. The initial state, denoted as $|s\\rangle$, is a uniform superposition over computational basis states.\n", + "\n", + "$$\n", + "|s\\rangle=\\frac{1}{\\sqrt{2^n}}\\sum_z|z\\rangle\n", + "$$\n", + "\n", + "This state is then evolved by a unitary operator that consists of $q$ layers, denoted as\n", + "\n", + "$$\n", + "U(\\vec{\\beta}, \\vec{\\gamma}) = V_{p}U_{p} \\cdots V_{1}U_{1},\n", + "$$\n", + "\n", + "where $U_{j}= e^{-i\\gamma_{j}H_{C}}$ and $V_{j}= e^{-i \\beta_{j} H_m}$. $H_C$ is the cost Hamiltonian introduced in previous section and the mixer Hamiltonian $H_m=\\sum_j\\sigma^j_x$ is used to mix the quantum state to explore different solutions. The unitary operator is parameterized by $2p$ angle parameters $\\gamma_1, \\gamma_2, \\dots, \\gamma_p$ and $\\beta_1, \\beta_2, \\dots ,\\beta_p$. It is worth noting that every $\\gamma$ is restricted to lie between $0$ and $2\\pi$, and every $\\beta$ is restricted to lie between $0$ and $\\pi$ due to the integer eigenvalues of $H_C$.\n", + "\n", + "It is important and also tricky to find a proper $p$. As introduced by [Farhi, Goldstone, and Gutmann (2014)](https://arxiv.org/abs/1411.4028), $p$ should be equal to the maximum steps between any pair of nodes. For example, in the graph above, the max steps are found between node 3 and node 1 or 0, and this number is 2. Therefore, a 2-layer PQC should be used.\n", + "\n", + "Begin with a set of initial parameters, the quantum state is obtained from the PQC and then the expected value of the cost Hamiltonian is calculated. A classical optimizer is then used to vary the parameters until a lower exptected value is found. This process is iterated a certain number of times, and the lowest expected value is approximated as the ground state energy of the cost Hamiltonian. By using the parameters that correspond to the lowest expected value, an approximate solution to the Max-Cut problem can be obtained.\n", + "\n", + "In summary, a general QAOA algorithm follows these steps:\n", + "\n", + "1. Define the cost fucntion according to the problem.\n", + "\n", + "2. Define the parameterized quantum circuit with cost Hamiltonian and mixer Hamiltonian.\n", + "\n", + "3. Define a group of initial parameters.\n", + "\n", + "4. calculate the cost function of this group of parameters.\n", + "\n", + "5. If a lower cost is found, accept it. Otherwise, keep the previously found cost.\n", + "\n", + "6. Find a new group of parameters with an optimizer.\n", + "\n", + "7. Repreat procedures 4-6 for given times. Then output the lowest cost and corresponding parameters." + ] + }, + { + "attachments": {}, "cell_type": "markdown", "id": "940fa22b", "metadata": {}, "source": [ - "## Setup" + "## The code" ] }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 103, "id": "b0def04d", "metadata": {}, "outputs": [], @@ -46,32 +167,47 @@ "import tensorcircuit as tc\n", "import tensorflow as tf\n", "import networkx as nx\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "from IPython.display import clear_output\n", + "import random\n", "\n", "K = tc.set_backend(\"tensorflow\")\n", "\n", "nlayers = 3 # the number of layers\n", - "ncircuits = 2 # the number of circuits with different initial parameters" + "ncircuits = 6 # six circuits with different initial parameters are going to be optimized at the same time\n", + "nnodes = 8 # the number of nodes" ] }, { + "attachments": {}, "cell_type": "markdown", "id": "6e407437", "metadata": {}, "source": [ - "## Define the Graph" + "### Define the Graph" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "c82972a4", + "metadata": {}, + "source": [ + "The degree of a graph is defined as the maximum number of edges connected to single nodes. For example, the graph below has a fixed degree of 3." ] }, { "cell_type": "code", - "execution_count": 2, - "id": "14a19854", + "execution_count": 104, + "id": "f1532831", "metadata": {}, "outputs": [ { "data": { - "image/png": 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Dhg2VLk8UgIODA4sXLyYoKIhHjx7h6urK4sWLefz4sdKlCVFqGW3wFbbHB6VnW0Nqair/93//x4svvsiIESPo1KkTERERLFq0iKpVqypdniiCatWqsWnTJo4ePcq5c+dwdnbmk08+ISUlRenShCh1jPaQ6ooVK3LhwgUqV65c4M+kpaVRtWpVTpw4YZSP0Hn06BFbtmxh9erVVK1alalTp+Lt7S1770qhf/75Bz8/PyIiIli4cCGDBg0yuof6CmGojPJvklarLfSqTnh6uHDPnj2Nbrjz9u3b+Pn5Ubt2bQ4fPkxAQEDmEKeEXunUokUL9u7dyyeffMLy5ctp2bIle/fuVbosIUoFowy+x48fY2FhgZWVVaE/a0zbGs6fP8/IkSNxd3fn8ePHnDhxgsDAQF588UWlSxMlpHPnzpw4cYIZM2Ywfvx4OnfuzMmTJ5UuSwijZpTBV9itDM/q0qULJ0+e5MGDBzquSje0Wi2//fYbr7zyCt26dcPNzY3w8HDWrl0rzxQ0UWZmZgwaNIiLFy8yaNAg+vbty6BBgwgNDVW6NCGMklEGX1EWtmQoU6YM7du359dff9VxVcWTnJzMV199RZMmTZg2bRrDhg3j2rVr+Pn5Ub58eaXLEwbAwsKCcePGERYWhoeHB23btmXcuHHcvn1b6dKEMCpGGXxF2crwLEPa1hAbG8vixYupU6cO3377LStWrOD8+fO8/vrrRRrKFaWfjY0Nfn5+hIaGYm9vT6NGjfDz8yMuLk7p0oQwCkYZfMXp8cHTQ6t/++03RR8XEx4ezsSJE3FyciI0NJQ9e/bw+++/88orr8iGc1Eg5cuX56OPPuLcuXNERUXh4uLC8uXLSUxMVLo0IQyaUQZfcXt8VapUwc3NjUOHDumuqAI6duwYAwYMoHXr1tja2nLhwgW++uorGjduXOK1iNKhRo0abN68mUOHDnHs2DFcXFzYvHkzqampSpcmhEEyyuArbo8PSnYze1paGtu3b6dt27YMHz4cLy8vIiIiWLJkCdWqVSuRGkTpV79+fXbs2EFgYCABAQE0atSIHTt2lPrzaYUoLKMMvuL2+KBkDq1+/Pgx69evx8XFhRUrVjBlyhTCwsKYOHEitra2eruvMG2tW7dm//79rFq1ivnz59OmTRuTfCSXELkx2uArbo+vfv36WFlZcfbsWd0U9Yw7d+4wc+ZMateuzf79+9m6dSvHjh1j4MCBsuFclAiVSkW3bt04ffo0kyZNYvTo0XTr1o0zZ84oXZoQijPK4NPFUKdKpdL5cOeFCxd44403cHd3Jz4+nmPHjrFjxw7atm2rs3sIURhmZmYMGzaMkJAQevXqRY8ePRg2bBjh4eFKlyaEYowy+HQx1Am62dag1WrZu3cv3bp1o0uXLjg5OREWFsb69etxcnIqdo1C6IKlpSUTJkwgLCwMNzc3WrVqxYQJE7h7967SpQlR4owy+HTR4wNo27YtN27c4MaNG4X+7JMnT/jmm29o2rQp7777Lq+++ioRERHMmjULR0fHYtcmhD7Y2toyZ84cQkJCsLCwwN3dndmzZxMfH690aUKUGKMMPl31+NRqdaEPrX7w4AFLly6lTp06bN26lWXLlhEUFMQbb7whG86F0ahYsSKrVq3i1KlT3LhxA2dnZ1atWkVSUpLSpQmhd0YZfLrq8UHBhzuvXbvGpEmTqFevHpcuXWL37t2ZQ5yy4VwYq9q1a/P111/zxx9/cODAAVxdXfnqq69IS0tTujQh9MYog09XPT6AV155hePHj/Pw4cMc3//7778ZNGgQLVu2xNramqCgIL755huaNGmik/sLYQgaNWrErl27CAgIYPPmzTRp0kTv232EUIrRPYg2JSUFa2trUlJSdNbT6tmzJyNGjODVV18Fnm4437VrFytXruTWrVtMnjyZUaNGUbZsWZ3cTwhDptVq+fnnn/Hz88PBwYGlS5fSrl07pcsSQmeMrscXFxeHvb29TocXM7Y1/Pvvv2zcuBE3NzeWLl3KpEmTCAsLY9KkSRJ6wmSoVCp69+7NuXPnGDNmDMOHD6d3794EBQUpXZoQOmF0waeLzevPa926NTt37uSFF15g7969fPnllxw/fpxBgwahVqt1ei8hjIW5uTkjR44kNDSUTp060blzZ0aMGEFERITSpQlRLEYXfLpc2HLx4kVGjx5Nhw4dsLOzY+XKlezcuZN27drJghUh/sfKyorJkycTFhZG7dq1ad68OZMnTyYqKkrp0oQoEqMJvuhHyWw6FM6KI9E8bjGCydvOsOlQODGPkgvVjlarZd++ffTo0YNOnTpRu3ZtwsLCeOeddzh16pSeqhfC+NnZ2TF//nwuXbpEWloabm5uzJs3j4SEBKVLE6JQDH5xy7mbcWw4eIVDoU9/u0xOTc98T6M2Qwt4uVbEt70TTWo65NrOkydP2LZtGx9//DHJyclMnTqV4cOHo9FogKfHjfXq1Ytr165Jb0+IArh69SqzZ89m3759zJo1i3HjxmFpaal0WULky6CDz/94BIt2h5CUmkZeVapUoFGbM6uHGz5tamd5Ly4ujs8++4y1a9fi6urK1KlT6datG2ZmWTu7Wq2WevXqsXPnTtmqIEQhnD17Fj8/Py5fvsyCBQsYOnRotr9fQhgSg/3T+TT0gklMyTv0ALRaSExJY9HuYPyPRwAQERHB5MmTqVu3LkFBQfz000+ZQ5w5/aVUqVQ6ObtTCFPTtGlTfv31V7Zs2cK6devw8PDg119/lT2AwmAZZI/v3M04hnx+nMSUnE+PSIm9xe0vJlDGzZMKvadlec/SHJyv/8Lx3dsYPXo077zzDjVq1CjQfQ8cOMB7773HP//8U+zvQQhTpNVq+eGHH5g5cyaVK1dm6dKltGnTRumyhMjCIHt8Gw5eISk19yOTYn/fhFVV5xzfe5KSTlK99kRERPDRRx8VOPQA2rVrx7Vr14iMjCx0zUKIpyMn/fr1IygoiNdee41BgwbRr18/goODlS5NiEwGF3zRj5I5FBqV6/Dm40uHMNOUQVMrl3k4MzMi0+x4oir8JLuFhQXdu3fnp59+KvRnhRD/UavVjB49mtDQUNq2bcvLL7/M6NGjuXnzptKlCWF4wRd4KvfeVnryv8T9GUC5jm/m2YYKCDxdtF6bt7e3Th9OK4Qps7a25r333iMsLIxKlSrRtGlT3nvvPWJiYpQuTZgwgwu+kLvxWbYsPCvu8FZsm7yC2q5Cnm0kpaYTcqdoe4u6devGkSNH5PlkQuiQg4MDS5YsISgoiISEBFxdXVm8eDGPHz9WujRhggwu+OKTUnN8/cm9qyRdP4ddS+8CtpNSpPuXLVsWT09PfvvttyJ9XgiRu2rVqrFp0yaOHj3K2bNncXFxYdOmTaSkFO3vqxBFYXDBZ6fJ+WzMpBtBpD68R+TGN7i5zof4Ezv59/JR7nw5KZd2LIpcg2xrEEK/XFxc+P777/nxxx8JDAzE3d2d77//nvT0nEd7hNAlg9vOsOlQOKv+CM023JmekoQ2OTHz6/gTO0h9eI/yXcdjbmOf5VqN2ox3u7gw7uV6RaohMjKSJk2acPfuXSwsih6gQoiC+eOPP5gxYwYAS5YsoUuXLgpXJEozg+vxDWye8/YDMwsN5rblMv9RWWhQqS2zhR6AFhjoUfBtDM+rUaMGderU4a+//ipyG0KIguvcuTMnTpzg/fffx9fXl86dO8t+WqE3Bhd8FWytaO9SkfyOy3R4aXi2zevw9PiyDq4VcbS1KlYdMtwpRMkyMzNj8ODBXLp0iYEDB9KnTx8GDx5MaGio0qWJUsbggg9gvJcTGrV5kT6rUZvj6+VU7BoyHk5rYCPBQpR6FhYWvPXWW4SFhdGsWTPatm3LuHHjuH37ttKliVLCIIOvSU0HZvVww9qicOVZW5gxq4cbjWs4FLuGxo0bk56ezsWLF4vdlhCi8MqUKZN5+LWdnR2NGjXCz8+PuLg4pUsTRs4ggw/Ap01tZvWoj7WFeb7DnqSno7EwY1aP+tmezlBUKpUqs9cnhFCOo6Mjy5cv5+zZs9y/fx9nZ2eWL19OYmJi/h8WIgcGG3zwNPy2jW1D1waVsVKboVFnLVejNsNKbYb9o+u8YnZRZ6GXQeb5hDAcNWvW5IsvvuDw4cMcO3YMFxcXNm/eTGpqznt/hciNwW1nyE3Mo2QCT0cScieB+KQU7DQWuFUty0CPGjyKuYuHhwcnT56kbt26OrtnSkoKlStX5sKFC1SrVk1n7Qohiu/48ePMmDGDe/fusWjRIvr16ycPkRYFYjTBl58lS5Zw9OhRnR8wPWzYMNq3b8+4ceN02q4Qovi0Wi179uzBz88PKysrli5dSocOHZQuSxg4gx7qLIwpU6YQGhqq86FJGe4UwnCpVCq6d+/O6dOnmTRpEqNHj6Zbt26cOXNG6dKEASs1PT54evrDmDFjuHjxIjY2Njpp8+HDh9SsWZPbt29ja2urkzaFEPrx5MkTPvvsMxYtWkSHDh1YsGAB9eoV7QQnUXqVmh4fPD39oVWrVixZskRnbdrb29OmTRt+//13nbUphNAPS0tLJkyYQFhYGG5ubrRq1YoJEyZw7949pUsTBqRUBR/AypUr+eSTTwgLC9NZm7KtQQjjYmtry5w5cwgJCcHCwoIGDRowZ84cedyYAErZUGeGFStWsHfvXvbs2aOTVV43btzAw8ODu3fvolbn/PQIIYThioiI4MMPP2TPnj3MmDEDX19frKwKdqxh9KNkAk9FEnI3nvikVOw0atyq2DGoeY1iH40olFEqgy8lJYWmTZsyf/58BgwYoJM2mzVrxpo1a3j55Zd10p4QouQFBQUxc+ZMgoKCmDdvHj4+Ppib53w84rmbcWw4eIVDoVEAWZ4Yo1GboQW8XCvi296JJjUdSqB6oSulMvgADh48yIgRI7h06ZJOFqXMnTuXhIQEVq5cqYPqhBBK+uuvv5g+fTrx8fEsXryYXr16ZRkd8j8ewaLdISSlppHXT0iV6un5wLN6uOn8AA2hP6U2+AB8fHyoXr06y5YtK3ZbZ86cYdCgQYSFhckmWSFKAa1Wy88//4yfnx8ODg4sXbqUdu3a/S/0gklMKfhDca11fGSi0K9SHXx3796lYcOG/Pnnn9SvX79YbWm1WmrVqsWePXto0KCBjioUQigtLS0Nf39/5syZg1PrTkS6DCQ57b8fi9rUFGJ+30hSxFnSkx6hdqhCufYjsa7XIks71hbmbBvbRieH5Av9KnWrOp9VpUoVZs+ezfjx44v9eKGMQ6tlM7sQpYu5uTkjR47k8uXLUP8VklLSsryvTU9DXbYCVYYtpea723B4+TWiflxGalzWLRJJqWlsPHilJEsXRVSqgw9g/PjxxMbG8t133xW7LdnWIETp9ShVRWS6PSqzrD8WzSw1OLw0HLVDZVQqM2ycWqG2r0zy3awhp9XCgctRxDxKLsmyRRGU+uBTq9Vs3LiRadOmFXsPj5eXFyEhIdy9e1dH1QkhDEXgqcgCXZf2+AEpsbewrPhCtvdUQODpgrUjlFPqgw+gbdu2dO3alblz5xarHUtLS7p27crPP/+sm8KEEAYj5G58li0LOdGmpRK9awW2jTph4Vgz2/tJqemE3EnQV4lCR0wi+ACWLl2Kv78/QUFBxWpHhjuFKJ3ik/J+rp9Wm070zyvBXE35Lm/l0U6KrksTOmYywVepUiXmzZuHr69vsRa6dO/enUOHDvH48WMdVieEUJqdJvdTmbRaLTG715L2OI6K/WaiMs/9WjuNhT7KEzpkMsEHMHbsWBITE9m6dWuR2yhXrhwtW7Zk7969OqxMCKE0typ2WKlz/pEY+9sGUmJuUmngHMwscj+mTKM2w61qWX2VKHSkVO/jy8mJEyfw9vYmODgYBweHIrWxdu1azp49y5YtW3RbnBBCMdGPkvFctj/bPF/qw/vc+mQUmFugMvvveLPy3cZj6571obdWajOOTu8oZ3gaOJMLPoBx48ZhaWnJunXrivT5iIgIWrVqxZ07d3I9508IYXzGbv2HvcH38jymLDcqFXRtUJlNPi3yv1goyqSGOjMsXryY77//ntOnTxfp87Vr16Zq1aocO3ZMx5UJIZQ03ssJjbpov8xq1Ob4ejnpuCKhDyYZfI6OjixatAhfX1/S0wt+Ht+zvL295RQXIUqZJjUdmNXDDWuLwv1otFKrmNXDTY4rMxImGXwAo0aNQqVS8eWXXxbp87KtQYjSyadNbWb1qI+1hTn5nUevUoFalY729Ha83R1LpkBRbCY5x5fh9OnTdO/enUuXLuHoWLg/tFqtlho1arB//35cXV31VKEQQinnI+PYePAKBy5HoeLp5vQM5qShVlvQwbUib7evx4YF07l//z47duzAzMxk+xNGw6SDD2DChAmkpKTw6aefFvqzb7/9NnXq1OH999/XQ2VCCEMQ8yiZwNORhNxJID4phccPogj5ez/7Pl+UuXrzyZMndOrUiQ4dOjB//nyFKxb5Mfngi4uLo379+vz444+0atWqUJ/ds2cPCxYs4MiRI3qqTghhaOLj46lWrRqxsbFYWlpmvn7//n1atmzJihUrGDRokIIVivyYfJ/cwcGBZcuW4evrS1paWv4feEaHDh24ePEi9+/f11N1QghDY2dnh7Ozc7ZV4ZUqVeKHH37A19eXs2fPKlOcKBCTDz6A1157DWtraz777LNCfc7KyoouXbrIodVCmJh27drx119/ZXu9WbNmbNiwgb59+8ovxAZMgo+nD5nduHEjH374IVFRUYX6rGxrEML0tGvXLtcpjsGDB+Pj48OAAQN48uRJCVcmCsLk5/ieNWXKFOLi4gp1FFlsbCy1a9fm7t272NjY6LE6IYShiIyMpFmzZty/fx9VDnse0tPT6d+/P5UrV2bTpk05XiOUIz2+Z8ydO5fffvutUItVypcvT/Pmzdm3b58eKxNCGJIaNWpQpkwZQkNDc3zfzMyMrVu3cuTIET755JMSrk7kR4LvGXZ2dqxYsYLx48eTmpr3s7meJZvZhTA9eQ13ApQtW5Yff/yR+fPnc+DAgRKsTORHgu85Q4YMoXz58mzcuLHAn/H29uann34q9KpQIYTx8vT0zHGBy7Pq1avHt99+y9ChQ7l27VoJVSbyI8H3HJVKxYYNG5g/fz537twp0Gfq1q1LpUqVOHHihJ6rE0IYitxWdj6vY8eOzJo1iz59+pCQkFAClYn8SPDloH79+owePbpQJ7LIcKcQpsXd3Z2oqKgCbVuYMGECbdq0YcSIEUU+GF/ojgRfLmbPns2hQ4c4dOhQga6XbQ1CmBYzMzNefPHFAi2GyxhJioqKYt68eSVQnciLBF8ubG1tWbVqFePHjyclJSXf61u0aEFcXBxhYWElUJ0QwhAUdLgTwNLSku3bt/PVV18RGBio58pEXiT48tC/f3+qV6/O2rVr873WzMyM3r17S69PCBOS38rO51WuXJmdO3fy9ttvy7FmCpIN7PkICwvjxRdf5Ny5c1SvXj3Pa3/55ReWLVvG4cOHS6g6IYSSEhMTqVChAlFRUYU6wGLbtm3MmDGDEydOULFiRT1WKHIiPb58ODs78/bbbzNlypR8r+3UqRPnzp0jOjq6BCoTQijN2tqaxo0bF3pF96uvvsqwYcMYOHCgHGumAAm+AvDz8+PEiRP88ccfeV6n0Wjo3Lkzv/zySwlVJoRQWmHm+Z61YMEC7O3teeedd/RQlciLBF8B2NjYsGbNGiZMmEBycnKe18q2BiFMi6enZ5GeyWlmZoa/vz9//vmnHGtWwmSOrxB69+5N27Zt8fPzy/Wa6Oho6tWrx71799BoNCVYnRBCCVFRUTg7OxMTE4O5uXmhPx8eHk7btm3Ztm0bXl5eui9QZCM9vkJYs2YNK1as4MaNG7leU6FCBZo0aSKHVgthIipWrEiVKlW4cOFCkT6fcazZkCFD5FizEiLBVwh169Zl0qRJTJ48Oc/rvL29ZbhTCBNS1OHODJ06dWLmzJl4e3vz6NEjHVYmciLBV0jvv/8+58+f59dff831mj59+vDTTz/J0URCmIiiLnB51sSJE2nZsqUca1YCJPgKSaPRsG7dOiZOnEhSUlKO1zg7O1OuXDlOnjxZwtUJIZSgi+BTqVRs3LiRe/fuMX/+fB1VJnIiwVcE3bt3p3Hjxnz00Ue5XiNndwphOpycnEhKSspz/r8grKys2LFjB1u2bGH79u06qk48T4KviFavXs3atWu5evVqju/LtgYhTIdKpSr08WW5yTjW7K233uLcuXM6qE48T4KviF544QWmTZvGpEmTcny/devWREdHEx4eXsKVCSGUoIvhzgzNmzdn3bp19O3bl6ioKJ20Kf4jwVcMU6ZMISwsLMchTTMzM3r16iXDnUKYCF31+DIMGTKEoUOHyrFmeiDBVwyWlpZs2LCBSZMm8e+//2Z7X7Y1CGE6mjVrRnh4OA8fPtRZmwsXLsTe3j7XkSVRNBJ8xdSpUydat27NkiVLsr3XuXNnTp8+TUxMjAKVCSFKkoWFBS1atODYsWM6azPjWLPDhw+zadMmnbVr6iT4dGDlypV88skn2R5Ca21tTceOHdm9e7dClQkhSpKuhzsB7Ozs+PHHH/nwww85dOiQTts2VRJ8OlC9enX8/PyYMGECzx99KtsahDAdnp6eOlvg8iwnJycCAgIYMmQIEREROm/f1Mgh1TqSkpJCs2bNmDdvHgMGDMh8/f79+7i4uHDv3j2srKwUrFAIoW8PHz6kRo0axMbGYmFhofP216xZw5YtWzhy5Ai2trY6b99USI9PRywsLNiwYQPvvvtulrP2KlWqRMOGDTlw4ICC1QkhSoK9vT316tXjzJkzemn/nXfeoXnz5rz++utyrFkxSPDpUPv27Wnfvj0LFizI8rpsZhfCdOhruBOebpT/5JNPuH37drafM6LgJPh0bPny5WzZsoXg4ODM1zLm+eQ3NCFKP11uZM9JxrFmX3zxBTt27NDbfUozCT4dq1KlCrNnz2b8+PGZC11cXV0pW7Ysp0+fVrg6IYS+Zazs1OfyiSpVqrBz507GjRvH+fPn9Xaf0kqCTw98fX158OAB3333XeZrMtwphGmoWbMmVlZWXLlyRa/3ad68OWvXrsXb25vo6Gi93qu0keDTA7VazYYNG5g2bRrx8fGAbGsQwpToe7gzw9ChQxkyZAiDBg0iJSVF7/crLST49KRt27Z07dqVuXPnAtCmTRvu3LnDtWvXlC1MCKF3JRV88PRYszJlyjB58uQSuV9pIMGnR8uWLcPf35+goCDMzc3l0GohTISnp6fOT3DJjbm5Od9++y0HDhzg008/LZF7GjsJPj2qWLEi8+fPx9fXF61WS58+fST4hDABDRs25O7duyX2SKGMY83mzJnD4cOHS+SexkyCT8/GjBlDUlISW7dupUuXLpw8eZIHDx4oXZYQQo/Mzc158cUXS6zXB+Ds7MzWrVt59dVX5VizfMiRZSXg5MmT9OnTh+DgYIa9MZYXvAajqVKP+KRU7DRq3KrYMah5DRxt5UgzIUqLhQsX8vDhQ5YvX16i9129ejVffvklR48epUyZMiV6b2MhwVdCho6fzjUbV6IsKpGelobWTJ35nkZthhbwcq2Ib3snmtR0UKxOIYRuHDx4ED8/P50+pqggtFoto0aNIiEhge+//x4zMxnYe54EXwnwPx7Bwl+CSXySiiqPP4QqFWjU5szq4YZPm9olV6AQQuf+/fdfKlasSHR0NNbW1iV67+TkZLy8vOjevTtz5swp0XsbA/lVQM/8j0ewaHcwSanpeYYegFYLiSlpLNodjP/xiJIpUAihFzY2NjRs2JCTJ0+W+L0zjjX7/PPP2blzZ4nf39Cp879EFNW5m3Es2h1CYkrWMzpvrByY5Wtt6hPKNutB+VfeAiAxJZ1Fu0NoXMOBxjUcSqpcIYSOZezne/nll0v83lWrVmXnzp10794dJycnGjVqVOI1GCrp8enRhoNXSEpNy/b6C1MDM/+pMXErKrUlNm7tslyTlJrGxoP6PfJICKFfJbmRPSctWrRgzZo1cqzZcyT49CT6UTKHQqPIbwb138tHMbexx6qme5bXtVo4cDmKmEfJeqxSCKFPbdu25dixY4o+mWXYsGEMHjxYjjV7hgSfngSeiizQdY+C9lGmYUdUKlW291RA4OmCtSOEMDyVK1emYsWKXLx4UdE6Fi1aRJkyZXj33XcVrcNQSPDpScjdeJJT8/4tL/XhfZJvXqBMo045vp+Umk7InQR9lCeEKCFKD3fC0w31AQEB7Nu3j88++0zRWgyBBJ+exCel5nvNowv7sarRAAuHKnm0I0MTQhizjOfzKc3e3p5du3Yxe/Zs/vzzT6XLUZQEn57YafJfMPv4wn5sG3bMpx0LXZUkhFCAp6en4j2+DBnHmg0ePJjr168rXY5iJPj0xK2KHVbq3P/zJkUGk/YoJttqzmdp1Ga4VS2rj/KEECXExcWFx48fExlpGPP1r7zyCu+//z7e3t48fvxY6XIUIcGnJwOb18jz/ccX9mHj0hYzK5tcr0l68oTK/0Ygh+sIYbxUKpXBDHdmmDx5Mk2bNuWNN94wyZ8vEnx6UsHWivYuFclhsSYAjt0mUKH31Fw/r1JBA/s03n/nbby8vDhw4ICeKhVC6JshDXfC0zDetGkTN27cYNGiRUqXU+Ik+PRovJcTGrV5kT6rUZuzdERHLl26xOjRoxk7dixeXl4cPHhQt0UKIfTOEFZ2Pk+j0bBz504+/fRTfvjhB6XLKVFySLWeZZzV+fyxZXmxtjBjVo/6WQ6qTk1NJSAggAULFlCzZk3mzZunyDFIQojCe/LkCY6Ojty6dQs7Ozuly8ni5MmT9OjRgwMHDtCwYUOlyykR0uPTM582tZnVoz7WFua5DntmUKnA2sI8W+gBqNVqRo4cSUhICCNHjuSNN96gY8eOJr8sWQhjYGlpiYeHB8ePH1e6lGxatmzJ6tWr8fb2JiYmRulySoQEXwnwaVObbWPb0LVBZazUZmieW+2pUZthpTaja4PKbBvbJs9HEqnVal5//XVCQkJ47bXXGDlyJJ06dTK4YRQhRFaGONyZYfjw4QwcONBkjjWToc4SFvMomcDTkYTcSSA+KQU7jQVuVcsy0KNoT2BPSUlh69atLFy4kLp16zJv3jw8PT31ULkQojh+/fVXli9fzv79+5UuJUdpaWn06dOHunXrsm7dOqXL0SsJvlIiJSWFb775hoULF+Lk5MS8efNo27at0mUJIf4nLi6OmjVrEhsbi4WFYR5M8fDhQ1q3bs3UqVMZM2aM0uXojQx1lhIWFhaMHj2ay5cvM3jwYIYNG0bXrl05duyY0qUJIQAHBwfq1KnD2bNnlS4lVxnHmn3wwQcGOyyrCxJ8pYylpSVjxowhNDSUAQMGMGTIELp162aQk+pCmBpDnufL4OLiwjfffMPgwYO5ceOG0uXohQRfKWVpacnYsWMJCwujX79+vPrqq3Tv3p2///5b6dKEMFmenp4GdYJLbrp27crUqVNL7bFmMsdnIpKTk/nyyy9ZvHgxDRs2ZO7cubRq1UrpsoQwKdevX6d169bcuXMnx2dwGhKtVsvrr79OYmIi27ZtM/h6C0N6fCbCysqKt956i7CwMHr37s2AAQPo2bMnJ0+eVLo0IUzGCy+8gIWFBeHh4UqXki+VSsWnn37KjRs3WLx4sdLl6JT0+ExUcnIyX3zxBUuWLKFJkybMnTuXFi1aKF2WEKXekCFD6N69OyNHjlS6lAK5ffs2rVq1YsOGDXh7e2e+Hv0omcBTkYTcjSc+KRU7jRq3KnYMal60rVklSYLPxCUlJWUGYLNmzZg7dy7NmzdXuiwhSq3169dz7tw5Pv/8c6VLKbATJ07Qq1cv9u/fT5p9DTYcvMKh0CgAklP/O45RozZDC3i5VsS3vRNNajooU3A+JPgE8DQAP//8c5YuXUrz5s2ZO3cuHh4eSpclRKlz9uxZhg4dSnBwsNKlFIq/vz+zv/4dqzZDSU5LJ6/kUKmeHrQ/q4dbnidRKUXm+ATw9KT2iRMnEh4eTufOnenduzd9+/blzJkzSpcmRKnSqFEjbt++TXR0tNKlFI5TO8yaDyQpNe/QA9BqITEljUW7g/E/HlEi5RWGBJ/IQqPR8M4773DlyhU6dOhAz5496devn0FvuhXCmJibm9OmTRuOHj2qdCkFdu5mHIt2h5Cm+u8xa/GnfuLOV5O5vrwv0T+vyvFziSnpLNodwvnIuBKqtGAk+ESOrK2tmTRpEuHh4bRv354ePXrQv39/zp07p3RpQhg9Y9jI/qwNB6+QlJqW5TW1rSP2bV/FtnGXPD+blJrGxoNX9FleoUnwiTxZW1szefJkrly5wksvvUS3bt0YMGAA58+fV7o0IYxWu3btjGIjOzxdvXkoNCrb8KaNa1tsXF7EzDrv5wtqtXDgchQxj5L1WGXhSPCJArGxseHdd98lPDwcT09PunbtysCBAwkKClK6NCGMTqtWrTh79iyJiYlKl5KvwFORxW5DBQSeLn47uiLBJwrFxsaGKVOmcOXKFV588UW6dOnCoEGDuHDhgtKlCWE0ypQpg7u7O//884/SpeQr5G58li0LRZGUmk7InQQdVVR8EnyiSMqUKcPUqVMJDw+ndevWdO7cmcGDB3Px4kWlSxPCKBjLcGd8UqqO2jGcB9xK8IliKVOmDNOmTSM8PJyWLVvSsWNHXn31VQlAIfLh6elpFAtc7DRqHbVjOM8glOATOlGmTBnee+89wsPD8fDwoEOHDgwZMoRLly4pXZoQBsnT05OjR4+Snl68YUR9un79OneC/4HU7L01bXoa2tQnkJ4G2nS0qU/Qpqfl0MrTE13cqpbVd7kFJsEndMrW1pbp06dz9epVmjZtipeXF8OGDTO6UyqE0LcqVarg6OhocH83YmNj+fTTT3n55Zdp3rw5Ze5fwMIye2/t4ZHvuLGiP/HHA3l88QA3VvTn4ZHvcmxTCwz0qKHnygtOjiwTepWQkMD69etZtWoVXbp0Yfbs2bi5uSldlhAG4fXXX+fFF19k3LhxitaRlJTEzz//jL+/PwcOHKBr1674+PjQrVu3p8/23PoPe4Pv5XtiS05UKujaoDKbfAznEHzp8Qm9Klu2LH5+foSHh+Pu7s7LL7+Mj48Ply9fVro0IRSn5Eb2tLQ09u/fz+jRo6lWrRqbNm3C29ubGzdu8P3339OnTx8sLS0BGO/lhEZtnk+LOdOozfH1ctJl6cUmwSdKRNmyZZk5cyZXrlyhfv36tGvXjtdee43Q0FClSxNCMSUdfFqtlrNnz/Lee+9Rq1Ytpk2bRoMGDQgKCuKPP/7gjTfewN7ePtvnmtR0YFYPN6wtChcZ1hZmzOrhRuMaDjr6DnRDgk+UKDs7O2bNmsWVK1dwdXXF09OTESNGEBYWpnRpQpQ4V1dXEhISuHXrll7vc/36dZYsWUKjRo3o27cvlpaW/P7775w+fZqpU6dSvXr1fNvwaVObsS0rok1JJr9nsatUYG1hzqwe9eXpDEJksLe354MPPuDKlSs4OzvTtm1bRo4cyZUrhnWmnxD6pFKp8PT01Mt+vtjYWD777LPMRSrXr19n06ZNXL16lUWLFtGgQYNCt3l4yyL621+nq3tlrNRmaNRZI0SjNsNKbUbXBpXZNraNQYYeyOIWYSDi4uJYu3Yta9eupVevXnzwwQc4ORnWvIAQ+rB8+XJu3rzJ2rVri91WxiKVgIAA9u/fT9euXRk+fDjdu3fPnK8rqoz5wODgYDQaDTGPkgk8HUnInQTik1Kw01jgVrUsAz3kCexCFEpcXByrV69m/fr19O7dmw8++IB69eopXZYQenP06FEmTpzIqVOnivT59PR0Dh06hL+/Pzt37qRZs2b4+PjQv3//HOfriiI1NRUPDw8+/PBDBgwYoJM2lSTBJwzSgwcPWL16NRs2bMDb25tZs2ZRt25dpcsSQueSk5NxdHTkzp07lC1bsE3eWq2W8+fPExAQwLfffkvFihUZPnw4Q4cOLdB8XWFt2rSJ7777jgMHDqBS5TfDZ/hkjk8YpHLlyjFv3jzCwsKoXr06LVu25M033+TatWtKlyaETllZWeHh4cHx48fzvfbGjRssXbqUxo0b4+3tjVqt5rfffuPMmTNMmzZNL6H34MEDPvzwQ1avXl0qQg8k+ISBK1euHPPnzycsLIyqVavSokULxowZQ0REhNKlCaEzeS1wefDgAZ9//jnt27fHw8ODiIgINm7cyNWrV1m8eDHu7u56rW3+/Pl4e3vTtGlTvd6nJEnwCaNQvnx5FixYQFhYGJUrV6Z58+aMHTtWAlCUCs/v50tKSmL79u3079+f2rVr8/vvvzNlyhRu3brFpk2beOmllzAz0/+P75CQELZu3crChQv1fq+SJHN8wijFxMTw8ccfs2nTJgYOHMjMmTOpVauW0mUJUSQPHjygVq1a7Nixg++++44dO3bQrFkzhg8fzoABA3S2SKWwevbsSceOHZk6daoi99cX6fEJo+To6MiiRYu4fPkyjo6OeHh48NZbb3Hjxg2lSxOiUM6fP8+SJUtITEzE19cXNzc3zp8/z759+xg1apRiobdnzx7CwsKYOHGiIvfXJwk+YdQqVKjA4sWLuXz5MuXKlaNZs2a8/fbb3Lx5U+nShMjVzZs3WbZsGY0aNaJ3796Ym5vTr18/xo8fz7Rp06hRQ9knGaSkpPDuu++ycuXKYu//M0QSfKJUqFChAkuWLCEkJAR7e3uaNm2Kr6+vBKAwGBmLVLy8vGjatClXr15lw4YNXLt2jSVLltCnTx+DeTDtxo0bqVmzJr169VK6FL2QOT5RKkVFRbF8+XI2b97M0KFD8fPzU/y3aGF6kpKS2L17N/7+/uzbt48uXbrg4+ND9+7dsbLKerpJREQEbdu25datW4puG4iOjqZ+/focPHhQ7ytGlSI9PlEqVaxYkY8++oiQkBBsbGxo3LgxEydO1PthwEKkp6dz8OBBxowZQ/Xq1Vm/fj29evXi+vXrBAYG0rdv32yhB1CrVi1UKpXie1U//PBDhgwZUmpDDyT4RClXqVIlli9fTnBwMFZWVjRq1Ih33nmH27dvK12aKGWCgoKYPn06tWrVYvLkybi4uHDu3Dn279/PqFGjcHBwyPPzKpVK0efzAVy4cIH/+7//Y+7cuYrVUBIk+IRJqFy5MitWrCA4OBgLCwsaNmzIpEmTJABFsdy8eZOPPvqIxo0b07NnT8zMzPj1118zn3lX2OH1du3a6eVJDQWh1Wp59913mT17No6OjorUUFIk+IRJqVy5MitXruTSpUuYm5vTsGFDJk+ezJ07d5QuTRiJuLg4Nm/eTIcOHWjatClXrlxh/fr1REREsGTJEho2bFjktj09PRXr8f3000/cunWLt956S5H7lyRZ3CJM2p07d/joo4/4+uuvGTlyJNOnT6dKlSpKlyUMTHJyMr/88gsBAQH88ccfdOnSheHDh9OjR48c5+uKKjU1lfLlyxMREUH58uV11m5+kpOTcXd3Z8OGDXTt2rXE7qsU6fEJk1a1alVWrVrFxYsX0Wq1NGjQgClTpnD37l2lSxMKy3jcz5gxY6hWrRrr1q2jR48emYtU+vXrp9PQA1Cr1bRp04ajR4/qtN38rF27Fjc3N5MIPZDgEwJ4GoCrV6/mwoULpKWl0aBBA6ZOncq9e/eULk2UsKCgIGbMmEHt2rV55513cHZ25uzZsxw4cIDRo0fnu0iluEp6uPPevXssW7aMjz/+uMTuqTQJPiGeUa1aNdasWUNQUBBPnjyhfv36TJs2jfv37ytdmtCjjEUqTZo0oWfPngD88ssvnDt3jvfff5+aNWuWWC0lvbLzgw8+YOTIkbi4uJTYPZUmc3xC5CEyMpKlS5fy7bff8uabbzJt2jQqVaqkdFlCB+Li4ti+fTv+/v6cP3+eAQMGMHz48BJ78kFuHj16RJUqVYiOjkaj0ej1XmfOnKF79+6EhITovSdrSKTHJ0QeatSowfr16zl//jyPHz/Gzc2N6dOnExUVpXRpogiSk5PZuXMnAwcOpFatWuzevTtzX+dnn31G+/btFQ09AFtbW9zc3Dh16pRe76PVapk0aRLz5s0zqdADCT4hCqRGjRps2LCBc+fOkZCQgJubGzNmzCA6Olrp0kQ+MhapjB07lmrVqrF27Vq6detGREQE27dv18sileIqieHOwMBAHj58yJtvvqnX+xgiCT4hCqFmzZps3LiRM2fO8PDhQ1xdXfHz85MANEAXLlzIXKQyceJEnJycMhepvPnmm5QrV07pEnOl7+BLTEzkvffeY/Xq1Zibm+vtPoZKgk+IInjhhRf45JNPOH36NA8ePMDV1ZWZM2cSExOjdGkmLTIykuXLl9OkSRO6d++OVqvl559/5vz58yW+SKU4PD09OXr0KOnp6Xpp/+OPP6Z58+Z06NBBL+0bOlncIoQOXL9+ncWLFxMYGMhbb73F1KlTS3QDsinLWKQSEBDA2bNnMxepvPzyy4rP1xVHvXr1+Omnn2jQoIFO2719+zaNGzfmxIkT1K1bV6dtGwvj/VMhhAGpVasWn376KadOnSIqKgpnZ2c++OADYmNjlS6tVEpOTuaHH37IXKTyyy+/MGHCBG7fvp35zDtjDj3Q33Cnn58fY8aMMdnQAwk+IXSqdu3afPbZZ/zzzz/cu3cPZ2dnZs+ezYMHD5Quzeilp6dz+PBhxo0bR7Vq1Vi9enXmIpUdO3bQv39/vS//L0menp46P7D677//Zu/evcycOVOn7RobCT4h9KBOnTp8/vnnnDx5ktu3b+Pk5MScOXMkAIvg4sWL+Pn5UadOHcaPH0/dunU5c+YMBw8eNPhFKsWh6x6fVqtl8uTJLFq0iLJly+qsXWMkwSeEHtWtW5cvvviCkydPEhkZibOzM3PnziUuLk7p0gzarVu3WLFiBU2bNqVr166kp6fz008/ZT7z7oUXXlC6RL1zc3MjLi5OZ08O+fbbb0lJSWHkyJE6ac+YSfAJUQLq1q3Lli1b+Pvvv7l+/TpOTk7MmzdPAvAZDx8+ZMuWLXTs2JFGjRoREhLC6tWruXHjBsuWLaNx48ZKl1iizMzMaNu2rU6GOx8/fsyMGTNYs2aN0c996oL8FxCiBNWrV48vv/yS48ePc+3aNZycnJg/fz4PHz5UujRFZCxSGTRoEC+88AI///wz48eP5/bt22zevLlULFIpDl0Nd3700Ue0a9cOT09PHVRl/GQ7gxAKCgsLY+HChZlHZ02aNAk7Ozuly9Kr9PR0jhw5gr+/P9u3b8fd3R0fHx8GDhxYaufriurIkSNMmjSJf/75p8htXL9+HQ8PD86cOWMSQ8QFIcEnhAEIDQ1l4cKF/Prrr0yaNIl33nmn1AXgxYsXCQgIICAggLJly+Lj48OwYcPkh3EekpOTcXR05O7du9ja2hapjSFDhuDq6sq8efN0XJ3xMt0xBCEMiIuLC9988w1//fUXly9fpl69eixatIj4+HilSyuWjEUqzZo1o2vXrqSmprJr167MZ95J6OXNysqKpk2b8vfffxfp83/99RdHjhzh/fff13Flxk2CTwgD4urqytatW/nzzz8JDg7GycmJxYsXk5CQoHRpBfbw4UO+/PJLOnXqRKNGjQgODubjjz/m+vXrmc+8U6lUSpdpNIo6z5eens7kyZNZtmwZZcqU0UNlxkuCTwgD5Obmhr+/P4cPH+bixYvUq1ePJUuWGGwAPnnyhB9//JHBgwfzwgsvsGvXLnx9fbl9+zZffPEFHTp0MMnDkHWhXbt2RVrZ+fXXX2NpacnQoUP1UJVxkzk+IYxAcHAw8+fPZ9++fUyZMoUJEyYUeM4n+lEygaciCbkbT3xSKnYaNW5V7BjUvAaOtkV/HE96ejpHjx7F39+fwMBA3N3dGT58OAMHDpRzSnUoNjaW2rVrExsbi1qtLtBn4uPjcXNz48cff6Rly5Z6rtD4SPAJYUQuXbrE/PnzOXDgAFOnTsXX1zfXADx3M44NB69wKPTpQ3OTU/876V+jNkMLeLlWxLe9E01qOhSqBn9/f7799ltsbW3x8fFh6NCh1KpVqzjfmsiDu7s7W7duxcPDo0DXz5gxgzt37vD111/ruTLjJMEnhBG6ePEi8+fP5+DBg0ybNg1fX98s8zj+xyNYtDuEpNQ08vobrlKBRm3OrB5u+LSpnet1t2/f5v/9v/+Hv78/UVFRDB06FB8fHxo3bizzdSVg3LhxNGzYkIkTJ+Z7bXh4OK1atSIoKIhq1aqVQHXGR4JPCCN24cIF5s+fz+HDh5k2bRpvv/02O4OiWLQ7mMSU/3p4aYkJxOxeQ1LEGcys7SjXfiRl3L0y37e2MGNWj/pZwi8+Pj7zcT+nT5+mX79+DB8+nPbt28t8XQn75ptv+OWXX9i2bVu+1/bv358WLVqY/EHUeZHgE6IUCAoKYv78+fwVfJMyvWeR+ty6tagfPwKtFsce7/Dk3lXuB86jis9yLCv+NzxpbWGO/xvNuRV0DH9/f3777Tc6dOiAj48PPXv2xNrauqS/LfE/V69e5aWXXiIyMjLPHvaBAwcYNWoUwcHBpepJFbomwSdEKTJk/T6OR/4Lqv+CL/1JEjdXD6HamxuwKF8dgOifVmJe1pFyXq//92FtOqkRp6h7ez/Dhw9n0KBBskjFQGi1WqpXr86RI0eoU6dOjtekpaXh4eHB7NmzGThwYAlXaFwKtkRICGHwoh8lc+bekyyhB5AaewuVmXlm6AFYVKpD8o2grA2ozLBxasXOzX7FWu0pdE+lUmU+ny+34Nu8eTMODg4MGDCghKszPrKPT4hSIvBUZI6vp6ckorLKOkxpZmVD+pPEbNeaqVQEns65HaGsvDayx8XFMWfOHFavXi2LjQpAenxClBIhd+OzbFnIYGZhjTY5a8hpk//FzDL7nF1Sajp7T16kgeo25cuXx9HRkfLly2Npaam3ukXBNGrxIhv2XWbytjPZ9mMumj+fPn360KxZM6XLNAoSfEKUEvFJqTm+ri5fHW16GimxtzKHO5/cv4ZFxZz33YVei8Rv50fExsYSExNDbGwsGo0mMwQdHR2z/Htur5UrV05Wf+rAf/sxY0h27cwPZ29nvqdR32Xl3ssk3rZnq98EBas0LhJ8QpQSdpqc/zqbWWqwcX2RuD8DcOz+Dk/uX+XfK39TxWd5jtd3eqktq9b7Zn6t1WpJSEjIDMGYmJgs/x4REcHp06ezvR8fH4+dnV2+Afn8a3Z2djJc9z/P78dUqbPOvSb9r4evrtMc3+2hzEo0y3M/pnhKgk+IUsKtih1W6rs5DneWf8WXmN1riFw3HDNrOxxf8c2ylSGDRm2GW9WyWV5TqVTY2dlhZ2eX68KKnKSlpREXF5djWMbExBAcHJxjmCYmJlKuXLlChaWjoyPW1talKjCfhl7W/Zi5U5GYksai3cEAEn75kO0MQpQS0Y+S8Vy2P8fgKygrtRlHp3dUdFXnkydPiI2NzTLU+nxw5vSaVqst9HCso6OjQc5fnrsZx5DPj5OYkpbl9eifVpAUcY70lCTMy5TDrs0AyjbpmuUaawtzto1tQ+MaDiVYsXGRHp8QpUQFWyvau1Rkb/C9PI8py41KBR1cKyq+lcHS0pIqVapQpUqVQn3u33//zTUY79+/T3BwcLb3M+Yv8+tNPv++vucvNxy8QlJqWrbX7doMwrH7JFRqC1JibnL3Wz8sK9fDqopT5jVJqWlsPHiFTT4t9FafsZPgE6IUGe/lxJ9h0dl6CgWhUZvj6+WU/4UGysbGBhsbG2rUqFHgzzw7f5lTjzKv+cuyZcsWKiwLOn8Z/SiZQ6FROf7yknV4WoUKFakP7mQJPq0WDlyOIuZRsuK/xBgqCT4hSpEmNR2Y1cOtEHNDTz09q9PN5IbHijt/mdvwa8b85fPvZ8xf5hWQ51Mqk56e+/BrzG8beRy0D21qMpaV62FdL3vPTgUEno5k3Mv1ivKfpdSTOT4hSiFdP51B6EZB5i//sXAn1i7vnrc2PY3kWyEk3QjCvs1AVObZ+zD9mlZn1atN9fSdGDcJPiFKqfORcWw8eIUDl6NQ8d/Sd/jveXwdXCvi6+Vkcj09Qzbq65PsD7lfoGtj9qzHosIL2LXok+29Tm6V+GKkPIQ2JzLUKUQp1biGA5t8WhDzKJnA05GE3EkgPikFO40FblXLMtCjeE9gF/qR237MHKWnk/rgTi7tWOiootJHgk+IUs7R1krmeoxIbvsx0x7HkXT9HNZOrVCpLUmKOMvj4ENU6PN+tjZy2o8p/iPBJ4QQBmRg8xqs+iM0+xsqFQlnfiXmt42gTUdtX4lyncZg49w626VaYKBHwVe3mhoJPiGEMCC57cc0t7GnyvCl+X7eUPZjGjJ5LJEQQhiY8V5OaNRF2yBv7PsxS4IEnxBCGJiM/ZjWFoX7EW2q+zELS4Y6hRDCAGXsq5T9mLon+/iEEMKAyX5M3ZPgE0IIIyD7MXVHgk8IIYRJkcUtQgghTIoEnxBCCJMiwSeEEMKkSPAJIYQwKRJ8QgghTIoEnxBCCJMiwSeEEMKkSPAJIYQwKRJ8QgghTIoEnxBCCJMiwSeEEMKkSPAJIYQwKRJ8QgghTIoEnxBCCJMiwSeEEMKkSPAJIYQwKRJ8QgghTIoEnxBCCJMiwSeEEMKkSPAJIYQwKRJ8QgghTMr/B9gJF4Lp6pNNAAAAAElFTkSuQmCC", + "image/png": 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", "text/plain": [ - "
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" ] }, "metadata": {}, @@ -79,15 +215,6 @@ } ], "source": [ - "def dict2graph(d):\n", - " g = nx.to_networkx_graph(d)\n", - " for e in g.edges:\n", - " if not g[e[0]][e[1]].get(\"weight\"):\n", - " g[e[0]][e[1]][\"weight\"] = 1.0\n", - " nx.draw(g, with_labels=True)\n", - " return g\n", - "\n", - "\n", "# a graph instance\n", "# each node is connected to three nodes\n", "# for example, node 0 is connected to nodes 1,7,3\n", @@ -95,48 +222,44 @@ " 0: {1: {\"weight\": 1.0}, 7: {\"weight\": 1.0}, 3: {\"weight\": 1.0}},\n", " 1: {0: {\"weight\": 1.0}, 2: {\"weight\": 1.0}, 3: {\"weight\": 1.0}},\n", " 2: {1: {\"weight\": 1.0}, 3: {\"weight\": 1.0}, 5: {\"weight\": 1.0}},\n", - " 4: {7: {\"weight\": 1.0}, 6: {\"weight\": 1.0}, 5: {\"weight\": 1.0}},\n", - " 7: {4: {\"weight\": 1.0}, 6: {\"weight\": 1.0}, 0: {\"weight\": 1.0}},\n", " 3: {1: {\"weight\": 1.0}, 2: {\"weight\": 1.0}, 0: {\"weight\": 1.0}},\n", - " 6: {7: {\"weight\": 1.0}, 4: {\"weight\": 1.0}, 5: {\"weight\": 1.0}},\n", + " 4: {7: {\"weight\": 1.0}, 6: {\"weight\": 1.0}, 5: {\"weight\": 1.0}},\n", " 5: {6: {\"weight\": 1.0}, 4: {\"weight\": 1.0}, 2: {\"weight\": 1.0}},\n", + " 6: {7: {\"weight\": 1.0}, 4: {\"weight\": 1.0}, 5: {\"weight\": 1.0}},\n", + " 7: {4: {\"weight\": 1.0}, 6: {\"weight\": 1.0}, 0: {\"weight\": 1.0}},\n", "}\n", + "pos = nx.spring_layout(nx.to_networkx_graph(example_graph_dict))\n", + "colors = [\"c\" for key in example_graph_dict.items()]\n", "\n", - "example_graph = dict2graph(example_graph_dict)" + "# convert to a NetworkX graph\n", + "example_graph = nx.to_networkx_graph(example_graph_dict)\n", + "nx.draw_networkx(example_graph, with_labels=True, node_color=colors, pos=pos)\n", + "ax = plt.gca()\n", + "ax.set_facecolor(\"w\")" ] }, { + "attachments": {}, "cell_type": "markdown", "id": "c944f6dd", "metadata": {}, "source": [ - "## Parameterized Quantum Circuit (PQC)" - ] - }, - { - "cell_type": "markdown", - "id": "021d2cb8", - "metadata": {}, - "source": [ - "The PQC with $p$ layers can be written as:\n", - "$$\n", - "U(\\vec{\\beta}, \\vec{\\gamma}) = V_{p}U_{p} \\cdots V_{1}U_{1},\n", - "$$\n", - "where $U_{j}= e^{-i\\gamma_{j}H_{C}}$ and $V_{j}= e^{-i \\beta_{j} \\sum_{k} \\sigma^{x}_{k}}$." + "### Parameterized Quantum Circuit (PQC)" ] }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 105, "id": "055d1257", "metadata": {}, "outputs": [], "source": [ - "def QAOAansatz(params, g=example_graph):\n", + "def QAOAansatz(params, g=example_graph, return_circuit=False):\n", " n = len(g.nodes) # the number of nodes\n", " c = tc.Circuit(n)\n", " for i in range(n):\n", " c.H(i)\n", + "\n", " # PQC\n", " for j in range(nlayers):\n", " # U_j\n", @@ -151,106 +274,498 @@ " for i in range(n):\n", " c.rx(i, theta=params[2 * j + 1])\n", "\n", + " # whether to return the circuit\n", + " if return_circuit is True:\n", + " return c\n", + "\n", " # calculate the loss function\n", " loss = 0.0\n", " for e in g.edges:\n", - " loss += c.expectation_ps(z=[e[0], e[1]])\n", + " loss += c.expectation_ps(z=[e[0], e[1]]) * g[e[0]][e[1]].get(\"weight\", 1.0)\n", "\n", " return K.real(loss)" ] }, { + "attachments": {}, "cell_type": "markdown", "id": "5b159920", "metadata": {}, "source": [ - "## Main Optimization Loop" + "### Optimization" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "6d07ee61", + "metadata": {}, + "source": [ + "Here, several circuits with different initial parameters are optimized/trained at the same time.\n", + "\n", + "Optimizers are used to find the minimum value." ] }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 106, "id": "b8d63c5d", "metadata": {}, "outputs": [], "source": [ "# use vvag to get the losses and gradients with different random circuit instances\n", - "QAOA_vvag = K.jit(tc.backend.vvag(QAOAansatz, argnums=0, vectorized_argnums=0))" + "QAOA_vvag = K.jit(\n", + " tc.backend.vvag(QAOAansatz, argnums=0, vectorized_argnums=0), static_argnums=(1, 2)\n", + ")" ] }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 107, "id": "c51b17a7", "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "params = K.implicit_randn(\n", + " shape=[ncircuits, 2 * nlayers], stddev=0.1\n", + ") # initial parameters\n", + "opt = K.optimizer(tf.keras.optimizers.Adam(1e-2))\n", + "\n", + "list_of_loss = [[] for i in range(ncircuits)]\n", + "\n", + "for i in range(300):\n", + " loss, grads = QAOA_vvag(params, example_graph)\n", + " params = opt.update(grads, params) # gradient descent\n", + "\n", + " # visualise the progress\n", + " clear_output(wait=True)\n", + " list_of_loss = np.hstack((list_of_loss, K.numpy(loss)[:, np.newaxis]))\n", + " plt.xlabel(\"Iteration\")\n", + " plt.ylabel(\"Cost\")\n", + " for index in range(ncircuits):\n", + " plt.plot(range(i + 1), list_of_loss[index])\n", + " legend = [\"circuit %d\" % leg for leg in range(ncircuits)]\n", + " plt.legend(legend)\n", + " plt.show()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "98a6b152", + "metadata": {}, + "source": [ + "### Results" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "fc1c257d", + "metadata": {}, + "source": [ + "After inputing the optimized parameters back to the ansatz circuit, we can measure the probablitiy distribution of the quantum states. The states with highest probability are supposed to be the ones corresponding to Max Cut." + ] + }, + { + "cell_type": "code", + "execution_count": 108, + "id": "843c0ad3", + "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "[-0.23837963 -1.1651934 ]\n", - "[-0.5175445 -1.4539642]\n", - "[-0.7306818 -1.6646069]\n", - "[-0.91530037 -1.8384367 ]\n", - "[-1.0832287 -1.9884492]\n", - "[-1.2398103 -2.120449 ]\n", - "[-1.3878661 -2.2374902]\n", - "[-1.5290209 -2.341291 ]\n", - "[-1.6642232 -2.4328852]\n", - "[-1.7940071 -2.5128942]\n", - "[-1.9186544 -2.5888019]\n", - "[-2.0382538 -2.6627793]\n", - "[-2.152771 -2.735217]\n", - "[-2.2620971 -2.8060198]\n", - "[-2.3657765 -2.8749723]\n", - "[-2.4635859 -2.942443 ]\n", - "[-2.5571456 -3.0074604]\n", - "[-2.6474872 -3.071116 ]\n", - "[-2.7343643 -3.1320357]\n", - "[-2.8174913 -3.1904984]\n", - "[-2.896546 -3.2464304]\n", - "[-2.971222 -3.298626]\n", - "[-3.0411685 -3.3485155]\n", - "[-3.1060221 -3.3945203]\n", - "[-3.1671162 -3.4365993]\n", - "[-3.2244647 -3.47741 ]\n", - "[-3.2800133 -3.51378 ]\n", - "[-3.328074 -3.5467668]\n", - "[-3.3779154 -3.5716858]\n", - "[-3.42378 -3.6026983]\n", - "[-3.4665916 -3.6264663]\n", - "[-3.5065007 -3.6452012]\n", - "[-3.5436964 -3.6676104]\n", - "[-3.5783873 -3.6827888]\n", - "[-3.6107998 -3.696251 ]\n", - "[-3.6411772 -3.710956 ]\n", - "[-3.6697989 -3.725151 ]\n", - "[-3.6969085 -3.739223 ]\n", - "[-3.7227716 -3.753837 ]\n", - "[-3.747642 -3.7637105]\n", - "[-3.7717733 -3.7778597]\n", - "[-3.7953677 -3.7897499]\n", - "[-3.8185773 -3.8026254]\n", - "[-3.8415692 -3.8186839]\n", - "[-3.864397 -3.8288355]\n", - "[-3.887118 -3.8470592]\n", - "[-3.9089546 -3.8578553]\n", - "[-3.9298224 -3.8789082]\n", - "[-3.9531326 -3.898365 ]\n", - "[-3.9759274 -3.9132624]\n" + "Circuit #0\n", + "cost: -6.011465 \n", + "bit strings: ['01010101', '10101010'] \n", + "\n", + "Circuit #1\n", + "cost: -6.0114813 \n", + "bit strings: ['01010101', '10101010'] \n", + "\n", + "Circuit #2\n", + "cost: -6.0113897 \n", + "bit strings: ['01010101', '10101010'] \n", + "\n", + "Circuit #3\n", + "cost: -6.001644 \n", + "bit strings: ['01010101', '10101010'] \n", + "\n", + "Circuit #4\n", + "cost: -6.011491 \n", + "bit strings: ['01010101', '10101010'] \n", + "\n", + "Circuit #5\n", + "cost: -5.1607475 \n", + "bit strings: ['01010101', '10101010'] \n", + "\n" ] } ], "source": [ + "# print all results\n", + "for num_circuit in range(ncircuits):\n", + " c = QAOAansatz(params=params[num_circuit], g=example_graph, return_circuit=True)\n", + " loss = QAOAansatz(params=params[num_circuit], g=example_graph)\n", + "\n", + " # find the states with max probabilities\n", + " probs = K.numpy(c.probability()).round(decimals=4)\n", + " index = np.where(probs == max(probs))[0]\n", + " states = []\n", + " for i in index:\n", + " states.append(f\"{bin(i)[2:]:0>{c._nqubits}}\")\n", + " print(\"Circuit #%d\" % num_circuit)\n", + " print(\"cost:\", K.numpy(loss), \"\\nbit strings:\", states, \"\\n\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "c27fb3f6", + "metadata": {}, + "source": [ + "Based on the results, quantum states with the highest probabilities are $\\ket{01010101}$ and $\\ket{10101010}$. This outcome aligns with our intuition, as swapping the labels of the groups would have an impact on the final result.\n", + "\n", + "The network plot corresponding to $\\ket{01010101}$ is:" + ] + }, + { + "cell_type": "code", + "execution_count": 109, + "id": "fb183e97", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "colors = [\"r\" if states[0][i] == \"0\" else \"c\" for i in range(nnodes)]\n", + "nx.draw_networkx(example_graph, with_labels=True, node_color=colors, pos=pos)\n", + "ax = plt.gca()\n", + "ax.set_facecolor(\"w\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "4ae99ab9", + "metadata": {}, + "source": [ + "## Classical Method" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "720dd1a4", + "metadata": {}, + "source": [ + "In classial method, all situation will be checked one-by-one (brutal force). " + ] + }, + { + "cell_type": "code", + "execution_count": 110, + "id": "2115bb6d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "bit string: ['01010101', '10101010'] \n", + "max cut: 10.0\n" + ] + } + ], + "source": [ + "def classical_solver(graph):\n", + " num_nodes = len(graph)\n", + " max_cut = [0]\n", + " best_case = [0] # \"01\" series with max cut\n", + " for i in range(2**num_nodes):\n", + " case = f\"{bin(i)[2:]:0>{num_nodes}}\"\n", + " cat1, cat2 = [], []\n", + " for j in range(num_nodes):\n", + " if str(case)[j] == \"0\":\n", + " cat1.append(j)\n", + " else:\n", + " cat2.append(j)\n", + "\n", + " # calculate the cost function\n", + " cost = 0\n", + " for node1 in cat1:\n", + " for node2 in cat2:\n", + " if graph[node1].get(node2):\n", + " cost += graph[node1][node2][\"weight\"]\n", + " cost = round(cost, 4) # elimate minor error\n", + " if max_cut[-1] <= cost:\n", + " max_cut.append(cost)\n", + " best_case.append(case)\n", + "\n", + " # optimal cases maybe more than 1, but they are all at the end\n", + " index = max_cut.index(max_cut[-1])\n", + "\n", + " return max_cut[-1], best_case[index:]\n", + "\n", + "\n", + "max_cut, best_case = classical_solver(example_graph_dict)\n", + "print(\"bit string:\", best_case, \"\\nmax cut:\", max_cut)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "e9b8619b", + "metadata": {}, + "source": [ + "## Weighted Max-Cut Problem" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "9f8cb1da", + "metadata": {}, + "source": [ + "When an edge is cut, the total cost increase a certain number instead of 1, we say that this edge has a \"weight\".\n", + "\n", + "Let's define a graph with random weights:" + ] + }, + { + "cell_type": "code", + "execution_count": 111, + "id": "b0a1f778", + "metadata": {}, + "outputs": [], + "source": [ + "weighted_graph_dict = {\n", + " 0: {1: {\"weight\": 0.1756}, 7: {\"weight\": 2.5664}, 3: {\"weight\": 1.8383}},\n", + " 1: {0: {\"weight\": 0.1756}, 2: {\"weight\": 2.2142}, 3: {\"weight\": 4.7169}},\n", + " 2: {1: {\"weight\": 2.2142}, 3: {\"weight\": 2.0984}, 5: {\"weight\": 0.1699}},\n", + " 3: {1: {\"weight\": 4.7169}, 2: {\"weight\": 2.0984}, 0: {\"weight\": 1.8383}},\n", + " 4: {7: {\"weight\": 0.9870}, 6: {\"weight\": 0.0480}, 5: {\"weight\": 4.2509}},\n", + " 6: {7: {\"weight\": 4.7528}, 4: {\"weight\": 0.0480}, 5: {\"weight\": 2.2879}},\n", + " 5: {6: {\"weight\": 2.2879}, 4: {\"weight\": 4.2509}, 2: {\"weight\": 0.1699}},\n", + " 7: {4: {\"weight\": 0.9870}, 6: {\"weight\": 4.7528}, 0: {\"weight\": 2.5664}},\n", + "}\n", + "\n", + "weighted_graph = nx.to_networkx_graph(weighted_graph_dict)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "264289c1", + "metadata": {}, + "source": [ + "The classical algorithm is used to find the corresponding maximum cut" + ] + }, + { + "cell_type": "code", + "execution_count": 112, + "id": "f9f5ce41", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "bit string: ['00010101', '11101010'] \n", + "max cut: 23.6685\n" + ] + } + ], + "source": [ + "max_cut, best_case = classical_solver(weighted_graph_dict)\n", + "print(\"bit string:\", best_case, \"\\nmax cut:\", max_cut)" + ] + }, + { + "cell_type": "code", + "execution_count": 113, + "id": "35dea0fb", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "colors = [\"r\" if best_case[0][i] == \"0\" else \"c\" for i in range(nnodes)]\n", + "weighted_graph = nx.to_networkx_graph(weighted_graph_dict)\n", + "nx.draw_networkx(weighted_graph, with_labels=True, node_color=colors, pos=pos)\n", + "ax = plt.gca()\n", + "ax.set_facecolor(\"w\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "d62faa79", + "metadata": {}, + "source": [ + "The quantum algorithm is then used, and the same result is supposed to be found." + ] + }, + { + "cell_type": "code", + "execution_count": 114, + "id": "22db40be", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "QAOA_vvag = K.jit(\n", + " tc.backend.vvag(QAOAansatz, argnums=0, vectorized_argnums=0), static_argnums=(1, 2)\n", + ")\n", "params = K.implicit_randn(\n", " shape=[ncircuits, 2 * nlayers], stddev=0.1\n", ") # initial parameters\n", "opt = K.optimizer(tf.keras.optimizers.Adam(1e-2))\n", "\n", - "for i in range(50):\n", - " loss, grads = QAOA_vvag(params, example_graph)\n", - " print(K.numpy(loss))\n", - " params = opt.update(grads, params) # gradient descent" + "list_of_loss = [[] for i in range(ncircuits)]\n", + "\n", + "for i in range(300):\n", + " loss, grads = QAOA_vvag(params, weighted_graph)\n", + " params = opt.update(grads, params) # gradient descent\n", + "\n", + " # visualise the progress\n", + " clear_output(wait=True)\n", + " list_of_loss = np.hstack((list_of_loss, K.numpy(loss)[:, np.newaxis]))\n", + " plt.xlabel(\"Iteration\")\n", + " plt.ylabel(\"Cost\")\n", + " for index in range(ncircuits):\n", + " plt.plot(range(i + 1), list_of_loss[index])\n", + " legend = [\"circuit %d\" % leg for leg in range(ncircuits)]\n", + " plt.legend(legend)\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 115, + "id": "d2cf1b57", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Circuit #0\n", + "cost: -15.938664 \n", + "bit strings: ['00110101', '11001010'] \n", + "\n", + "Circuit #1\n", + "cost: -17.461643 \n", + "bit strings: ['00010101', '11101010'] \n", + "\n", + "Circuit #2\n", + "cost: -16.610685 \n", + "bit strings: ['00010101', '11101010'] \n", + "\n", + "Circuit #3\n", + "cost: -16.61402 \n", + "bit strings: ['00010101', '11101010'] \n", + "\n", + "Circuit #4\n", + "cost: -14.814039 \n", + "bit strings: ['00010101', '11101010'] \n", + "\n", + "Circuit #5\n", + "cost: -14.7950735 \n", + "bit strings: ['00010101', '11101010'] \n", + "\n" + ] + } + ], + "source": [ + "# print all results\n", + "for num_circuit in range(ncircuits):\n", + " c = QAOAansatz(params=params[num_circuit], g=weighted_graph, return_circuit=True)\n", + " loss = QAOAansatz(params=params[num_circuit], g=weighted_graph)\n", + "\n", + " # find the states with max probabilities\n", + " probs = K.numpy(c.probability()).round(decimals=4)\n", + " index = np.where(probs == max(probs))[0]\n", + " states = []\n", + " for i in index:\n", + " states.append(f\"{bin(i)[2:]:0>{c._nqubits}}\")\n", + " print(\"Circuit #%d\" % num_circuit)\n", + " print(\"cost:\", K.numpy(loss), \"\\nbit strings:\", states, \"\\n\")" + ] + }, + { + "cell_type": "code", + "execution_count": 116, + "id": "492d215f", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "OS info: macOS-13.3.1-arm64-arm-64bit\n", + "Python version: 3.10.10\n", + "Numpy version: 1.23.2\n", + "Scipy version: 1.10.1\n", + "Pandas version: 2.0.1\n", + "TensorNetwork version: 0.4.6\n", + "Cotengra is not installed\n", + "TensorFlow version: 2.12.0\n", + "TensorFlow GPU: [PhysicalDevice(name='/physical_device:GPU:0', device_type='GPU')]\n", + "TensorFlow CUDA infos: {'is_cuda_build': False, 'is_rocm_build': False, 'is_tensorrt_build': False}\n", + "Jax is not installed\n", + "JaxLib is not installed\n", + "PyTorch is not installed\n", + "Cupy is not installed\n", + "Qiskit version: 0.23.3\n", + "Cirq is not installed\n" + ] + } + ], + "source": [ + "tc.about()" ] } ], @@ -270,7 +785,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.10.10" } }, "nbformat": 4, diff --git a/docs/source/tutorials/qaoa_bo.ipynb b/docs/source/tutorials/qaoa_bo.ipynb index cd6e97e4..240bf374 100644 --- a/docs/source/tutorials/qaoa_bo.ipynb +++ b/docs/source/tutorials/qaoa_bo.ipynb @@ -3,32 +3,71 @@ { "cell_type": "markdown", "source": [ - "# Optimizing QAOA using BO" + "# Optimizing QAOA by Bayesian Optimization (BO)" ], "metadata": {} }, { "cell_type": "markdown", "source": [ - "## Setup" + "## Overview" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "In this tutorial, we show how to use Bayesian optimization to optimize QAOA. For the introduction of QAOA, please refer to the [previous tutorial](qaoa.ipynb). Bayesian optimization in this tutorial is based on $\\text{ODBO}$, please refer to [Cheng, Yang, Hsieh, Liao and Zhang](https://doi.org/10.48550/arXiv.2205.09548) for details and this [repository](https://github.com/tencent-quantum-lab/ODBO) for source code and [installation](https://github.com/tencent-quantum-lab/ODBO#installation). In this tutorial, the updated modules of BO, TuRBO and DARBO are packaged." ], "metadata": {} }, + { + "cell_type": "markdown", + "source": [ + "## Setup" + ], + "metadata": { + "collapsed": false + } + }, { "cell_type": "code", "execution_count": null, "source": [ "import tensorcircuit as tc\n", - "import tensorflow as tf\n", - "import cotengra as ctg\n", + "from jax import numpy as jnp\n", "import optax\n", + "import torch\n", "import networkx as nx\n", - "import time\n", + "import matplotlib.pyplot as plt\n", "import numpy as np\n", - "import torch\n", - "import os\n", + "import cotengra as ctg\n", + "from typing import Union\n", + "import time\n", + "import odbo\n", + "from IPython.display import clear_output\n", + "\n", + "K = tc.set_backend(\"jax\")\n", + "tc.set_dtype(\"complex128\")\n", + "dtype = torch.float64\n", "\n", - "K = tc.set_backend(\"tensorflow\")" + "# cotengra package to speed up the calculation\n", + "opt_ctg = ctg.ReusableHyperOptimizer(\n", + " methods=[\"greedy\", \"kahypar\"],\n", + " parallel=True,\n", + " minimize=\"combo\",\n", + " max_time=20,\n", + " max_repeats=128,\n", + " progbar=True,\n", + ")\n", + "\n", + "tc.set_contractor(\"custom\", optimizer=opt_ctg, preprocessing=True)\n", + "\n", + "nlayers = 10\n", + "device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n", + "acqfn = \"ucb\"" ], "outputs": [], "metadata": {} @@ -36,257 +75,847 @@ { "cell_type": "markdown", "source": [ - "## QAOA blackbox" + "## MAX-CUT Hamiltonian" ], "metadata": {} }, + { + "cell_type": "markdown", + "source": [ + "### Define the Graph" + ], + "metadata": { + "collapsed": false + } + }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 3, "source": [ - "# Generate a graph\n", - "def dict2graph(d):\n", - " g = nx.to_networkx_graph(d)\n", - " for e in g.edges:\n", - " if not g[e[0]][e[1]].get(\"weight\"):\n", - " g[e[0]][e[1]][\"weight\"] = 1.0\n", - " nx.draw(g, with_labels=True)\n", - " return g\n", - "\n", - "\n", "# a graph instance\n", - "example_graph_dict = {\n", - " 0: {1: {\"weight\": 0.9}, 7: {\"weight\": 0.4}, 3: {\"weight\": 0.38}},\n", - " 1: {0: {\"weight\": 0.44}, 2: {\"weight\": 0.67}, 3: {\"weight\": 0.62}},\n", - " 2: {1: {\"weight\": 0.21}, 3: {\"weight\": 0.87}, 5: {\"weight\": 0.72}},\n", - " 4: {7: {\"weight\": 0.34}, 6: {\"weight\": 0.53}, 5: {\"weight\": 0.45}},\n", - " 7: {4: {\"weight\": 0.45}, 6: {\"weight\": 0.63}, 0: {\"weight\": 0.59}},\n", - " 3: {1: {\"weight\": 0.12}, 2: {\"weight\": 0.21}, 0: {\"weight\": 0.68}},\n", - " 6: {7: {\"weight\": 0.34}, 4: {\"weight\": 0.33}, 5: {\"weight\": 0.96}},\n", - " 5: {6: {\"weight\": 0.18}, 4: {\"weight\": 0.79}, 2: {\"weight\": 0.17}},\n", + "graph_dict = {\n", + " 0: {1: {\"weight\": 1.0}, 7: {\"weight\": 1.0}, 3: {\"weight\": 1.0}},\n", + " 1: {0: {\"weight\": 1.0}, 2: {\"weight\": 1.0}, 3: {\"weight\": 1.0}},\n", + " 2: {1: {\"weight\": 1.0}, 3: {\"weight\": 1.0}, 5: {\"weight\": 1.0}},\n", + " 3: {1: {\"weight\": 1.0}, 2: {\"weight\": 1.0}, 0: {\"weight\": 1.0}},\n", + " 4: {7: {\"weight\": 1.0}, 6: {\"weight\": 1.0}, 5: {\"weight\": 1.0}},\n", + " 5: {6: {\"weight\": 1.0}, 4: {\"weight\": 1.0}, 2: {\"weight\": 1.0}},\n", + " 6: {7: {\"weight\": 1.0}, 4: {\"weight\": 1.0}, 5: {\"weight\": 1.0}},\n", + " 7: {4: {\"weight\": 1.0}, 6: {\"weight\": 1.0}, 0: {\"weight\": 1.0}},\n", "}\n", "\n", - "example_graph = dict2graph(example_graph_dict)" + "graph = nx.to_networkx_graph(graph_dict)\n", + "pos = nx.spring_layout(graph)\n", + "nx.draw_networkx(graph, with_labels=True, pos=pos)\n", + "ax = plt.gca()\n", + "ax.set_facecolor(\"w\")" ], "outputs": [ { - "output_type": "display_data", "data": { - "text/plain": [ - "
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" 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" }, - "metadata": {} + "metadata": {}, + "output_type": "display_data" } ], - "metadata": {} + "metadata": { + "ExecuteTime": { + "end_time": "2023-07-15T07:42:26.571397400Z", + "start_time": "2023-07-15T07:42:26.444088200Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "### Brutal Force Result" + ], + "metadata": { + "collapsed": false + } }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "bit string: ['01010101', '10101010'] \n", + "max cut: 10.0\n" + ] + }, + { + "data": { + "text/plain": "
", + "image/png": 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62rZt65hW6N69O9WrV1e73FKRnJzMmjVrMJlMrF+/nqysLEJDQzEYDAwdOpTatWurXaLL2rhxI4899hgJCQnMnj2bsWPHyp4dQhUSBgRWq5WRI0fy7bff8s0332A0GtUuyamcO3cux7TC6T/a2bZu3doxrRAWFkaNGjVUrrT4pKamsnbtWsxmM+vWrSMjI4POnTs7AoD04C8+SUlJvPzyyyxYsICePXvyxRdf0LhxY7XLEhojYUDjrFYro0aN4uuvv+bbb7+VIFAAFy5cyHG3wokTJwBo1aqVIxiEhYW53BVzWloa69atw2w2s3btWtLT0wkKCnIEAFnsVrI2bdrE6NGjuXHjBu+88w5PPPGEjBKIUiNhQMOsViujR4/mq6++4ptvvuFf//qX2iW5pMuXL+eYVjh+/DgAzZs3d0wrhIWFUTeXFsxqysjI4Oeff8ZsNrNmzRpSU1Pp2LEjRqORYcOGyRVqKUtOTuaVV15h/vz59OjRg4ULF8q/gSgVEgY0ymq18thjj/Hll1/y9ddf8+9//1vtksqMK1eusGXLFkc4OHLkCABNmzbNMa2gVovazMxMNmzYgNlsZvXq1SQnJxMQEOAIAPfcc48qdYk/bd68mdGjRxMfH8/bb7/Nk08+KaMEokRJGNAgm83GY489xtKlS/nqq6/4z3/+o3ZJZdr169fZsmWLY83BwYMHAWjcuLEjGISHh5foavKsrCw2bdqEyWRi1apVJCUl0aZNGwwGAwaDgRYtWpTYe4uiSU5O5tVXX+XTTz8lLCyMRYsW0aRJE7XLEmWUhAGN+WsQ+PLLL/m///s/tUvSnPj4eKKiohxTC7GxsSiKQoMGDXKEgyZNmtzV/efZ2dn8+uuvmEwmfvjhB27dukXLli0xGo0YDAbuvffeYvyuREn59ddfGT16NNeuXePtt9/mqaeeklECUewkDGjIX4PA0qVLeeSRR9QuSWBv3nM7HERERLB//35sNht169bNseagWbNm+YYDi8VCREQEZrOZlStXcuPGDZo1a+YIAG3atJEGNy4oJSWFV199lU8++YTu3buzaNEimjZtqnZZogyRMKARNpuNMWPGsGTJEgkCTu7WrVts3brVMXIQHR2NzWajdu3aOe5WaNmyJTqdDqvVypYtWzCbzaxYsYLr16/TpEkTRwAICAiQAFBG/Pbbb4waNYpr167x1ltv8fTTT8sogSgWEgY0wGazMXbsWBYtWsSXX34pQcDFJCUlsW3bNkc42LNnD1arlcqVK1OtWjWuXbtGcnIyDRs2xGAwYDQa6dixowSAMiolJYXx48fz8ccf0717dxYuXCiLPsVdK+j5W6Kni7LZbDz++OMsWrRIRgRcVKVKlejbty8zZ87k3XffZezYsVStWpVbt25x4cIFUlNTAftJ4tSpU2zfvp2DBw9isxV2j0nhCipWrMi8efP47bffuHDhAu3atePDDz+Uf29RKiQMuCCbzcYTTzzBwoULWbJkCY8++qjaJYlCUhSFXbt28eKLL9KwYUO6du3Kjz/+yKOPPsr27dtJT08nOTmZTZs28eSTT3L9+nXGjRtHQEAA/v7+DBo0iPfff599+/Zhtea316RwJeHh4Rw4cIDRo0fz3HPPER4ezsmTJ9UuS5RxMk3gYmw2G08++SSff/45ixcvZvjw4WqXJApIURSio6MxmUwsW7aMc+fOUatWLYYOHYrBYKBr1655zhOnp6ezc+dOx7TCjh07yMzMpHLlynTr1s2x5qB9+/Z4eHiU4ncmSkpkZCSjRo0iLi6OmTNn8uyzz8paAlEosmagDLLZbDz11FMsWLCARYsWMWLECLVLEvlQFIX9+/djNpsxm82cPn0af39/RwDo1q0b7u7uRXrtjIwMdu/e7bhbYceOHaSnp1OpUiVCQ0Mddyx07NhRwoELS01N5bXXXuPDDz8kNDSURYsW0axZM7XLEi5CwkAZY7PZePrpp/nss89YuHAhI0eOVLskkQtFUTh48KAjAJw4cYJq1aoxZMgQDAYDYWFhJXJyzsrKYs+ePY4mSNu2bSMtLY2KFSvStWtXx62MnTp1oly5csX+/qJkbdmyhVGjRnHp0iXHKEFRg6TQDgkDZYiiKDz99NPMnz+fL774glGjRqldkriDw4cPOwLAsWPHqFKlCoMGDcJoNNKjR49SPwFnZ2cTHR3tCAdbt24lJSWFChUq0LVrV8e0gl6vx8vLq1RrE0WTmprKxIkT+fDDD+ncuTOLFy+mefPmapclnJiEgTLidhD49NNPWbhwoQQBJ3P8+HFMJhNms5nDhw/j5+fHwIEDMRqN3HfffXh6eqpdooPFYiEmJsax5iAqKoqkpCTKly9P586dHdMKQUFBeHt7q12uyENUVBSjRo3i4sWLvPnmmzz33HMySiDuSMJAGaAoCv/73//45JNP+OKLLxg9erTaJQng5MmTjgBw4MABfH19efjhhzEYDPTp08dlrrKtViv79+93rDmIiori1q1beHl5ERIS4phWCAkJoXz58mqXK/4mLS2NiRMn8sEHHxASEsLixYtlLwrxDxIGXNxfg8Dnn3/OY489pnZJmnb69GmWLVuGyWRi3759+Pj48NBDD2EwGHjggQfKxJW01Wrl4MGDjmmFLVu2cPPmTTw9PQkKCnKEg86dO+Pj46N2ueIPW7duZeTIkVy8eJEZM2bw/PPPyyiBcJAw4MIUReGZZ57h448/ZsGCBYwZM0btkjTp3LlzjgCwd+9eKlSoQP/+/TEYDPTt25cKFSqoXWKJstlsHDp0yDGtEBkZSXx8PB4eHgQFBTnWHHTt2pWKFSuqXa6mpaWlMWnSJN5//32Cg4NZvHgxLVu2VLss4QQkDLgoRVF49tlnmTdvngQBFVy4cIHly5djMpnYtWsX3t7ePPjggxgMBh588EFNXxErisKRI0cc0wqRkZFcu3YNd3d3OnXq5Fhz0LVrV/k9oZJt27YxcuRIzp8/z4wZM3jhhRdklEDjJAy4IEVReO655/joo4/47LPPGDt2rNolacLly5dZvnw5ZrOZbdu24enpSd++fTEajfTv3x9fX1+1S3RKiqJw/PjxHOEgLi4ONzc3Onbs6JhWCA0NpXLlymqXqxlpaWlMnjyZuXPnyiiBkDDgahRF4fnnn+fDDz9k/vz5PP7442qXVKZdvXrVEQCioqLw8PDg/vvvx2g0MmDAAPz8/NQu0eUoisLJkycdwSAiIoJLly6h0+no0KGDY1qhW7duVK1aVe1yy7zt27czcuRIzp07xxtvvMFLL70kowQaJGHAhSiKwgsvvMAHH3zAp59+yhNPPKF2SWXS9evXWbFiBWazmcjISNzc3OjduzcGg4GBAwfK1WsxUxSF06dPO9YbREREcP78eXQ6He3atXNMK3Tv3p1q1aqpXW6ZlJ6ezuuvv867775LUFAQixcvplWrVmqXJUqRhAEXoSgKL774Iu+//z6ffPIJTz75pNollSk3btzghx9+wGQy8dtvvwFw3333YTAYGDRokFyhlrKzZ8/mmFY4c+YMAG3atHFMK3Tv3p0aNWqoXGnZsmPHDkaOHMnZs2eZNm0aL730krSo1ggJAy5AURReeukl5s6dy8cff8xTTz2ldkllQkJCAqtWrcJsNrNp0yZsNhvh4eEYjUYGDRqEv7+/2iWKP5w/fz7H3Qq3d+e79957HdMKYWFh1KpVS+VKXV96ejpTpkzh3XffJTAwkCVLlnDvvfeqXZYoYRIGnJyiKIwbN4733nuPefPm8fTTT6tdkktLTEzkxx9/xGw2s3HjRiwWC927d8doNDJ48GBq1qypdomiAC5dupRjWuH3338HoEWLFo5phbCwMOrUqaNypa5r586djBw5ktOnTzNt2jTGjRsnowRlmIQBJ6YoCi+//DLvvvuuBIG7kJyczOrVqzGbzaxfv56srCxCQ0MxGo0MGTKE2rVrq12iuEtxcXFs2bLFEQ6OHj0KwD333OMIBmFhYdSvX1/lSl1LRkYGU6ZMYc6cOXTs2JElS5bQunVrtcsSJUDCgJNSFIVXXnmFOXPm8NFHH/G///1P7ZJcSkpKCmvXrsVsNrNu3ToyMzPp3LkzBoOBYcOGUbduXbVLFCXo2rVrbNmyxbHm4NChQwA0adIkx7RCo0aN1C3URezatYuRI0dy6tQppkyZwiuvvCKjBGWMhAEnpCgKr776KrNnz+bDDz/kmWeeUbskl5CWlsa6deswmUz89NNPpKenExQU5AgADRo0ULtEoZL4+PgcIwcHDhwAoGHDho5gEB4eTuPGjdHpdCpX65wyMjKYOnUqs2fPpkOHDixZsoQ2bdqoXZYoJhIGnMxfg8AHH3zAs88+q3ZJTi09PZ3169djMplYs2YNaWlpBAYGOgJA48aN1S5ROKGbN28SFRXlGDnYv38/iqJQr169HGsO7rnnHgkHf7N7925GjBghowRljIQBJ6IoCuPHj+edd96RIJCHzMxMNmzYgMlkYvXq1aSkpNC+fXtHALjnnnvULlG4mFu3bhEVFeVYlBgTE4PNZqN27do51hy0aNFCwgH2UYJp06bxzjvv0KFDBxYvXkzbtm3VLkvcBQkDTkJRFCZMmMDbb7/N+++/z3PPPad2SU4lKyuLX375BbPZzKpVq0hKSqJNmzYYjUaGDRsmW7KKYpWYmMi2bdsc4WDv3r1YrVZq1qyZY1qhVatWmg4He/bsYcSIEZw4cYLXX3+dV199lXLlyqldligCCQNOQFEUXnvtNd566y3mzp3L888/r3ZJTiE7O5vNmzdjNpv54YcfuHXrFi1btsRoNGIwGOTeZ1FqkpOT2b59u2PNwZ49e7BYLPj7+9O9e3fH6EHr1q1xc3NTu9xSlZmZyRtvvMHbb79NQEAAixcvpl27dmqXJQpJwoDKFEVh4sSJzJo1i/fee48XXnhB7ZJUZbFY+O233zCbzaxcuZKbN2/SrFkzjEYjRqOR1q1ba/pKTDiH1NRUduzY4VhzsGvXLrKzs6lWrRrdu3d3jB60a9dOM+Fg7969jBgxgt9//53Jkyczfvx4GSVwIRIGVKQoCpMmTWLmzJm8++67vPjii2qXpAqr1cqWLVswmUysWLGC+Ph4mjRp4hgBCAgIkAAgnFpaWho7d+50TCvs3LmTzMxMKleunCMctG/fvkxvApSZmcn06dN56623aNeuHYsXLyYgIEDtskQBSBhQiaIoTJ48mTfffJM5c+bw0ksvqV1SqbJarWzbts0RAK5evUqjRo0wGAwYDAY6duwoAUC4rIyMDHbt2uWYVtixYwcZGRn4+fkRGhrqWHPQoUOHMrkSPzo6mhEjRnDs2DEmT57MhAkTZJTAyUkYUIGiKLz++uvMmDGD2bNnM27cOLVLKhU2m40dO3ZgNptZtmwZcXFx1K9f3xEA9Hq9BABRJmVmZrJnzx7HtML27dtJS0vD19eXrl27OtYcBAYGlpmTZmZmJjNmzGDWrFm0bduWxYsX0759e7XLErmQMFDKFEVhypQpTJ8+nXfeeYeXX35Z7ZJKlKIo7Nq1yxEALl68SN26dRk2bBgGg4Hg4GDNzKkKcVtWVhbR0dGOcLB161ZSU1Px8fGha9eujmkFvV6Pp6en2uXelZiYGEaMGMHRo0eZOHEir732mst/T2WRhIFSNmXKFMfK21deeUXtckqEoijs3bsXs9mM2Wzm/Pnz1KpVi6FDh2I0GunSpYsEACH+Ijs7m5iYGMeag6ioKJKTkylfvjxdunRxTCsEBQXh5eWldrmFlpWVxYwZM5g5cyZt2rRhyZIlMkrgZCQMlKKpU6cybdo03nrrLV599VW1yylWiqKwb98+RwA4c+YM/v7+jgAQGhpaphdOCVGcLBYL+/fvd6w5iIqKIjExEW9vb0JCQhzTCiEhIXh7e6tdboHFxMQwcuRIjhw5wmuvvcbEiRNllMBJSBgoJbeDwKxZsxg/frza5RQLRVE4ePAgJpMJs9nMyZMnqVatGkOGDMFgMBAWFlYmF0cJUdqsVisHDhxwTCts2bKFhIQEPD09CQ4OdoSDzp07U6FCBbXLzVNWVhZvvvkmM2fO5N5772XJkiV06NBB7bI0T8JAKZg2bRpTp04tM0Hg8OHDjgBw/PhxqlSpwuDBgzEYDPTo0aPMLIASwlnZbDYOHjzomFaIjIzkxo0blCtXjqCgIMeagy5dulCxYkW1y72jffv2MXLkSA4fPsyECROYNGmSjBKoSMJACXvjjTeYMmUKM2fOZMKECWqXU2THjh3DbDZjMpk4cuQIfn5+DBo0CIPBwH333Sf/EwuhIpvNxpEjRxzTCpGRkVy/fh0PDw86derkWHPQtWtXfH191S7XISsri1mzZjFjxgxatWrFkiVL6Nixo9plaZKEgRI0ffp0Xn/9dd58801ee+01tcsptBMnTjgCwMGDB/H19eXhhx/GaDTSu3dvl1zIJIQWKIrCsWPHcoSDK1eu4O7uTseOHR3TCqGhofj5+aldLvv372fEiBEcOnTIMUogv19Kl4SBEjJjxgwmT57MjBkzmDhxotrlFNjp06cdiwD37duHj48PDz30EEajkfvvv9+lFisJIewUReHEiROOYBAZGcmlS5dwc3OjQ4cOjmmFbt26UaVKFVVqzM7OZtasWUyfPp2WLVuyZMkSAgMDValFiyQMlIA333yTSZMmMX36dCZNmqR2Ofk6d+6cIwDs3buXChUq0L9/f4xGI3379qV8+fJqlyiEKEaKonDq1ClHMIiIiODChQvodDoCAgIc0wrdunWjWrVqpVpbbGwsI0eO5MCBA4wfP57JkyfLKEEpkDBQzGbOnMnEiRN54403mDx5strl5OrChQssW7YMs9nMrl278Pb25sEHH8RgMPDggw/i4+OjdolCiFKiKApnz57NMa1w9uxZANq2beuYVujevTv+/v4lXk92djZvvfUW06dPp3nz5ixZsoROnToV7cUUBU6fhosXwWKBihWhdWv7Z+FQ4PO3UgCJiYkKoCQmJhbk8DJn5syZCqBMmzZN7VLu6NKlS8oHH3ygdOnSRQEULy8vZeDAgcq3336rJCcnq12eEMKJnD17Vlm6dKkyatQopWnTpgqgAErr1q2Vp556SjGZTMqVK1dKtIbY2FilY8eOiru7uzJhwgQlIyOjYE/MzlaUH35QlL59FcXXV1HskeDPD51OUe65R1Fee01Rzp0r0e/BVRT0/C1hIB+zZs1SAGXq1Klql5JDXFycMm/ePKVbt26KTqdTypUrpwwYMED56quvNPnvJIQomgsXLihff/21MmbMGKVZs2aOcNCyZUvl8ccfV7777jvl8uXLxf6+WVlZyowZM5Ry5cop9957r7J79+68n7BmjaLUqWM/6bu7/zMI/PXD3d0eDEaMUJSbN4u9dlciYaAYvPXWWwqgTJkyRe1SFEVRlKtXryqffvqpEh4eruh0OsXDw0Pp27evsmTJEiUhIUHt8oQQZcClS5eU7777TnniiSeUli1bOsJBs2bNlDFjxihff/21cuHChWJ7vwMHDigdO3ZU3NzclPHjx/9zlCAtTVH++1/7Sd7NLe8QcKdQUKOGomzeXGz1uhoJA3fpdhB4/fXXVa3j+vXryoIFC5RevXopbm5uiru7u9KnTx9l4cKFyo0bN1StTQhR9l25ckUxm83KU089pbRu3doRDpo2baqMGjVKWbp0qXL27Nm7eo+/jxLs2rXL/oXUVEXp3r3wIeCvH25uiuLhoSirVxfD34brKej5WxYQ3sE777zDq6++yuTJk5k2bVqpb7+bkJDADz/8gNlsZtOmTSiKQo8ePTAYDAwePJjq1auXaj1CCHHb9evX2bJli2NR4sGDBwFo1KiR41bG8PBwGjVqVOjfnYcOHWLEiBHs27ePl8eN482jR3H/6Sew2e6uaJ0OPDxg2zbQ6+/utVyM3E1QRLNnz+aVV14p9SCQmJjIqlWrMJvN/PLLL1gsFsLCwjAYDAwZMoQaNWqUSh1CCFEYN27cICoqynG3QmxsLIqiUL9+fUcwCAsLo2nTpgX6fWqxWJg9eza/T57MYqs11+MygdeBr4AEoB0wA+id2xPc3aFpUzhwADR0S6OEgSKYM2cOL7/8MpMmTeKNN94o8SCQlJTEmjVrMJlMbNiwgezsbEJDQx0BoHbt2iX6/kIIUdwSEhKIiopy9DrYt28fNpuNOnXqOIJBWFgYzZs3z/137K1bWOvVQ5eaSm6bov8bWA48DzQDlgB7gN+A0NyK0+lg2jRw4tvDi5uEgUJ69913GTduHBMnTmT69OklFgRSUlJYu3YtJpOJn3/+mczMTDp37ozRaGTo0KHUrVu3RN5XCCHUkJiYyNatWx3hIDo6GqvVSq1atXJMK7Rs2fLP37sffgjPP2+f9b+D3UAwMBsY98djGUAboAawPa+CqlWDy5dBI/uuSBgohPfee4+XXnqJ1157jRkzZhR7EEhNTWXdunWYTCZ++uknMjIyCAoKcgSABg0aFOv7CSGEs0pOTmbbtm2ONQd79+7FYrFQo0YNunfvTnh4OI+98w6eFy6gy+X09ArwHnAT+OsZaRbwGnAeqJ9XESYTGAzF8w05Oe2EAUWBQ4dg927Ytw+uXbM/Vq0adOhgXyzSoYN9eOgO5s6dy4svvsiECRN48803iy0IpKen8/PPP2M2m1mzZg1paWkEBgZiMBgwGAw0atSoWN5HCCFcWUpKCjt27HCsObiwaxfnLJY8n9MbuAQc+dvjm4FewGpgQG5P9vCA0aNh/vy7rNw1FPT87VGKNRWvrCxYutQ+nHTokP2xcuXsbSnB/g9usdiDwT33wLPP2n8AKlRwvMTtIDB+/PhiCQIZGRls2LABs9nM6tWrSUlJoX379kyaNAmDwUDTpk3v6vWFEKKsqVixIr1796Z3b/vSv8zly2HYsDyfEwfcaUXV7ccu5/VkiwV27SpCpWWba4aBmBh45BE4ehTc/rK8JDv7zn8+dQqeew7eew++/BK6deP999/nxRdf5NVXX2XmzJlFDgJZWVls3LgRs9nMjz/+SFJSEm3btuXVV1/FYDDQvHnzIn6TQgihPV4XLth/r+dxO2E6cKf7Abz/8vU8nTxZtOLKMNcLAwsXwtixfw77F+T+09szIRcuQFgYUQMG8MLq1bzyyivMmjWr0EEgOzubzZs3YzKZWLVqFbdu3aJVq1a8+OKLGAwGWrVqVchvSgghBACZmfmGgfLYby38u4y/fD1PWVlFq60Mc60wsHAhPPZY0Z//xz2r3Vav5qfu3en71lsFDgIWi4XffvsNs9nMypUruXnzJs2bN+eZZ57BYDDQunXrUm9OJIQQZU758vle5NXGvmbg7+L++Fwnv/fQUJ+BgnKdMBATYx8RKCb9tmyBX3+F++7L9Rir1UpkZCRms5kVK1YQHx9P06ZNeeKJJzAYDLRr104CgBBCFKcWLfINA+2x9xNIIufdBLv+8vU8tWxZtNrKMNcIA1lZ9jUCuZx49wBLsf9wnAWqASHYu1HlOmPv5gbDh9vXHfj6Oh62Wq1s3boVs9nM8uXLuXbtGo0aNWLUqFEYjUY6dOggAUAIIUpKYGC+hwwF5gAL+LPPQCawGHv/gTxvKyxXDoKD767GMsg1wsCXX9pP2rl4G9gGDMPekvIKMA/oCOzE3ojiH2w2iIuDjz7CNn4827dvdwSAuLg46tevz6OPPorRaKRTp04SAIQQojT4+0O7dva7xHIZIQjG/vt+AnANuAf7BeFZYGF+r5+dDX36FFu5ZYXz9xlQFPsPxpEjuf5gbAc6AX/tJ3UCaIs9QX6d20sDST4+tPXz48Lly9StW5dhw4ZhMBgIDg7GzS23RphCCCFKzBdfwJgxeR6SAUzG/vv99t4E04H783vtOnXg/Hn7XgUaUHaaDh06BG3bFumptwebovM57qOBA+nw0kt06dJFAoAQQqgtNRUaN4YbN+5+x8K/mzvX3upYIwp6/nb+M18Rm0MowFUgv81+FXd3ngkOJjQ0VIKAEEI4Ax8f+91jxRkEPDygUyd45pnie80yxPnPfjEx9gUfhfQN9ltPjPkcp1MU+3sIIYRwHgMG2G8lL471Wm5u9tsJv/xSM9MDheX8YeD69T9bDBfQMeBpoDMwPL+DbTa4cqVotQkhhCg5n34KgwbdXSBwdwdvb1i/HqQhXK6cPwzkv6QhhyvAg4Af9r2uC5QBC/keQgghSoGHh32HwVdftQeCwl7Vu7lBkyawdSuEhpZMjWWE84eBqlXtPxAFkAj0BW4B6ylAFyqw/7D4+xe1OiGEECXJwwNmzYIdO6BNmz8fy4UC9uDg7W0PEQcO2HeuFXly/jDQoUOBpgkysG9Z+TuwFri3oK+v00HHjkUuTwghRCkIDrZvU79zp71h3D33/GP6IBk437ixfTfbq1dh5kx7KBD5cv6mQ3p9vsP4VuwLBXcAP2JfK1BgVqt9hakQQgjnptPZQ8HtDoIpKXDpkv33eMWKPPTf/1K1WjVW/O9/6tbpgpw/DHTsCE2bwunTuYaCl4DV2EcGbvLPJkOP5PX61apBz57FUakQQojSVLGifS+DP+iDgvj+++9VLMh1Of80gU4Hzz6b5yH7//i8Bnj0Dh+5cneHJ58ET8+8jhJCCOECgoKCuHDhAlfkDrFCc/4wADB6NDRokOtK0gjsi0Zy+7gjnQ4qV9ZUJyohhCjL9Ho9AHv27FG5EtfjGmHAx8feLMJqLb7XVBR7/+tq1YrvNYUQQqimQYMG+Pv7SxgoAtcIAwDdu8Pbbxff640bBwMHFt/rCSGEUJVOpyMoKEjCQBG4ThgAeOUV+/2mYO8PUFi3b0MZNw7eeaf46hJCCOEU9Ho9u3fvpgB78Im/cK0wADB+PPzyC9SqVbhA4O4OVarAypUwe3bx9LsWQgjhVPR6PTdv3uTMmTNql+JSXC8MAPTqBUePwvTpULu2/TF39xzhQHFzI/v2f1SrBhMmwO+/2/tcCyGEKJNkEWHR6JQCjKUUdD9kVVgssGUL7N4N0dH2rlM2G0r16rz58880+89/MH72mdw+KIQQGtG4cWMGDx7Mu+++q3Ypqivo+dv5mw7lx8PD3jTob42DdEBEr17sTUjAKEFACCE0Q6/Xy8hAIbnmNEEBhYSEsHPnTllIIoQQGqLX64mJicFanLejl3FlPgxcvXqVc+fOqV2KEEKIUhIUFERqaipHjx5VuxSXUabDQPAfm1ns2rVL5UqEEEKUlo4dO6LT6di9e7fapbiMMh0G/P39adq0KTt37lS7FCGEEKXE19eXVq1aybqBQijTYQDsowMSBoQQQlukE2HhlPkwEBISQkxMDJmZmWqXIoQQopTo9XpiY2PJyMhQuxSXoIkwkJWVxf79+9UuRQghRCnR6/VYLBZiY2PVLsUllPkwEBAQgJeXl0wVCCGEhrRr1w5PT0+ZKiigMh8GPD09CQwMlDAghBAa4uXlRUBAgNxRUEBlPgzAn82HhBBCaId0Iiw4zYSBs2fPcvXqVbVLEUIIUUr0ej3Hjx8nKSlJ7VKcnmbCAEjzISGE0JKgoCAURSE6OlrtUpyeJsJAvXr1qF27tkwVCCGEhrRo0YKKFSvKuoEC0EQY0Ol0sm5ACCE0xt3dncDAQFk3UACaCANgnyrYvXu37GIlhBAaIp0IC0ZTYSA1NZXDhw+rXYoQQohSotfrOX/+vCwgz4dmwkBgYCDu7u4yVSCEEBqi1+sBZHQgH5oJAz4+PrRr107CgBBCaEjDhg3x9/eXMJAPzYQBkOZDQgihNTqdDr1eL3cU5ENzYeDo0aPcunVL7VKEEEKUktudCBVFUbsUp6WpMBAcHAzI3JEQQmhJUFAQN27c4OzZs2qX4rQ0FQaaNWtGlSpVZKpACCE0RBYR5k9TYcDNzY3g4GAJA0IIoSH+/v40bNhQ1g3kQVNhAP5cRChzR0IIoR2yg2HeNBkGbt68ycmTJ9UuRQghRCkJCgoiOjpautDmQnNhICgoCECmCoQQQkP0ej2pqakcPXpU7VKckubCQJUqVWjZsqWEASGE0JDAwEB0Op1MFeRCc2EApPmQEEJoja+vL61atZIwkAtNhoHg4GAOHDhAWlqa2qUIIYQoJdKJMHeaDAMhISFYLBZiYmLULkUIIUQp0ev1HDhwgMzMTLVLcTqaDANt2rShQoUKMlUghBAaEhQURHZ2NrGxsWqX4nQ0GQY8PDzQ6/USBoQQQkPatWtHuXLlZKrgDjQZBkAWEQohhNZ4eXkREBAgiwjvQNNh4NKlS1y8eFHtUoQQQpQS6UR4Z5oNA7d3MJTRASGE0I6goCCOHTtGUlKS2qU4Fc2Ggdq1a9OgQQMJA0IIoSF6vR5FUYiOjla7FKei2TAA9qmCXbt2qV2GEEKIUtKyZUt8fHxkquBvNB8G9u7dS3Z2ttqlCCGEKAXu7u506tRJwsDfaD4MZGRkcODAAbVLEUIIUUqkE+E/aToMdOjQgXLlysm6ASGE0BC9Xs/58+e5du2a2qU4DU2HAW9vbzp06CBhQAghNOT2VvYyVfAnTYcBkOZDQgihNQ0bNqR69eoyVfAXEgZCQjh58iTx8fFqlyKEEKIU6HQ6aT70N5oPA7ebD8kthkIIoR23w4CiKGqX4hQ0HwYaN26Mv7+/hAEhhNCQoKAg4uPjOXfunNqlOAXNhwGdTifrBoQQQmP0ej2ArBv4g+bDAPzZidBms6ldihBCiFJQo0YNGjRoIOsG/iBhAHsYSEpK4tixY2qXIoQQopQEBQVJGPiDhAHsw0U6nU6mCoQQQkP0ej179+7FarWqXYrqJAwAvr6+tGnTRsKAEEJoiF6vJzU1VUaFkTDgIIsIhRBCWwIDA9HpdDJVgIQBh+DgYA4dOkRycrLapQghhCgFlSpVomXLlnJHARIGHEJCQlAURRKiEEJoiHQitJMw8IdWrVpRqVIlaT4khBAaEhQURGxsLJmZmWqXoioJA39wc3MjKChI1g0IIYSG6PV6srOziY2NVbsUVUkY+IvbiwilV7UQQmhDQEAA5cqV0/xUgYSBvwgJCeHatWucPXtW7VKEEEKUAi8vL9q1aydhQO0CnMntHQxlqkAIIbRDOhFKGMihevXq3HPPPRIGhBBCQ/R6PUePHtX0reUSBv4mODhYwoAQQmiIXq9HURSio6PVLkU1Egb+JiQkhH379pGRkaF2KUIIIUpBq1at8PHx0fRUgYSBvwkJCSE7O5v9+/erXYoQQohS4O7uTmBgoKY7EUoY+Jt27drh7e0tUwVCCKEhWu9EKGHgbzw9PQkMDJQwIIQQGhIUFMS5c+e4du2a2qWoQsLAHcgOhkIIoS16vR5As6MDEgbuICQkhHPnzhEXF6d2KUIIIUpBo0aNqFatmoQB8aeQkBAA2bRICCE0QqfTaXrdgISBO6hXrx516tSRqQIhhNCQ250Itbg/jYSBXMi6ASGE0Ba9Xs/169c5d+6c2qWUOgkDuQgJCWHPnj1YLBa1SxFCCFEKtLyIUMJALkJCQkhLS+Pw4cNqlyKEEKIU1KxZkwYNGkgYEH8KDAzE3d1dpgqEEEJD9Hq9JjsRShjIRYUKFQgICJAwIIQQGqLX64mOjsZqtapdSqmSMJAHWUQohBDaEhQUREpKCsePH1e7lFIlYSAPISEhHDt2jISEBLVLEUIIUQoCAwPR6XSamyqQMJCH4OBgAM39UAghhFZVqlSJFi1aaG4RoYSBPDRr1owqVarIVIEQQmiIFjsRShjIg06nk3UDQgihMUFBQcTGxpKZmal2KaVGwkA+QkJC2LVrlybbUwohhBbp9XqysrI4cOCA2qWUGgkD+QgJCSEhIYETJ06oXYoQQohSEBAQgIeHh6amCiQM5CMoKAhApgqEEEIjvL29CQgIkDAg/lS5cmVatWolYUAIITREa50IJQwUgCwiFEIIbdHr9Rw9epTk5GS1SykVEgYKIDg4mAMHDpCamqp2KUIIIUpBUFAQiqIQExOjdimlQsJAAYSEhGC1WomOjla7FCGEEKWgVatW+Pj4aGaqQMJAAbRu3RofHx+ZKhBCCI1wd3enY8eOmllEKGGgADw8PNDr9ezatUvtUoQQQpSSoKAgCQMip5CQEHbs2CHNh4QQQiP0ej1nz57l+vXrapdS4iQMFFBISAhxcXFcvHhR7VKEEEKUAr1eD6CJ0QEJAwV0ewdDWTcghBDa0LhxY6pVqyZhQPypVq1aNGrUSMKAEEJohE6n08wOhhIGCiE4OFjCgBBCaMjtToRlfb2YhIFCCAkJITo6mqysLLVLEUIIUQr0ej3Xr1/n/PnzapdSoiQMFEJISAiZmZnExsaqXYoQQohSoJVFhBIGCqFDhw54enrKVIEQQmhErVq1qF+/fpnvRChhoBC8vLzo0KGDNB8SQggN0cIiQgkDhSQ7GAohhLYEBQURHR2N1WpVu5QSI2GgkEJCQjh16pQmOlIJIYSwjwwkJydz/PhxtUspMRIGCikkJARApgqEEEIjAgMDgbK9iFDCQCE1bNiQGjVqyFSBEEJohJ+fHy1atJAwIP6k0+lk3YAQQmhMWd/BUMJAEYSEhLB79+4yvZhECCHEnzrp9ey7fJllcXEsjItjUVwca+LjuZSZWSa6E3qoXYArCgkJITk5maNHj9KmTRu1yxFCCFFCjqel8emlSyxq25bsr77CcIdFhDXLlWNk7do8Xrs2jcqXV6HKuycjA0XQqVMn3NzcZBGhEEKUUbeysxl57Bgtd+/m40uXSM7j2KvZ2cw+f54mu3bx/IkTpLngqLGEgSLw9fWlTZs2sm5ACCHKoB2JibTcvZuvrlwBwFKA51gBBfjo0iVa79nDoZSUkiyx2EkYKCJZRCiEEGVP1K1b9IyN5Xp2NkW5vrcBFzIy6LpvH7EuFAgkDBRRSEgIhw8fJikpSe1ShBBCFIOz6en0PXCALJsN2128jhVItVrpFRtLvIvscisLCIsoODgYRVHYs2cP9913n9rlCCGEuAuKojDy+HEycwsCb70FGzbk/gJmM/j7O/7TCiRkZ/O/Eyf4vnXr4i632EkYKKKWLVtSqVIldu7cKWFACCFc3PfXrhFx61buBwwYAH90InRQFJg7F2rWzBEEbrMCpuvXGZOQwH1VqhRrvcVNwkARubm5ERwcLOsGhBCiDJh78SJukPv0QOvW9o+/OngQMjKgV69cX9cD+ODiRQkDZVlISAifLFzI9lu3uGGxoADVy5WjnY8PFT3kr1YIIVzBwZQU9iTndfNgLjZtAp0uzzBgAdbeuMHlzEzqeHkVvcgSJmesIriRnc3iuDiWhIdzIzycrvv35/i6DmhevjzDa9VidO3a1PD0VKVOIYQQ+duSmIgO+62BBWaxQESEfbSgVq08D1WA7YmJDK1Ro+hFljC5m6AQsm02pp89S53t23n19GkuuLmB2z//ChXgeHo6k86coe6OHUw8fZpM292sTRVCCFFSopOTcdfpCvekPXsgKSnPUYHbyul07C3KyEMpkjBQQKfS0wmMjmbK2bNkKUqBbjuxARZFYdb58wTs2cPR1NSSLlMIIUQhnU5Px1LY/QU2bQIPDwgPz/dQq6JwLjOzaMWVEgkDBfB7WhohMTEcTUsr3DDSHxTgZHo6XWJiOOhCTSiEEEILsgobBNLTYft20OvBzy/fwxXsI8vOTMJAPm5lZ9Nz/34SsrMLnxz/wgokW632zlYu0oRCCCG0wNfdvXBP2Lo137sI/sod8Cnse5QyWUCYj+dPnuRKVtad21Lu3w8vvHDnJ378Mdx7b46HbjeheOr331kmux0KIYRTaOvjw2+3bpFd0Au+TZugfHno0qVAh9uANj4+RS+wFEgYyMOWW7dYevVq/gcOHgwtW+Z8rG7dOx5qBZbHx/PzjRv0rVbt7osUQghRZIqiUPXGjYIHgVu3IDoaevYEb+8CPcUGBPr6FrnG0iBhIA9zL17EQ6fLf3qgXTsICyvw67oD7128KGFACCFUoCgKBw8exGQyYTabOXntGqxYYV8QmJ/ffgOrtcBTBAB+7u50rlTpLiouebJmIBdxmZmsjo8v+DqBtDT7D0gBWIFNCQmcTk8veoFCCCEK5fDhw0yZMoVWrVoREBDAp59+SlhYGBuXL+eR2rXxKMjthZs2QZUq/2xNnAt3YGydOpSXNQOuaWtiYsF3rXr7bfvqUjc3+yjBE09Aixb5Pi3y1i2alC9/V3UKIYTI3fHjxzGbzZhMJg4fPoyfnx+DBg1i7ty59OrVi3LlygFQKyWF765fz/8FP/64UO9fzs2N/+UybexMJAzkIjo5Of8pAg8P6N4dgoPtt5ecOwcmEzz7LMybB82a5frUcjod0cnJjKxduwSqF0II7Tp16pRjCiA2NhZfX18efvhhZs2aRZ8+ffC6Q1vgthUrMrFhQ6afO1ekW8hzM6dpUxoUcG2BmiQM5OJkejrW/KYI2rSxf9zWtat97cDo0fD55/DOO7k+NVtROCnTBEIIUSzOnj2L2WzGbDYTHR2Nj48PAwYMYOrUqTzwwAN4F+CEPLFhQ368dInYzEy4y2F9N+CBqlV5sk6du3qd0iJhIBdZilK0dFi3rj0UREXZ1xDk8QOV4eRNKIQQwplduHCBZcuWYTKZ2L17N+XLl+fBBx9k/Pjx9OvXjwoVKhTq9c6cOEHc8OGUf/11Mhs2LPhU8d+4AT0rV2Z569a4FbbNsUokDOSigptb3ttZ5sXfH7Kz7U0p8ri31NmbUAghhLO5fPkyy5cvx2QysX37dry8vOjbty/fffcd/fv3p2LFikV63RMnTtCjRw+qV6nCzvvvZ1ZiIp/HxRXqPOD+x7Ev1a/P9MaN8brD3jXOSsJALlr5+OAWH4+tKF0H4+LA09PelCIXbjYbVZKSyM7OdixgEUII8U9Xr15lxYoVmEwmoqKi8PDw4P777+err77ioYceotJd3rZ36tQpevTogZ+fH7/++is1a9ZkQa1aDPP35+VTp4hNTc1zDdntrwVXqsScpk3pXIAWxc5GwkAuAitWzP+2wlu3oHLlnI+dPGnvWR0UdMcdDW+zubnxzeuvs2r3bkJDQwkLCyM8PJxOnTpJOBBCaF58fDwrV67EZDIRERGBm5sbvXv3ZtGiRQwcOJDKf//dW0RnzpyhR48e+Pj4OILAbb2rVmV/1arsSUrim6tX2ZmURGxqqmOKt4KbGx0rVqSznx+P1qxJ2yKOSjgDnaLkf+mblJSEn58fiYmJd53AXEWixUKt7dvzntd/8UX7CECbNvZQcO4crF1rXyfw8cfQsGGuT/XQ6Vjt6cmBLVuIiIhg69atpKSkUKFCBbp27eoIB3q9Hk9Pz+L/BoUQwsncvHmTH374AbPZzObNmwHo2bMnBoOBQYMGUa2YG7WdO3eO8PBw3N3diYyMpG4BbgFUFIUMmw03nQ5PnQ6dk68JKOj5W8JAHh4/fpxFV67kPkKwYoW9AcXly5Caag8EHTvC8OG5tiMG+3CMoUYNvvnL3gUWi4WYmBgiIyOJiIggKiqK5ORkypcvT5cuXRzhICgo6I63xQghhCtKTExk1apVmM1mNm7ciNVqJTw8HIPBwJAhQ/D39y+R971w4QLh4eEoikJkZCT169cvkfdRm4SBYnAkNZV2e/bceZOiu6BTFHYHBtIpj79Li8XC/v37c4SDxMREvL296dy5syMcBAcHF+iWGSGEcBbJycmsXr0as9nM+vXryc7OJjQ0FIPBwNChQ6lVq1aJvv+lS5cIDw8nOzubyMhIGuYxiuvqJAwUk2lnzzLt7Nnia0KhKGAy0f/SJRYsWEDtAjYdslqtxMbGOsLBli1buHXrFl5eXoSEhBAeHk5YWBghISGUl66GQggnk5qaytq1azGZTKxbt47MzEw6d+6M0Whk6NChBRqiLw5xcXGEh4eTnp5OZGQkjRs3LpX3VYuEgWKSbbMRum8f0cnJdz1C4IH9LoXX4+L439ixZGVlMW/ePP79738Xet7JarVy8ODBHOHg5s2beHp6Ehwc7AgHnTt3LvS9tkIIURzS09NZt24dJpOJtWvXkp6ejl6vx2g0MmzYMBo0aFCq9Vy9epXw8HCSk5OJjIykadOmpfr+apAwUIwSsrPpGRvLwZSUIgcCd6B5hQpEtG9PDU9Pbty4wTPPPMN3333HoEGDmD9/PjVq1ChyjTabjUOHDjnCQWRkJDdu3KBcuXIEBQU5wkGXLl3wcfJ9tYUQrisjI4MNGzZgMplYvXo1qampdOjQAaPRiMFgUO1K/Nq1a/To0YOEhAQiIyNplke7+LJEwkAxS7JYeOr33/nm2jV0UOBpg9vHDq5enc9btKDq324bXLFiBU888QQAn3zyCcOGDSuWem02G0eOHMkRDq5fv46Hhwd6vd4RDrp27VrkJh1CCAGQlZXFxo0bMZvN/PjjjyQlJdGuXTsMBgMGg0H1E298fDw9e/bk2rVrREZG0qIAG8mVFRIGSsjq+HhePHmSUxkZeACWXI5zx75VcQMvL2Y3bYohj6v+a9eu8dRTT7FixQqMRiPz5s2jevXqxVq3oigcPXo0Rzi4evUq7u7udOrUybEgsWvXrpr/NxZC5C87O5vNmzdjNpv54YcfuHXrFq1atXKMALRq1UrtEgH77Yo9e/YkLi6OiIgIp6mrtEgYKEGKovDrrVt8deUK2xITOZWRkWOkoLG3N10qVeLRWrXoXaVKgXpTK4qCyWTi6aefxsPDg88++4yBAweW6Pdw/PjxHOEgLi4ONzc3AgMDHeEgNDQUPxfspiWEKH4Wi4WIiAjMZjMrV67kxo0bNGvWDKPRiNFopM1fN25zAgkJCfTq1Yvz588TERFB69at1S6p1EkYKEWpVisJ2dkoQBUPDyp6FL2x45UrV3j88cdZvXo1jzzyCB9++CFVqlQpvmJzoSgKJ06cyBEOLl26hJubGx06dHCEg27duhVb5y8hhPOzWq1ERUVhMplYsWIF169fp0mTJo4RgICAAKdsvHPr1i169+7NmTNn+PXXX2nXrp3aJalCwoALUxSFr7/+mmeeeYYKFSrw+eef8+CDD5Z6DadOnXKEg4iICC5evIhOp6N9+/Y5wkHVqlVLtTYhRMmy2Wxs374dk8nE8uXLuXLlCg0bNnSsAQgMDHTKAHBbUlISffr04ffff+fXX3+lffv2apekGgkDZcClS5cYM2YMP//8MyNHjmTu3LmqDdkrisKZM2dyhIPz58+j0+lo166dIxx079692FuGCiFKnqIo7Nq1C5PJxLJly7h06RJ169Z1BIDg4GCnDgC3JScn88ADD3DkyBE2b95Mx44d1S5JVRIGyghFUVi8eDHPP/88fn5+LFy4kD59+qhdFgBnz57NMa1w5swZANq2bZsjHJRUO1EhxN1RFIW9e/diNpsxm82cP3+eWrVqMWzYMIxGI507d8bNhbbhTUlJoW/fvhw4cIBNmzah1+vVLkl1EgbKmPPnzzN69Gg2bdrE2LFjmTNnDr6+vmqXlcP58+dzhINTp04B0Lp1a0c4CAsLu6t+CkKIu6MoCvv373cEgNOnT+Pv78/QoUMxGo2Ehobi7u6udpmFlpqaSr9+/di3bx8bN24kJCRE7ZKcgoSBMkhRFBYsWMBLL71E9erVWbRoET179lS7rFxdvHgxRzg4ceIEAK1atcoRDkq6D7kQWqcoCocOHcJsNmMymThx4gTVqlVj8ODBGI1GwsLC8LiLhc9qS0tLo3///uzZs4cNGzbQpUsXtUtyGhIGyrAzZ84watQoIiIiePrpp3n77bddoqvg5cuXc4SD48ePA9CiRYsc4aBOnToqVypE2XD06FFHADh69CiVK1dm0KBBGI1GevbsSbm/NUFzRenp6Tz00ENs376d9evX061bN7VLcioSBso4m83Gxx9/zKuvvkrt2rVZsmSJy/1PEBcXx5YtWxzh4OjRowA0a9YsRzioV6+eypUK4TpOnDiByWTCbDZz8OBBKlWqxMCBAzEYDPTu3RtPT0+1Syw2GRkZDBo0iMjISNatW0d4eLjaJTkdCQMacfLkSUaMGMH27dt5/vnnefPNN11218KrV6/mCAeHDx8GoGnTpjnCQWlvbiKEszt9+rRjDcC+ffuoWLEiDz30EAaDgfvvv79MbnOemZnJkCFD2Lx5M2vXruW+++5TuySnJGFAQ6xWKx988AGvvfYaDRs2ZOnSpWVi8cz169dzhIODBw8C0Lhx4xzhoFGjRuoWKoQKzp8/75gC2Lt3LxUqVKB///4YjUb69u3rshcFBZGVlcWwYcPYsGEDq1evdpo7rJyRhAENOnbsGMOHD2fv3r2MGzeOadOmlakrgvj4eKKiohzhIDY2FoCGDRs6gkF4eDiNGjVyifuhhSisS5cusWzZMkwmEzt37sTb25t+/fphNBp58MEHXWLt0N3Kzs7GaDTy008/sWrVKvr27at2SU5NwoBGWSwW5syZw5QpU7jnnntYunQpnTp1UrusEnHz5s0c4WD//v0oikL9+vVzhIMmTZpIOBAuKy4ujhUrVmAymdi6dSuenp488MADGI1GBgwY4HS3GJcki8XCv//9b3788UdWrlxJ//791S7J6UkY0LhDhw4xfPhwYmNjmTBhApMnTy5TC4fuJCEhga1btzrCwb59+7DZbNStWzfHtEKzZs0kHAindu3aNVauXInJZCIyMhJ3d3f69OmD0WjkoYce0uT+IBaLhUcffZTly5ezfPlyHn74YbVLcgkSBgTZ2dm89dZbvPHGG9x7770sXbpUUz26ExMTc4SD6OhobDYbtWvXzhEOWrRoIeFAqO7GjRusXLkSs9nMr7/+ik6no1evXhgMBgYOHKjpPUCsVivDhw/n+++/x2w2M3jwYLVLchkSBoTD/v37GT58OEeOHGHy5MlMmDChTNxfXFhJSUls27bNEQ727t2L1WqlZs2aOcJBq1atJByIUpGQkMCqVaswm81s2rQJm81Gjx49MBgMDB48mOrVq6tdouqsViujRo3im2++4bvvvmPYsGFql+RSJAyIHLKyspgxYwYzZ84kICCApUuXOt3e46UtOTmZ7du3O8LBnj17sFgs1KhRg+7duzvCwb333utS/dmFc0tKSuLHH3/EZDKxceNGLBYL3bt3x2AwMGTIEGrWrKl2iU7DZrMxZswYlixZwtdff82///1vtUtyORIGxB3t3buX4cOHc/LkSaZOncrLL7/s0m1Ii1NqamqOcLB7926ys7OpXr16jnDQpk0bCQeiUFJSUlizZg0mk4n169eTmZlJ165dMRqNDBkyRLpu3oHNZuOJJ57giy++4Msvv+SRRx5RuySXJGFA5CojI4Np06bxzjvv0KlTJ5YsWUKrVq3ULsvppKWlsWPHDkc42LVrF1lZWVStWjVHOGjXrp2EA/EPqamprFu3DpPJxE8//URGRgbBwcEYjUaGDh1K/fr11S7RaSmKwtNPP838+fNZvHgxw4cPV7sklyVhQORr586djBgxgrNnzzJjxgxeeOEFl9ytrLSkp6ezc+dORzjYuXMnmZmZVKlShW7dujnCQUBAgPw9alR6ejrr16/HZDKxZs0a0tLSCAwMxGg0MmzYMGmQVQCKovDcc8/x0Ucf8cUXXzB69Gi1S3JpEgZEgaSnpzNp0iTmzp1L586dWbJkCc2aNVO7LJeQkZHBrl27HOFgx44dZGRk4OfnlyMctG/fXqZiyrDMzEw2bNiA2Wzmxx9/JCUlhYCAAIxGIwaDgaZNm6pdostQFIUXX3yR999/n88++4yxY8eqXZLLkzAgCmXr1q2MGDGCy5cvM2vWLJ555hkZ+i6kzMxMdu/e7QgH27dvJz09nUqVKhEaGuoIBx07dpRw4OKysrLYtGkTZrOZVatWkZiYSJs2bTAYDBgMBlq0aKF2iS5HURReeeUV5syZw8cff8xTTz2ldkllgoQBUWipqalMmDCBjz76iO7du7N48WKaNGmidlkuKysriz179jjCwbZt20hLS8PX15euXbs6wkFgYKAmb/V0NRaLhV9//RWz2czKlStJSEigRYsWjhGA1q1bq12iy1IUhddee4233nqLDz74gGeffVbtksoMCQOiyCIiIhg5ciTXr19n9uzZPP744zJKUAyysrKIjo52hIOtW7eSmpqKj49PjnDQqVOnMt8t0lVYrVYiIyMxmUysXLmS+Ph4mjZtitFoxGg00rZtW+lJUQxef/11pk+fznvvvccLL7ygdjllioQBcVeSk5N55ZVXmD9/Pvfddx8LFy6kYcOGapdVpmRnZxMTE+MIB1FRUaSkpFChQgW6dOniCAdBQUESDkqRzWZj69atmEwmli9fzrVr12jUqJFjBKBDhw4SAIrRG2+8wZQpU3jnnXd4+eWX1S6nzJEwIIrFL7/8wujRo7l16xbvvfceo0ePll+EJcRisbBv374c4SApKYny5cvTuXNnRzgIDg7Gy8tL7XLLFJvNxs6dOzGZTCxbtoy4uDjq16/vWAOg1+vl574EvPnmm0yaNImZM2cyYcIEtcspkyQMiGKTmJjIiy++yKJFi3jggQf4/PPPqVevntpllXlWq5X9+/c7wsGWLVtITEzE29ubkJAQRzgICQkpU1tVlxZFUdi9ezdms5lly5Zx4cIF6tSpw7BhwzAYDISEhMj0WAl6++23GT9+PNOnT2fSpElql1NmSRgQxW7dunWMGTOG1NRUPvzwQx599FG5WipFVquVAwcO5AgHCQkJeHl5ERwc7AgHnTt3pnz58mqX65QURSEmJgaz2YzZbObs2bPUrFmToUOHYjQa6dq1qwSAUvDuu+8ybtw4pkyZwtSpU9Uup0yTMCBKREJCAs899xxfffUVAwYMYMGCBdSqVUvtsjTJZrNx8OBBRziIjIzk5s2beHp6EhQU5AgHXbp0oUKFCmqXqxpFUThw4IAjAJw8eZLq1aszZMgQjEYj3bt3lyZRpeiDDz7g+eefZ+LEiUyfPl0uKEqYhAFRon788UfGjh2LxWJh3rx5/Otf/5L/qVVms9k4fPhwjnAQHx9PuXLl0Ov1OcJBxYoV1S63xB0+fBiTyYTZbOb48eNUqVKFwYMHYzQa6dGjh/R6UMHHH3/M//73P1599VVmzZolvzNKgYQBUeLi4+N55pln+P777xkyZAiffPIJNWrUULss8QebzcbRo0cd4SAiIoLr16/j4eFBp06dHOGga9eu+Pr6ql1usTh+/LgjABw+fBg/Pz8GDRqEwWCgV69e0s9BRfPnz+fJJ5/kpZdeYvbs2RIESomEAVFqli1b5ugW9umnnzJ06FCVKxJ3oigKx44dyxEOrl69iru7O4GBgY5wEBoa6lL/n588edIxBRAbG4uvry8PP/wwBoOBPn36yJ0XTuCLL75gzJgxPPfcc8ydO1eCQCmSMCBK1bVr13jyySdZuXIl//rXv5g3bx7VqlVTuyyRB0VR+P3333OEg7i4ONzc3OjYsaMjHHTr1g0/Pz+1y83hzJkzLFu2DJPJRExMDD4+PgwYMACDwcADDzwgCyidyOLFixk9ejRPPfUUH330kQSBUiZhQJQ6RVH4/vvvefrpp/H09OSzzz7j4YcfVrssUUCKonDy5Mkc4eDSpUu4ubnRvn37HOGgSpUqpV7fhQsXHAFg9+7dlC9fngcffBCDwcCDDz6o6UWSzuqrr75i+PDhPP7443zyyScSBFQgYUCoJi4ujscff5w1a9bw6KOP8sEHH6hy8hB3R1EUTp8+nSMcXLhwAZ1OR0BAgCMcdO/enapVq5ZIDZcvX2b58uWYTCa2b9+Ol5cXffv2xWg00r9/f00shHRV3377LY8++iijRo3is88+k1s2VSJhQKhKURS++uornn32WXx8fPj888/p16+f2mWJu6AoCmfPns0RDs6dO4dOp6Nt27Y5wkH16tWL/D5Xr15l+fLlmM1moqKi8PDw4P7778doNPLQQw/J7yAXYDKZ+M9//sN///tfFi5cKEFARRIGhFO4ePEiY8aMYf369YwaNYr33nvP6eafRdGdPXvWcRtjREQEZ86cAaBNmzaOcBAWFoa/v3+erxMfH8+KFSswm81ERETg5uZGr169MBqNDBw4kMqVK5fCdyOKw4oVKzAajfznP/9h8eLF0sNBZRIGhNNQFIVFixbxwgsvULlyZRYuXEjv3r3VLkuUgPPnz+cIB6dOnQLg3nvvzREOatasyc2bN/nhhx8wm81s3rwZgJ49e2IwGBg0aJAsQHVBq1atcrRz/vLLLyUIOAEJA8LpnDt3jtGjR7N582Yef/xxZs+eXWbubxd3dvHixRzh4MSJEwD4+PiQlpaGoih06dKFRx99lCFDhuQ7giCc15o1axgyZAiDBg3im2++kaZOTqKg52/51xKlpmHDhvzyyy/Mnz+fl19+mQ0bNrBo0SJ69OihdmmihNSrV48BAwYAcOXKFc6ePUt2dja+vr74+Phw7do1tm/fTnx8PPv27XOMHNStW1flykVhrFu3jqFDh/LQQw/x9ddfSxBwQbKqQ5QqnU7Hk08+yYEDB2jYsCE9e/bk2WefJTU1Ve3SRDFKTU3FZDIxePBgatSowSOPPEJ8fDyzZ8/m4sWLxMXFcfXqVeLi4vj++++57777iIqK4v/+7/+oV68ezZo1Y8yYMXz99ddcvHhR7W9H5GHDhg0MHjyYfv368d1330mXRxcl0wRCNTabjXnz5jF+/Hjq1q3L4sWLCQ0NVbssUURpaWn8/PPPmEwm1q5dS3p6Onq9HqPRyLBhw2jQoEG+r3H16lW2bNnimFY4fPgwAE2aNHGsOQgPDy/Qa4mSt2nTJgYMGEDv3r1Zvnw5np6eapck/kbWDAiX8fvvvzNy5Eh27NjBCy+8wIwZM6SDnIvIyMhg/fr1mM1mVq9eTWpqKh06dHAEgCZNmtzV61+/fj1HODh48CAAjRo1yhEOGjVqVAzfjSiMX3/9lQcffJCePXuycuVKafvspCQMCJditVqZO3cukyZNolGjRixdupTg4GC1yxJ3kJWVxcaNGzGbzfz4448kJSXRtm1bjEYjBoOBZs2aldh737hxI0c4OHDgAIqi0KBBgxzhoHHjxtLtrgRFRkbSr18/QkND+fHHH/H29la7JJELCQPCJR09epThw4cTHR3NK6+8wtSpU+WKwwlkZ2ezefNmTCYTq1at4tatW7Rq1coRAFq1aqVKXTdv3iQqKsoRDvbv34+iKNSrVy9HOGjatKmEg2KydetWHnjgAUJCQlizZo2M4jk5CQPCZVksFmbPns2UKVNo3rw5S5cuJTAwUO2yNMdisRAREYHJZGLlypXcvHmTZs2aYTQaMRqNtG7d2ulOsLdu3coRDvbt24fNZqNOnTo5wkGzZs2crnZXsGPHDvr06UOnTp346aefZD8IFyBhQLi8gwcPMmLECGJjY3nttdeYNGmSLFAqYVarlaioKEwmEytWrOD69es0adIEg8GA0WgkICDApU6iiYmJbN261REOYmJisFqt1KpVK0c4aNGihUt9X2rYtWsXvXv3pn379vz888/4+PioXZIoAAkDokzIzs5m1qxZTJ8+ndatW7N06VICAgLULqtMsdlsbN++HZPJxPLly7ly5QoNGzbEYDBgMBgIDAwsMyfKpKQktm3b5ggHe/fuxWq1UrNmTUePg/DwcFq1alVmvufisHfvXnr16kWbNm34+eefpVmYC5EwIMqU/fv3M3z4cI4cOcLrr7/O+PHj5X7mu6AoCjt37sRsNrNs2TIuXbpE3bp1HQEgODhYEyfD5ORktm/f7ggHe/bswWKx4O/vnyMc3HvvvZrdbCcmJob77ruPli1bsmHDBjkHuBgJA6LMycrKYvr06cyaNYv27duzZMkS2rRpo3ZZLkNRFPbu3YvZbMZsNnP+/Hlq1arFsGHDMBqNdO7cWbMnvNtSU1NzhIPdu3eTnZ1NtWrVcoSDNm3auNbfVWoq7N8Ply6B1Qp+ftCuHdStC3mEvtjYWHr27EnTpk355ZdfZJMxFyRhQJRZe/bsYcSIEZw8eZJp06Yxbtw4aX+aC0VR2L9/PyaTCbPZzJkzZ/D392fo0KEYjUZCQ0NlM5k8pKWlsWPHDkc42LVrF1lZWVStWpXu3bs7wkG7du2cLxwkJcFXX8Fnn8Hhw2Cz/fOYatXAaIQnn4S/BeuDBw/So0cPGjVqxKZNm2TnSBclYUCUaRkZGUydOpXZs2ej1+tZsmQJLVu2VLssp6AoCocOHXIEgBMnTlC1alWGDBmC0WgkLCxMwlMRpaens3PnTkc42LlzJ5mZmVSuXDlHOAgICFAvZNls9gAwbhykp9sfy+vXvIcHWCwwaBB8+inUrMmRI0cIDw+nbt26bN68mapVq5ZO7aLYSRgQmrBjxw5GjBjBuXPnePPNN3n++ec1e6V79OhRRwA4evQolStXZtCgQRiNRnr27ClrLEpARkYGu3btcoSDHTt2kJGRgZ+fH926dXOEg/bt25dOAIuPh6FDITKy8M91dwdfXy689Rb6KVOoWbMmv/76q2wl7eIkDAjNSE9PZ+LEibz//vt06dKFxYsXl2gXPGdy4sQJTCYTJpOJQ4cOUalSJQYOHIjBYKB3795yK2Ypy8zMZPfu3Y5wsH37dtLT0/H19c0RDjp27Fj84eD6dQgNhVOn7OsCikDR6bApCi/Xr8+E6GjZUroMkDAgNCcqKoqRI0dy+fJl3n77bZ5++mnnm8ctBqdPn8ZsNmMymdi/fz8VK1bkoYcewmAwcP/990trWCeSlZXFnj17HOFg27ZtpKWlUbFiRUJDQx3hIDAw8O5GbiwW6NIFYmKKHARuswE6d3d027dDUNBdvZZQn4QBoUmpqamMHz+eefPmER4ezqJFi2jcuHHBX8BigU2bYNcuiI6Gy5ftc7D+/tCxI3TqBA88AKXccOXcuXMsW7YMk8nE3r17qVChAv3798dgMNCvXz9pCesisrOz2bt3b45wkJKSgo+PD127dnWEg06dOhVuVOftt2HChDzXBsQAU4GtQAbQBBgLPHung93doUkTOHAAJFy6NAkDQtN+/fVXRo0aRXx8PHPmzOHxxx/P+775pCR4/334+GO4ds3+y1BR/lyBrdPZH7NYoGJFGD0aXn7ZfmtWCbl48SLLly/HZDKxc+dOvL296devHwaDgf79+0sHuDIgOzubmJgYRzjYunUrycnJlC9fPkc40Ov1ue/RceGC/cRtseT6PhuBAUAHwAhUBE5hHwV4J7cnubnBG2/AxIlF/waF6iQMCM1LTk5m3LhxLFiwgF69erFw4UIaNGjwzwN/+QVGjIArV+58+9WduLtD+fIwbx7897953qtdGHFxcSxfvhyz2czWrVvx9PTkgQcewGg0MmDAAOn8VsZZLBb27dvnCAdRUVEkJSXh7e1Nly5dHOEgKCjoz+mgSZPgrbdynR5IApoDXYDlQKEmzmrUgIsXQRafuqwCn7+VAkhMTFQAJTExsSCHC+FUNmzYoNSrV0+pVKmSsnDhQsVms/35xXfeURRQFDc3++fCfOh09s+jRimKxVLk+q5evap88sknSnh4uKLT6RQPDw+lX79+ytKlS5WEhIS7/wsQLstisSh79+5V3n33XWXAgAFK5cqVFUDx8vJSwsPDlamTJytZlSrl+XP6KSiAcuSP/04BxVqYn/OVK9X+axB3oaDnbwkDQhMSEhKUkSNHKoDSr18/5eLFi4oyZ07hA0BuoWDUKEX5a8jIR3x8vLJgwQKlV69eipubm+Lu7q706dNHWbhwoXLjxo0S/JsQrsxisSgxMTHK3LlzlYcfflgJyScIKKAMAaUSKL+A0vyPYOADyhOgpOf3s12unKI895za37a4CwU9f8s0gdCUtWvXMnbsWNomJ7M+JYVi7b6/eLF9uiEXCQkJrFq1CpPJxKZNm1AUhR49emAwGBg8eDDVq1cvzmqEBtiWLsUtj585gADg5B9/Hg2EAxHAR8C/gO/ye5POnWH79ruoUqipoOdvaUMmNKV///4c2rOH7JYtsVLw/wHeBCYBrYFDdzpAp4NnnoHevXMsKkxMTGT16tWYTCY2btyIxWKhW7dufPjhhwwZMoSaNWve7bckNMzt7Nk/OwjmIgVIA54APvzjscFAFvAZ8AaQZ1eOkyfz+qooIyQMCM2punatfeOWAroIzATyXLuvKPbWr7Nnkzx9OmvXrsVkMrF+/XoyMzPp2rUrc+bMYejQodSpU+cuvwPhbKxWK5mZmWRkZOT6kd/Xi3LcSwkJPGuxkNdNiLdvOv333x7/D/YwsIN8wkAeQUOUHRIGhLYoCnz4Yf7H/cU4IASwAvF5HWi1kj5vHo3mz+dmZibBwcHMmjWLoUOHUr9+/aLXLPKkKArZ2dklcrIt6HHZ2dmFrrtcuXJ4e3vj5eWFt7d3rh++vr74+/vf8bjgbdvw2Lgxz7tg6gCHgb+PQdX443NCfoVKDwtNkDAgtOXoUThypMCHb8F+O9Y+4JkCHF/eamXRv/9NwPTpNGrUqGg1uhibzZbjxKnGSbkAS5/+4e8n1txOytWqVSvQcQV9vdtfK5Y9NFatgvXr8zwkEPgFuAS0+Mvjl//4nGfDYZ3OvtWxKPMkDAht2bOnwIdasQeAx4C2BX1SuXI8XLculGIQsFgspXYFfKfHs7KyCl2zm5sb5cuXz/ckWqFCBapWrVrok21+x3l6eubdhMpVBAbme4gBeAtYCPT8y+NfYD8BhOf1ZHd30OuLXp9wGRIGhLbs329voFKAYd35wDlgUyFeXsnOJm3LFk7GxpbaSdlahF70np6eBTqJVq5c+a6ugHM7TrZQLib16kGrVnDsWK6tiDsAo4BFgAUIw343wTJgAvZphFxZLNCvX3FWLJyU/B8ptOXmzQJ1GbwBvA5MJp9h1L/RASd27KBD+/a5H6PTFejk6e3tTaVKle56SPpOV8VlcQMnTdLp4Nln4amn8jxsPtAAWAz8ADQE5gLP5/fabdtCcHDx1CqcmoQBoS0FHBqeBFSlYOsE/u6eZs3Y/c03uZ6MPTw8ysYQtXAOjzwCU6ZAfHyuQbccMOWPjwJTFHjttWJrtS2cm4QBoS01a9o3YMljaP0EsAB4nz8XWYF9p7ds4CxQCXtY+AedjorNmqGXeVZRWipWhEWLoH//4ntNd3f79IDBUHyvKZyajBUKbenYMd/1Apew7+b2LND4Lx+7gN//+PMbuT1ZFlwJNTz4IDz5ZPFcxbu727fsXrBARgU0REYGhLYEBeV7SBvs86p/NwlIBj4Amub2ZIulQO8hRLH76CP7VtzffFP01/DwgGrVICICatUqttKE85MwILSlcWPo2hV27Mh1frU6MPAOj7//x+c7fc3B39/ekliI0ubuDl9+ab+7YOpU+2OF7R7YpQt89RXcaatvUabJNIHQnmeeKdAdBYXm5mYfqpW934Va3Nxg4kSIiYFu3eyP5XUb5+3GR7Vqwaefwm+/SRDQKNm1UGiP1Wq/AoqJKb6+625uUKOG/X5vP7/ieU0h7taxY/bFhVu3wr59kJFhf1yns4+ShYTAsGH2xYfS+6FMKuj5W8KA0Kbjx+1tVrOzc23WUmg//wwPPFA8ryVEcbNa7WsKrFbw8ZE9BzSioOdvmSYQ2tSiBXz7rf3PxbFi+s03JQgI5+buDlWqQPXqEgTEP0gYENo1ZAgsW2af4y/KEKm7uz1IvP22vTmLEEK4KAkDQtuGDIEDB+z9B+DPBVV50ensH/Xrw5Yt8MorJVujEEKUMAkDQrRoAdu3w3ff2RdU3VaunD0cuLvnvEOgRQv4+GM4fBhCQ0u/XiGEKGaygFCIvzt9GnbvhuhouHbNfhtilSrQoQN06gRt2khnNiGESyjo+VvuJRHi75o0sX/8619qVyKEEKVCpgmEEEIIjZMwIIQQQmichAEhhBBC4yQMCCGEEBonYUAIIYTQOAkDQgghhMZJGBBCCCE0TsKAEEIIoXESBoQQQgiNkzAghBBCaJyEASGEEELjJAwIIYQQGidhQAghhNA4CQNCCCGExkkYEEIIITROwoAQQgihcRIGhBBCCI3zKMhBiqIAkJSUVKLFCCGEEKL43D5v3z6P56ZAYSA5ORmA+vXr32VZQgghhChtycnJ+Pn55fp1nZJfXABsNhuXL1/G19cXnU5XrAUKIYQQomQoikJycjJ16tTBzS33lQEFCgNCCCGEKLtkAaEQQgihcRIGhBBCCI2TMCCEEEJonIQBIYQQQuMkDAghhBAaJ2FACCGE0DgJA0IIIYTG/T9aBCqtuZzSNAAAAABJRU5ErkJggg==" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def classical_solver(graph):\n", + " num_nodes = len(graph)\n", + " max_cut = [0]\n", + " best_case = [0] # \"01\" series with max cut\n", + " for i in range(2**num_nodes):\n", + " case = f\"{bin(i)[2:]:0>{num_nodes}}\"\n", + " cat1, cat2 = [], []\n", + " for j in range(num_nodes):\n", + " if str(case)[j] == \"0\":\n", + " cat1.append(j)\n", + " else:\n", + " cat2.append(j)\n", + "\n", + " # calculate the cost function\n", + " cost = 0\n", + " for node1 in cat1:\n", + " for node2 in cat2:\n", + " if graph[node1].get(node2):\n", + " cost += graph[node1][node2][\"weight\"]\n", + " cost = round(cost, 4) # elimate minor error\n", + " if max_cut[-1] <= cost:\n", + " max_cut.append(cost)\n", + " best_case.append(case)\n", + "\n", + " # optimal cases maybe more than 1, but they are all at the end\n", + " index = max_cut.index(max_cut[-1])\n", + "\n", + " return max_cut[-1], best_case[index:]\n", + "\n", + "\n", + "max_cut, best_case = classical_solver(graph_dict)\n", + "print(\"bit string:\", best_case, \"\\nmax cut:\", max_cut)\n", + "\n", + "colors = [\"r\" if best_case[0][i] == \"0\" else \"c\" for i in graph.nodes]\n", + "weighted_graph = nx.to_networkx_graph(graph_dict)\n", + "nx.draw_networkx(weighted_graph, with_labels=True, node_color=colors, pos=pos)\n", + "ax = plt.gca()\n", + "ax.set_facecolor(\"w\")" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-15T07:42:29.489809800Z", + "start_time": "2023-07-15T07:42:29.368921400Z" + } + } + }, + { + "cell_type": "markdown", "source": [ - "def QAOAansatz(params, g=example_graph):\n", - " n = len(g.nodes) # the number of nodes\n", - " c = tc.Circuit(n)\n", + "## QAOA Ansatz" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 46, + "outputs": [], + "source": [ + "def QAOAansatz(params, each=1, return_circuit=False):\n", + " n = graph.number_of_nodes() # the number of nodes\n", + "\n", + " # PQC loop\n", + " def pqc_loop(s_, params_):\n", + " c_ = tc.Circuit(n, inputs=s_)\n", + " for j in range(each):\n", + " # driving layer\n", + " for a, b in graph.edges:\n", + " c_.RZZ(a, b, theta=graph[a][b][\"weight\"] * params_[2 * j])\n", + " # mixing layer\n", + " for i in range(n):\n", + " c_.RX(i, theta=params_[2 * j + 1])\n", + " s_ = c_.state()\n", + " return s_\n", + "\n", + " c0 = tc.Circuit(n)\n", " for i in range(n):\n", - " c.H(i)\n", - " # PQC\n", - " for j in range(nlayers):\n", - " # U_j\n", - " for e in g.edges:\n", - " c.exp1(\n", - " e[0],\n", - " e[1],\n", - " unitary=tc.gates._zz_matrix,\n", - " theta=g[e[0]][e[1]].get(\"weight\", 1.0) * params[2 * j],\n", - " )\n", - " # V_j\n", - " for i in range(n):\n", - " c.rx(i, theta=params[2 * j + 1])\n", + " c0.H(i)\n", + " s0 = c0.state()\n", + " s = K.scan(pqc_loop, K.reshape(params, [nlayers // each, 2 * each]), s0)\n", + " c = tc.Circuit(n, inputs=s)\n", + "\n", + " # whether to return the circuit\n", + " if return_circuit is True:\n", + " return c\n", "\n", " # calculate the loss function\n", " loss = 0.0\n", - " for e in g.edges:\n", - " loss += g[e[0]][e[1]].get(\"weight\") * c.expectation_ps(z=[e[0], e[1]])\n", + " for a, b in graph.edges:\n", + " loss += c.expectation_ps(z=[a, b]) * graph[a][b][\"weight\"]\n", "\n", " return K.real(loss)" ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-15T05:12:41.534488800Z", + "start_time": "2023-07-15T05:12:41.483853500Z" + } + } + }, + { + "cell_type": "code", + "execution_count": 47, "outputs": [], - "metadata": {} + "source": [ + "QAOA_vag = K.jit(\n", + " tc.backend.value_and_grad(QAOAansatz, argnums=0), static_argnums=(1, 2)\n", + ")\n", + "QAOA_nograd = K.jit(QAOAansatz, static_argnums=(1, 2))\n", + "\n", + "\n", + "def eval_objective(x):\n", + " \"\"\"This is a helper function we use to unnormalize and evalaute a point\"\"\"\n", + " return -torch.from_numpy(np.asarray(QAOA_nograd(jnp.asarray(x.ravel()))))" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-15T05:12:41.541255500Z", + "start_time": "2023-07-15T05:12:41.484406100Z" + } + } }, { "cell_type": "markdown", "source": [ - "## Using BO optimizer from ODBO\n" + "## Adam Optimizer" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 48, + "outputs": [], + "source": [ + "opt = K.optimizer(optax.adam(1e-2))" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-15T05:12:41.603802800Z", + "start_time": "2023-07-15T05:12:41.585764800Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "## BO Optimizer" ], "metadata": {} }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 49, "source": [ - "import odbo\n", + "class BO_optimizer:\n", + " def __init__(self, eval_func, batch_size: int = 1, device=\"cpu\"):\n", + " self.eval_func = eval_func\n", + " self.device = device\n", + " self.batch_size = batch_size\n", + " self.best_dict = {\"X\": None, \"Y\": torch.tensor(-float(\"inf\"))}\n", "\n", - "# BO settings\n", - "device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n", - "dtype = torch.float\n", + " def compute_Y(self, X):\n", + " return torch.tensor(\n", + " [self.eval_func(x) for x in X], dtype=X.dtype, device=self.device\n", + " ).unsqueeze(-1)\n", + "\n", + " def update_best(self, X_next, Y_next):\n", + " new_Y, new_idx = torch.max(Y_next, dim=0)\n", + " new_Y = new_Y.squeeze()\n", + " if new_Y > self.best_dict[\"Y\"]:\n", + " self.best_dict[\"Y\"] = new_Y\n", + " self.best_dict[\"X\"] = X_next[new_idx]\n", + "\n", + " def update(\n", + " self,\n", + " X,\n", + " Y=None,\n", + " acqfn: str = \"ucb\",\n", + " normalize: bool = False,\n", + " verbose: bool = False,\n", + " ):\n", + " if Y is None:\n", + " Y = self.compute_Y(X)\n", + " X_next = odbo.run_exp.bo_design(\n", + " X=X,\n", + " Y=Y,\n", + " batch_size=self.batch_size,\n", + " acqfn=acqfn,\n", + " normalize=normalize,\n", + " verbose=verbose,\n", + " )[0].reshape(self.batch_size, X.shape[-1])\n", + " Y_next = self.compute_Y(X_next)\n", + "\n", + " self.update_best(X_next, Y_next)\n", + "\n", + " # Update training set\n", + " X = torch.cat((X, X_next), dim=0)\n", + " Y = torch.cat((Y, Y_next), dim=0)\n", + "\n", + " return X, Y, Y_next.mean()" + ], + "outputs": [], + "metadata": { + "scrolled": false, + "ExecuteTime": { + "end_time": "2023-07-15T05:12:41.603802800Z", + "start_time": "2023-07-15T05:12:41.586291Z" + } + } + }, + { + "cell_type": "code", + "execution_count": 50, + "outputs": [], + "source": [ "batch_size = 1\n", - "acqfn = \"ucb\"\n", "\n", - "QAOA_nograd = K.jit(QAOAansatz)\n", + "bo_opt = BO_optimizer(eval_objective, batch_size, device)" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-15T05:12:41.603802800Z", + "start_time": "2023-07-15T05:12:41.586291Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "## TuRBO Optimizer" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 51, + "outputs": [], + "source": [ + "class TuRBO_optimizer(BO_optimizer):\n", + " def __init__(\n", + " self, eval_func, num_params, tr_length, failure_tolerance, device=\"cpu\"\n", + " ):\n", + " super(TuRBO_optimizer, self).__init__(eval_func, device=device)\n", + " self.batch_size = 1 # There is a bug in odbo.run_exp.turbo_design, batch_size can only be 1 right now.\n", + " self.tr_length = tr_length\n", + " self.state = odbo.turbo.TurboState(\n", + " dim=num_params,\n", + " batch_size=batch_size,\n", + " length=tr_length,\n", + " n_trust_regions=len(tr_length),\n", + " failure_tolerance=failure_tolerance,\n", + " )\n", "\n", + " def inverse_transform(self, X):\n", + " \"\"\"\n", + " Note TuRBO is working on only [0,1] parameter range\n", + " We need to transform parameters from [0,1] to [-pi,pi] before using eval_func\n", + " \"\"\"\n", + " return X * 2 * np.pi - np.pi\n", "\n", - "def eval_objective(x, example_graph):\n", - " \"\"\"This is a helper function we use to unnormalize and evalaute a point\"\"\"\n", - " a = tf.convert_to_tensor(np.array(x).ravel())\n", - " return -QAOA_nograd(a, example_graph).numpy()\n", + " def transform(self, X):\n", + " \"\"\"\n", + " Note TuRBO is working on only [0,1] parameter range\n", + " We need to transform parameters from [-pi,pi] to [0,1] before using odbo.run_exp.turbo_design\n", + " \"\"\"\n", + " return X / 2 / np.pi + 0.5\n", + "\n", + " def compute_Y(self, X, transformed_input: bool = True):\n", + " if transformed_input:\n", + " X = self.inverse_transform(X)\n", + " return torch.tensor(\n", + " [self.eval_func(x) for x in X], dtype=X.dtype, device=self.device\n", + " ).unsqueeze(-1)\n", + "\n", + " def get_next(self, X, Y, acqfn, normalize, verbose):\n", + " X_next = odbo.run_exp.turbo_design(\n", + " state=self.state,\n", + " X=X,\n", + " Y=Y,\n", + " n_trust_regions=len(self.tr_length),\n", + " batch_size=self.batch_size,\n", + " acqfn=acqfn,\n", + " normalize=normalize,\n", + " verbose=verbose,\n", + " )[0].reshape(len(self.tr_length) * self.batch_size, X.shape[-1])\n", + " Y_next = self.compute_Y(X_next)\n", + " return X_next, Y_next\n", + "\n", + " def update_state(self, Y_next):\n", + " self.state = odbo.turbo.update_state(\n", + " state=self.state,\n", + " Y_next=Y_next.reshape(len(self.tr_length), self.batch_size, 1),\n", + " )\n", + "\n", + " def preprocess(self, X, Y, transformed_input):\n", + " if not transformed_input:\n", + " X = self.transform(X)\n", + " if Y is None:\n", + " Y = self.compute_Y(X)\n", + " best_Y, best_idx = torch.max(Y, dim=0)\n", + " best_Y = best_Y.squeeze()\n", + " if best_Y > self.best_dict[\"Y\"]:\n", + " self.state.best_value = best_Y.item()\n", + " self.best_dict[\"Y\"] = best_Y\n", + " self.best_dict[\"X\"] = X[best_idx]\n", + " return X, Y\n", + "\n", + " def postprocess(self, X, Y, X_next, Y_next, transformed_output):\n", + " X = torch.cat((X, X_next), dim=0)\n", + " Y = torch.cat((Y, Y_next), dim=0)\n", + " if not transformed_output:\n", + " X = self.inverse_transform(X)\n", + " return X, Y\n", + "\n", + " def update(\n", + " self,\n", + " X,\n", + " Y=None,\n", + " acqfn: str = \"ucb\",\n", + " normalize: bool = False,\n", + " verbose: bool = False,\n", + " transformed_input: bool = False,\n", + " transformed_output: bool = False,\n", + " ):\n", + " X, Y = self.preprocess(X, Y, transformed_input)\n", + "\n", + " X_next, Y_next = self.get_next(X, Y, acqfn, normalize, verbose)\n", "\n", + " self.update_best(X_next, Y_next)\n", "\n", - "X_new = np.random.uniform(low=0, high=1, size=[1, 2 * nlayers])\n", - "X_bo = torch.tensor(np.vstack([initial_X, X_new]))\n", - "Y_bo = torch.tensor(\n", - " [eval_objective(x, example_graph) for x in X_bo], dtype=dtype, device=device\n", - ").unsqueeze(-1)" + " self.update_state(Y_next)\n", + "\n", + " X, Y = self.postprocess(X, Y, X_next, Y_next, transformed_output)\n", + "\n", + " return X, Y, Y_next.mean()" ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-15T05:12:41.603802800Z", + "start_time": "2023-07-15T05:12:41.586798100Z" + } + } + }, + { + "cell_type": "code", + "execution_count": 52, "outputs": [], + "source": [ + "failure_tolerance = 10\n", + "tr_length = [1.6]\n", + "\n", + "turbo_opt = TuRBO_optimizer(\n", + " eval_objective, 2 * nlayers, tr_length, failure_tolerance, device\n", + ")" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-15T05:12:41.645737200Z", + "start_time": "2023-07-15T05:12:41.586798100Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "## DARBO Optimizer" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "Please refer to [Cheng, Chen, Zhang and Zhang](https://doi.org/10.48550/arXiv.2303.14877) for details." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 53, + "outputs": [], + "source": [ + "class DARBO_optimizer(TuRBO_optimizer):\n", + " def __init__(\n", + " self,\n", + " eval_func,\n", + " num_params,\n", + " tr_length,\n", + " failure_tolerance,\n", + " mode: Union[bool, str] = True,\n", + " device=\"cpu\",\n", + " ):\n", + " super(DARBO_optimizer, self).__init__(\n", + " eval_func, num_params, tr_length, failure_tolerance, device\n", + " )\n", + " self.switch_counter = 0\n", + " if mode == True or mode == \"large\":\n", + " self.mode = True\n", + " else:\n", + " self.mode = False\n", + " self.best_dict = {\n", + " \"X\": None,\n", + " \"Y\": torch.tensor(self.state.best_value),\n", + " \"mode\": self.mode,\n", + " }\n", + "\n", + " def get_mode(self):\n", + " return \"large\" if self.mode else \"small\"\n", + "\n", + " def compute_Y(self, X, transformed_input: bool = True, mode=None):\n", + " if transformed_input:\n", + " X = self.inverse_transform(X, mode)\n", + " return torch.tensor(\n", + " [self.eval_func(x) for x in X], dtype=X.dtype, device=self.device\n", + " ).unsqueeze(-1)\n", + "\n", + " def inverse_transform(self, X, mode=None):\n", + " \"\"\"\n", + " Note TuRBO is working on only [0,1] parameter range\n", + " We need to transform parameters from [0, 1] to [-pi, pi] or [-pi / 2, pi / 2] before using eval_func\n", + " \"\"\"\n", + " if mode is None:\n", + " mode = self.mode\n", + " if mode: # [0, 1] to [-pi, pi]\n", + " return X * 2 * np.pi - np.pi\n", + " else: # [0, 1] to [-pi / 2, pi / 2]\n", + " return X * np.pi - np.pi / 2\n", + "\n", + " def transform(self, X, mode=None):\n", + " \"\"\"\n", + " Note TuRBO is working on only [0,1] parameter range\n", + " We need to transform parameters from [-pi,pi] or [-pi / 2, pi / 2] to [0,1] before using odbo.run_exp.turbo_design\n", + " \"\"\"\n", + " if mode is None:\n", + " mode = self.mode\n", + " if mode: # [-pi, pi] to [0, 1]\n", + " return X / 2 / np.pi + 0.5\n", + " else: # [-pi / 2, pi / 2] to [0, 1]\n", + " return X / np.pi + 0.5\n", + "\n", + " def update_best(self, X_next, Y_next):\n", + " new_Y, new_idx = torch.max(Y_next, dim=0)\n", + " new_Y = new_Y.squeeze()\n", + " if new_Y > self.best_dict[\"Y\"]:\n", + " self.best_dict[\"Y\"] = new_Y\n", + " self.best_dict[\"X\"] = X_next[new_idx]\n", + " self.best_dict[\"mode\"] = self.mode\n", + " else:\n", + " self.switch_counter += 1\n", + "\n", + " def update(\n", + " self,\n", + " X,\n", + " Y=None,\n", + " acqfn: str = \"ucb\",\n", + " normalize: bool = False,\n", + " verbose: bool = False,\n", + " transformed_input: bool = False,\n", + " transformed_output: bool = False,\n", + " frequency: int = 4,\n", + " ):\n", + " X, Y = self.preprocess(X, Y, transformed_input)\n", + "\n", + " # check if we need to switch the searching parameter range.\n", + " if self.switch_counter >= frequency:\n", + " if self.mode:\n", + " X = X * 2 - 0.5\n", + " self.mode = False # small\n", + " else:\n", + " X = X / 2 + 0.25\n", + " self.mode = True # large\n", + " self.switch_counter = 0\n", + "\n", + " X_next, Y_next = self.get_next(X, Y, acqfn, normalize, verbose)\n", + "\n", + " self.update_best(X_next, Y_next)\n", + "\n", + " self.update_state(Y_next)\n", + "\n", + " X, Y = self.postprocess(X, Y, X_next, Y_next, transformed_output)\n", + "\n", + " return X, Y, Y_next.mean()" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-15T05:12:41.645737200Z", + "start_time": "2023-07-15T05:12:41.627215300Z" + } + } + }, + { + "cell_type": "code", + "execution_count": 54, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "initial mode: small\n" + ] + } + ], + "source": [ + "mode = \"small\"\n", + "\n", + "darbo_opt = DARBO_optimizer(\n", + " eval_objective, 2 * nlayers, tr_length, failure_tolerance, mode, device\n", + ")\n", + "print(f\"initial mode: {darbo_opt.get_mode()}\")" + ], "metadata": { - "scrolled": false + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-15T05:12:41.645737200Z", + "start_time": "2023-07-15T05:12:41.627726200Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "## Optimization" + ], + "metadata": { + "collapsed": false } }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 55, + "outputs": [ + { + "data": { + "text/plain": "
", + "image/png": 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" + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 299 min loss: -5.837215998677346\t-6.87628698348999\t-6.8708058821631575\t-7.000515157123274\n", + "Epoch 299 time: 13.83302903175354\tTotal time: 2123.8649847507477\n" + ] + } + ], "source": [ - "# BO Optimizer\n", - "for i in range(100): # run 100 iter optimizations\n", - " X_next, acq_value, ids = odbo.run_exp.bo_design(\n", - " X=X_bo,\n", - " Y=Y_bo,\n", - " batch_size=batch_size,\n", - " acqfn=acqfn,\n", - " normalize=False,\n", - " verbose=False,\n", + "# initial parameters\n", + "params = K.implicit_randu(shape=(2 * nlayers,))\n", + "initial_X = torch.from_numpy(np.asarray(params)).type(dtype)\n", + "\n", + "# First point by BO is actually just a random selection, to have a better search, we pick the most distant point\n", + "X_new = []\n", + "for i in initial_X:\n", + " if i <= 0.5:\n", + " X_new.append(i + 0.5)\n", + " else:\n", + " X_new.append(i - 0.5)\n", + "X_new = torch.tensor(X_new)\n", + "\n", + "X_bo = torch.stack((initial_X, X_new), dim=0)\n", + "Y_bo = None\n", + "X_turbo = X_bo.clone()\n", + "Y_turbo = None\n", + "X_darbo = X_bo.clone()\n", + "Y_darbo = None\n", + "\n", + "losses, losses_bo, losses_turbo, losses_darbo = [], [], [], []\n", + "t0 = ts = time.time()\n", + "\n", + "for i in range(300):\n", + " loss, grads = QAOA_vag(params)\n", + " params = opt.update(grads, params) # gradient descent\n", + " losses.append(loss)\n", + "\n", + " X_bo, Y_bo, _ = bo_opt.update(X_bo, Y_bo, acqfn)\n", + " losses_bo.append(-bo_opt.best_dict[\"Y\"].item())\n", + "\n", + " X_turbo, Y_turbo, _ = turbo_opt.update(\n", + " X_turbo,\n", + " Y_turbo,\n", + " acqfn,\n", + " transformed_input=False if i == 0 else True,\n", + " transformed_output=True,\n", + " )\n", + " losses_turbo.append(-turbo_opt.best_dict[\"Y\"].item())\n", + "\n", + " X_darbo, Y_darbo, _ = darbo_opt.update(\n", + " X_darbo,\n", + " Y_darbo,\n", + " acqfn,\n", + " transformed_input=False if i == 0 else True,\n", + " transformed_output=True,\n", " )\n", - " X_next = torch.reshape(X_next, [batch_size, 2 * nlayers])\n", - " Y_next = torch.tensor(\n", - " [eval_objective(x, example_graph) for x in X_next], dtype=dtype, device=device\n", + " losses_darbo.append(-darbo_opt.best_dict[\"Y\"].item())\n", + "\n", + " # visualise the progress\n", + " clear_output(wait=True)\n", + " plt.figure()\n", + " plt.xlabel(\"Iteration\")\n", + " plt.ylabel(\"Cost\")\n", + " plt.plot(range(i + 1), losses, c=\"r\", label=\"Adam\")\n", + " plt.plot(range(i + 1), losses_bo, c=\"b\", label=\"BO\")\n", + " plt.plot(range(i + 1), losses_turbo, c=\"g\", label=\"TuRBO\")\n", + " plt.plot(range(i + 1), losses_darbo, c=\"y\", label=\"DARBO\")\n", + " plt.legend()\n", + " plt.show()\n", + "\n", + " print(\n", + " f\"Epoch {i} min loss: {min(losses)}\\t{losses_bo[-1]}\\t{losses_turbo[-1]}\\t{losses_darbo[-1]}\"\n", " )\n", - " # Update training set\n", - " X_bo = torch.cat((X_bo, X_next), dim=0)\n", - " Y_bo = torch.cat((Y_bo, Y_next.unsqueeze(-1)), dim=0)\n", - " print(f\"{i+1}) New loss: {-Y_next.item(): .4e} Best loss: {-Y_bo.max():.4e}\")" + "\n", + " te = time.time()\n", + " print(f\"Epoch {i} time: {te - ts}\\tTotal time: {te - t0}\")\n", + " ts = te" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "## Results" ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "After inputting the optimized parameters back to the ansatz circuit, we can perform the projective measurement on the output quantum state to get the solution. Here we directly use the bit string with the maximum probability as the solution since we know all information of the probability distribution of the output quantum state, but which is not feasible in the experiment." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 56, "outputs": [ { + "name": "stdout", "output_type": "stream", + "text": [ + "Adam\n", + "loss: -5.837558827215271\tprob: 0.318607790021735\tbit strings: ['10101010']\n", + "\n", + "BO\n", + "loss: -6.876287191047742\tprob: 0.3434109359024678\tbit strings: ['10101010']\n", + "\n", + "TuRBO\n", + "loss: -6.8708058821631575\tprob: 0.3339171040448526\tbit strings: ['10101010']\n", + "\n", + "DARBO\n", + "loss: -7.000515157123274\tprob: 0.36778546095898973\tbit strings: ['01010101']\n" + ] + } + ], + "source": [ + "params_bo = jnp.asarray(bo_opt.best_dict[\"X\"])\n", + "params_turbo = jnp.asarray(turbo_opt.inverse_transform(turbo_opt.best_dict[\"X\"]))\n", + "params_darbo = jnp.asarray(\n", + " darbo_opt.inverse_transform(\n", + " darbo_opt.best_dict[\"X\"], mode=darbo_opt.best_dict[\"mode\"]\n", + " )\n", + ")\n", + "\n", + "\n", + "# find the states with max probabilities\n", + "def find_max(params):\n", + " loss = QAOA_nograd(params)\n", + " c = QAOAansatz(params, return_circuit=True)\n", + " probs = K.numpy(c.probability())\n", + " max_prob = max(probs)\n", + " index = np.where(probs == max_prob)[0]\n", + " states = []\n", + " for i in index:\n", + " states.append(f\"{bin(i)[2:]:0>{graph.number_of_nodes()}}\")\n", + " return loss, max_prob, states\n", + "\n", + "\n", + "loss, prob, states = find_max(params)\n", + "loss_bo, prob_bo, states_bo = find_max(params_bo)\n", + "loss_turbo, prob_turbo, states_turbo = find_max(params_turbo)\n", + "loss_darbo, prob_darbo, states_darbo = find_max(params_darbo)\n", + "print(f\"Adam\\nloss: {loss}\\tprob: {prob}\\tbit strings: {states}\\n\")\n", + "print(f\"BO\\nloss: {loss_bo}\\tprob: {prob_bo}\\tbit strings: {states_bo}\\n\")\n", + "print(f\"TuRBO\\nloss: {loss_turbo}\\tprob: {prob_turbo}\\tbit strings: {states_turbo}\\n\")\n", + "print(f\"DARBO\\nloss: {loss_darbo}\\tprob: {prob_darbo}\\tbit strings: {states_darbo}\")" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-15T05:48:09.478379400Z", + "start_time": "2023-07-15T05:48:05.566717500Z" + } + } + }, + { + "cell_type": "code", + "execution_count": 57, + "outputs": [ + { "name": "stdout", + "output_type": "stream", "text": [ - "1) New loss: 1.3437e+00 Best loss: 1.2106e+00\n", - "2) New loss: 8.7936e-01 Best loss: 8.7936e-01\n", - "3) New loss: 7.1789e-01 Best loss: 7.1789e-01\n", - "4) New loss: 6.1326e-01 Best loss: 6.1326e-01\n", - "5) New loss: 5.8545e-01 Best loss: 5.8545e-01\n", - "6) New loss: 2.7606e-01 Best loss: 2.7606e-01\n", - "7) New loss: 1.7849e-02 Best loss: 1.7849e-02\n", - "8) New loss: -1.1042e-01 Best loss: -1.1042e-01\n", - "9) New loss: -1.1939e-01 Best loss: -1.1939e-01\n", - "10) New loss: -2.5096e-01 Best loss: -2.5096e-01\n", - "11) New loss: -5.6989e-01 Best loss: -5.6989e-01\n", - "12) New loss: -7.5698e-01 Best loss: -7.5698e-01\n", - "13) New loss: -8.6725e-01 Best loss: -8.6725e-01\n", - "14) New loss: -9.1735e-01 Best loss: -9.1735e-01\n", - "15) New loss: -9.2709e-01 Best loss: -9.2709e-01\n", - "16) New loss: -9.3580e-01 Best loss: -9.3580e-01\n", - "17) New loss: -9.1267e-01 Best loss: -9.3580e-01\n", - "18) New loss: -9.4420e-01 Best loss: -9.4420e-01\n", - "19) New loss: -9.4391e-01 Best loss: -9.4420e-01\n", - 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"92) New loss: -1.0050e+00 Best loss: -1.0052e+00\n", - "93) New loss: -1.0052e+00 Best loss: -1.0052e+00\n", - "94) New loss: -1.0050e+00 Best loss: -1.0052e+00\n", - "95) New loss: -1.0049e+00 Best loss: -1.0052e+00\n", - "96) New loss: -1.0051e+00 Best loss: -1.0052e+00\n", - "97) New loss: -1.0051e+00 Best loss: -1.0052e+00\n", - "98) New loss: -1.0051e+00 Best loss: -1.0052e+00\n", - "99) New loss: -1.0052e+00 Best loss: -1.0052e+00\n", - "100) New loss: -1.0051e+00 Best loss: -1.0052e+00\n" + "OS info: Linux-5.4.119-1-tlinux4-0010.2-x86_64-with-glibc2.28\n", + "Python version: 3.10.11\n", + "Numpy version: 1.23.5\n", + "Scipy version: 1.11.0\n", + "Pandas version: 2.0.2\n", + "TensorNetwork version: 0.4.6\n", + "Cotengra version: 0.2.1.dev15+g120379e\n", + "TensorFlow version: 2.12.0\n", + "TensorFlow GPU: []\n", + "TensorFlow CUDA infos: {'cpu_compiler': '/dt9/usr/bin/gcc', 'cuda_compute_capabilities': ['sm_35', 'sm_50', 'sm_60', 'sm_70', 'sm_75', 'compute_80'], 'cuda_version': '11.8', 'cudnn_version': '8', 'is_cuda_build': True, 'is_rocm_build': False, 'is_tensorrt_build': True}\n", + "Jax version: 0.4.13\n", + "Jax installation doesn't support GPU\n", + "JaxLib version: 0.4.13\n", + "PyTorch version: 2.0.1\n", + "PyTorch GPU support: False\n", + "PyTorch GPUs: []\n", + "Cupy is not installed\n", + "Qiskit version: 0.24.1\n", + "Cirq version: 1.1.0\n", + "TensorCircuit version 0.10.0\n" ] } ], + "source": [ + "tc.about()" + ], "metadata": { - "scrolled": false + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-15T05:48:09.478379400Z", + "start_time": "2023-07-15T05:48:09.477371900Z" + } } } ], @@ -311,4 +940,4 @@ }, "nbformat": 4, "nbformat_minor": 5 -} \ No newline at end of file +} diff --git a/docs/source/tutorials/qaoa_nae3sat.ipynb b/docs/source/tutorials/qaoa_nae3sat.ipynb new file mode 100644 index 00000000..51937c93 --- /dev/null +++ b/docs/source/tutorials/qaoa_nae3sat.ipynb @@ -0,0 +1,1102 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "dc0db886", + "metadata": {}, + "source": [ + "# Quantum Approximation Optimization Algorithm (QAOA) for Not-all-equal 3-satisfiability (NAE3SAT)" + ] + }, + { + "cell_type": "markdown", + "id": "aecf6615", + "metadata": {}, + "source": [ + "## Overview" + ] + }, + { + "cell_type": "markdown", + "id": "b533d43e", + "metadata": {}, + "source": [ + "Quantum Approximation Optimization Algorithm (QAOA) is a hybrid classical-quantum algorithm used for solving the combinatorial optimization problem, which is proposed by [Farhi, Goldstone, and Gutmann (2014)](https://arxiv.org/abs/1411.4028). In QAOA, the parameterized quantum circuit is regarded as an oracle, we sample the circuit to obtain the gradient of the parameters, and update them through the classical optimizer. Before this tutorial, there was already a tutorial of [QAOA for Max-Cut](qaoa.ipynb). In this tutorial, we will focus on another combinatorial optimization problem - Not-all-equal 3-satisfiability (NAE3SAT), and discuss the performance of QAOA in different hardness cases." + ] + }, + { + "cell_type": "markdown", + "id": "16ad937f", + "metadata": {}, + "source": [ + "## Not-all-equal 3-satisfiability (NAE3SAT)" + ] + }, + { + "cell_type": "markdown", + "id": "c2321b00", + "metadata": {}, + "source": [ + "[Not-all-equal 3-satisfiability (NAE3SAT)](https://en.wikipedia.org/wiki/Not-all-equal_3-satisfiability) is a variant of 3-satisfiability (3-SAT) and 3-SAT is a subset of [Boolean satisfiability problem (SAT)](https://en.wikipedia.org/wiki/Boolean_satisfiability_problem). SAT is, given a Boolean expression, to check whether it is satisfiable, where the Boolean expression is a disjunction of clauses (or a single clause) and each clause is a disjunction of literals (or a single literal). Here is an example of Boolean expression of SAT,\n", + "$$\n", + "(x_1\\lor x_2\\lor\\cdots\\lor x_m)\\land(\\lnot x_5\\lor x_9\\lor\\cdots\\lor x_m)\\land\\cdots\\land(x_m\\lor \\lnot x_{m+3}\\lor\\cdots\\lor \\lnot x_n),\n", + "$$\n", + "where $(x_i\\lor x_j\\lor\\cdots\\lor x_k)$ is a clause and $x_i$ is a literal. SAT with $k$ literals in each clause is called $k$-SAT, thus in 3-SAT, there are only three literals in each clause, for example\n", + "$$\n", + "(x_1\\lor x_2\\lor x_m)\\land(\\lnot x_5\\lor x_9\\lor x_m)\\land\\cdots\\land(x_m\\lor \\lnot x_{m+3}\\lor \\lnot x_n).\n", + "$$\n", + "When $k$ is not less than 3, SAT is NP-complete. On the other hand, NAE3SAT requires the three literals in each clause are not all equal to each other, in other words, at least one is true, and at least one is false. It is different from 3-SAT, which requires at least one literal is true in each clause. However, NAE3SAT is still NP-complete, [which can be proven by a reduction from 3-SAT](https://en.wikipedia.org/wiki/Not-all-equal_3-satisfiability)." + ] + }, + { + "cell_type": "markdown", + "id": "4d28f719", + "metadata": {}, + "source": [ + "Now we use the spin model to represent a NAE3SAT. Let the set of clauses in the NAE3SAT be $\\mathcal{C}$. In each clause, there are three literals and each literal is represented by a spin. Spins up ($s=1$, $\\text{bit}=0$) and down ($s=-1$, $\\text{bit}=1$) represent false and true respectively. For the clause $(s_i,\\ s_j,\\ s_k)\\in\\mathcal{C}$, $s_i,\\ s_j,\\ s_k$ cannot be 1 or -1 at the same time. The Hamiltonian of the NAE3SAT is as follows\n", + "$$\n", + "\\begin{split}\n", + " \\hat{H}_C&=\\sum_{(i,j,k)\\in\\mathcal{C}}\\left[(s_i+s_j+s_k)^2-1\\right]/2\\\\\n", + " &=\\sum_{(i,j,k)\\in\\mathcal{C}}(s_i s_j+s_j s_k+s_k s_i)+|\\mathcal{C}|,\n", + "\\end{split}\n", + "$$\n", + "where $|\\mathcal{C}|$ is the number of clauses in $\\mathcal{C}$. When all clauses are true, $\\hat{H}_C$ takes the minimum value 0, and the corresponding bit string is the solution of the NAE3SAT." + ] + }, + { + "cell_type": "markdown", + "id": "871bff2e", + "metadata": {}, + "source": [ + "## QAOA for NAE3SAT" + ] + }, + { + "cell_type": "markdown", + "id": "598dc69e", + "metadata": {}, + "source": [ + "QAOA utilizes a parameterized quantum circuit ([PQC](https://tensorcircuit.readthedocs.io/en/latest/textbook/chap5.html?highlight=变分)) to generate a quantum state that represents a potential solution. The initial state, denoted as $|s\\rangle$, is a uniform superposition over computational basis states.\n", + "$$\n", + "|s\\rangle=\\frac{1}{\\sqrt{2^n}}\\sum_z|z\\rangle\n", + "$$\n", + "This state is then evolved by a unitary operator that consists of $p$ layers, denoted as\n", + "$$\n", + "U(\\boldsymbol{\\beta}, \\boldsymbol{\\gamma}) = V_{p}U_{p} \\cdots V_{1}U_{1},\n", + "$$\n", + "where $U_{j}= e^{-\\text{i}\\gamma_{j}\\hat{H}_{C}}$ is the driving layer and $V_{j}= e^{-\\text{i}\\beta_{j} \\hat{H}_m}$ is the mixing layer. $\\hat{H}_C$ is the driving and cost Hamiltonian introduced in previous section and the mixing Hamiltonian $\\hat{H}_m=\\sum_{j=1}^{n}\\sigma_j^x$ is used to mix the quantum state to explore different solutions. The unitary operator is parameterized by $2p$ angle parameters $\\gamma_1, \\gamma_2, \\dots, \\gamma_p$ and $\\beta_1, \\beta_2, \\dots ,\\beta_p$ and each $\\gamma$ and $\\beta$ are restricted to lie between $0$ and $2\\pi$." + ] + }, + { + "cell_type": "markdown", + "id": "949be36e", + "metadata": {}, + "source": [ + "Begin with a set of initial $\\boldsymbol{\\gamma}$ and $\\boldsymbol{\\beta}$, the quantum state is obtained from the PQC and then the expectation value of $\\hat{H}_C$ is calculated. A classical optimizer is then used to vary the parameters until a lower expectation value is found. This process is iterated a certain number of times until the expectation value of $\\hat{H}_C$ is approximated to 0. Then we perform projective measurement on the quantum state output by PQC, and obtain a bit string, which is very likely to be the solution of NAE3SAT. Since NAE3SAT is an NP-complete problem, we can verify whether the solution is correct in polynomial time on classical computer. Even if this bit string is not the correct solution, we can repeat the projective measurement and verify the obtained solution until we get the correct solution.\n", + "\n", + "For other details of QAOA, such as the selection of $p$ and the overall algorithm loop, please refer to [Farhi, Goldstone, and Gutmann (2014)](https://arxiv.org/abs/1411.4028) or the tutorial of [QAOA for Max-Cut](qaoa.ipynb)." + ] + }, + { + "cell_type": "markdown", + "id": "940fa22b", + "metadata": {}, + "source": [ + "### Setup" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "b0def04d", + "metadata": { + "ExecuteTime": { + "end_time": "2023-07-03T11:21:55.043565200Z", + "start_time": "2023-07-03T11:21:54.946406500Z" + } + }, + "outputs": [], + "source": [ + "import tensorcircuit as tc\n", + "import optax\n", + "import tensorflow as tf\n", + "import networkx as nx\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "from IPython.display import clear_output\n", + "import random\n", + "\n", + "K = tc.set_backend(\"jax\")\n", + "\n", + "nlayers = 30 # the number of layers\n", + "ncircuits = 6 # six circuits with different initial parameters are going to be optimized at the same time" + ] + }, + { + "cell_type": "markdown", + "id": "6e407437", + "metadata": {}, + "source": [ + "### Define the Graph" + ] + }, + { + "cell_type": "markdown", + "id": "c82972a4", + "metadata": {}, + "source": [ + "The graph of NAE3SAT is constructed by the set $\\mathcal{C}$ of clauses. When a clause is violated, the energy will increase by 4, so the upper bound of $\\hat{H}_C$ will not exceed $4|\\mathcal{C}|$. In practice, we multiply $\\hat{H}_C$ by a normalization factor $1/(4|\\mathcal{C}|)$." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "f1532831", + "metadata": { + "ExecuteTime": { + "end_time": "2023-07-03T11:21:55.148550800Z", + "start_time": "2023-07-03T11:21:54.965499300Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": "
", + "image/png": 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" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# an easy graph instance\n", + "easy_clauses = [\n", + " [4, 7, 6],\n", + " [0, 5, 9],\n", + " [2, 6, 9],\n", + " [2, 6, 7],\n", + " [3, 1, 9],\n", + " [5, 9, 11],\n", + " [4, 8, 9],\n", + " [5, 1, 9],\n", + " [3, 8, 6],\n", + " [2, 8, 10],\n", + " [5, 6, 8],\n", + " [2, 9, 6],\n", + " [2, 6, 8],\n", + " [5, 3, 9],\n", + " [4, 11, 7],\n", + " [3, 11, 10],\n", + " [5, 10, 7],\n", + " [3, 9, 8],\n", + " [3, 6, 9],\n", + " [2, 4, 7],\n", + " [4, 0, 6],\n", + " [3, 4, 6],\n", + " [3, 11, 6],\n", + " [4, 5, 6],\n", + " [4, 0, 10],\n", + " [5, 4, 10],\n", + " [3, 7, 9],\n", + " [0, 11, 6],\n", + " [5, 11, 9],\n", + " [3, 5, 9],\n", + " [3, 4, 7],\n", + " [3, 4, 7],\n", + " [3, 0, 7],\n", + " [1, 7, 8],\n", + " [0, 3, 10],\n", + " [0, 8, 9],\n", + " [5, 7, 8],\n", + " [2, 9, 6],\n", + " [0, 8, 6],\n", + " [4, 6, 8],\n", + " [3, 2, 9],\n", + " [4, 3, 8],\n", + " [0, 2, 8],\n", + " [4, 5, 10],\n", + " [2, 4, 8],\n", + " [5, 8, 9],\n", + " [4, 8, 9],\n", + " [3, 5, 11],\n", + " [5, 4, 10],\n", + " [2, 7, 9],\n", + " [3, 0, 7],\n", + " [2, 8, 6],\n", + " [5, 3, 6],\n", + " [0, 6, 10],\n", + " [3, 2, 8],\n", + " [4, 6, 9],\n", + " [3, 2, 6],\n", + " [1, 5, 6],\n", + " [2, 8, 11],\n", + " [2, 10, 8],\n", + " [2, 0, 6],\n", + " [2, 6, 9],\n", + " [0, 8, 7],\n", + " [0, 10, 8],\n", + " [3, 5, 7],\n", + " [2, 10, 8],\n", + " [5, 7, 9],\n", + " [0, 1, 6],\n", + " [0, 3, 8],\n", + " [0, 6, 9],\n", + " [0, 5, 11],\n", + " [1, 2, 10],\n", + "]\n", + "factor = 1 / len(easy_clauses) / 4\n", + "\n", + "# convert to a NetworkX graph\n", + "easy_graph = nx.Graph()\n", + "for i, j, k in easy_clauses:\n", + " easy_graph.add_edge(i, j, weight=0)\n", + " easy_graph.add_edge(j, k, weight=0)\n", + " easy_graph.add_edge(k, i, weight=0)\n", + "for i, j, k in easy_clauses:\n", + " easy_graph[i][j][\"weight\"] += 1\n", + " easy_graph[j][k][\"weight\"] += 1\n", + " easy_graph[k][i][\"weight\"] += 1\n", + "pos_easy = nx.spring_layout(easy_graph)\n", + "nx.draw_networkx(easy_graph, with_labels=True, pos=pos_easy)\n", + "ax = plt.gca()\n", + "ax.set_facecolor(\"w\")" + ] + }, + { + "cell_type": "markdown", + "id": "c944f6dd", + "metadata": {}, + "source": [ + "### Parameterized Quantum Circuit (PQC)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "055d1257", + "metadata": { + "ExecuteTime": { + "end_time": "2023-07-03T11:21:55.167476700Z", + "start_time": "2023-07-03T11:21:55.166422100Z" + } + }, + "outputs": [], + "source": [ + "def QAOAansatz(params, g, each=1, return_circuit=False):\n", + " n = g.number_of_nodes() # the number of nodes\n", + "\n", + " # PQC loop\n", + " def pqc_loop(s_, params_):\n", + " c_ = tc.Circuit(n, inputs=s_)\n", + " for j in range(each):\n", + " # driving layer\n", + " for a, b in g.edges:\n", + " c_.RZZ(a, b, theta=g[a][b][\"weight\"] * params_[2 * j] * factor)\n", + " # mixing layer\n", + " for i in range(n):\n", + " c_.RX(i, theta=params_[2 * j + 1])\n", + " s_ = c_.state()\n", + " return s_\n", + "\n", + " c0 = tc.Circuit(n)\n", + " for i in range(n):\n", + " c0.H(i)\n", + " s0 = c0.state()\n", + " s = K.scan(pqc_loop, K.reshape(params, [nlayers // each, 2 * each]), s0)\n", + " c = tc.Circuit(n, inputs=s)\n", + "\n", + " # whether to return the circuit\n", + " if return_circuit is True:\n", + " return c\n", + "\n", + " # calculate the loss function\n", + " loss = 0.25\n", + " for a, b in g.edges:\n", + " loss += c.expectation_ps(z=[a, b]) * g[a][b][\"weight\"] * factor\n", + "\n", + " return K.real(loss)" + ] + }, + { + "cell_type": "markdown", + "id": "5b159920", + "metadata": {}, + "source": [ + "### Optimization" + ] + }, + { + "cell_type": "markdown", + "id": "6d07ee61", + "metadata": {}, + "source": [ + "Here, several circuits with different initial parameters are optimized/trained at the same time.\n", + "\n", + "Optimizers are used to find the minimum value." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "690b8b67", + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": "
", + "image/png": 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oirmcawFSVIqt0gUmhBCicun1eoKCgjAYDJc9r6oqNput3M+xWCwEBASU+r7Y2FgefPBBVq1axcaNGwkNDaVv374kJiaWu05XIwGoirl4aAHIoTiwSQuQEEKICuBwOJg8eTKRkZGYzWbq1q3L+PHjgUu7wGJjY1EUhUWLFtGmTRvMZjPr1q27ahnn7snMzCx5ZlxcHIqikJCQAFzcBRYTE8Pbb7/Njh07UBQFRVGIiYm5bN2/++47nn32WaKjo2ncuDFffPEFDoeDFStWVMa3qsTl46CoNBYPrQvModixW2UMkBBCVGeqqlJgK6jy51oMFhRFue7rR40axaxZs/jggw/o0qULycnJxMfHX/WekSNHMnXqVMLDw/Hx8SlTGVcyZMgQdu/ezeLFi1m+fDkAXl5e13Vvfn4+VqsVX1/fMj37ekkAqmKunmdbgLBCsSJdYEIIUY0V2Aro8H2HKn/uXw/9havR9doXAjk5OUyfPp0ZM2YwbNgwACIiIujSpctV7xs7dix9+vQpVxlXYrFYcHd3x2AwEBQUVKp7X3vtNWrXrk3v3r3L9OzrJQGoirl5ewKgqlYoMkgXmBBCiHLZt28fRUVF9OrVq1T3tW3bttxlVLSJEycyd+5cYmNjcXFxqdRnSQCqYu4+WheYqhais1qkBUgIIaoxi8HCXw/95ZTnXve1luu/9kJubm7XXYZOpw0ZVlW15JjVai3Tc69k6tSpTJw4keXLlxMVFVWhZV+OBKAqdm4MEGoRpmIX8gtPcX2NnEIIIaqaoijX3RXlLA0aNMBisbBixQqeeOKJSinD398fgOTkZHx8fACuua6QyWTCbrdf1/MnT57M+PHjWbJkyUUtU5VJAlAVM7meS9w2XIotZBRnSwASQghRZi4uLrz22muMGDECk8lE586dSUtLY8+ePQwfPrxCyoiMjCQ0NJQxY8Ywfvx4Dhw4wHvvvXfVMsPCwjh69ChxcXGEhITg4eGB2Wy+5LpJkyYxevRovv/+e8LCwkhJSQHA3d0d97NLx1QGmQZfxcyW83HHbDOTgR2sVT/DQAghxI3jzTff5OWXX2b06NE0adKEIUOGcOrUqQorw2g0MmfOHOLj44mKimLSpEmMGzfuquUNHjyY/v3707NnT/z9/ZkzZ85lr/vkk08oLi7m3nvvJTg4uOQzderUUtW/tBT1wg49AUB2djZeXl5kZWXh6elZ4eW//8DdqKqVWsUWwm9ZQ7dn4sAzuMKfI4QQ4voVFhZy9OhR6tevX+kDcEXZXe3nVJq/39IC5AQ6vfYD0ztMZOr1shaQEEIIUcUkADmB3qAFIEU1kqWT1aCFEEKIqiYByAmM5nPTDQ1aAJKp8EIIIUSVkgDkBEYXbSC0QzFIC5AQQgjhBBKAnMDkenZHeL2OfJu0AAkhhBBVTQKQE7i4a4sh2vQKRbIjvBBCCFHlJAA5gfns8uM2HVilBUgIIYSochKAnMDFXQtAdsWBvVgn0+CFEEKIKiYByAlcz+4H5lAcOIp1kH/GyTUSQgghbi4SgJzA4nU2AGFDV6xgz09zco2EEELcqBISElAU5Zqbl5ZXTEwM3t7elfqMiiQByAncvM8HINdCyM477eQaCSGEuFGFhoaSnJxM8+bNK/U5Q4YM4cCBAyVfjxkzhujo6Gve98svv9C2bVu8vb1xc3MjOjqab775phJrqpHd4J3A3ccLAFUtxK3IRFbhKXxUFRTFyTUTQghxo9Hr9QQFBV3xvKqq2O12DIbyRQKLxYLFYrn2hf/D19eX119/ncaNG2MymViwYAGPPfYYAQEB9OvXr1x1uhppAXKCcwEItRC3IguZajEU5zm3UkIIIWosh8PB5MmTiYyMxGw2U7duXcaPHw9c2gUWGxuLoigsWrSINm3aYDabWbdu3VXLOHdPZmZmyTPj4uJQFIWEhATg4i6wmJgY3n77bXbs2IGiKCiKQkxMzGXr3qNHD+6++26aNGlCREQEL7zwAlFRUaxbt64yvlUlpAXICVxLdqi141LsSrpeD3mnwOzu1HoJIYS4mKqqqAUFVf5cxWJBKUWvwKhRo5g1axYffPABXbp0ITk5mfj4+KveM3LkSKZOnUp4eDg+Pj5lKuNKhgwZwu7du1m8eDHLly8HwMvL65r3qarKypUr2b9/P5MmTSrTs6+XBCAnMLpY0BrfHJjtrqTrdZB3GnzDnV01IYQQF1ALCtjfuk2VP7fRtq0orq7XdW1OTg7Tp09nxowZDBs2DICIiAi6dOly1fvGjh1Lnz59ylXGlVgsFtzd3TEYDFftfjsnKyuLOnXqUFRUhF6v5+OPPy6pW2WRAOQEiqKg07vgsOdjcFg4o9dD7ilnV0sIIUQNtG/fPoqKiujVq1ep7mvbtm25y6goHh4exMXFkZuby4oVK3jppZcIDw+nR48elfZMCUBOYjBYKLbno3OYSdfpITfV2VUSQgjxPxSLhUbbtjrluderLAOPAdzO7kpwPWXodNqQYVVVS45ZrdYyPfdK5UdGRgIQHR3Nvn37mDBhQqUGIBkE7SQGk9a0qSpGzuh10gIkhBDVkKIo6Fxdq/xTmvE/DRo0wGKxsGLFijK/57XK8Pf3ByA5Obnk2LXWFTKZTNjt9jLVx+FwUFRUVKZ7r5e0ADmJyeJGfg6oGM52gaU4u0pCCCFqIBcXF1577TVGjBiByWSic+fOpKWlsWfPHoYPH14hZURGRhIaGsqYMWMYP348Bw4c4L333rtqmWFhYRw9epS4uDhCQkLw8PDAbDZfct2ECRNo27YtERERFBUVsXDhQr755hs++eSTMn0/rpcEICdxcdMWQ7TrdGTo9JAjXWBCCCHK5s0338RgMDB69GiSkpIIDg7mn//8Z4WVYTQamTNnDs888wxRUVG0a9eOcePGcd99912xvMGDB/PLL7/Qs2dPMjMz+eqrr3j00UcvuS4vL49nn32WkydPYrFYaNy4Md9++y1DhgwpVf1LS1Ev7NATAGRnZ+Pl5UVWVhaeJVPWK9bPE6aTELcMN7UuP/dYxTJDIDwVWynPEkIIcW2FhYUcPXqU+vXr4+Li4uzqiCu42s+pNH+/ZQyQk7h5a+sh2BUVu1WPVVqAhBBCiCojAchJSgKQzo5rEWQUngaHw8m1EkIIIW4OEoCcxM3HGwA7NtwKVdIVFfLPOLdSQgghxE1CApCTeAX4AqBSiFuh7uxMMOkGE0IIIaqCBCAn8QmsBYDqyMezwE2mwgshhBBVSAKQk7j7+p79lw2PQk/SdTqZCi+EEEJUkWoRgGbOnElYWBguLi506NCBzZs3X/HaWbNm0bVrV3x8fPDx8aF3796XXK+qKqNHjyY4OBiLxULv3r05ePBgZb9GqWgbouoBcC1ylxYgIYQQogo5PQDNmzePl156ibfeeott27bRsmVL+vXrx6lTl98aIjY2lgcffJBVq1axceNGQkND6du3L4mJiSXXTJ48mQ8//JBPP/2Uv/76Czc3N/r160dhYWFVvdY1KYqCXq/tveJiPbsjvLQACSGEEFXC6QHo/fff58knn+Sxxx6jadOmfPrpp7i6uvLll19e9vrvvvuOZ599lujoaBo3bswXX3yBw+Eo2b9EVVWmTZvGG2+8wV133UVUVBRff/01SUlJzJ8//7JlFhUVkZ2dfdGnKhgN2n5gBodZWoCEEEKIKuTUAFRcXMzWrVvp3bt3yTGdTkfv3r3ZuHHjdZWRn5+P1WrF9+yYmqNHj5KSknJRmV5eXnTo0OGKZU6YMAEvL6+ST2hoaDne6vqZzVoA0jlMpOtlOwwhhBAVLyEhAUVRrrl5aXnFxMTg7e1dqc+oSE4NQKdPn8ZutxMYGHjR8cDAQFJSrq815LXXXqN27dolgefcfaUpc9SoUWRlZZV8Tpw4UdpXKZNz+4Epqu7sjvASgIQQQlSs0NBQkpOTad68eaU+Z8iQIRw4cKDk6zFjxhAdHV2qMubOnYuiKAwaNKhiK3cZNXoz1IkTJzJ37lxiY2PLtW+L2Wy+7A61lc3dx4fUZHAA6Xo9jtxUdKoKilLldRFCCHFj0uv1BAUFXfG8qqrY7XYMhvJFAovFgsViKfP9CQkJvPLKK3Tt2rVc9bheTm0B8vPzQ6/Xk5p6cctHamrqVX9YAFOnTmXixIksXbqUqKiokuPn7itLmVXNI8AfAIfiwA7k2AuhKMe5lRJCCFHjOBwOJk+eTGRkJGazmbp16zJ+/Hjg0i6w2NhYFEVh0aJFtGnTBrPZzLp1665axrl7MjMzS54ZFxeHoigkJCQAF3eBxcTE8Pbbb7Njxw4URUFRFGJiYq5Yf7vdztChQ3n77bcJDw+v6G/PZTm1BchkMtGmTRtWrFhR0tx1bkDzc889d8X7Jk+ezPjx41myZAlt27a96Fz9+vUJCgpixYoVJU1v2dnZ/PXXXzzzzDOV9Spl4h1aGwC7YsW9AM7odXjlpoJL5exAL4QQonRUVcVWXPX7NBpMOpRS9AaMGjWKWbNm8cEHH9ClSxeSk5OJj4+/6j0jR45k6tSphIeH4+PjU6YyrmTIkCHs3r2bxYsXs3z5ckAbj3slY8eOJSAggOHDh7N27doyPbO0nN4F9tJLLzFs2DDatm1L+/btmTZtGnl5eTz22GMAPPLII9SpU4cJEyYAMGnSJEaPHs33339PWFhYybged3d33N3dURSFF198kXHjxtGgQQPq16/Pm2++Se3ataukT7E0fOpo45RUtRDfHCNn9HrCc1LAr4GTayaEEALAVuzg8xdWV/lzn5reHaNZf13X5uTkMH36dGbMmMGwYcMAiIiIoEuXLle9b+zYsfTp06dcZVyJxWLB3d0dg8Fwzd6XdevW8d///rfSB2n/L6cHoCFDhpCWlsbo0aNJSUkhOjqaxYsXlwxiPn78ODrd+Z66Tz75hOLiYu69996LynnrrbcYM2YMACNGjCAvL4+nnnqKzMxMunTpwuLFi8s1TqgyeAdqXWCqIw//LHfOeMt+YEIIIUpn3759FBUV0atXr1Ldd2EPSlnLKK+cnBwefvhhZs2ahZ+fX5U+2+kBCOC55567YpdXbGzsRV+f62u8GkVRGDt2LGPHjq2A2lUej1q1zv7LSq08T9J9dZAjawEJIUR1YTDpeGp6d6c893qVdeCxm5vbdZdxriFCVdWSY1artUzPvdDhw4dJSEjgjjvuKDnmcGhdjgaDgf379xMREVHu51xOtQhANyuj2QVFMaGqxXjly4aoQghR3SiKct1dUc7SoEEDLBYLK1as4IknnqiUMvz9tR6L5ORkfHx8AK7ZZWUymbDb7Ve9pnHjxuzateuiY2+88UZJl1xlrssnAcjJjHo3im3FuBaeC0CX3wJECCGEuBwXFxdee+01RowYgclkonPnzqSlpbFnzx6GDx9eIWVERkYSGhrKmDFjGD9+PAcOHOC99967aplhYWEcPXqUuLg4QkJC8PDwuGTJGRcXl0vWJzo3k6yy1y2SAORkZrMbxbYMzDYzx/TSBSaEEKL03nzzTQwGA6NHjyYpKYng4GD++c9/VlgZRqOROXPm8MwzzxAVFUW7du0YN24c99133xXLGzx4ML/88gs9e/YkMzOTr776ikcffbQ8r1mhFPXCDj0BaNPmvby8yMrKwtOzcqekf/vCSFJTduOiC2NDj6V8Z/OBf/1Vqc8UQghxqcLCQo4ePUr9+vWr3aQZcd7Vfk6l+fvt9M1Qb3ae/tqodxXl7I7w0gIkhBBCVDYJQE7mW08b4GVTbGSqOtTCTLAWOrdSQgghxA1OApCT+UfWA8Ch5uOVbSZdJ5uiCiGEEJVNApCT+Z9tAVIdWdRJ9yHZYJAAJIQQQlQyCUBO5hUQCCiAjaAsX5IMesg87uxqCSGEEDc0CUBOpjcYMOjdAfDJ9dZagM4ccnKthBBCiBubBKBqwNWiTdUzWy0kGQxw+oCTaySEEELc2CQAVQNetQIAUBx6rQvs9EEn10gIIYS4sUkAqgb8I8IAsCs2UnVnu8DObgYnhBBCiIonAagaCG3dAgC7moma5QnWfMhOdHKthBBC3AgSEhJQFOWam5eWV0xMTMk+XjWBBKBqoHbDhgCojkyCTgeSqyhwRrrBhBBClF9oaCjJycmVvrnokCFDOHDg/BjWMWPGEB0dfc37YmJiUBTlok9VbEUim6FWA65e3uh1FuyOAoIzapHkbaDh6YMQcauzqyaEEKKG0+v1BAUFXfG8qqrY7XYMhvJFAovFgsViKdO9np6e7N+/v+RrRVHKVZfrIS1A1YSriy8A7oUeJBv0MhNMCCGqAVVVsRYWVvmntPuUOxwOJk+eTGRkJGazmbp16zJ+/Hjg0i6w2NhYFEVh0aJFtGnTBrPZzLp1665axrl7MjMzS54ZFxeHoigkJCQAF3eBxcTE8Pbbb7Njx46SVp2YmJgr1l9RFIKCgko+gYGBpXr/spAWoGrCr3Ydcg4lojh0JBoMMhNMCCGqAVtRER8Ou7fKn/vv2T9hLEU30KhRo5g1axYffPABXbp0ITk5mfj4+KveM3LkSKZOnUp4eDg+Pj5lKuNKhgwZwu7du1m8eDHLly8HwMvL64rX5+bmUq9ePRwOB61bt+bdd9+lWbNmZXr29ZIAVE2EtYvm6KHNWMkjxeaKemofld8AKIQQoqbLyclh+vTpzJgxg2HDhgEQERFBly5drnrf2LFj6dOnT7nKuBKLxYK7uzsGg+Gq3W8AjRo14ssvvyQqKoqsrCymTp1Kp06d2LNnDyEhIWV6/vWQAFRNRHTqwKo5n6Pa07ClRqJ4boCcVPCo/GZAIYQQl2cwm/n37J+c8tzrtW/fPoqKiujVq1epntG2bdtyl1EROnbsSMeOHUu+7tSpE02aNOGzzz7jnXfeqbTnSgCqJrwCAtHrXLE78jFl1AXPDZCyEzz6OLtqQghx01IUpVRdUc5Q1oHHbm5u112GTqcNGb5wbJLVai3Tc6/FaDTSqlUrDh2q3G2hZBB0NeLjrTUTGoosWAGSdzi1PkIIIaq/Bg0aYLFYWLFiRaWV4e/vD0BycnLJsWutK2QymbDb7aWui91uZ9euXQQHB5f63tKQFqBqpFGXTpz+/QhWNZOjdg/Ck3bID0gIIcRVubi48NprrzFixAhMJhOdO3cmLS2NPXv2MHz48AopIzIyktDQUMaMGcP48eM5cOAA77333lXLDAsL4+jRo8TFxRESEoKHhwfmy3TtjR07lltuuYXIyEgyMzOZMmUKx44d44knnijT9+N6SQtQNRJ1x22Aguo4zZ6U9lgTNkEpp0IKIYS4+bz55pu8/PLLjB49miZNmjBkyBBOnTpVYWUYjUbmzJlDfHw8UVFRTJo0iXHjxl21vMGDB9O/f3969uyJv78/c+bMuex1GRkZPPnkkzRp0oQBAwaQnZ3Nhg0baNq0aanqX1qKWtrFBm4C2dnZeHl5kZWVhaenZ5U+e/o/hmKzZuGmj+SfDb+C57dBrYgqrYMQQtyMCgsLOXr0KPXr16+SlYhF2Vzt51Sav9/SAlTNmJtrfZ75ZJOT50Xu/lVOrpEQQghx45EAVM00GtQHUFDtp1iXfCvJ2xc7u0pCCCHEDUcCUDXTol4bilxMABxUvQlI3kRhQZ6TayWEEELcWCQAVTN+Fj+2tskEwGo7wvYTPVm1cJ5zKyWEEELcYCQAVUN+TSKxG02Agx02P4q2LOR0bpGzqyWEEDcFmRtUvVXUz0cCUDXUyLcRS1ofA8BmO0heYgPG/rJV/kcphBCVyGg0ApCfn+/kmoirOffzOffzKitZZ68aauzTmK9qFWPzdsGQWUiKLYE669fwQ5MQhrSr6+zqCSHEDUmv1+Pt7V2y9o2rqyuKIttSVxeqqpKfn8+pU6fw9vZGr9eXqzwJQNVQC/8WAPzU4TCPLK1PsSMHU+5Jvv9mC+H+7rQL83VyDYUQ4sZ0bufy0i4iKKqOt7f3NXeYvx4SgKqhEPcQ/Cx+nC44TfNhA9j+1e84bAn0TN/COx+bmfJSdxoFeTi7mkIIccNRFIXg4GACAgIqbbNPUXZGo7HcLT/nSACqhhRFIdo/muXHl3MkRKFvcwtL9uRht+7m1mSFN9+D0S92pXkdL2dXVQghbkh6vb7C/tCK6kkGQVdT0QHRAGxN3Urz5ybQzeMEqGAv3kXH5Fg+nriSVfGpzq2kEEIIUUNJAKqmbgm+BYC/U/+myKsO7e69nVu9DoMKDms8kWcWEPveSj5bekBmhwkhhBClJAGommro0xB/iz8FtgK2pW6Dbq/QqkERgwL2oFd1qPZUPHN+pWDOKka8v4H0vGJnV1kIIYSoMSQAVVOKotC5TmcA1ieuB1dfuP09IvzSeaT+37jrjKDmY8//gzo7FjF15FKWb01ycq2FEEKImkECUDXWpU4XANYlrtMONLsbmt+LryWPx6L30qRufQDsRXH4nf6B3R8vY+ykDaRlFTqrykIIIUSNIAGoGrsl+BYMioHDWYc5mnVUO3jHdAhoiqkghQEN93DHPx7HpOpQHenYc3/Ec89CvnptOd/9Eo/D4XDuCwghhBDVlASgaszL7EWnOp0A+PPIn9pBszs88B24eEPiVhpmfsPwjz8nok49QGsN0md9x5k/1zPx1Vj++jvZSbUXQgghqi8JQNXcwPCBACw4suD8bC/fcHjoBzC6wuGVuC5/mUGTP+Cup17AVdGDIwdr7q9YTi1ky+dbmfLWOhKOZTnxLYQQQojqRQJQNdcjtAeuBlcScxPZfmr7+RN1O8AD34PeBPELYO6DRHbtxPCv5tKiRWttunxxPEXZMZiPb+f3d7fwyQdbyM6U8UFCCCGEBKBqzmKw0DesLwDfx39/8cmInvDgHK0l6NBy+HoQJrWAvm+M5cGxk/Dx8AK1EGv+Euy5v2Dbe4KvRq1nbswuigttTngbIYQQonqQAFQD/KPJPwBYdmwZibmJF5+M7A2P/KaNCTq5Gb7oBWkHqN24GcM+nU3nu+5Dryg4bMcpzp4NBX9zemMqM19Zw9LfD2G3y0BpIYQQNx8JQDVAI99GdAzuiEN18M3eby69ILQ9PLYIvEIh/YgWgg4uQ28wcMtDwxg27TPq1I8E7NgK1mLLmo2hMIWDC4/z0Str+HvtSVlNWgghxE1FUeUv3yWys7Px8vIiKysLT09PZ1cHgI1JG3lq2VMYdUZ+H/Q7IR4hl16UmwY/PAzHN4Kig+6vQbdXQadHVVX2xC4n9qtPKSoqAhWMxubo3HuiKEYcPkZuG9qEyOZ+Vf9yQgghRAUozd9vaQGqIW4JvoVbgm/B6rDy4fYPL3+Ruz888ju0HgaqA2InwDeDICcFRVFo3rMPj3/0Xxp17AoKWG27sad/glp0AF2GlSUzdjJr3CZSj+dU6bsJIYQQVU1agC6jOrYAAcSnx3P/H/ejovJZn8/oVLvTlS/eMRcWvATWPHDzh7s/g8heJaePbv+bZZ9/RE76GQDcbb7YfO4DgxsqKr5NfBg4tAmefpbKfi0hhBCiQpTm77cEoMuorgEIYPym8czdP5cgtyB+vfNX3E3uV7447QD8+Cic2qN93f4p6P02mFwBKC4sYP28b9m+6HdUVcVkc+BJC3L9+wHgUKB+x0D63NcIs8VQyW8mhBBClI8EoHKqzgEo35rP4N8HczL3JLeH386ELhNQFOXKN1gLYOkbsOUL7etakVprUEjbkkuSD+5n8ccfkJ50EoCAHAeKR3+yfJoDYDfp6HR3BG26h6DorvIsIYQQwokkAJVTdQ5AAFtTtzJ8yXDsqp3X2r3GP5r+49o3HVoOvz0HOcnaAOnOL2qDpI0uAFiLi9jww3f8veBXUFXMVhthmS6cCnmAAtcArQw/M3cPb07t+l6V93JCCCFEGUkAKqfqHoAAvtn7DZO3TEav6Pm498dXHw90TkEGLHwVdv2ofV0rEu74EMI6l1ySdGAfiz+eRkaytt5QnfRcPGjOsbCBqHoTKhDQshZ3PtwUF3djJbyZEEIIUTYSgMqpJgQgVVV5fd3r/HHkDywGC5/3+ZzogOjru3nv71oQyk3Rvm77OPQeAy5ay461uIj1875l65/zQVVxs9ppejKb1Dp3ciqwHQB2o0LXIQ2J7lz76l1wQgghRBWRAFRONSEAARTbi3l+5fNsSNqAh8mDr/p9RSPfRtd3c0EmLBsN22ZrX3sEw+3vQePbSy45uXc3f86YSu6Z0+iAhomn8bb6sbfRUIpdAwEw1XPjwX+2xN3HpWJfTgghhCglCUDlVFMCEGiDop9e9jRxaXF4mjz5pPcnRPlHXX8BR9fCHy9A+mHt6yZ3wm2TwLM2AAW5OSz99EMObdkIQECRjeaHkkgM6UtCvf4oig6bHtrfHcEtvepKa5AQQginqVELIc6cOZOwsDBcXFzo0KEDmzdvvuK1e/bsYfDgwYSFhaEoCtOmTbvkmjFjxqAoykWfxo0bV+IbOJer0ZWZvWcS5R9FdnE2Tyx9go1JG6+/gPpd4Zn10OUlUPSw73eY0Q42fAR2KxZ3D+58+T/0fuJfGIwmTpkN/NUyAv+UZXT4ewKG/BQMdtj202G+nLyFgtziyntZIYQQooI4NQDNmzePl156ibfeeott27bRsmVL+vXrx6lTpy57fX5+PuHh4UycOJGgoKArltusWTOSk5NLPuvWrausV6gWPE2ezOozi47BHSmwFfDsimeZf2j+9RdgtEDvt+Dp1RDaAYpztanzn3WDYxtQFIWWfW7jwXFT8QoIJM9mZVPT+uS4FdJly3hCjy/EoaoUHs3l09fXc3D36Up7VyGEEKIiOLULrEOHDrRr144ZM2YA4HA4CA0N5fnnn2fkyJFXvTcsLIwXX3yRF1988aLjY8aMYf78+cTFxZW5XjWpC+xCxfZi/rPuPyxJWALAsKbD+L82/4dep7/+QhwOiPtOGx9UkK4da/kg9HkH3P0pyM3hz+mTObZzOwBNHAbCdu0n26Mem6L/hVHvhgOIuLUOt93XULrEhBBCVJka0QVWXFzM1q1b6d279/nK6HT07t2bjRtL0YVzGQcPHqR27dqEh4czdOhQjh8/ftXri4qKyM7OvuhTE5n0JiZ3m8w/W/4TgNl7Z/PcyufIKsq6/kJ0Omj9MDy/Fdo8CiiwYw7MaAObZ2GxWLhn1Bja3TkYgH06Gwe7tscz5xi9NryJLu8QOuDoykRmTdmCtdhe4e8phBBClJfTAtDp06ex2+0EBgZedDwwMJCUlJQyl9uhQwdiYmJYvHgxn3zyCUePHqVr167k5Fx5g88JEybg5eVV8gkNDS3z851Np+j4V/S/mNJtCma9mXWJ67j3j3uJOxVXuoJcfeGO6fDEcgiKgsIsWPgKfNoZ3eFVdBv6GL0efwYUhUPZZ9jTtxs6rPTY8gF+Z1ZjR8V6JJeP31hPbmZRpbyrEEIIUVZOHwRd0W677Tbuu+8+oqKi6NevHwsXLiQzM5MffvjhiveMGjWKrKysks+JEyeqsMaVo3/9/nw74FvqedYjJS+FxxY/xle7v8KhOkpXUEhbeCoWBkwFiy+kxcN3g+HbwUS3CufO/xuF3mjkeGoiBwbdBq6uRO36gcanfqUAB4ZsG5+/vZEzp/Iq5T2FEEKIsnBaAPLz80Ov15OamnrR8dTU1KsOcC4tb29vGjZsyKFDh654jdlsxtPT86LPjaCxb2Pm3j6X28Juw6baeH/r+zy74llO5V9+kPkV6fTQ/kn49zbo+BzojNrWGp90osGxzxj0xMPo9AaOHIrn8D0DUDw9Cd27go4p35GtODAXOPh6/GYyTxdUzosKIYQQpeS0AGQymWjTpg0rVqwoOeZwOFixYgUdO3assOfk5uZy+PBhgoODK6zMmsTd5M6kbpMY3XE0Jp2J9Ynrufu3u1l4ZCGlHv9u8YF+4+Fff0HjgaA6YO98wmIfY2C/pig6Hft3bSfj6cfQeXnhG7+JWwv+IEPnwFSkEjNhM4V51sp5USGEEKIUnNoF9tJLLzFr1ixmz57Nvn37eOaZZ8jLy+Oxxx4D4JFHHmHUqFEl1xcXFxMXF0dcXBzFxcUkJiYSFxd3UevOK6+8wurVq0lISGDDhg3cfffd6PV6HnzwwSp/v+pCURTua3gf8wbOo2mtpmQXZ/Pa2td4efXLpBeml77AWhHwwHfw+FLwawhAg6MzubW+Nth647KF6F57BcVkwnPTUrp6bidHUTHm2fnmva04HLL2phBCCOdyagAaMmQIU6dOZfTo0URHRxMXF8fixYtLBkYfP36c5OTkkuuTkpJo1aoVrVq1Ijk5malTp9KqVSueeOKJkmtOnjzJgw8+SKNGjbj//vupVasWmzZtwt/fv8rfr7qJ9Ink2wHf8mz0sxgUA8uOLePu3+5m+bHlZSuwbgd4dhP0Gg1mL1oa42jqlYqqOli17HdqjXkLgIDfviKoQTbFqBQn5bPi54MV+FZCCCFE6ZVpHaCxY8fyyiuv4OrqetHxgoICpkyZwujRoyusgs5QU9cBKo09Z/bwxro3OJSptZ71DO3Jfzr8hyC3Mo6/yk+HVeOxbo5h9uFosqwWopsF0aSgFlm//o6hdm0+ufUNIk6qqMC9r7UhqL5Xxb2QEEKIm16l7wWm1+tJTk4mICDgouNnzpwhICAAu71mr/1yMwQggCJ7EZ/t+Iyvdn+FTbXhZnTj+VbP80CjB0q3eOKFUnZz7NvX+GmLAqg81PAEuass2E5nY3joET4605ZGRXqMtcwMH9sRvf6Gm4gohBDCSSp9IURVVS+7wu+OHTvw9fUtS5HCCcx6M/9u/W9+uOMHWvq3JM+ax8TNE3l40cPsT99ftkKDmlPv5QU0bh4OKKw56Ulg46MA2OZ+S3S0Qr6iYj1TxOaFCRX2LkIIIURplCoA+fj44Ovri6IoNGzYEF9f35KPl5cXffr04f7776+suopK0sCnAV/f9jVvdHgDd6M7u07v4oEFD/DB1g8osJVh6rqi0PWZNzAYTZzM9ya1VgAeIQXgcNDrx1Ek1soAYOuiBLLPyNR4IYQQVa9UXWCzZ89GVVUef/xxpk2bhpfX+TEcJpOJsLCwCp3C7iw3SxfY5aTmpTJx80SWH9cGRoe4h/BmxzfpVLtTqcta/8O3bPp5Ll7+/gxtY+HYlJWoDoXa3TP5zjgF1VabOlG1GPRsy4p+DSGEEDehSh8DtHr1ajp37ozBYChzJauzmzkAnbPy+ErG/zW+ZNHEgeEDebXdq/i6XH8XZ3FhAV+++DR5Gen0eORJQrZsIn3ufEyeVjx7ufFjxnuo6Bj0YhR1GvtV1qsIIYS4SVT6GCAPDw/27dtX8vVvv/3GoEGD+M9//kNxcXFZihTVzK11b+X3Qb8ztMlQFBQWHFnAnfPv5LdDv133AoomFwud7hsKwKZf5uL+z3+j9/amONuIekahqWUZAGs+WYxjfxmn4gshhBBlUKYA9PTTT3PgwAEAjhw5wpAhQ3B1deXHH39kxIgRFVpB4TxuRjdGth/JdwO+o5FPI7KKsnhj/Rs8ufRJjmUfu64ymvfoTa2QuhTm5rB15RL8nnsOgMzdbpwJtWBU8kgvqs2+/34K394LaWUcfC2EEEKUQpkC0IEDB4iOjgbgxx9/pHv37nz//ffExMTw888/V2T9RDXQwr8FcwbO4f/a/B8uehf+SvmLe367h893fo7VfvWtLXR6Pd2Gait7b1v4G/pePTHVr489PZ3WBRbWu2mzCTfl/oPCAxvg446wcIS2rpAQQghRSco8Dd7h0HYVX758OQMGDAAgNDSU06dPV1ztRLVh1Bl5vPnj/HLXL3Sq3YliRzEfbf+I+xfcz74z+656b/1WbQlt2gK71cqGX+YSMOJVAIrmfkenNp6c1jkodHiy2fgaqHbY/Bl82Ao2fQLXCFhCCCFEWZQpALVt25Zx48bxzTffsHr1am6//XYAjh49WrKNhbgxhXqE8mnvT5nYdSK+Lr4cyjzEQ38+xKc7PsXmsF32HkVR6PaPxwHYu3YV+WF1cevUEdVqpf/GX9jpp7UC7UxqQfqA3yCwORRmwuKRWovQkdVV9XpCCCFuEmUKQNOmTWPbtm0899xzvP7660RGRgLw008/0alT6adLi5pFURRuD7+dX+/6lT71+mBTbcyMm8nDCx/mSNaRy94TFNGAxp27g6qy9vsYAl57DXQ68pcu4elmNg4a7CgqLF/tjvrUarhjOrj6wZmD8PWd8POTkHuqit9UCCHEjapM0+CvpLCwEL1ej9ForKginUKmwV8/VVX58+ifvPvXu+QU52AxWHjzlje5I+KOS67NOpXCly/+E4fdxuBRb2P++Tcyf/wRlxYtGN35edrEF2NEoe/wZjRoFwiFWbByHGyeBahg9oLeo6HNY1DWrTqEEELcsCp9Gvw5W7du5dtvv+Xbb79l27ZtuLi41PjwI0pHURQGhg/klzt/oUNwBwpsBfxn3X8YvX70JatIewUE0aq/1l265ruvqPXcv9C5ulK4axcjvBP5y0XrQls17wDFhTZw8YIBU+DJlRAcDUVZ8OfL8EVvSNlV1a8qhBDiBlKmAHTq1Cl69uxJu3bt+Pe//82///1v2rZtS69evUhLS6voOooaIMgtiM96f8az0c+ioPDroV956M+HLpku3+GeBzC7uZF2PIGD8bup9fTTALjEfEZoa28ydA6suVY2Lzh6/qY6rbUQdNsUMHlA0jb4vAfETpJB0kIIIcqkTAHo+eefJzc3lz179pCenk56ejq7d+8mOzubf//73xVdR1FD6HV6nmn5DLP6zqKWS62SAdKbkzeXXGNx96DDIG2/uHXzvsHzoQcw1q6NLSWFZ5PXsd7DDsCOFSc4k5R7vnCdHjo8Bc9tgcYDwWGD2Hdh1q2QsrtK31MIIUTNV6YAtHjxYj7++GOaNGlScqxp06bMnDmTRYsWVVjlRM3UIbgDP935E1F+UWQXZ/P0sqf56cBPJedb9b8DDz9/cs+cZvvyxQSMGglAwbezeaSNCweNdlBhYcxeVMf/DFHzDIYh38I9X4DFB1J2aq1BqyeD/fKz0IQQQoj/VaYA5HA4LjvWx2g0lqwPJG5ufhY//tvvv9xW/zZsqo23N77Ne3+/h6qqGEwmujzwCACbfp2HI6o57t27g9VKxwVfktvEnWJUso/nsntt4qWFKwpE3QfP/gWNbgeHFVaNh9kDIetkFb+pEEKImqhMAejWW2/lhRdeICkpqeRYYmIi//d//0evXr0qrHKiZnMxuDCp6ySejX4WgJg9MYzZOAa7w06Tzt0JadocW1ERi2Z+gN9/RqG4uFCweTMjPE+w1qKN7Vn70yFy0gsv/wCPQHjgO7j7c21s0PGN8GkXiF9YVa8ohBCihipTAJoxYwbZ2dmEhYURERFBREQE9evXJzs7m48++qii6yhqMEVReKblM7zT+R10io5fDv7CiDUjsKl2+j79bwxGE0n793LgwB78nnlGu+mTD+ncuRaJejuq1cHyr/ddeQNWRYGWQ+Cfa6B2KyjIgLkPwqLXwFZUdS8qhBCiRinzOkCqqrJ8+XLi4+MBaNKkCb17967QyjmLrANUOZYfW86INSOwOqx0rdOVaT2nsXX+z2z44Ttc3Nx5/L1PSPrHwxQfPozbwIH8y+c2ep9QMaDQa1gTGncMvvoDbMWwfAxsmql9Xbu11kLkWbvS300IIYTzVdo6QCtXrqRp06ZkZ2ejKAp9+vTh+eef5/nnn6ddu3Y0a9aMtWvXlqvy4sbVu15vZvSagYvehbWJaxmxZgTRA+/COyiYwrxc1v7wDcHvvAM6HXkLFvBOrRNsPLc20Pf7yUoruPoDDCbo/y48OE8bIH1uuvyJzVe/TwghxE2nVAFo2rRpPPnkk5dNVV5eXjz99NO8//77FVY5cePpVLsTH976ISadiRXHV/DWpjH0fOyfAOxauZR0FyP+zz8HgOW/M2l3iycn9XYcVgcLP9uF3XYdg+wb9YcnV0FAU8hNhZjbYfu3lflaQgghaphSBaAdO3bQv3//K57v27cvW7duLXelxI2tY+2OfNDzAww6A4sSFvFl7q80v7UvAIs/nYbHIw/j0rQpjpwc7vv7F/bVNVKgqKSfzGXjr4ev7yG+9WH4Mm3NIHsx/PYvWDYaZJaiEEIIShmAUlNTr7rVhcFgkJWgxXXpFtKNKd2moFf0/Hb4N3Y1y8fDz5+s1BTWzplN4JtvlHSFvRt8iuXuWlfYjhUnSNh1+voeYnaH+7+BHqO0r9dPh1+f1sYKCSGEuKmVKgDVqVOH3buvvOruzp07CQ6+xkBVIc7qXa8373R+B4DZh79Dua0pADuWLeKU4sDvuX8BoP9wCk9182KrSQtBS77cQ27Gdc7w0umgx0i462PQGWDXD/DdvVCYXfEvJIQQosYoVQAaMGAAb775JoWFl67LUlBQwFtvvcXAgQMrrHLixndHxB281OYlAD488zXeHZsDsOTT6bg9+ACW1q1x5OYS/eUk/Nt7k6p3YCuws3DWLhz/u0r01bQaCg/NA6MbHF2tLZqYn14ZrySEEKIGKNU0+NTUVFq3bo1er+e5556jUaNGAMTHxzNz5kzsdjvbtm0jMDCw0ipcFWQafNVSVZUpf0/hm73fYHYYeWxbcwpPpRPeuh23D3uahHsGY09Px/3ue3jRpy9djtgwodD29jA63BFeuoclbYdv74X80xDQDB6ZD+4BlfJeQgghqlZp/n6Xeh2gY8eO8cwzz7BkyZKSxekURaFfv37MnDmT+vXrl73m1YQEoKrnUB2MXDuSRUcXEZznwW3rA3DYbPR45Eka+wZw/PHhoKoYRr7JiL1+9M42oAK3PxtF/Si/0j0sbT/MvhNyU8CvITzym6wVJIQQN4BKDUDnZGRkcOjQIVRVpUGDBvj4+JSpstWRBCDnsNqtPLviWTYlb6J1YiBRO1zQ6fXc/9ZEzCtjSZv+IYrZzMl3PuKH5QW0LDagGBQGv9yGwPql/DmdOayFoOyT4FMfHlsoIUgIIWq4SlsI8UI+Pj60a9eO9u3b31DhRziPUW9kWs9pNPFtwrbaqaSEOnDY7fzxwQRchtyPW/duqEVFhM0YR/3O3hwx2FFtKr99FEdWWn7pHlYrQgs93vUg4yh8fRfkXefsMiGEEDVemQOQEJXBzejGx70/JtQzlOVNTpLnBXkZ6SyYPpmg8eMx1q6N9fhxhq76iowW7qTqHVjzbfw6LY6CnFJOb/epB8P+AM86cPoAfHM3FGRWynsJIYSoXiQAiWrHz+LH530+x9fDnyUtE7EbITF+D6t++o7a06ahmEzkxcbydtoqdtU3kaU4yDtTyO8zdmAttpfuYT71tDFAbv6QshO+vx+K8yrnxYQQQlQbEoBEtRTiEcJnfT5DqeXGypapqArsXrWMXUfiqT1xAgC5337DNJ+jrA5WKFBUTh/LYckXu0s3PR7ArwE8/Cu4eMGJv2DOg7KTvBBC3OAkAIlqK9Inko97fUx6bYW/mpwBYN2c2ST7eOL/4osA5L83mWnNC1nibceGyrGdZ1gzdz+lHtsf1AKG/nx+naBf/ynbZgghxA1MApCo1qL8o5jeczqHw4vYG6at3rxo5vsU9uiC1+B7wOFAeft1xrVTWHJ2u4w9a5LYtvR46R8W2g4e+E5bMXrPL7B8dEW+ihBCiGpEApCo9jrW7sjkbpPZ1jSb4wH52K3F/DrpbfSPDcP91ltRi4rwHjeS17q6EOtqBWDTr4eJ35Rc+odF9NS2zQDY8BFs+rQC30QIIUR1IQFI1Ai96/VmSo+prG+dSYpPIcX5+fw86W1cR7yCa4cOOPLzCX73NYb38mCrWWsJWh6zj70bkkr/sJZDoNdb2r8Xj4S9v1XgmwghhKgOJACJGqN3vd5M6fUeq9unc8aziILsLH6eMhavd97GJSoKe1YWERNHcsetbsSZbCjAyq/j2b02sfQP6/J/0HY4oMIvT8GJLRX9OkIIIZxIApCoUXrW7cnUvtOI7ZBJlpuVnNNp/DhlLD4T38XcoAG2tDSaTRnJXb0sbDdrIWj1d/vZGXuidA9SFBgwBRreBrZCmPMApB+tlHcSQghR9SQAiRqnW0g3pg6YzupOWeRYrGSfSmXe++Pwfn8K5saNsZ8+TcOJrzGkl4VtZ7vD1s49yOZFCaWbHabTw+AvILiltnnq9/dDQUYlvZUQQoiqJAFI1Eidanfi40H/ZWP3IrJdreSmpTH3/XF4TZmIS7Nm2DMyqDv+VR6+1cTfLloI2vLbEVbO2Y9amnWCzO7w4DzwDNFWi573MNhKueK0EEKIakcCkKixmvk144vB37Czl54sNysF6Rl8P2UM7u++g6VlSxxZWQS//TLPdLGzwV1bITp+TRK/fboTu7UUa/x4BsPQH8DkAQlr4Y9/Q9n2EBZCCFFNSAASNVqoZyhfDP6G47fXItO9mOKsHL559z/oRr2K6y234MjPx2PMCN5omcG6Wip2VBJ3nmHue1spzLNe/4MCm8H9s0HRw445sHpy5b2UEEKISicBSNR4tSy1+HxQDLoH25LmXYRaaOWHyWPIfeIfeA4YADYbjH+Ld4MPsjlETzEqmQk5fD32LzJSSrHvV2QvGPi+9u/Yd2HHvMp5ISGEEJVOApC4IZj0Jsb0Gk+zZ//ByYACFLvKohkfsLdbC3wffRSAwhnTGV+4kv2NtQ1UrVnFfDduM0d3nr7+B7V5FDq/oP37t39BwvoKfxchhBCVTwKQuGEoisLDLYfxwGvjORZmRVFh55yf+N0tA78Rr4KikP/Tj4zcOgtDJzdO6O0oNpU/P97Jxj+PXP8MsV5joOkgcFhh7kNw+mBlvpYQQohKIAFI3HA6hNzCm299y5nWngBkr9vN5/uW4DF1PDo3Nwq2bOGemDfpfKuJXS52FGDbHwn8+skOrMX2az9Ap4O7P4WQdlCYCd/dC3mlaEUSQgjhdBKAxA3J39WfcSO+xe2eDth0DlyO5/HfX2dx4u2nMNatizUxkQbjX+KZ9nn85aPiQCV5Zzr/fWsj6UnXMS7IaIEH5oB3PchIgDkPgrWw0t9LCCFExVDUUq0Md3PIzs7Gy8uLrKwsPD09nV0dUU7rti1m9Ucf4ZKvUGxwYO9ZjwfX5lL8198AWIY+whRLF+oeLsZdVXDooPtDjYjqUufahacdgP/20VqCmt0Ng7/UWoiEEEJUudL8/Zbf1OKG16V1f/459QvUOp6YbDpclh1nSlgq2Xf3AKDgu695ZduneHexcMxgR+eAtd/u5+dPdmAtukaXmH9DGPIt6Iyw51dYObbS30cIIUT5SQASN4VatYJ5cdJsandui4JCg3gTP2QdYMGjTcHNlcJt2+g54xXu625ju5cDByopO87w+ZsbSD2WffXC63eFOz/S/r3uA9gaU+nvI4QQonykC+wypAvsxrYjdinLv5gBVgf5Zhv7GmTw4nozHglpoCi4PjyM6ZbOBB4o0rrEFGjaJ5SegyLR6ZQrF7xqAqyeqC2W+I+fIOLWqnspIYQQpfr7LQHoMiQA3fjOnDzBL++NJTspGQcquyIy6XKiiK5btAHQ5iaNiXvoJdavKyK8SGsoNQS68MDz0Xj5uV6+UFWFX5+GnfPA7AmPL4HAplX1SkIIcdOTAFROEoBuDtaiQlZ8+Sl7YpcDkOpTSJZnGk8ut+OWb0cxmzE8+wLTT0cQfsKKCQW7HtrfE0GHW+uiKJdpDbIVwTd3w7H12gaqw5eC13UMphZCCFFuEoDKSQLQzWXP6hWs+PJTrIUFWPUOdoenc9u2bFof0f6n4dalC8v7PMnhtdnUtp1tDapt4YFnovHyt1xaYH66NjPszCHwjYBH/9Q2VBVCCFGpJACVkwSgm0/WqVQWzXyfxPg9AJwIzMdkT2PoahsmG+DtCf/3Op/u8yI8xYYBBZsOom6vR4/bwlH+d2xQ5nH46nbIOg5+DWHYAvAIrPoXE0KIm4gEoHKSAHRzcjjsbF0wn3Vzv8Fht2G36NkZksRDa3Opn6pdo+/djfXdnuLwmgyCz7YG4W9myLMt8Qt2v7jAjAQtBGWfBP/GMOwPcA+o0ncSQoibiQSgcpIAdHM7lXCERTPe4/SJYwDkNnRHf3IXgzY50KtQ6G5G/fcLzDnZgNrHi7SxQQpE9KrDbfc0vHimWPoRLQTlJGndYY/MB++6znkxIYS4wdWohRBnzpxJWFgYLi4udOjQgc2bN1/x2j179jB48GDCwsJQFIVp06aVu0wh/ldAWDhD3/2ANgPvBkXB/UAuPuZW/PxYCxICwCW3CMu7k+m96y28+thINGnBKGF5ItNHruXogYzzhfmGw6MLtNCTfhj+2w9OxTvv5YQQQgBODkDz5s3jpZde4q233mLbtm20bNmSfv36cerUqcten5+fT3h4OBMnTiQoKKhCyhTicgwmEz0eHs59b4zH0z+QwoxM3Lfmk37HPazvVxebDupuT6LFOy9SO3AWxxsUUoiKKdvGgve38eWMbRTmW7XCakVoU+L9G2stQV/dBif/du4LCiHETc6pXWAdOnSgXbt2zJgxAwCHw0FoaCjPP/88I0eOvOq9YWFhvPjii7z44ovlLrOoqIiioqKSr7OzswkNDZUuMAFAcWEB6+d9y7ZFv4Oq4urlTWTndhi//Y7AEzkA7AxT2HB3V1wOD6RuthsAhUZod08E3XrW0wrKT9d2jk/cCgYXuGsmtLjXWa8lhBA3nBrRBVZcXMzWrVvp3bv3+crodPTu3ZuNGzdWaZkTJkzAy8ur5BMaGlqm54sbk8nFQs9hT/Lg2CnUCqlLflYmOxcuI7PPQIoeH4LNqCMqQeXxj9ZgzhrJ380XkWUoxsUKu+Yd5oO31pOcnAOuvvDI79CwP9gK4efh2urRMgxPCCGqnNMC0OnTp7Hb7QQGXjw1ODAwkJSUlCotc9SoUWRlZZV8Tpw4Uabnixtb7YaN+cfE6dwy+EF0ej2Ht25m3b592Ea/gdIuGpMNHlzt4IG5C9geOIrddf7GjgNTahHzxm7mq1lxFGOBB76HTs9rha6eCD88AoVZzn05IYS4yTh9EHR1YDab8fT0vOgjxOUYjEY63z+Uf0ycTlBEA4ry81j503fsbFAft9Gvo3h7Ufc0jPmukMZ7Y1jQeCLJ7icxqgr5W9OZ9upqlq48AX3HaRuo6oyw73f4rDskxTn79YQQ4qbhtADk5+eHXq8nNTX1ouOpqalXHODsjDKFuBz/umE8OG4q3R8ejsFk5sSenfy68BfSn38a97sHoQP6bld5+5sk0pnE8sjZ5BlzcCuGgz8dYeLra9jvNRAeXwxedSHjqLZ69OZZ0iUmhBBVwGkByGQy0aZNG1asWFFyzOFwsGLFCjp27FhtyhTiSnQ6PW0H3s2wKTOo2yIam7WYjb//zPLCDAzj3sYUFoZ3nsrzCxw8smwra0LHEhe8Ajt2PM7YWDxlO9N/Usl+eDk0GgD2Ylj4Cnx7D2RKN6wQQlQmp84CmzdvHsOGDeOzzz6jffv2TJs2jR9++IH4+HgCAwN55JFHqFOnDhMmTAC0Qc579+4FYMCAAQwdOpShQ4fi7u5OZGTkdZV5PWQhRFFaqqoSv341sV9/QX5WJgBNu/SkBSZy//slamEhDr2OZe2NLIiuRbukewnJagRAjl6lbq/aDAlahX7l29oAaZMH9BsPrR+By226KoQQ4hI1aiXoGTNmMGXKFFJSUoiOjubDDz+kQ4cOAPTo0YOwsDBiYmIASEhIoH79+peU0b17d2JjY6+rzOshAUiUVWFuLuvmzmbH8sWgqri4e9B5wCB8V64hb8VKAIp83fmqp0qCb2M6Hrsbj2IfAE67K/QfaKHDoTfh5NnFO+t3g9umQEBjZ72SEELUGDUqAFVHEoBEeSUdiGf5FzNJO3YUgODIRtzSsh2OL77Cevw4AGdahPB+p1x8cnvQMqknetWAA5WMQCOPt9lGyM4JWmuQzgAd/gndXwMX+e+jEEJciQSgcpIAJCqCw25n26Lf2fjT9xQXFICi0LxbL5oWOsiLmY1aXAwGA4f7Nuaj+pk0Tx5AeHpLAIoUB7owB08GfoVbwkKtQPdA6D4CWg8DvdGJbyaEENWTBKBykgAkKlJuRjprv/uKvWtXAWB2c+OWvgPxX7mO/DVrAFB8vPn7jgZ8755Du2N3EZCnbZiao7MT2jidBxwT0Wce0Qr0qQ+3vgHN7gGdrGQhhBDnSAAqJwlAojIkxu9lxVefkpagBRn/umF0bNMR3dffU3xEO6ZEhvHHAD825hvocHwg7mfHB6UZ7XRpvp9e2dNQ8tK0AgObQ9eXoOkg0Omd8UpCCFGtSAAqJwlAorI4HHZ2Ll/C+rlfU5iXC0DjTt1o6eZD/qz/Ys/SVoS2dW7FzFsKKTgVRnRib0wOFwCS3OzcG7WF6KRPUIqytUJ9w6HzC9DyQTCYnfJeQghRHUgAKicJQKKy5WdnsX7uN+xcuQRUFaOLhQ4D7iLkYALZc+eBzQYGA+kDb2FqRBK1T3Sk8alb0KHDhoMkHzvDWmyiyYmvUAoytEI9gqHtcGjzKLj7O/X9hBDCGSQAlZMEIFFVUo8cYsWXn5B8cD8APsF16Nx3IK6//Unu6tUA6Ly92HdPNB97nKR1wgBCs7Qp8fmKgxMBKs9GbaNRQgxKTpJWqN6kjQ9q/xTUaS3rCAkhbhoSgMpJApCoSqrDwZ41K1n7fUzJIoph0W1o36w1xZ/PovjQYQB04fVYekcdFhXl0PHYXfgWBANwRmfnZB09L7Q+TNOTc1ASt54vPKAZtH4YooZou9ELIcQNTAJQOUkAEs5QlJ/Ppl/msm3h7zjsNnR6PdF9BtBYMZPz6WfYMzMBUDu1ZlZXG0mnfGh34jYsNg8AjuvtpNR34cXORUQnz0PZ8xvYi7TC9SZoPBBa/QPCe8igaSHEDUkCUDlJABLOlJGcSOw3/+XIVm01aIuHJx3vvJeg3fvJ/P77kvFB2QNuYWLDY/gmtSEquQcGVVsbKN5oIzPSlWd7BXNL3gqU7d9Ays7zD3ALgGZ3Q4t7IaSddJEJIW4YEoDKSQKQqA4Sdmwj9usvOHNSWznav24Ynfvdgenn38hdpa0ppHi4s//OFkz3T6B5Yh8aprVDQYcdlTiTnfwGbjzbryFd3U+ibP8Wdv8M5wZNg7YTffN7tDAU2FzCkBCiRpMAVE4SgER1YbfZ2LFsERt+/JaivDwAGnToRLsm0RR8Noui+HgAlNpBLLstgJ9dM+hw4k7qZjYFoAiVzS42iiPceL5vQ3pEeKEciYVdP0H8n2DNO/+wWg2gyR3QZCDUlsHTQoiaRwJQOUkAEtVNQU42G378jh1LF6GqDvRGI20G3EVjnYXMjz/GduoUALYm4XzR3cp+nQe3HLsT/7xQAHIUlfUuVvThbjzfuyG3Ng5AsRbAwSVaGDq47Px4IQDPEGh8uxaG6nYCvcEZry2EEKUiAaicJACJ6irteAKxs2dxfPcOANx8fOly70MExB8i/cuvUPPzAci4pTGT2iSjK2pM+xO341lUC4DTOgdrLFYs9dz4d6+G9GkaiKIoUJgFB5ZC/B9wcPnFLUMWX2jYT/tE3AouXlX+3kIIcT0kAJWTBCBRnamqyuG//yL2my/ISk0BtN3mu951L4Y/FpL58y/gcIDBwP5bI5jSOIGwrK60TuyLi80NgBN6O6stVrxDPXihVyR9mwah053t8rIWwJFY2LcA9i+EgvTzD9cZoF4naNhf+9SKqOK3F0KIK5MAVE4SgERNYLNa2bbwNzb9Mg9rYQEATbv2pF2HruR/+jl569cDoHq4s7S3L9+GpxOd3IeolO7oHdqMsf1GO2tcrATVcef5WxtwW/MLghCA3QYnNsGBJXBgMZw+cHElakWeDUP9oG5H2aVeCOFUEoDKSQKQqElyM9JZN/dr9sQuB8BodqHD3ffTyDuA9Pffp+jgQQCKIurw0a1F7PGAdicG0CitPQoKdlR2mOysc7FSL9idUbc1oUcjf61r7H+dOQwHl2phKGE9OKznz5k9IbKXFogi+4Bbrap4fSGEKCEBqJwkAImaKOXQAVbO/pzkA9rMME//QLoNfRS/I8c5Pf1DHNna5qknezbhneijKPYAOh6/k9DMJgAU6FRWuVjZY7TTtaEf/xnQhCbBV/nvf2E2HFl1tnVoCeSfvuCkAqHttZahBv0gsJnMKhNCVDoJQOUkAUjUVKqqEr9+NWu+jyH3jBZIQptFcev9/6A45huy5s/XLvT0IPaOED4OPUCd7EZ0S7gfr3xtA9VEg4OllmLSDSpD2tVlZP/GeLleo2vL4YCkbVrL0IHFkLLr4vOeIecHUtfvBkZLBb+5EEJIACo3CUCiprMWFrL595/5+/efsVmLMZpd6Db0MRrUCiD1nfEU7dc2X7W2a87k3nnsciQRldyddokD0NuNqMBms5X1LjZ8PMyMvasZtzUPuny32OVkJWpB6OBSOLIabAXnzxksEN4dGvTVApFXSMV/A4QQNyUJQOUkAUjcKLJOpbDkk+mc2Ku1yNRt3pK+T/wL26IlpE2bhlpcjM7Tg0OP9WSc52rIM9Ep4W7C01sCkG2E382FJBtUejcJ5N17mhPg4VK6SlgL4Ojas61DSyD75MXnA1tAo9u0RRiDWkhXmRCizCQAlZMEIHEjUR0Oti/5k7Xfx2ArLsLs6ka/f75AXb9AkkaOonCXFo5MPbsy7y4f5qYuom56M7ofGYKr1RMV+NvFxhqzFV8PE+/fH023hv5lrIwKp/aeD0MnNgMX/Aryrnd2Neo7IKQ96HTlfn8hxM1DAlA5SQASN6KM5EQWzXyf5INa91d0v4F0e3AYWbNnkzbzY7BaMQQGUvzWc0wonE980kE6Jwym4em22v0u8KOxkCy9ytPdwnm5byNMhnIGlLwzWjdZ/AI4tOLirjL3QGg0QAtDYV3BYCrfs4QQNzwJQOUkAUjcqOw2G+vnfcOW338GIKB+BHf83yhc0jNIfOllio8eBb0e/xdeYGPPAD7YPh23k8H0OPwALnY37AaVBaZiDpgctAvzYebQ1qXvEruS4jwtBO37Q2sdKso6f87sBY36a2EooheYXCvmmUKIG4oEoHKSACRudEe2b2HRzA8ozMnGxc2dgS+OJDSiAclvjSF7wQIA3Hv0wHv8W/w3YS4/b/+dHvsfIignHIA9rkUsMTrw93Lh04fbEB3qXbEVtBVDwhptNer4PyHv1PlzBou23lCTO7RB1Bafin22EKLGkgBUThKAxM0g58xp/nh/AsmH9qMoOro//DitbruTrB9/InX8eNTiYkxhYYR8/DGpfnqm/DWV/I1utE7qA0C6Sw4/GRUKTEbG3d2c+9uGVk5FHXZtrFD8Atj3O2QeP39OZ9Cm1Te7B5reKfuUCXGTkwBUThKAxM3CVlzM8i8+Zs9qbRXppl170vup57AdPMTJ557HlpyMzt2dOu9Nxb17dzYmbeTLRfNotL0nFpsHhYZ8/vQ+yRFbCI90DOPNgU0x6itx4LKqQspOrWVo3x+Qtu/8Ob0ZGvaFFvdpiy8aK6hrTghRY0gAKicJQOJmoqoq2xf/QezXX6A6HASGN+CuV1/H4oCTL7xIwdatoCgEvPwSvsOH41Ad/LL9d+Ln5uKbUwcHDjYGrWeTGkTb4ChmDm2Nv4e5aip/+hDs/RV2/QRp8eePmz2hyZ3Q4l6thUinr5r6CCGcSgJQOUkAEjej47t38McHEynMzcHNx5e7XnmdoLr1SRk3nswffgDAc+BAgse9g87Fhaz8HL75bCnKfm0MzuFa21nmtxdL0QA+e+hWWtWtwrE5qgqpu2HXj7Dr54vXGnIPhOaDIWoI1I6uujoJIaqcBKBykgAkblaZqSnMnzyWMyePozca6fv0v2nSpQeZc+eSMv5dsNlwadqUkJkzMAYHo6oqG5fvY9uvSSgOHWcsSSxuOJuMgub8p/M/ebhDo6p/CYdD28F+5w+wdz4UZJw/F9QCWj2sdZO5+lZ93YQQlUoCUDlJABI3s6L8fBbOmMqRrZsBaHfnYLo8+AgFf28l8YUXsWdkoK9Vi5APp+Papg0AyYezWPDJdopzHRTp81nR4BsS3E/QymMIn9/9DK4mJ63hYyuGwyth5zxtELW9WDuuN0OTgdDqH1C/hyy4KMQNQgJQOUkAEjc71eFg3bxv2Dz/RwDCW7djwPOvoqRncPK55yiKjwejkaDXX8fngSEA5GUWsejzXaQeyUZF5e+QxWwNWYJJDeT1ji9zd6N+17+XWGXIT9e6yLZ9A6kXbNbqVRdaDYXoh8C7rvPqJ4QoNwlA5SQBSAjNvnWxLP30Q2zWYnzrhDJoxJt4eXqT9Prr5CxaDID3/fcT9MbrKCYTdpuDdT8eZPfqRAASvPexssFsig0FRHg2563OI2gV0MqZr6SNF0reAdu/gZ0/XrDgogLhPbRWocYDZRaZEDWQBKBykgAkxHkphw7w29Rx5Gak4+Lmzh0vjSK0WRRnZn1B2gcfgKpiad2akOnTMPhre4Tt25DM6u/3Y7c5yDblsajRJ2S4nwCgR0gPXmzzIhHeEc58LY21QJtSv/1rOLrm/HEXb23QdOuHtXFDQogaQQJQOUkAEuJiueln+O298aQcOoCi09Hz0aeI7ns7eWvWkPjKqzhycjAEBhIy4yMsLbTAkHY8h0Wf7iInvRCHDpYGreNo3Z9RFAc6dAxqMIhnWj5DkFuQk9/urIwE2P4dxH0H2YnnjwdHQ9vHtSn1Jjdn1U4IcR0kAJWTBCAhLmUtLmLZZx+xb10sAFG9+tPzsaexnzzJyX89R/GRIygmE4FvvoH3vfeiKAoFucUs/WIPJ+O1mVi7XHNZW28eOu+dAJh0Ju5rdB9PtHgCP4ufs17tYg47HF6ldZHF/wkOq3bc7AUtH9DCUEBj59ZRCHFZEoDKSQKQEJenqipbfv+ZtXNmg6oSFNGAO/5vFG4WV5JGvEbuypUAeN11F0FvjUbn6orDobL5jyNsXXwMVMgyw0+ehykI/gOD21EAXPQuPND4AR5r/hi+LtVoenreaa1F6O+vIOPo+eP1OmtBqMkdYKiiRR+FENckAaicJAAJcXVHt//NwhnvUZibg4ubO7c9/zL1W7bRxgVNnw4OB+YGkdSZPh1zuLaB6vE9Z1j21V4Kc6049Ap/mAs57L0frzorsRq0cGExWBjaZCiPNnsUL3M12tfL4YAjq+DvL2H/QlAd2nFXP22cUJtHwSfMmTUUQiABqNwkAAlxbdlpp/jjgwmkHD4IwC33DKHjfQ9p6wW9/DL2tNMorq4Ejx2L18DbAcjNKGTpf/eQfEibebXPzcEiQyFGz4PUCV/DqeJDALgZ3Xi46cM83PRhPE3V7H+DWYmw7WvYNhtyks8eVCCyt9Yq1LCfbL0hhJNIAConCUBCXB+b1Urs11+wY+mfANRtEc3t/34VU1Exia+8Sv5ffwHg/eADBI4ahc5kwmF38NfvR9i2RNvVvcBVx1x9Pqf1DppGnsBQaylHs7Ug5GHyYFjTYfyj6T9wM1azAch2GxxYBFv+q7UOneMZorUItX4EPAKdVj0hbkYSgMpJApAQpbNvXSxLP/8IW1ER7r61GPjiSGpHNiRtxgzOfPIpAC5Nm1Ln/fcwhYUBcGz3GVbM3ktBjhX0CmssVv7SW/Fw0TG4WwZxOT9wOOswAF5mL4Y2HspDTR6qXl1j55w5DFu/0maRFaRrx3QGbYxQuye0MUPOXARSiJuEBKBykgAkROmdOXmc3997l/Skkyg6HZ3v/wft7hpM/voNJL06AntmJoqrK0Gj38TrrrtQFIX87GJWfr2PY7vPAHDaQ8c8JY98HXRp4Ev/DqnMO/hfErITAG2M0P0N7+eRZo8Q4BrgxLe9Amsh7P0NtnwBJzefP+7fGNoOh5ZDwKUaBjghbhASgMpJApAQZVNcWMCyz2cQv341AHWbR3Hbv17GbLWR9OoI8jdrocBz4ECCxryF3t0dVVXZFZvIhp8PYbc5wEXHb6YiDuhsuJsN/GdAQ3z84/nv7v+yP2M/AEadkbsi7+LxZo8T6hnqtPe9quSd8Pd/tU1ZrfnaMaMbRN2nhaHgKOfWT4gbkASgcpIAJETZqarKntUrWPHlJ9iKirB4eNL/2f+jfsvWnJk1i7SPZoDdjjE0lDpTJmOJjgbgTGIuy77cw5nEPABO1NLzky0XmwJdG/gx4Z4WHMn7my92fcH2U9sB0Ck6+tXrxyPNHqG5X3NnvfLVFWbBjnlaGEqLP3+8dmtoMwyaDwazh/PqJ8QNRAJQOUkAEqL80pNOsmD6ZNISjgDQ6rY76PbQYxTv3kPSK69gTUoCnQ6/fz6N3zPPoBiN2Kx2Nv16hB0rtW0zFA8D83T5HFPsuJsNvH57Ex5oF8q2U9v4YtcXrEtcV/K8VgGteLjpw/QM7YlBZ3DKO1+VqsKx9dqg6X1/nF9g0egGLQZD60ehTmsZKyREOUgAKicJQEJUDJvVytrvvmLbot8BqBVSl9v+9RJ+fgGkvDOO7D/+AMClWTNqT5l80ZpBK7/eR15WMShw3E/Pz8Vaa1CXSD/G392cerXciE+P5+s9X7MoYRE2hw2A2m61eajJQ9zT4B48TNW0ZSXvNMR9r02nP3Pw/PHA5tB6mNZNZvFxXv2EqKEkAJWTBCAhKtaRbVtY8ul08rMy0en13DL4AToMup/cJUtIfnssjqwsFLOZgFdfxWfoQyiKQlG+lXU/HiR+YwoAiqeBeYrWGmQ26Ph3rwY82TUck0FHWn4ac/fP5Yf9P5BZlAmAq8GVgeEDub/R/TTybeTEt78KVYVjG7Q1hfb+BrZC7bjBBZoO0rrI6naUViEhrpMEoHKSACRExcvPzmL5FzM5+NcGAIIiG3Lbv17CQ28kedR/yNugHXfr1Ingd8ZirFMHgIRdp1n1bTz5Z1uDEgMMzCvMwa5Ao0AP3r2nOW3qadtnFNoKWXBkAd/u/bZkCj1AS/+W3N/ofvrW64uLwaWK3/w6FWTAzh+1MJS6+/xxv4bamkItHwS3arJfmhDVlASgcpIAJETlUFWV+HWxrPjyU4ry8zAYTXQd+hjRfW4jc85cTk2dilpUhM7VlYBXX8F7yBAUnY7CPCvrfjjI/r+01iCDt4lfjAXstxYDMLRDXUb0b4yXxVjynC0pW/jhwA+sOLYCm6p1j3maPLkr8i7uibyHSJ9I53wTrkVVIXEbbIuBXT+DVRsUjs4ITQZqXWT1u4NO59RqClEdSQAqJwlAQlSunDOnWfzJNI7vigO06fL9nnkRc04eya+/QcG2bQC4duhA8Lh3MIVqU92P7kgj9rv95GcXoyiQGeLCV9kZWBXw9zDz1h1Nub1FMMoFXUanC04z/9B8ftz/I0l5SSXHm9Zqyp0Rd3Jb/duq1wasFyrKgd0/w9bZkLTt/HHvetoeZNFDwbO28+onRDUjAaicJAAJUflUh4O4ZQtZ8+1X2IqLMLpY6PrQMFre2k9rDfrgA9SCAhSLhYD/+z98/jG0pDVo7bwDHNicCoDRw8gaNxvrCvJBgZ6N/Bl7V3NCfV0vep7dYWdD0gZ+PPAja0+uLWkVMigGuoR04a6Iu+gW0g2T3lTl34vrkrJLC0I7f4CirLMHFajfDaKGaKtOu8jvK3FzkwBUThKAhKg66UmJLP7kA5IPaGvkBDdsTN+nnsdTVUh+482SxRMtrVsTNOYtXBo2BLStNNbM3U/2aW3gsCPYhZiCLM7gwMWo45nukTzVLRyL6dKNSTMKM1h4dCF/HP6DPWf2lBz3MnvRP6w/d0bcSQu/Fhe1JFUbxfnagOltX8PxDeePGyzQeIAWhiJuBb3ReXUUwkkkAJWTBCAhqta51qC138/GWliATm+g/aD7aH/XveT++iunJk/BkZ8Pej2+w4bh/69n0bm5YS22s3VhAtuXHcdhV9EbdRz01/FrXg4OBYK9XBh5W2PubFn7imHmUMYh/jjyBwsOL+BUwamS46EeofQL60ffen1p7Nu4eoahjATY9aO20OKF0+ld/bQFFqOGyNpC4qYiAaicJAAJ4RzZp9NY8eUnHNmqtfr41g6hz5PPEejtS+qECeQsWw6AITCQwFGj8OjXF0VRSE/KI/b7eJIPaV1DRl8zC01FxBUWANCqrjejBzalVd0rr61jd9j5K+Uvfj/8OyuOraDQXlhyrq5HXS0MhfWlkU+j6heGVBWStmvdY7t/gry08+dqRUKze7QusqAWEobEDU0CUDlJABLCeVRV5cCm9az86lPyszIBaNy5O92GPga7dpM6bjzWkycBcOvShaA3XscUFqbNMNuYwoafD1GYp62yrIZa+CY/i1S7HYC7W9VhRP9GBHtZrlqHfGs+a06uYUnCEtYmrqXIXlRyrp5nPfrW60u/sH409GlY/cKQ3QZHVsHOebBvAdgKzp/zrqcFoSZ3Qkg7mUkmbjgSgMpJApAQzleYm8vaOTHsXLEEVBWj2YUOd99Pq963kfVVDGdmzUK1WlGMRmo9+QS1nngCnasrBbnFbJp/hL3rk0AFnUHHmRAzszPSsSrgYtTxVLcInuxaHw+Xa4+Tybfms/rkapYmLL0kDIV5htGzbk96hvYkyi8Kve7S8UZOVZQD8Qth3+9waPn5hRYB3IO0afVN7oB6nWXMkLghSAAqJwlAQlQfqUcOsfKrz0g6sA8A78Bgegx7ktBa2nYaeevXA2AICMD/hRfwGnQXil5P2okc1v94kMQDmQCYPIzs9FZZkJ2DqoC3q5F/do9gWMewyw6Uvpw8ax6rT6xm6bGlrD25lmJHcck5XxdfuoV0o2doTzrW7ojFcPVWpipXnKeFoH1/wIElUJR9/pzFBxoN0MJQeE8wVtPFIoW4BglA5SQBSIjqRVVV9q2LZc13X5GXkQ5A/VZt6Tb0MUx74jk1dWpJt5i5SRMCXxuB2y23oKoqR+LS2PDzoZLZYkZfM2tcrKzLy4Oz6wc91zOSB9qHYjZcfwtOnjWPtSfXsurEKtaeXEuONafknFlvpmNwR3rW7Um3kG74WarZCs62Iji6RmsZiv8T8s+cP2d0g4Z9tTDUoK/sVC9qlBoXgGbOnMmUKVNISUmhZcuWfPTRR7Rv3/6K1//444+8+eabJCQk0KBBAyZNmsSAAQNKzj/66KPMnj37onv69evH4sWLr6s+EoCEqJ6KC/LZ+PNcti38HYfdhqLoaN6zN7fcdR/WPxdx+tNPceRoQcS9Rw8CRryKOTwcm9XOzpUn2bbkGEX52vo/xkALC/UFxOVrY2TqeFt4/tZI7mkdgslQurExVoeVbanbWHViFauOr7powUUFhSj/KHqE9qBHSA8ivCOq17ghuw1ObNJahvb9AdmJ58/pzRDeAxr0gche4BvutGoKcT1qVACaN28ejzzyCJ9++ikdOnRg2rRp/Pjjj+zfv5+AgIBLrt+wYQPdunVjwoQJDBw4kO+//55Jkyaxbds2mjdvDmgBKDU1la+++qrkPrPZjI/P9e2uLAFIiOotPSmRtd/HcGjLRgAMJjOtB9xJ6+69yfkyhoy5c8FmA70er0F34f/ssxjr1KEwz8q2JcfYueokdqtDuzfUlV+suewv1Mb2BHm68ETX+jzYvi5uZkOp66aqKgcyDrDqxCpiT8RetM4QaLvVdw3pSreQbrQLale9uspUVVtxet8fsPd3SD988XmfMIjopa0zVL+bLLwoqp0aFYA6dOhAu3btmDFjBgAOh4PQ0FCef/55Ro4cecn1Q4YMIS8vjwULFpQcu+WWW4iOjubTTz8FtACUmZnJ/Pnzy1QnCUBC1AyJ+/ex5ruvSNq/FwAXD0863HUvTRo1I336R+SuWAGAYjTiff/91Hr6KYwBAeRmFLLlzwT2bUhGdWi/AnWhrvxmzSX+bBDyshgZ1imMxzqF4eNW9tWhU/NSWX1yNStPrGRL8paLxg2Z9WbaBbWjW0g3uoV0o457nTI/p8KpKqTFa11kh1fCib/AYTt/XtFDaPvzgah2NFS3QeDiplNjAlBxcTGurq789NNPDBo0qOT4sGHDyMzM5Lfffrvknrp16/LSSy/x4osvlhx76623mD9/Pjt27AC0ADR//nxMJhM+Pj7ceuutjBs3jlq1al22HkVFRRQVnZ/ZkZ2dTWhoqAQgIWoAVVU5/PdfrP0+hvSks9PjvX1oP+h+GvgHkT7zY/I3bgJAcXHBZ+hD1HriCQw+PmSk5LF5wVEObT0FZ38TGuu6sdCRR1yu1jVmMep5sH1dnuhan9re5WutybfmsyVlC2tOrmFN4hpS8lIuOh/uFU63kG50rdOVVgGtMFanmVlFOXB0rRaGDq+A9CMXn7f4aN1lEb0goid4hTilmuLmVmMCUFJSEnXq1GHDhg107Nix5PiIESNYvXo1f/311yX3mEwmZs+ezYMPPlhy7OOPP+btt98mNVXbG2ju3Lm4urpSv359Dh8+zH/+8x/c3d3ZuHEjev2l/w9lzJgxvP3225cclwAkRM3hsNvZs3oFm36ZS3aatqKzey0/brn7fuq7epP+0UcUxMUBoHNzw2foUHwfHYbB15f0pDz+XniUgxcEIUuYO8uUQjZmaGOKjHqFQdF1eLp7BJEB7uWur6qqHMo8xNrEtaw5uYa4U3HYVXvJeTejGx2DO9I1pCtd6nQhwPXSIQFOlX70bBhaqQ2ovnBWGYBPfW16fb1O2scnTBZhFJXupg9A/+vIkSNERESwfPlyevXqdcl5aQES4sZht1nZvWoZm36ZR266NrvJ0z+Q9ncNJkxv5syMmRTt1abUKxYLPkOG4Pv4YxgDAkhPzuPvhQkc/Du1JAh51PdgnaGIpaeyQNH+hvdrGsSzPSOICvGusHpnF2ezIWkDa0+uZV3iOtIL0y8639i3MV3rdKVrSFda+LXAoCv9+KRKY7dC4lY4tEILREnbQHVcfI1H7fNhqF5n8G8kgUhUuBoTgCqrC+xy/P39GTduHE8//fQ16yVjgISo+WzFxexcsYTN838gLzMDAHcfX9oMvJtwoytZs76gcPduABSTCe9776XWE8Mx1q5NRsrZILQllXO/Id1ru7LLXeXn1HTUs3+324f58mjnMPo2DcSgr7hVlR2qg31n9rEmcQ3rTq5j1+ldqJz/Ve1p8qRz7c50DelK5zqd8XXxrbBnV4jCLDixGY6th2MbIHEbOKwXX+Na63wYqnsLBDaXxRhFudWYAATaIOj27dvz0UcfAdog6Lp16/Lcc89dcRB0fn4+f/zxR8mxTp06ERUVVTII+n+dPHmSunXrMn/+fO68885r1kkCkBA3DmtxEbuWL2bLH7+UtAi5eHjS+rY7aejlR86XX1GwbZt2scGA1113Umv4E5jD65OZms/25cfZvzEFu01r0bD4mDnup2fO6XSKzv76rO3lwj861uOBdnXxLceA6StJL0xnfeJ61iauZX3ierKLz3c3KSg092te0jrUtFZTdEo12+KiOB8S/9bCUMI6OLnl4lWpAQwuENwS6rSFkDbaf3rXlVYiUSo1KgDNmzePYcOG8dlnn9G+fXumTZvGDz/8QHx8PIGBgTzyyCPUqVOHCRMmANo0+O7duzNx4kRuv/125s6dy7vvvlsyDT43N5e3336bwYMHExQUxOHDhxkxYgQ5OTns2rULs9l8zTpJABLixmOzWtm7ZiVbfvuJzNRkAEwWCy373k7T4Hrkff11yWBpFAX3W2+l1vDHcW3dmvzsYnbFnmTX6pMU5WkzoUyuBvLqWvgxM5PEQm1ml9mgY1B0HYZ1CqNp7cr53WFz2Nh9ejdrTq5hXeI69qXvu+i8n8WvZFZZx+COuBpdK6Ue5WIr1jZvPbZe+5zcorUa/S83/4sDUZ3W4OJV9fUVNUaNCkAAM2bMKFkIMTo6mg8//JAOHToA0KNHD8LCwoiJiSm5/scff+SNN94oWQhx8uTJJQshFhQUMGjQILZv305mZia1a9emb9++vPPOOwQGBl5XfSQACXHjctjt7N+0js2//sDpE8cAMBhNNOvRi6b1G2L/eT65K1eWXG+JjsZ3+ON49OqFzaqyb0MyO1YcL1lZWm/UYYr0YFFxHlvOnF8NukN9Xx7rHEbvJhXbPfa/TuWfYn3ietacXMOGpA3k2/JLzpl0JtoFt6N7SHe6h3SntnvtSqtHuTgc2ppDJ//WWopO/g2puy+edg+AAn4NIeRsGKrTFgKbSdeZKFHjAlB1IwFIiBuf6nBweNsW/vp1HimHDmgHFYWINu2JatUel9i1ZP/2O6pVG7tiCgvD99FH8brrTjCZObw9jbhlxzl17GzoUcCngRfbLXZ+OX4a+9lfrXW8LTzcsR4PtAvF27Xiu8cuVGwv5u/Uv1lzcg2xJ2JJzE286Hwjn0baitShPapnV9mFrAWQvPN8IErcCpnHLr3OYDnbddYagqK0f/s1BH01GiQuqowEoHKSACTEzUNVVU7u283fC37lyNbNJccDwyOJ7norfnsPkvXDDziytXE3Oi8vfO6/D5+HHsIQFETSwUy2LzvOsV3n99PyDHLldJCROSlnOFWoBSizQcftLYJ5sENd2tbzqfTtMFRV5WjWUVafXE3siVji0uJwXDAzy9/iT/fQ7vQI6UGH4A64GGrABqi5aVoQKglF26DoMl1nBhetZehcIAqOgoBmssnrTUACUDlJABLi5pSedJJtC39jT+wKbFZtXI9HLX+ievShbnYe+fN+xHrihHaxXo9H3z74PvwIllbRpCfnsXPFCQ5sTsV2dpsNo4sefbg7Swrz2Jx+vnssMsCdB9qFMrh1SLlWmS6NjMIM1iauJfZELOsT11/UVeaid6Fj7Y70CO1RPTdvvRKHA84c0gJR8g6txShlJxTnXnqtogf/xucDUXBLCGohm73eYCQAlZMEICFubvnZWexYtpC4JX+Sn5UJgN5opFHHrjSqFYh+0TLyL1inzNykCT5D7sdz4B3YdCbiN6awe00imannQ4ZnXXeOeCn8kHyGPJu24KFJr6N/8yAeaB9Kx/BaVbZJarG9mC0pW4g9EUvsydiLVqRWUGjh34KeoT2r5+at1+JwQMZRSI7TAlHyDi0UXbjj/YV8w7Up+EEttFajwOYy+6wGkwBUThKAhBCgrSUUv34125cs4NTR8xuDBkU2pFlUG2rF7Sbvz4WoxVprkc7VFc+BA/Eecj8uTZtycn8Gu2MTObojrWQ9IYunEUd9dxbl57A17XyrUL1argyKrsPdreoQ5udWZe+oqir7M/YTeyKWVSdWsffM3ovOh7iHlLQMtQlsg0lfNS1WFUpVtV3uLwxEyTu0Y5dj9jrbhdb8bDhqDgFNwViNNq4VlyUBqJwkAAkhLqSqKskH9xO39E8ObFyL3abNTrJ4eNK4Q2fqFdph4WKKjx4tucelRQutVWjAAPKLdOxZm8TedUnkZ2thSVHAJ8KLA24qPyWdJsd6fhuMVnW9uadVHQZG1a6yLrJzzm3euvrkajYlbbpo81aLwUKHoA50rtOZLnW6EOJRw/f7yjsNKbu0GWcpu7X/TNt/6aKNAIoOfCMuCEUttP/0rC2tRdWIBKBykgAkhLiS/KxMdq1cyo5li8g5k1ZyPLhBIxqGNcBv934KVqyAs7PHdO7ueN15J95D7scY0YAjcWnsXp1I0sHMknvNbkYM4e5sVAtZlpiO49zGrHqFHo0CuLtVHW5tHICLsWp3W8+35rMxeSOxJ2JZl7iO0wWnLzof5hlGlzpd6FynM20D29aMgdTXYiuG0wfOhqILwlH+6ctfb/G5tAvNv7EMuHYSCUDlJAFICHEtDrudo3Fb2b1qKYe3bkZ1nB34bHahQet21LOBcelKbMePl9xjbtIEr7vuxGvgQHLtruzbkEz8pmTys863sviEuJETZGZxdjbbT53vIvNwMTAwKpg7W9ahfX1f9LqqbXVwqA4OZBxgXeI61iWuu2TzVrPeTNugtnSprQWiMM+wmjV26GpUFXJPQequ8y1FKbu1oHTB96CEotem4l/YhRbYHNwDpbWokkkAKicJQEKI0sjLzGDP6hXsXrWMjOTz40p8a4fQMLwhAfGHsa1ZW9IqhF6Pe5cueA26C9fuPTl5OJf4Dckc3Xkah137lazoFHzDPTjpoeP30xkczzm/dYSfu5n+zQMZ0CKYDvVrVXkYAsgpzuGv5L9KAlFq/sWbUddxr0OXOl3oUqcL7YPaV88VqcvLWghp8ZC65+IWo4KMy1/v6ndpF5pfQzDUwHFV1ZQEoHKSACSEKAtVVUncv5fdK5exf9NabEVF2glFIaRhY+q6eOC7YzeOHbtK7tF5eODZvx+eA+9AadSCg1tPc2BzyvkFFtFWm/ao78FBs535aZlkFp4fo+LnbqJfsyBuj3JeGFJVlUOZh1ifuJ51SevYmroV2wWrOBt0BtoEtCnpLov0jrxxWof+l6pCdtIFgehsODpzCC5Yh6mEzqh1mV006LoFuNWQpQiqGQlA5SQBSAhRXkX5+ezfuIbdsctJPhBfclynN1C3QSNCbAqeGzdDUnLJOUNAAJ4DBuA5cCCF/mEc+vsUBzanXjSd3sXdiCXcg30mG7+fTCfrf8JQn6aB9GkaSKcIvyofM3ROvjWfzSmbS1qH/ndF6kDXQG4JvoV2Qe1oH9SeYPdgp9SzShXnQ9q+i7vQUvdcfiFHAPeg84HoXDdarQaywvU1SAAqJwlAQoiKlHUqlfgNa9i/fjVpxxNKjhvMZuqFRVI7Ox/3DZtRss/v8m4KC8Pz9tvxuH0A2Xo/Dm87RfzGlJJZZABuPmYsER7s0llZcOIMmQXnw5CrSU+3Bv70aRrIrY0Dqnw22TmqqnIs+5gWhpLW8XfK3xTZiy66JsQ9hPbB7UsCUYBrgFPqWuVUFbJOXBCKznahpR8FLvOnWW+GgMYQ2OKCcNQMXH2rvOrVlQSgcpIAJISoLGdOHid+/Wri168p2ZUewOzqRljd+gSnZeK64S8oPD/mx6VZMzwHDsS9X39SM4wc3JLK4bg0rIXnB+C6+5oxh7lzwGhnYVIGKReMGdLrFNrW86FvsyD6Ng0k1Nd543EKbYVsTd3K5pTNbEnZwp4zey7aogO02WVtg9rSPkgLRTVmZeqKUpQLp/ZdPOg6dc/lV7gG8Kxz8WDroBbaAo8657QAOpMEoHKSACSEqGyqqpJ6+CDxG1azf8NacjPSS865enlTPyiEwMRUzJu2oNjPBh1FwdKqFR59+mDpcSvJGS4c3JLKsT1nsBWfDxGunia8Ij05ZlFZejqTfakX/+FsHORR0lXWoo6XU8fj5Bbnsu3UNjYnb2ZL6hb2ndmH+j+tH+Fe4bQNbEvrwNa0CWxDkFuQk2rrRA4HZCac7zo712J0uQ1iQdskNrDp2an551qMmoGLV5VWu6pJAConCUBCiKrkcNhJ3LeH+PVrOPDXegpzzw+A9vTzJ8w3gIAjxzFtjbvoPnOTJnj06Y2l+62kFvtyJC6NhJ1nKC44PwDZ7GogoLE3qR46YrNy2HQ8A7vj/K/9IE8XejcNoE/TIDqG18JkcO4O8dnF2WxNOd9CtD9j/yXX1HarTXRANK0CWhEdEE0D7wbob8LWDgAKsyB178WDrk/tBWv+5a/3rntpF5pPfdA59+deUSQAlZMEICGEs9htVo7tjCN+/WoObdmEteh8V5ZPYBChHr74nUjCvDXufMsQYKpXD48+vXG9tTdnTCEc2XGao3FpFOScHxdkMOup3cSHnFpGNuTnserwafKKL+hGMxvo1tCPHg0D6NbQnyAv5y/ml1mYydbUrWw9tZVtqdvYl77vki4zV4MrUf5RRAdEE+0fTZR/FB6mm3iTU4ddG0f0v+sWZZ+8/PUmd22rjwtDkV/DGjm2SAJQOUkAEkJUB9aiQo5s20L8+tUc3f53yRYcAO7ePoTWCsT/1BncNm9DKT4/ONoQEIBH79649epFtm9DjuxK58j2NHIzzg8+1ht01G7sjb22ha3WQpYeSuNUzsWDkxsFetC9kT/dG/rTNswHs8H5rSx51jx2pO1gx6kdxKXFsSNtB3nWvIuuUVCI9Ikk2j+alv4taVarGfW96v9/e3ceHEWZ/w/83T33PZkcM0mYXNxHREBhowKW5CewruK6VSLLF8V1cVGs1fKi3K1dXWtdUGtR11XXPxZx1fLYWsUq19Xi9goISIAkEJKQi9zX3PfM5/fHJANNwiEJyYR8XlVdM3Q/M/M8eZLpN08/3T12R4n6+HviI0StZafDUfsx4KxJ6QnaNCB9cjwM9T2mTQJM45L2go4cgAaJAxBjLNkEfV7UHjqAqv17UXvoAMIBf2KbUqOFPXMcrA4PjPsPQfScnvMjM5mgv+km6IuL4bMXorbchZpD7XC2n369IArInGCCMkeHKlkEe1ocONzowBlHyqBRyHDd+NREIMpNHb4btp5PNBZFtaMahzsOo7S9FKUdpWh0N/Yrp5FrMMUyBdNSp2F66nRMS52GPGMeh6JoJH6NorYzRoo6jsfPTjsXhQ5Im9g/HFkKAJli+Oo+AA5Ag8QBiDGWzCLhMBrLDqN6/15UH9gLn9OR2CZTKJCdZYfNH4b5hyOQd52eXC1otdDPnw998f9DeMo1qDvhQ80PHehqkk6SNmVoYJuSgh6TDPs8Xuyp7kTHWaNDealaLJyUjgWT0lE0PhVaZfJcn6bT34nD7YdxqP0QyrrKcKzrGHyR/nNiNHINplqmYlrqtEQwyjXmcigC4meidVXHb/fRUQl0VgIdJ4DuGuCMi1xKiPJ4CDp7xChtEqDSD0u1OQANEgcgxthoEYtF0VJ1AtX7S1C9vwSO1tOn1kMQYMsch0wSYS47DvWpZiQOXMjl0F59NXTz5yNW+BM0+8yoL+tCc5UjcTsOAFCoZciZZoHSrkOlGMFX9d04UN+N8BlllDIR1+anYOGkdCyclIFJVn1SXek5RjHUuepQ3lmOiq4KVHRV4Fj3Mfgj/n5ltXItplimYHra9MRIUa4xF6JwZUwSHrRoGOipk4aizkqgs+rcp+kDgHEckH5GIEqfHJ93NMTzjDgADRIHIMbYaERE6G5qRPX+vaj6vgRtJ6sk2w2mFGSqdUipbYSpphbyM45xyVJTob/heijmzUdP2jQ01gVRf7RTMokaAmDNM8I22YxuvQzfu9zYXdWJUz3SIGEzquNhaHI6rh+fBpN2ZA+LDCQai6LOVYeKrgqUd8WD0fHu4wOGIp1Ch6mWqZhimYKJKRMxKWUSxpvHQyPXjEDNk1TfLUDODEUdJ+IjSN72gV9zzX3AzzYNaTU4AA0SByDG2JXA1dmBmoP7UHNgH05VHJVMohZlctgsaUj3BmGuqITW6T49OiQIUE+fDu0NNyAwpQitQQvqy3vQ0eCWvL9CLUP2RDM0dh1q5VF83erA3tpuBMKnz9ISBWBWTnx0aP7ENBRmmyCXJedoSjQWRa2zNhGIyrvKcbz7eL8rVwPxidZ2gx2TUiZhYsrE+GKeCLvBzofQzubrjo8QdVb2jhz1BqOih4C5a4b0ozgADRIHIMbYlSYcCKCh/DBqDx1EbelBuDqkd283GM3IVOtgaWqF4Xg1FLEzQozBAF1REYS589GdMg3NLTGcOtaDgDcseQ+dSYnMySkIWBQoiwSxu6EbVe3SwyI6pQyzc1MwL9+CufmpuGqcacTuWXYxIrEITjpPoryzHCd6TqDKUYWqnip0B7oHLK+SqVBgKkCBuQATzBNQYIo/ZuuzORgNAw5Ag8QBiDF2JSMidDefQl3pQZw8dABNx8oko0OCICA1JQ1poShMNbUwtXdJDpcpJ4yH7vr5CE4rQqeYiaaTHjRXOxENS6/PY8nSISXfiDYtsNftwXf1PXD6paFJKRcxy25OBKLZueakmlB9Lp3+TlT1xMNQlaMKJ3pOoMZRM+BoEQAoRSVyTbnIN+Yj33R6yTPmQasYuVuTXGk4AA0SByDG2FgSCvjRWH4EtYcOov7oIelEagCiKCJVb4TF5YPpZD1SPH7I+nYdMhnU06dDNftaeHJno0OwoumkDx2Nbsn9PEVRgLXACKVNgzYl4bDPj+9OOdDpkQYGuShgRrapNxBZcE2eBSZN8s0hGkg0FkWTpwnVjmqcdJ5EjaMGNY4anHSePGcwAgCbzoZ8Yz7yTHnINebGF0MuMvWZkIvJHwaTCQegQeIAxBgby9xdnWgsP4KG8iNoLD/a73CZKIpIVWpg6XLA3NIOsy8AWd+eRBCgmjQJslk/gcs+Cx1kRVOdD67OQL/PMdu00Gdp0aMVUREK4ptWB5pd0nKCAEy1GTE334J5+RZcm29Bml51uZp+WURjUTR7m1HrrJUsda66cx5KAwC5KMc4/TjkGHOQY8hBrjEXOcb4o01r40NqA+AANEgcgBhj7DRnexsay4/EQ1HFUXi6OiXbZTIZLEoNzA43jE2tsPgCUERPHw5T5uWBZs+HI+tq9IjpaG+PwtHa/7o8Kq0cZrseXoMMJymM73rcqOruX258ug5z8y24apwZM7JMmGTTJ8VVqi+FI+BAnasuEYrqXfVocDegwdWAUCx0ztf1haNsQzbsejvshtNLtiF7zJ6hxgFokDgAMcbYwIgIjtZmNJYf7R0hOiK5EGMfk0oDsy8AY0s7TN4A9IEQ+s79Ek0myArnwJt/DRz6XHQFdOg45UfkrDlEgijAlKlF1KJEoxjFAY8Xhzo9wFmXGFLIBEyyGjAjy4QZ40yYkWXE1ExjUk+uvpAYxdDmbUO9ux4NroZ4MHI1oN5dj0Z3IyLnuhhhr3RNOrL0WcjWZyeWLH0WxunHwaazQTHCV2y+XDgADRIHIMYYuzhEhJ6WJjRXHkNTZQWajlegp6WpXzmZKMIcA4xdTpg8Pph8AWhDkUSWkWXbEZxxHTzWGeiRW9HRLcDj6D8CojEpIUtTo1NJqI2EcNDlRUsw3K+cTBQwMUOP6VkmFGYbMSPbhGlZxlExwfpCorEo2nxtaHQ34pT7FBrdjYnllPsU3GH3eV8vCiIytBn9wlHf8wxtxqide8QBaJA4ADHG2KXzOR1orqpEy4ljaK05gdaaKoT8/S8wqBRlMIeiMHb1wOgLwhAIng5FMhliE2fCmzsbDmM+uqNmdDuAs24EDwBQ6RUQLUq41ALqYhGUur2oC4T6jRQJAjA+XY8ZWfFANCPbhOlZRhjUV85oCBHBGXSiydOEU55TaPY0o8nTlFiaPc3nnZANnA5ImbpM6aLPhFVrhU1ng1FpTKqrfffhADRIHIAYY2zoUCyG7pYmtFbHw1BrzQl01J2UnHrfRw4BhlAYercPBn8QhkAIhkAIymgMUVEBT8YUeHNnwWvOg1O0wB1QYKC9mFwlgyJVBY9GRCNFcNTnwwl/ELEB9tm5qVpMzzJiepYJk6wGTLLqYU/RQhSTbwc/WESErkAXTrkHDkfN3uYLHl4D4vdRs2qtsOqs8cfeYGTT2UY0JHEAGiQOQIwxdnlFI2F01NedEYhq0XWqfsBQBACaGKD3+mHwB2Dwx0ORPhgCCUp49Fnw2abCa5sCt9oGZ0SH2ABJR5QJUKSo4NeIaBOiqPIHURkIwCkS6KziaoWIiRkGTLTqE6GoIE2PcSmapL2S9VCIUQxd/i60eFvii6cl8bzV24pWbyt6gj0X9V6JkKS1IkObgQxtBtK16bBqrUjXpsNusMOi5nuBJRUOQIwxNvxi0Sh6WprR0VCLzob63sc6uDoGvpeUCEAfiUHv9iZCkSEQgjISg19rhVtvhy9rWny0SLAgHBt4UrQgF0B6OVwKoJWiqAkG0U5R9MgI4QEmXOem6lCQpsP4DD0K0nQoSNdjfLoOZq1yiH8iySkYDaLN24Y2Xxtava2nH89YdzEh6f+m/h/Wz10/pHXjADRIHIAYYyx5BH1edDbUo7OxDh31dehoqENnQx1C/v6nyAOADIAuFIHWF4AuGIY+GII2GIaM9AhpbPCa7PCnT4BXlwk3jIjRuUd0SCODVyWgXYiiIRRCO2LoEQnuAUaNLDolxqfrUJCmR366DjkWLewpWuRYtEl5Q9jLaaCQ1OHrQLuvHe3+drT72rFq6ircPf3uIf1cDkCDxAGIMcaSGxHB3dmRCEN9jz0tzYhFzz2HRRmJQhcMQRuMQBMKQxOKQBR0gNyCiMoGv9EOvykbXmUaQjjPBRdFIKKRwSUntMeiaA6H4RQJLpHgFAnBszKVUS1HTurpQGS3nH7MNmuglF+5h9WGEwegQeIAxBhjo1MsGoWzow09zU3oaWlCd/Mp9LQ0o6f5FDw9577qMgAIRNCE4sFIG4pAGRUgQg/ILYgqrQhqshHQZ8KvSkVMOP81hqIyAT4F0CPE0B6NwiXGEuHIKRKCAhJnqYkCkGnSYFyKBjkWLTLNGtiMaliNKliNaliNaqTqlFfkpOyhxgFokDgAMcbYlScU8MfDUEsTnO1tcLW3wdnRBmd7K1wdHecdOQIAMRaDNhSBJhSBMipCBi0gGkGKVEQVaQipbAjqbAjLdResS1QGeORAF0XhAMEjxhe30PsoSucfyUUBGQYVMnqDkc2oRoZR3RuUesOSSQ2DSp6Up6cPFw5Ag8QBiDHGxpZYLApvTw+c7a1wtrfFA1JHW+K5u7sTA55vfxZlOAJVJNYbkJQQBB0gMyAmtyCizEBYnYmwMuOiQkpEBDwiwYEYPEI8FHlFglcgeEX0PkqDkkYhk4wc2UxqZBhUiedWgxoZRtWovkr2+XAAGiQOQIwxxs4UjYTh6uyQBCNXRzs83V1wd3fC092FaLj/FakHIhBBESXIY7J4SIIaEHWAzIioPBVRZRpiihQIghYQVBcMS1GB4BMIrrOCkVcg+PoCkwD4RUIYAATArFXAalDDalLDalAhw6hCml6FVL0KaTolUvUqpOqVSNEqIRtFh95+zP57dF7rmjHGGBtGMrkCKbYspNiyBtxORPC7XfFA1BUPRJ7uTnh6euDt6YLH0QNvTzd8TgdIEBCSCwiBAAR7FyeAZiAKwN+7ABAIkMdEyEgOQVBDEDQgUQeSGxCVmwCZHhA00Alq6EUNIGgAnPswWJRiCAox+J2Aty0AvxiEQyC0CAS/QAiIgL/3uV8AAiJBo1XAolciVadCik4Bi06FVJ0Slt7FrFUgRRsPS2adYtQchuMAxBhjjA2SIAjQGk3QGk3IyCs4Z7loJAKf0wGf0wGvswc+hwNepwM+R48kJHkdPQj5fSABCMtiCCMEIATAFX+jSO8yUF1IgAg5RKgAQd0bmPSAqIMgqKEUNFAJaqSIGqA3VMVHmgY+E40chIAQhl8IwycCfgGoEgmB3pCUCEwiEBAIIRmg1ilg0imRolXArI0/pmiVp5/rlJiYoUdBun5QP/fB4ADEGGOMDROZXA5DahoMqWkXLBsJhxNhyedywOdwwO9xI+B29T664fe44o9uF/xuN2LRCEggRBFGFGEAHiDWGc9O50OACDkEKCEIakDUADI9qDc0KUQNlIIaJkETH4kS46EJUAw82uMAwhRCUAjALxC8ooBGUcCJ3kNxAYFQdE0m1q+ceQk/xaHBAYgxxhhLQnKFAsa0dBjT0i+qPBEhHAycDkTnCkseN/wuFwKueKAKBQKAAMQSw0o+IIb4csEPBUQoAEEJQVABohokauPPBRXUvYul99/x9WpAUCLlhzKAAxBjjDHGBkMQBCjVGijVGhjTMy76ddFIBEGvB35JSJKOLPk9LgQcDvhdTvg9bgT9PsRisd7gFAYQBsgbn8MUvbjPVSgmAlh5KU0dEhyAGGOMsTFMJpdDazJDazJf9GuICJFgEEGfF0GfFwGvF0GfB0GvF0GfD0GvJ77N60XA60GwdzQqvt6HUDCA7KsnXL5GXQQOQIwxxhj7UQRBgEKthkKtht6SeknvQbGLOcZ2+fDNRxhjjDE27ARxZCMIByDGGGOMjTkcgBhjjDE25nAAYowxxtiYwwGIMcYYY2MOByDGGGOMjTkcgBhjjDE25nAAYowxxtiYwwGIMcYYY2MOByDGGGOMjTkcgBhjjDE25nAAYowxxtiYwwGIMcYYY2MOByDGGGOMjTnyka5AMiIiAIDL5RrhmjDGGGPsYvXtt/v24+fDAWgAbrcbAGC320e4Jowxxhj7sdxuN0wm03nLCHQxMWmMicViaG5uhsFggCAIQ/reLpcLdrsdjY2NMBqNQ/reyYDbN/pd6W280tsHXPlt5PaNfperjUQEt9uNrKwsiOL5Z/nwCNAARFHEuHHjLutnGI3GK/YXG+D2XQmu9DZe6e0Drvw2cvtGv8vRxguN/PThSdCMMcYYG3M4ADHGGGNszOEANMxUKhWefvppqFSqka7KZcHtG/2u9DZe6e0Drvw2cvtGv2RoI0+CZowxxtiYwyNAjDHGGBtzOAAxxhhjbMzhAMQYY4yxMYcDEGOMMcbGHA5Aw+i1115DXl4e1Go15s2bh++//36kq3RRNmzYgGuvvRYGgwEZGRm4/fbbUVlZKSlz4403QhAEybJ27VpJmYaGBtxyyy3QarXIyMjAE088gUgkMpxNGdAzzzzTr+5TpkxJbA8EAli3bh1SU1Oh1+vxi1/8Am1tbZL3SNa29cnLy+vXRkEQsG7dOgCjr/+++uor3HrrrcjKyoIgCNi6datkOxHhj3/8IzIzM6HRaFBcXIyqqipJme7ubqxcuRJGoxFmsxn33XcfPB6PpMyRI0cwf/58qNVq2O12vPDCC5e7aQnna2M4HMb69etRWFgInU6HrKws3H333Whubpa8x0D9vnHjRkmZkWrjhfpw9erV/eq+ZMkSSZlk7sMLtW+gv0dBEPDiiy8myiRz/13MfmGovjt3796N2bNnQ6VSYcKECdiyZcvQNILYsPjggw9IqVTS5s2bqby8nNasWUNms5na2tpGumoXtHjxYnrrrbeorKyMSktL6ac//Snl5OSQx+NJlFm4cCGtWbOGWlpaEovT6Uxsj0QiNGPGDCouLqZDhw7R559/TmlpafTUU0+NRJMknn76aZo+fbqk7h0dHYnta9euJbvdTjt27KADBw7QT37yE7ruuusS25O5bX3a29sl7du2bRsBoF27dhHR6Ou/zz//nH7/+9/Txx9/TADok08+kWzfuHEjmUwm2rp1Kx0+fJhuu+02ys/PJ7/fnyizZMkSmjlzJu3du5e+/vprmjBhAq1YsSKx3el0ktVqpZUrV1JZWRm9//77pNFo6M033xzxNjocDiouLqYPP/yQjh8/TiUlJTR37lyaM2eO5D1yc3Pp2WeflfTrmX+3I9nGC/XhPffcQ0uWLJHUvbu7W1ImmfvwQu07s10tLS20efNmEgSBampqEmWSuf8uZr8wFN+dJ0+eJK1WS48++ihVVFTQq6++SjKZjL744otBt4ED0DCZO3curVu3LvHvaDRKWVlZtGHDhhGs1aVpb28nALRnz57EuoULF9LDDz98ztd8/vnnJIoitba2Jta98cYbZDQaKRgMXs7qXtDTTz9NM2fOHHCbw+EghUJB//73vxPrjh07RgCopKSEiJK7befy8MMP0/jx4ykWixHR6O6/s3cusViMbDYbvfjii4l1DoeDVCoVvf/++0REVFFRQQBo//79iTL/+9//SBAEampqIiKi119/nVJSUiTtW79+PU2ePPkyt6i/gXagZ/v+++8JANXX1yfW5ebm0ksvvXTO1yRLG88VgJYtW3bO14ymPryY/lu2bBnddNNNknWjpf+I+u8Xhuq788knn6Tp06dLPmv58uW0ePHiQdeZD4ENg1AohIMHD6K4uDixThRFFBcXo6SkZARrdmmcTicAwGKxSNa/9957SEtLw4wZM/DUU0/B5/MltpWUlKCwsBBWqzWxbvHixXC5XCgvLx+eip9HVVUVsrKyUFBQgJUrV6KhoQEAcPDgQYTDYUnfTZkyBTk5OYm+S/a2nS0UCuHdd9/Fr371K8nNfkdz/52ptrYWra2tkj4zmUyYN2+epM/MZjOuueaaRJni4mKIooh9+/YlyixYsABKpTJRZvHixaisrERPT88wtebiOZ1OCIIAs9ksWb9x40akpqZi1qxZePHFFyWHF5K9jbt370ZGRgYmT56MBx54AF1dXYltV1IftrW14b///S/uu+++fttGS/+dvV8Yqu/OkpISyXv0lRmKfSffDHUYdHZ2IhqNSjoZAKxWK44fPz5Ctbo0sVgMjzzyCK6//nrMmDEjsf6Xv/wlcnNzkZWVhSNHjmD9+vWorKzExx9/DABobW0dsP1920bSvHnzsGXLFkyePBktLS3405/+hPnz56OsrAytra1QKpX9dipWqzVR72Ru20C2bt0Kh8OB1atXJ9aN5v47W199BqrvmX2WkZEh2S6Xy2GxWCRl8vPz+71H37aUlJTLUv9LEQgEsH79eqxYsUJyY8nf/va3mD17NiwWC7777js89dRTaGlpwaZNmwAkdxuXLFmCO+64A/n5+aipqcHvfvc7LF26FCUlJZDJZFdUH7799tswGAy44447JOtHS/8NtF8Yqu/Oc5VxuVzw+/3QaDSXXG8OQOxHWbduHcrKyvDNN99I1t9///2J54WFhcjMzMSiRYtQU1OD8ePHD3c1f5SlS5cmnl911VWYN28ecnNz8dFHHw3qjytZ/fOf/8TSpUuRlZWVWDea+2+sC4fDuPPOO0FEeOONNyTbHn300cTzq666CkqlEr/5zW+wYcOGpL/Nwl133ZV4XlhYiKuuugrjx4/H7t27sWjRohGs2dDbvHkzVq5cCbVaLVk/WvrvXPuFZMeHwIZBWloaZDJZv9nvbW1tsNlsI1SrH++hhx7CZ599hl27dmHcuHHnLTtv3jwAQHV1NQDAZrMN2P6+bcnEbDZj0qRJqK6uhs1mQygUgsPhkJQ5s+9GU9vq6+uxfft2/PrXvz5vudHcf331Od/fm81mQ3t7u2R7JBJBd3f3qOrXvvBTX1+Pbdu2SUZ/BjJv3jxEIhHU1dUBGB1t7FNQUIC0tDTJ7+SV0Idff/01KisrL/g3CSRn/51rvzBU353nKmM0Ggf9H1QOQMNAqVRizpw52LFjR2JdLBbDjh07UFRUNII1uzhEhIceegiffPIJdu7c2W/IdSClpaUAgMzMTABAUVERjh49KvnC6vvCnjZt2mWp96XyeDyoqalBZmYm5syZA4VCIem7yspKNDQ0JPpuNLXtrbfeQkZGBm655ZbzlhvN/Zefnw+bzSbpM5fLhX379kn6zOFw4ODBg4kyO3fuRCwWS4S/oqIifPXVVwiHw4ky27Ztw+TJk5Pi0Elf+KmqqsL27duRmpp6wdeUlpZCFMXEoaNkb+OZTp06ha6uLsnv5GjvQyA+IjtnzhzMnDnzgmWTqf8utF8Yqu/OoqIiyXv0lRmSfeegp1Gzi/LBBx+QSqWiLVu2UEVFBd1///1kNpsls9+T1QMPPEAmk4l2794tOR3T5/MREVF1dTU9++yzdODAAaqtraVPP/2UCgoKaMGCBYn36Dvd8eabb6bS0lL64osvKD09PSlOFX/sscdo9+7dVFtbS99++y0VFxdTWloatbe3E1H8VM6cnBzauXMnHThwgIqKiqioqCjx+mRu25mi0Sjl5OTQ+vXrJetHY/+53W46dOgQHTp0iADQpk2b6NChQ4kzoDZu3Ehms5k+/fRTOnLkCC1btmzA0+BnzZpF+/bto2+++YYmTpwoOYXa4XCQ1WqlVatWUVlZGX3wwQek1WqH7TT487UxFArRbbfdRuPGjaPS0lLJ32Xf2TPfffcdvfTSS1RaWko1NTX07rvvUnp6Ot19991J0cbztc/tdtPjjz9OJSUlVFtbS9u3b6fZs2fTxIkTKRAIJN4jmfvwQr+jRPHT2LVaLb3xxhv9Xp/s/Xeh/QLR0Hx39p0G/8QTT9CxY8fotdde49PgR6NXX32VcnJySKlU0ty5c2nv3r0jXaWLAmDA5a233iIiooaGBlqwYAFZLBZSqVQ0YcIEeuKJJyTXkSEiqquro6VLl5JGo6G0tDR67LHHKBwOj0CLpJYvX06ZmZmkVCopOzubli9fTtXV1Yntfr+fHnzwQUpJSSGtVks///nPqaWlRfIeydq2M3355ZcEgCorKyXrR2P/7dq1a8DfyXvuuYeI4qfC/+EPfyCr1UoqlYoWLVrUr91dXV20YsUK0uv1ZDQa6d577yW32y0pc/jwYbrhhhtIpVJRdnY2bdy4cbiaeN421tbWnvPvsu/aTgcPHqR58+aRyWQitVpNU6dOpb/85S+SADGSbTxf+3w+H918882Unp5OCoWCcnNzac2aNf3+w5jMfXih31EiojfffJM0Gg05HI5+r0/2/rvQfoFo6L47d+3aRVdffTUplUoqKCiQfMZgCL0NYYwxxhgbM3gOEGOMMcbGHA5AjDHGGBtzOAAxxhhjbMzhAMQYY4yxMYcDEGOMMcbGHA5AjDHGGBtzOAAxxhhjbMzhAMQYY4yxMYcDEGOMDSAvLw8vv/zySFeDMXaZcABijI241atX4/bbbwcA3HjjjXjkkUeG7bO3bNkCs9ncb/3+/ftx//33D1s9GGPDSz7SFWCMscshFApBqVRe8uvT09OHsDaMsWTDI0CMsaSxevVq7NmzB6+88goEQYAgCKirqwMAlJWVYenSpdDr9bBarVi1ahU6OzsTr73xxhvx0EMP4ZFHHkFaWhoWL14MANi0aRMKCwuh0+lgt9vx4IMPwuPxAAB2796Ne++9F06nM/F5zzzzDID+h8AaGhqwbNky6PV6GI1G3HnnnWhra0tsf+aZZ3D11VfjnXfeQV5eHkwmE+666y643e7L+0NjjF0SDkCMsaTxyiuvoKioCGvWrEFLSwtaWlpgt9vhcDhw0003YdasWThw4AC++OILtLW14c4775S8/u2334ZSqcS3336Lf/zjHwAAURTxt7/9DeXl5Xj77bexc+dOPPnkkwCA6667Di+//DKMRmPi8x5//PF+9YrFYli2bBm6u7uxZ88ebNu2DSdPnsTy5csl5WpqarB161Z89tln+Oyzz7Bnzx5s3LjxMv20GGODwYfAGGNJw2QyQalUQqvVwmazJdb//e9/x6xZs/CXv/wlsW7z5s2w2+04ceIEJk2aBACYOHEiXnjhBcl7njmfKC8vD3/+85+xdu1avP7661AqlTCZTBAEQfJ5Z9uxYweOHj2K2tpa2O12AMC//vUvTJ8+Hfv378e1114LIB6UtmzZAoPBAABYtWoVduzYgeeee25wPxjG2JDjESDGWNI7fPgwdu3aBb1en1imTJkCID7q0mfOnDn9Xrt9+3YsWrQI2dnZMBgMWLVqFbq6uuDz+S76848dOwa73Z4IPwAwbdo0mM1mHDt2LLEuLy8vEX4AIDMzE+3t7T+qrYyx4cEjQIyxpOfxeHDrrbfi+eef77ctMzMz8Vyn00m21dXV4Wc/+xkeeOABPPfcc7BYLPjmm29w3333IRQKQavVDmk9FQqF5N+CICAWiw3pZzDGhgYHIMZYUlEqlYhGo5J1s2fPxn/+8x/k5eVBLr/4r62DBw8iFovhr3/9K0QxPuD90UcfXfDzzjZ16lQ0NjaisbExMQpUUVEBh8OBadOmXXR9GGPJgw+BMcaSSl5eHvbt24e6ujp0dnYiFoth3bp16O7uxooVK7B//37U1NTgyy+/xL333nve8DJhwgSEw2G8+uqrOHnyJN55553E5OgzP8/j8WDHjh3o7Owc8NBYcXExCgsLsXLlSvzwww/4/vvvcffdd2PhwoW45pprhvxnwBi7/DgAMcaSyuOPPw6ZTIZp06YhPT0dDQ0NyMrKwrfffotoNIqbb74ZhYWFeOSRR2A2mxMjOwOZOXMmNm3ahOeffx4zZszAe++9hw0bNkjKXHfddVi7di2WL1+O9PT0fpOogfihrE8//RQpKSlYsGABiouLUVBQgA8//HDI288YGx4CEdFIV4IxxhhjbDjxCBBjjDHGxhwOQIwxxhgbczgAMcYYY2zM4QDEGGOMsTGHAxBjjDHGxhwOQIwxxhgbczgAMcYYY2zM4QDEGGOMsTGHAxBjjDHGxhwOQIwxxhgbczgAMcYYY2zM+f8LpqL+KQmmLQAAAABJRU5ErkJggg==" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# use vvag to get the losses and gradients with different random circuit instances\n", + "QAOA_vvag = K.jit(\n", + " K.vvag(QAOAansatz, argnums=0, vectorized_argnums=0), static_argnums=(1, 2, 3)\n", + ")\n", + "\n", + "params_easy = K.implicit_randn(\n", + " shape=[ncircuits, 2 * nlayers], stddev=0.1\n", + ") # initial parameters\n", + "if type(K).__name__ == \"JaxBackend\":\n", + " opt = K.optimizer(optax.adam(1e-2))\n", + "else:\n", + " opt = K.optimizer(tf.keras.optimizers.Adam(1e-2))\n", + "\n", + "list_of_loss = [[] for i in range(ncircuits)]\n", + "\n", + "for i in range(2000):\n", + " loss, grads = QAOA_vvag(params_easy, easy_graph)\n", + " params_easy = opt.update(grads, params_easy) # gradient descent\n", + "\n", + " # visualise the progress\n", + " clear_output(wait=True)\n", + " list_of_loss = np.hstack((list_of_loss, K.numpy(loss)[:, np.newaxis]))\n", + " plt.xlabel(\"Iteration\")\n", + " plt.ylabel(\"Cost\")\n", + " for index in range(ncircuits):\n", + " plt.plot(range(i + 1), list_of_loss[index])\n", + " legend = [f\"circuit {leg}\" for leg in range(ncircuits)]\n", + " plt.legend(legend)\n", + " plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "98a6b152", + "metadata": {}, + "source": [ + "### Results" + ] + }, + { + "cell_type": "markdown", + "id": "fc1c257d", + "metadata": {}, + "source": [ + "After inputting the optimized parameters back to the ansatz circuit, we can perform the projective measurement on the output quantum state to get the solution. Here we directly use the bit string with the maximum probability as the solution since we know all information of the probability distribution of the output quantum state, but which is not feasible in the experiment." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "8c5df93e", + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + }, + "ExecuteTime": { + "end_time": "2023-07-03T11:48:26.692908100Z", + "start_time": "2023-07-03T11:47:45.326665300Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Circuit #0\n", + "cost: 0.014918745495378971\n", + "max prob: 0.2869008183479309\n", + "bit strings: ['111111000000']\n", + "\n", + "Circuit #1\n", + "cost: 0.030193958431482315\n", + "max prob: 0.21499991416931152\n", + "bit strings: ['111111000000']\n", + "\n", + "Circuit #2\n", + "cost: 0.021412445232272148\n", + "max prob: 0.24743150174617767\n", + "bit strings: ['000000111111']\n", + "\n", + "Circuit #3\n", + "cost: 0.013799840584397316\n", + "max prob: 0.2941778600215912\n", + "bit strings: ['000000111111']\n", + "\n", + "Circuit #4\n", + "cost: 0.014260157942771912\n", + "max prob: 0.29104718565940857\n", + "bit strings: ['111111000000']\n", + "\n", + "Circuit #5\n", + "cost: 0.013322753831744194\n", + "max prob: 0.2968374788761139\n", + "bit strings: ['111111000000']\n", + "\n" + ] + } + ], + "source": [ + "# print QAOA results\n", + "for num_circuit in range(ncircuits):\n", + " print(f\"Circuit #{num_circuit}\")\n", + " c = QAOAansatz(params=params_easy[num_circuit], g=easy_graph, return_circuit=True)\n", + " loss = QAOAansatz(params=params_easy[num_circuit], g=easy_graph)\n", + "\n", + " # find the states with max probabilities\n", + " probs = K.numpy(c.probability())\n", + " max_prob = max(probs)\n", + " index = np.where(probs == max_prob)[0]\n", + " states = []\n", + " for i in index:\n", + " states.append(f\"{bin(i)[2:]:0>{c._nqubits}}\")\n", + "\n", + " print(f\"cost: {K.numpy(loss)}\\nmax prob: {max_prob}\\nbit strings: {states}\\n\")" + ] + }, + { + "cell_type": "markdown", + "id": "4ae99ab9", + "metadata": {}, + "source": [ + "## Classical Method" + ] + }, + { + "cell_type": "markdown", + "id": "720dd1a4", + "metadata": {}, + "source": [ + "Here we use two classical methods. The first is the brutal force method (BF), which is to check all bit string one-by-one and need exponential time, thus the obtained solution is guaranteed to be correct." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "2115bb6d", + "metadata": { + "ExecuteTime": { + "end_time": "2023-07-03T11:48:26.693910800Z", + "start_time": "2023-07-03T11:48:26.692908100Z" + } + }, + "outputs": [], + "source": [ + "def b2s(bit):\n", + " return 1 - 2 * int(bit)\n", + "\n", + "\n", + "def energy(cfg, graph, normalize=True):\n", + " E = 0.25\n", + " for a, b in graph.edges:\n", + " E += cfg[a] * cfg[b] * graph[a][b][\"weight\"] * factor\n", + " return E if normalize else E / factor\n", + "\n", + "\n", + "def brutal_force(graph):\n", + " num_nodes = graph.number_of_nodes()\n", + " min_cost, best_case = 1.0, []\n", + " for i in range(2**num_nodes):\n", + " case = f\"{bin(i)[2:]:0>{num_nodes}}\"\n", + "\n", + " cost = energy(list(map(b2s, case)), graph)\n", + "\n", + " gap = min_cost - cost\n", + " if gap > 1e-6:\n", + " min_cost = cost\n", + " best_case = [case]\n", + " elif abs(gap) < 1e-6:\n", + " best_case.append(case)\n", + "\n", + " return best_case, min_cost" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "b0cdc04f", + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + }, + "ExecuteTime": { + "end_time": "2023-07-03T11:48:27.165348700Z", + "start_time": "2023-07-03T11:48:26.692908100Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "cost: 0.000\n", + "bit string: ['000000111111', '111111000000']\n" + ] + }, + { + "data": { + "text/plain": "
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" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# print BF results\n", + "bf_best_cases, bf_best = brutal_force(easy_graph)\n", + "print(f\"cost: {bf_best:.3f}\\nbit string: {bf_best_cases}\")\n", + "\n", + "# plot NetworkX graph\n", + "colors = [\"r\" if bf_best_cases[0][i] == \"0\" else \"c\" for i in easy_graph.nodes]\n", + "nx.draw_networkx(easy_graph, with_labels=True, node_color=colors, pos=pos_easy)\n", + "ax = plt.gca()\n", + "ax.set_facecolor(\"w\")" + ] + }, + { + "cell_type": "markdown", + "id": "20324164", + "metadata": {}, + "source": [ + "Another method is the simulated annealing method (SA), which is an approximation method that can be done in polynomial time, so the obtained solution has only a certain probability of being correct." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "e1551fb4", + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + }, + "ExecuteTime": { + "end_time": "2023-07-03T11:48:27.165348700Z", + "start_time": "2023-07-03T11:48:27.164345100Z" + } + }, + "outputs": [], + "source": [ + "def sim_annealing(graph, t_max: int, T: float):\n", + " num_nodes = graph.number_of_nodes()\n", + " state = np.random.randint(0, 2, num_nodes)\n", + " next_state = state.copy()\n", + " E = energy(1 - 2 * state, graph, normalize=False)\n", + " t = 0\n", + " while t < t_max:\n", + " temper = (1 - t / t_max) * T\n", + " flip_idx = np.random.randint(num_nodes)\n", + " next_state[flip_idx] = 1 - next_state[flip_idx]\n", + " next_E = energy(1 - 2 * next_state, graph, normalize=False)\n", + " if next_E <= E or np.exp(-(next_E - E) / temper) > np.random.rand():\n", + " state[flip_idx] = 1 - state[flip_idx]\n", + " E = next_E\n", + " else:\n", + " next_state[flip_idx] = 1 - next_state[flip_idx]\n", + " t += 1\n", + " return \"\".join(map(str, state.tolist())), E" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "04596ec1", + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + }, + "ExecuteTime": { + "end_time": "2023-07-03T11:48:31.015863400Z", + "start_time": "2023-07-03T11:48:27.165348700Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "cost: 0.000\n", + "prob: 0.910\n", + "bit string: ['000000111111', '111111000000']\n" + ] + } + ], + "source": [ + "# print SA results\n", + "sa_best_cases, sa_best, n_exp = [], float(\"inf\"), 100\n", + "for _ in range(n_exp):\n", + " sa_case, sa_cost = sim_annealing(easy_graph, 200, 1)\n", + " gap = sa_best - sa_cost\n", + " if gap > 1e-6:\n", + " sa_best = sa_cost\n", + " sa_best_cases = [sa_case]\n", + " elif abs(gap) < 1e-6:\n", + " sa_best_cases.append(sa_case)\n", + "sa_prob = len(sa_best_cases) / n_exp\n", + "sa_best_cases = list(set(sa_best_cases))\n", + "print(f\"cost: {sa_best:.3f}\\nprob: {sa_prob:.3f}\\nbit string: {sa_best_cases}\")" + ] + }, + { + "cell_type": "markdown", + "id": "e9b8619b", + "metadata": {}, + "source": [ + "## Hard Problem" + ] + }, + { + "cell_type": "markdown", + "id": "9f8cb1da", + "metadata": {}, + "source": [ + "We call the above problem an easy problem, because the classical simulated annealing method has a high probability to obtain the correct solution. Now let's define another relatively hard problem." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "b0a1f778", + "metadata": { + "ExecuteTime": { + "end_time": "2023-07-03T11:48:31.522735600Z", + "start_time": "2023-07-03T11:48:30.976530700Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": "
", + "image/png": 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" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# a hard graph instance\n", + "hard_clauses = [\n", + " [4, 1, 7],\n", + " [5, 11, 8],\n", + " [4, 1, 8],\n", + " [4, 11, 8],\n", + " [4, 1, 10],\n", + " [5, 11, 8],\n", + " [4, 1, 8],\n", + " [1, 11, 8],\n", + " [4, 1, 7],\n", + " [0, 11, 8],\n", + " [4, 1, 10],\n", + " [4, 11, 8],\n", + " [5, 0, 10],\n", + " [0, 6, 7],\n", + " [5, 0, 11],\n", + " [0, 6, 7],\n", + " [5, 0, 9],\n", + " [3, 6, 7],\n", + " [5, 0, 8],\n", + " [5, 6, 7],\n", + " [5, 0, 10],\n", + " [3, 6, 7],\n", + " [5, 0, 10],\n", + " [1, 6, 7],\n", + " [2, 4, 6],\n", + " [1, 8, 11],\n", + " [2, 4, 6],\n", + " [2, 8, 11],\n", + " [2, 4, 9],\n", + " [5, 8, 11],\n", + " [2, 4, 10],\n", + " [2, 8, 11],\n", + " [2, 4, 10],\n", + " [4, 8, 11],\n", + " [2, 4, 8],\n", + " [4, 8, 11],\n", + " [3, 0, 9],\n", + " [5, 11, 7],\n", + " [3, 0, 10],\n", + " [2, 11, 7],\n", + " [3, 0, 9],\n", + " [0, 11, 7],\n", + " [3, 0, 9],\n", + " [5, 11, 7],\n", + " [3, 0, 10],\n", + " [3, 11, 7],\n", + " [3, 0, 7],\n", + " [4, 11, 7],\n", + " [5, 0, 10],\n", + " [4, 0, 10],\n", + " [2, 5, 6],\n", + " [2, 11, 10],\n", + " [2, 6, 10],\n", + " [2, 4, 9],\n", + " [0, 9, 10],\n", + " [3, 0, 7],\n", + " [2, 5, 6],\n", + " [1, 10, 9],\n", + " [1, 4, 11],\n", + " [5, 10, 11],\n", + " [0, 4, 8],\n", + " [0, 9, 8],\n", + " [2, 11, 10],\n", + " [2, 8, 6],\n", + " [3, 6, 7],\n", + " [0, 8, 10],\n", + " [4, 0, 9],\n", + " [3, 5, 8],\n", + " [5, 11, 10],\n", + " [2, 11, 10],\n", + " [4, 11, 8],\n", + " [1, 3, 11],\n", + "]\n", + "factor = 1 / len(hard_clauses) / 4\n", + "\n", + "# convert to a NetworkX graph\n", + "hard_graph = nx.Graph()\n", + "for i, j, k in hard_clauses:\n", + " hard_graph.add_edge(i, j, weight=0)\n", + " hard_graph.add_edge(j, k, weight=0)\n", + " hard_graph.add_edge(k, i, weight=0)\n", + "for i, j, k in hard_clauses:\n", + " hard_graph[i][j][\"weight\"] += 1\n", + " hard_graph[j][k][\"weight\"] += 1\n", + " hard_graph[k][i][\"weight\"] += 1\n", + "pos_hard = nx.spring_layout(hard_graph)\n", + "nx.draw_networkx(hard_graph, with_labels=True, pos=pos_hard)\n", + "ax = plt.gca()\n", + "ax.set_facecolor(\"w\")" + ] + }, + { + "cell_type": "markdown", + "id": "d37be898", + "metadata": {}, + "source": [ + "We first solve this problem by two classical methods." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "f22b5956", + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + }, + "ExecuteTime": { + "end_time": "2023-07-03T11:48:31.523763100Z", + "start_time": "2023-07-03T11:48:31.070473700Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "cost: 0.000\n", + "bit string: ['000000111111', '111111000000']\n" + ] + }, + { + "data": { + "text/plain": "
", + "image/png": 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oV68eypUrV6DtoLi4OPTt2xccDgfVqlXDvXv3spxPTU3FsmXLYGtrCw6Hg7Zt2+JBIUbAsLCUZORdv1lX7ZKAAvHyTkTUkIg6E9FhIkokomZE+WaaE0skFB0dLcvSx1IySU1NpcDAQNLV1aWtW7dmS67EMAytWrWK2rRpQ0ZGRnmO5eDgQAzDUFRUVJbjenp6FBISQsuXL6fJkyfTq1evaMGCBUrLrKenR4sXL6aLFy9SYmIiValShcaMGSPLKSESiah379704sULWr58OV27do1cXFyoTZs29ECajpuFhaVAsMpAScDERKEogp9pTUQ3iOh5Pu1eJySQtbU1aWpqkqOjIzVs2JC6d+9OkydPpo0bN9L58+cpMjJSVqGPpfgBgEJCQujRo0e0d+9eMjY2ztYmIiKCXr16Rb169cp3PGkyoDdv3mQ7N3DgQMrIyKBz585RSEiILESxINSqVYtu375NY8eOpbCwMHJ1daVz587JzguFQgoODqbnz5/TqlWr6ObNm1S5cmUKDAyke/fuFWhuFpY/HlWaGVjUxOXLSkUSgAjz//MfuJaXAyGPh29Nm+Lw4cNYvHgxhg8fjjZt2qBatWowMzPL4kjI4/FgZ2cHb29vdO7cGePGjcOaNWtw+vRpvHz5ko0eKEKke/gbN27MtU2bNm1QoUIFuZw+U1NTweFwsGrVqhzP9+7dG6ampoiOjoaJiQk6deqktOy/8vjxY9SuXRtEhJ49e+L79+/Z2qSnp2Pt2rUoU6YMiAgtWrTA7du3VSYDC8vvAJt06HciOZlIXz9P68BnIjL75VgGEdUgoif/ndfJpa+EiCYYGFBcp04UEBBAderUIf5P9QqSk5Pp3bt3FBkZSW/fvs328+PHjyT9GHE4HLK0tCR7e3uys7OT/ZT+bmtrS5qamkq/FSw5c+XKFfL29qZevXrRokWLcmzz6dMnsra2prCwMBo4cKBc49rY2FCXLl1yzCfw6tUrKleuHC1evJj4fD4FBwfTpUuXqFatWgW6FikMw9CKFSto5MiRpK2tTYsXL6ZWrVplS4MsFotpy5YtNGXKFHr58iU1a9aMxo8fT1WqVFGJHCwsJRk26dDvRocORLt25aoQBBBRPBHVJSIrIoohoi2UmWxoDhENyWNohsejMV260ObwcHr//j0ZGRlRs2bNKCAggBo1apTv4p2WlkZRUVG5Kgvv37/P4otgbm6eRVH49aeOTm5qC0tOxMTEUJUqVcjBwYHOnDlDQqEwx3azZs2icePG0YcPH/L1F5BSt25dsrGxoS1btuR4vn379nTt2jV68uQJ1a5dmwDQ9evXVVoI6v3799SvXz86cOAAtWjRgpYsWUJWOSTIEovFtG3bNpoyZQo9f/6c/P39afz48eTp6akyWVhYShqsMvC7cekSkZdXrqe3E9EaInpARLFEpEuZ2Qf7E1HzvMbl84natiXasoUA0M2bN2nfvn20b98+evr0KWlpaVHjxo0pICCA/P39ydDQUGHRxWIxRUdH56goREZG0rt372QZC4kyUxTnpSz8mjr3TyYjI4MaNGhAL168oNu3b5OFhUWO7RiGofLly1ONGjVo06ZNco/fuXNnevnyJV2+fDnH83fu3CEPDw/aunUr2dvbU61atWjFihUUHJxrAmylAEB79+6lfv36UXJyMs2YMYN69eqVY7pqiURC27dvp8mTJ9OzZ8/Iz8+Pxo8fT9WrV1epTCwsJQE2A+HvBsMAzZvnWqhImRdDBGhoALlkkXvy5AmmTZsGT09PEBH4fD7++usvLFmyBNHR0Sq7NLFYjPfv3+PixYvYsmULpk6diuDgYDRq1Ajly5eHhoZGFr8FfX19VK5cGc2bN0f//v0xZ84c7N69Gzdv3sSXL1/+qCRIAwcOBJ/Px8WLF/Nsd/r0aRCRrPCQvIwbNw6lSpXKs42vry9cXV3BMAw6d+4MY2NjfPv2TaF55OXbt2/o2bMniAi1a9fG48ePc20rFouxdetWODs7g4jg6+uLy5cvq0UuFpbiCptn4HckJgbQ11c6NXFOry/jx8s1dVRUFBYvXowGDRqAx+OBiFC9enXMmDEDz549U+tlS1MjX716FTt27MDMmTMREhKCJk2aoGLFitDW1s6iLGhra6NChQpo0qQJ+vTpg5kzZ2L79u24evXqb5UxcfPmzSAiLF68ON+2QUFBcHJyUvja161bByJCcnJyrm0iIiJkyYc+fPgAXV1d9OvXT6F5FOXs2bMoW7YshEIhJkyYgNTU1FzbisVibN++HRUrVgQRoWHDhrhw4YJa5WNhKS6wysDvypkzmQmICqgQMBwO9ujqwszEBFevXlVIhNjYWGzYsAEtW7aEpqYmiAgVKlTAmDFjcPPmzUJfbKVlkW/evIk9e/Zgzpw5GDBgAJo3bw5XV1fo6+tnURY0NDRQrlw5NGrUCD179sTUqVOxefNmXLx4EVFRUTkm6ilu3L17F5qamujSpUu+7/fnz58hEAgw95f6E/IgXejzSgfMMAyqV68uS108e/ZscLlc3L9/X+H5FCElJQWjR48Gn89HhQoV8qyzAAASiQS7du2Ci4sLiAj169fHuXPn1CojC0tRwyoDvzOnTgFaWkptGTAcDkCEay4u+BITg9q1a0NDQwN79uxRSpSkpCTs3bsXnTt3hqGhIYgINjY26N+/P86cOYOMjAwVX7xyfP/+HXfv3sWBAwewYMECDBkyBK1atUKVKlVgbGycRVkQCAQoXbo06tWrh27dumHChAlYv349IiIi8ObNmyK/ptjYWDg4OMDd3T3PJ3Yps2bNgkgkwtevXxWe6+3btyAiHD16NM92e/fuBRHh8uXLSEtLQ/ny5eHt7V0oiuG9e/dQrVo1cDgc9O3bN9/7lEQiwZ49e+Dq6goigo+PDyIiItQuJwtLUcAqA787b94APj6ZizyPJ58iwOUCBgY41LEjiAi7d+9GSkoKgoKCwOFwMGfOnALdvNPT03Hq1Cn07dsXVlZWICIYGxuja9euOHDggFwLV1GRkJCAhw8f4siRI1iyZAlGjBiBtm3bonr16jA3N8+iLHC5XNja2qJOnTro1KkT/v33X6xevRonT57Eixcv8jRZFxSxWAxfX18YGRnhzZs3+bZnGAaOjo74+++/lZ6Pz+dj6dKlebaTSCQoX748WrRoAQA4fvw4iAg7duxQal5FEYvFmD9/PrS1tWFlZYWDBw/m20cikWDfvn1wd3cHEaFu3bo4ffr0b7ONxMICsMrAnwHDALt3I6NWrf8v+tItBA4HDJ8P8X/HP3O5OFilCvD5MxiGQZs2baCjo4MnT55AIpEgNDQURISQkBCVPPlKJBJcu3YNoaGhKF++vGwvPzAwEJs3b84xiUxxJjk5GU+fPsWJEyewYsUKjB49Gh06dEDt2rVlhXSkygKHw4GlpSVq1qyJ9u3bIzQ0FMuXL8exY8fw5MkTJCUlKS3Hv//+Cy6Xi/DwcLnanzlzBkRUIHN46dKlMXz48HzbrV27FkQkc+pr0aIFrK2tkZiYqPTcivL27Vv4+fmBiNC2bVt8/Pgx3z4Mw+DAgQPw8PAAEcHLywsnT55klQKW3wJWGfiD2L59OxyI8GX+fGDwYKBtW6BVK6BbN4zV1YWfjg4mjR0LHR0dxMfHAwDi4+Ph7OwMZ2dn2bGVK1eCx+PB399f5ZUKc4tMWLp0qUojE4qKtLQ0vHr1CqdPn8batWsxbtw4dOnSBd7e3rC3t5c5XUpfZmZm8PT0RJs2bTBs2DAsXrwYhw4dwoMHD2T/j1/Zv38/iAjTp0+XW6527dqhfPnyBVrY6tevj9atW+fbLi0tDVZWVujatSsA4NWrVxCJRPj333+VnlsZGIbB1q1bYWJiAgMDA6xZs0au62cYBocOHULVqlVBRKhVqxZOnDjBKgUsJRpWGfiD6NChA9zc3HI817hxY5kDGJfLxfLly2Xnnjx5Ah0dHbRp00Z2wzt+/Dh0dXXh7u6utkX63bt3WLRoEerXry9bJGvUqIGZM2fi+fPnapmzqMnIyEBkZCTOnTuHjRs3YtKkSejevTsaNGgAR0dHCASCLMqCkZER3N3dERAQgEGDBmH06NHQ0NBAvXr1EBsbK9cC9fnzZwiFQsyZM6dAsnfv3h1VqlSRq+2cOXPA5/Px7t07AJmWDJFIhFevXhVIBmX48uULOnfuDCJCvXr15P5sMQyDI0eOoFq1arLP5rFjx1ilgKVEwioDfwjp6ekwMDDAuHHjcjy/aNEiEBG2bt2K5s2bw93dPctNbffu3SCiLAvGvXv3YG1tDRsbG7V7hH/9+hXr16/PEplQsWJF/Pvvv0USmVBUSCQSREdH49KlS9i6dSumTZuGXr16wdfXF+XKlcuyDUFE0NPTg4uLC5o2bYp+/fph9uzZ2LVrF65fv47P/20FhYWFQSgU4suXLwWSbcqUKTA2NparbXx8PAwNDTFo0CAAQGJiImxsbNC8efMCyVAQwsPD4eDgAA0NDUyfPj1bSebcYBgGx48fR82aNUFEqFatGg4fPvzHfCZZfg9YZeAPQbonfPPmzRzPx8TEgIjQpk0bHDlyBESEa9euZWkzfPhw8Hg8nD17Vnbs/fv3cHNzg66urtz70wUlMTERe/fuRadOnWBgYAAigq2tLQYMGICIiIgi9+IvChiGQevWraGjo4OLFy/i2rVr2LlzJ2bNmoW+ffvC398flSpVgo6OThZlQUtLC0KhEBYWFujduzemT5+Obdu24fLly/jw4QMkEoncMmzZsgVElOv2xa+MHTsW2trasuiFHTt2yPIQFBWJiYkYNmwYuFwuXF1dcf36dbn7MgyD8PBwWeGkqlWr4uDBg6xSwFIiYJWBP4RBgwbB0tIyzxuTlpYW7OzsIBaLYWtri3/++SfL+YyMDPj4+MDMzAzv37+XHY+Pj0eTJk3A5/OxevVqtV1DTqSnp+PkyZMICQmBpaWlLDKhW7duOHjwYLGOTFAls2bNAhFh7969ebZjGAaxsbG4desW9u7di759+0Kapc/NzU2mXElfQqEQZcuWRcOGDdGjRw9MnjwZmzZtwvnz5/Hu3bssuRYuXboEIsK9e/fkkvnz58/Q1NTExIkTZbL5+PigXLlyRV7V8ubNm3B3dweXy8XgwYMVcm5kGAanTp1CnTp1QETw8PDA/v37WaWApVjDKgN/AAzDwMHBAb17986znaurK3g8HsRiMaZMmQItLS38+PEjS5uYmBhYWVmhVq1aWW7YGRkZ6N27N4gIo0ePVuiJUlVIJBJcvXr1t4lMkJeTJ0+Cy+Vi9OjRCvdt3749ypUrl2Wh+vHjB+7du4eDBw9i4cKFGDp0KAIDA1G1alWYmJhkURb4fD4cHBzg4+ODtm3bgohkuSNev36dr6m9X79+MDY2li229+/fB4/Hw+zZsxW+FlWTkZGBWbNmQUNDA/b29jh+/LhC/RmGwZkzZ+Dt7Q0igpubG/bu3auy78bTpCQsjIpC58eP4XHjBpyuXUPl69cR9PAhZkdG4pacFhoWFoBVBv4IHj58KFdCmAEDBoCIcP36dXz48AF8Pj/HFLaXL1+GQCBA//79sxxnGAazZ88GEaF9+/ZqjaOXh8ePH2Pq1Kkyr2+BQIBGjRph2bJl+PDhQ5HKpirevn0LY2NjNGrUSOGMiF++fIFQKERYWJhC/RITE/Ho0SMcPXoUS5cuxciRIxEUFIQaNWpkURSkuRZsbGzg5eWFjh07YsyYMVi1ahXCw8Px7NkzPH36FDweDwsWLJCN379/f+jo6BSb/9HLly/RoEEDEBH+/vtvfP78WeExzp49i3r16oGIULlyZezevVtppeDY16/wuXMHFBEBTkQE+GfPgiIiZC9eRAS4//3ufuMGtsTEsFYJlnxhlYE/gGnTpkFbWxspKSl5trt48SKICMOGDQMAtGrVCi4uLjneSJYsWQIiwubNm7Od27VrFzQ0NFCnTh2lstmpg3fv3mHhwoWoV68eeDweOBwOatasWaIjE5KTk+Hh4QF7e3ul3uc5c+aoxHHwZ8qXL4++ffvi2bNnCA8Px8qVKzFmzBh07NgRXl5esLGxAZfLzaIwaGhoQCgUok2bNhg5ciTCwsKgp6eH5s2bF2rugbxgGAbr1q2DoaEhjI2NsWnTJqUW2PPnz8sUi0qVKmHHjh1yKwWx6en4+9Ej2YJPcrykSkHDO3cQmc/3n+XPRt71my1hXIKpWbMmWVpa0p49e/Jsl5GRQSKRiDw8POjmzZsUHh5Ovr6+dPnyZapZs2aWtgCoa9eutGvXLrp69SpVrlw5y/krV65Q8+bNydDQkI4ePUqOjo4qvy5liY2NpcOHD9O+ffvoxIkTlJqaShUrVqSAgAAKCAggd3d34nA4RS1mngCgf/75h7Zv306XL18md3d3hfs7OzuTu7s7bdu2TWVy+fn5kVAopAMHDuTaJiMjg96/fy8rTX3t2jVavnw5OTs7U2pqKkVFRZFYLJa1NzExybVMtb29faHeaz5//kyDBg2ibdu2ka+vLy1btowcHBwUHufSpUs0ceJEOnnyJFWoUIHGjh1Lbdq0IR6Pl2P7VykpVO/uXfqQlkYSJeTmczikzeVSuKsrVWPvzSw5IO/6zSoDJZSYmBiytLSkdevWUZcuXfJtb21tTT9+/KDExERiGIbKli1LderUofXr12drm5ycTLVq1aKkpCS6ceMGGRgYZDn/6tUratKkCX379o0OHjyYTaEoDiQlJdGJEydo3759dPjwYfrx4wfZ2dlRy5YtKSAggLy8vHK9QRcly5cvpz59+tDGjRupU6dOCvc/f/48eXt705kzZ6hevXoqkyskJIQuXbpE9+7dU6hf06ZN6e3bt3T//n0CQFFRUeTr60vp6enUrVs3ioqKkikPkZGRlJ6eLutrYGCQp7JgaGiocuXuyJEj1KdPH4qNjaXJkyfTgAEDiM/nKzzOlStXaOLEiXTixAlydnamf//9l4KCgrJ85t6nplL127fpU3q6UoqAFB4RafJ4dNHdnVx1dAowEsvviNzrtyrNDCyFx+rVq8HlcuXe52zevDmISLZfO336dGhoaORad/7ly5cwMDBAs2bNcjR3fv36FXXq1IFIJMLOnTuVv5BCID09HeHh4VkiE0xMTPDPP//g4MGD+W6zFBZSn42ClP/9+++/4ejoqPK95FmzZkFXV1fhcS9cuAAiylIrQBqdsHLlyixtJRIJPnz4gMuXL2Pbtm2YPn06evfujcaNG8PZ2VmWh0L60tHRQaVKleDv74++ffti1qxZ2LlzJ65du4ZPnz4p/R7Ex8djwIAB4HA4qFq1Ku7evavUOABw9epVNGnSBESE8uXLY9OmTcjIyICEYVD39u1sfgFZXitWgGrVAunqgkQikL09qF+/HNvyIiJQ+soVJJeAipsshQu7TfCb06JFC/r27RtduHBBrvZr166l7t270/Lly6lXr1706dMnsra2pjlz5tCAAQNy7HPkyBFq2rQpTZ06lUaPHp3tfFpaGv3zzz+0detWmjVrFg0bNqzYm+EZhqEbN27Qvn37aN++ffT8+XPS1tYmPz8/CggIIH9/f9LX1y90uWJiYqhKlSrk4OBAZ86cIaFQqPAYsbGxZGVlRZMnT6bhw4erVL5du3ZR27Zt6evXr2RsbKxQXy8vLyIiunjxouxY586d6dixY/T8+XMyNDSUaxwA9PXrV5klIaefCQkJsvaamppkZ2eXq2WhVKlSxOVyc53v6tWr1LNnT3ry5AkNHz6cxo0bR5qamgpdu5QbN27QpEmT6PDhw1S2bFmqOWMGbTQyyqsD0ZgxRI6ORPXqEWlqEn34QMQwRL1759iFS0SDra0prBht3bEUPew2wW9McnIymZiY0MSJE+W+6cfExJCFhQX5+/vT4cOHiYiobdu29OjRI3r48GGui/j48eNp8uTJdPz4cWrUqFG28wBo3LhxNGXKFOrduzctWrRIKbNqUQCAnjx5IlMMbt26RQKBgOrXr08BAQHUokULKlWqlNrlyMjIoAYNGtDLly/p1q1bZGFhodQ48+fPpxEjRlB0dDSZmpqqVMabN2+Sp6cn3bhxg6pWrapQ38OHD1OzZs3owoULMsXg48ePVL58eeratSstXLhQJTICoB8/fuSpLHz//l3WXigUkq2tbRYl4effraysiGEYmjVrFk2ePJlsbW1pxYoVVL9+faVlvHXrFk2YMoUOd+1KpKdHlNP3LimJqFMnokqViCZMIMpDYfkVPodD0TVrkpkSyiTL7wmrDPzGHDp0iJo3b05Pnz6l8uXLy91PR0eHdHV16ePHj0REdPr0aWrYsGGWm/SvSCQSatq0Kd24cYNu3bpFdnZ2ObZbu3Yt9erVi/766y/asWMH6erqKn5hRUxUVBTt37+f9u3bR+fPnyeGYahGjRoyB0R1OUsOGjSIli5dSmfPnqVatWopNQYAqlChArm6utL27dtVLGGm1cHExIR27dpFrVu3VqgvwzBUuXJlsre3lymiRERhYWEUGhpKd+7cIRcXF1WLnCPx8fEy/4SclIUvX77I2vJ4PLK2tiZ7e3syMDCgO3fu0Lt376hx48Y0ZcoUcnFxUcqCs/3TJ2r/5EnuDQ4eJJo3j2j9eiI7O6KUFCKRSC6lgEtEUxwcaFQu31OWPw9WGfiN6dmzJ50/f56ePXumUL+qVavS7du3KTExkbS0tIhhGCpfvjxVr16dNm/enGu/b9++UZUqVcjExIQuXLhAGhoaObY7deoUBQYGkoODAx05coSsrKwUkq84ERsbS4cOHaJ9+/ZReHg4paamUqVKlWSKgZubm0q2RDZv3kydOnWiJUuWUEhIiNLjXLhwgerWrUunT58u0JNrbgAgPT09GjdunFJbEJs2baLOnTvT/fv3ZQt/eno6Va5cmSwsLOjMmTPFYospOTk5T2VBqkgTEXE4HLK0tMzVydHW1jbHbYUWDx7Q4dhYYnITYvx4olu3iCZOJFqwgCgqikhDg6hRI6K+fYnyUUCctbTocbVqBXgXWH4nWAfC3xSJRAJzc3NZzgBFGDFiBIgIJ0+elB2bNWsWRCJRvvHst27dgkgkQs+ePfNs9+DBA9jY2MDKyqpAjlfFicTEROzevRsdO3aUpfW1s7PDoEGDcPbsWYWTAkm5c+cONDU10aVLlwI7/HXs2BGOjo5qzRDp4uKCPn36KNU3PT0dtra26NixY5bjx44dAxFhx44dqhBR7aSkpODChQvw8vICEaFs2bIICAhAnTp1YGtrmy3Xgrm5OapXr462bdtixIgRWLJkCQzOnMk7j0Dp0iANjcxXQABo4sTMn0Sg+vXlykGQxDoSsvyHvOu3/JtRLMWCGzdu0KdPn6h58+YK923ZsiUREe3du1d2rGvXrgSANmzYkGdfDw8PWrZsGa1atYrWrFmTa7tKlSrR1atXydzcnLy8vOj48eMKy1nc0NbWpsDAQNq0aRN9/vyZwsPDqUmTJrRjxw7y8fGhUqVKUffu3enw4cOUmpoq15jfvn2jVq1akZOTEy1btqxAT8Xfvn2jXbt2Uc+ePfN0iCsoDg4O9ObNG6X6CgQCGjZsGG3bto3evn0rO964cWNq3rw5DRs2jJKSklQkqfrQ0NAgLy8vunDhAu3du5cSExPp5MmTFBQURG/evKHU1FR68+YNRURE0Pr166lPnz5UoUIF+vLlC+3evZsGjB1LP/L7X6emZr4aNSIaMICobt3Mn82aEZ05Q/T+fZ7dGSJ6WALeS5Zihio1Cxb1M3r0aBgbGytVwS8tLQ0cDgcVKlTIcrx9+/YoX768XE+nwcHBEIlEuVZJlJKQkICmTZuCx+NhxYoVCstaEpBIJLhy5QpGjBiBsmXLysLd2rRpg61bt2ar/yBFLBbD19cXRkZGePPmTYHlmD9/PgQCAT59+lTgsfJi4MCBcHJyUrp/YmIijI2Ns4VOvnr1CiKRCP/++29BRSx0fvz4IavdUbNmTTx8+DDP9k8SEvLPMGhvn2kFmD8/6/H58zOPh4bmO8bx2NhCegdYijusZeA35eDBg+Tv76+Ux75QKCRra2t68eIFMcz/dyx79epFz549o3PnzuU7xsKFC6ly5coUGBhIsbGxubbT0dGh/fv3U+/evalXr14UGhqaZc7fAS6XSzVq1KCZM2fSs2fP6OHDhxQaGkqvX7+mDh06kKmpKTVu3JhWrFhBMTExsn4TJkygkydP0vbt28ne3r5AMgCglStXUsuWLcnMzKyAV5Q39vb29PbtW0L+bkY5oq2tTQMGDKA1a9ZkcdQrXbo0DRs2jGbPnk2vX79WlbiFgr6+Pi1btozOnz9P3759I3d3dxo/fjylpaXl2J4vj+XGxCTz568hl9K/fwqfzA32xs6iKOxnpgTx+vVrevjwoVJbBFKqV69OGRkZ9PTpU9mxunXrkpOTE61YsSLf/iKRiHbv3k2JiYn0999/k0SSe+40Ho9HixYtorlz59KsWbOoffv2cpvRSxocDocqVqxIY8aMoZs3b1JkZCSFhYVRWloahYSEkKWlJdWuXZu6du1KU6ZMoalTp9Jff/1V4HkvX75Mjx8/puDgYBVcRd44ODhQampqFsVGUfr27UtcLpcWLVqU5fioUaPI1NSUhgwZUlAxi4Q6derQ3bt3KTQ0lKZPn05ubm5Z8ipIkSvkr1y5zJ9fv2Y9Lv37l4ygOcGGFrIoCqsMlCAOHTpEQqEwx3h/eZEqEkePHpUd43A4FBwcTHv27MnyxJYbtra2tH37djp58iRNnDgxz7YcDocGDx5Me/bsoUOHDlGDBg3o6683ud8QW1tbGjBgAEVERNCnT59ozZo1JBKJZL4ZW7ZsofHjx9Pdu3eVftImIlqxYgWVKVNGLREEvyLN1f/znr+iGBsbU3BwMC1evDhLgiBtbW0KCwujAwcO0IkTJwoqapGgoaFBkyZNotu3b5OBgQHVqVOH+vTpQ3FxcbI2enw+2YtEeQ/k45P586fvKBERHTlCxOMRubnl2V3I4VAFLS3FL4Dlj4ZVBkoQBw8epPr16xcohl+6aBz95UbTpUsX4nK5OdYqyImGDRvSlClTaPLkyVlix3MjICCAIiIi6MWLF1SzZk168eKFwrKXVExMTKh169b06dMnKleuHG3atIlcXV1pwYIF5O7uTqVLl6bBgwfT+fPn87S0/Mq3b99o586dancclCLd0lDWiVDK4MGDKSEhgVatWpXleNu2bcnHx4cGDhyYpUZBSaNSpUp08eJFWrRoEW3evJkqVKhA+/fvl52vY2BAeW7ylS1L5OdHdPp0Znjh/v2ZyYfOnCEKCvr/NkIOcInIXUeHBIXweWD5vWA/MSWEHz9+0Pnz5wu0RUBEZGVlRdra2nTnzp0sx42MjKhNmza0cuVKuff2R44cSS1atKCOHTvSy5cv821fvXp1unr1KvH5fKpZs2aOZtTfEfxXiTAqKooOHDhAHTt2pM2bN9Pnz5/pxIkT1LhxY9qxYwd5e3uThYUF9ejRg44cOZLvlsrmzZtJIpFQ165dC+U69PT0yMjIqMDKgI2NDXXs2JHmzp2bZdHncDi0cOFCevHihcqyEhYVPB6P+vXrR48fPyYPDw8KCAigwMBAevToEQnPnCFxfgMMGULUtSvRkydES5YQvXyZmWOgZ888uzFE1NPSUkVXwfInwSYdKiFs376d2rdvT1FRUWRtbV2gsWrUqEHXrl2jmJgYMjc3lx2/ePEi1alTh06dOkUNGjSQa6y4uDiqWrUqaWlp0ZUrV0hLDvPk9+/fqVWrVnT58mXauHEjBQUFKX0tJYFZs2bRyJEjae/evRQQEJBjG4Zh6Nq1a7IMiC9evCAdHR1q0qQJBQQEUJMmTbJ89wCQi4sLOTs7065duwrrUqhq1ark5uZGq1evLtA4T548oQoVKtDatWupW7duWc7179+f1q9fT8+fP1c6NXNxAgAtXLiQRo0aRSkpKcTj80l7zx5K1NPLPfGQkujyeBRTqxZpFcOKnCxFg7zrN2sZKCEcPHiQPDw8CqwIEJHMce38+fNZjteuXZsqVKgglyOhFH19fdq7dy+9fPmSevXqJdf+t6GhIR0/fpzatm1L7dq1oxkzZhRo37w4c+rUKRo1ahSNHj06V0WAKDMyoWbNmlkiE0aOHEkvX76k9u3bk4mJCfn5+dHKlSvp06dPdOXKFXr06FGhOA7+jIODQ4F8BqQ4OztTy5YtaebMmdksUZMmTSKRSEShoaEFnqcoAUAXL16kwMBAGjx4MGlpaZGbmxtJxGKy3b9f5YoAEdHM0qVZRYBFKVhloASQkZFBR48eLfAWgZQmTZoQUaZD4s9wOBzq1asX7du3TyGPcRcXF1q9ejVt3ryZli1bJlcfkUhEGzdupHHjxtGoUaMoODiYMjIy5L+IEkBkZCS1a9eOGjZsSJMmTZK7nzQy4d9//6Vbt27R27dvafbs2ZSSkkJ9+vQhCwsLCggIICMjI5lTX2Fhb29f4G0CKSNHjqRnz57RgQMHshw3NDSkadOm0caNG+nKlSsqmaswEYvFtGPHDqpevTrVqVOHnjx5QitWrKCoqCi6c+cOnT59mlLOnyfu8ePEUVG4LUciIbp7l75t3PjbhfCyFA6sMlACuHDhAsXFxalMGXB3dycOh5Pjnn2nTp2Iz+fTunXrFBqzffv2NGDAABo0aJDcN3AOh0MTJ06k9evX0/r166lp06YUHx+v0LzFlZSUFGrVqhXp6urS1q1biVeApzU7OzsaOHAgnT17lj59+kQLFy6kr1+/UlxcHJUtW5YqV66sksgEeXBwcKB3794p5OiYGzVq1CBvb+8cLUPdu3cnDw8P6t+/v0rmKgzi4uJo7ty5VKZMGWrXrh3p6urSkSNH6NGjR9SzZ09ZnYL69evTgwcPyP/1a8Ljx0QFvD4+ETloa9PA+Hj6d/RoatWqVZYIBhYWeWCVgRLAwYMHydramtzyCSmSFw0NDbK1taXIyMhsTmqGhoYUFBREq1atUvgJY/bs2VStWjWZ57y8dOnShY4fP07Xrl0jLy8vioqKUmje4gYACgkJocePH9PevXvJ2NhYZWOb/OdJzuVy6dmzZ7Rr1y5ycXGh+fPnk7u7O5UpU4aGDBlCFy5cUMsi6uDgQGKxmKKjo1UyXmhoKF2/fj1bwitpjopbt24prJgWNpGRkTR06FCysbGhkSNHkre3t8wC0KRJkxwjPQ4dOkRH9+6leseOke6rV0rPzSEiJ21tuujuTvPHjaODBw/S2bNnqWrVqvTgwYMCXBXLH4cq0xmyqB6GYeDg4ICQkBCVjtu+fXsQES5cuJDt3JUrV0BEOH78uMLjRkdHw9zcHD4+PgqnTH706BHs7OxgaWmJ27dvKzx3cWHZsmUgImzatEnlYzMMg0qVKiEwMDDL8bS0NBw/fhy9e/dGqVKlQEQwMzNDjx49cOTIEaSmpqpk/idPnoCIcPbsWZWMxzAMXF1d4evrm+P5Tp06wcTEBN++fVPJfKrk2rVrCAoKAo/Hg4GBAUJDQ/H+/ft8+23atAlcLhedOnVCRkYG0tLT0WLDBtCJE6BTp/JPVxwRAf7Zs+BGRGD0q1dI/aU41YsXL1C5cmVoampi8+bN6rp8lhKCvOs3qwwUcx48eKD0wpwXW7ZsARHlmA+eYRhUrlwZAQEBSo197tw58Hg8DB8+XOG+Hz9+RNWqVaGtrY0jR44oNX9RcvnyZQgEAvTv319t4xMRTpw4kWsbiUSCy5cvY/jw4XB0dJTVTGjbti22bdtWoO9xcnIyiAjr1q1Teoxf2bp1K4goRwXww4cP0NHRUdv7qShisRh79+6VVS0sU6YMFi1ahISEBLn6r169GhwOB927d89S7fLLly/QtLeH/rBhoIMHMxf9M2cgOHsW/IgIUHg46PRpUEQENM+dQ8izZ3iUmJjrPElJSejUqROICP369UNaWlqBr52lZMIqA78JU6dOhY6Ojsqe7KS8ffsWRIRq1arleH7JkiXg8XiIjo5Wavy5c+eCiLB7926F+yYmJqJ58+bgcrlYunSpUvMXBR8/foSlpSW8vLzUdvPt2rUr7O3t5S5VzDAMHjx4gEmTJsHd3R1EBKFQCD8/P6xcuRIxMTEKy1CqVCmMGzdO4X65kZGRAQcHBwQFBeV4ftasWeDxeLh//77K5lSUxMRELFq0CGXKlAERwcvLC3v37lWofPWSJUtARAgJCcn2/xs1ahS0tbXx6dMnDBs1CuTsDI127dDgwAF0evAANGgQqE0bzIuIQKKcczIMg6VLl0IgEKBmzZqIiopS6JpZfg9YZeA3oXr16mjdurXKx2UYBjo6OtDU1MyxWuGPHz+gpaWFyZMnKz1+27ZtoaOjgydPnijcXywWY+DAgSAiDBs2TO7Fr6hIT0+Hl5cXLCws8OHDB7XM8f37d2hqamLq1KlKj/HmzRvMnz8f3t7e4HK54HA48PLywpw5c/Dq1Su5xqhZsyY6d+6stAw5sXTpUnC5XLx8+TLbubS0NJQrVw4+Pj5yVdZUJdHR0QgNDYWhoSF4PB6CgoJw7do1hceRKseDBw/Odg1fvnyBjo4ORo4cCQAYP348DA0N0aFDBxARGjZsCA0NDXC5XCxbtkzhua9cuQJra2uYmprizJkzCvdnKdmwysBvwMePH0FE2Lhxo1rGr1WrFogIT58+zfF89+7dYWtrq9DTz88kJCTA2dkZzs7OiI+PV2qM+fPng8PhIDAwEMnJyUqNURgMGDAAAoEAly5dUtscixcvBo/HU5my8fnzZ6xZswZNmzaFSCQCEaFy5coYP3487t69m+vC26FDB9SpU0clMkhJTk6GmZkZevfuneP5Y8eOgYiwc+dOlc6bG3fu3EGnTp0gEAigq6uLIUOG4O3bt0qNNX36dBARQkNDc3xPpVaBL1++AAB8fHzQokULAJnXbWdnBw6HAy0tLaW3Sz59+oT69euDy+Vi5syZha5UsRQdrDLwG7Bq1SpwuVx8/fpVLeNPmDABRISVK1fmeP769esgogLt3T958gS6urpo06aN0jeg/fv3Q1NTEzVq1MDnz5+VlkVdbNq0CUSEJUuWqG0OhmHg4uKitB9HfsTHx2Pnzp1o37499PT0QERwcHDAkCFDcOHChSwK4ejRo2Ftba1yGaZOnQqRSISPHz/meL558+awsbFBYh575QVBIpHgyJEjqF+/PogItra2mDNnDn78+KHUeAzDyL5jEyZMyPHzL7UKhIaGAgBSU1OhoaGBuXPnytokJCTInEJ1dXVx69YtpeTJyMhAaGgoiAitWrVi7+d/CKwy8BvQrFkz1K1bV23jnz9/HkSEli1b5nieYRi4u7ujefPmBZpnz549ICLMmTNH6TGuX78Oc3NzlC5dOldLRlFw584daGpqokuXLmp92rp69SqICMeOHVPbHFKkkQm9evXKMTJh6dKl4HA4Kvdj+f79O3R1dWUL46+8fPkSIpEIY8eOVem8ycnJWLlyJZydnUFE8PT0xPbt2xWOhvkZhmEwatQoEBGmTZuWa7vQ0NAsVgHpd/LXBb9Zs2awsrKCQCCQOecmJSUpJdu+ffugp6eHcuXK4eHDh0qNwVJyYJWBEk5SUhI0NDQwe/Zstc7B4XBgbm6ea5vly5eDy+UW2PloxIgR4PF4BQpJe/PmDZydnWFoaIhz584VSB5VEBsbCwcHB3h4eKh9C6Nbt26ws7NTestGWSQSCS5duoRhw4bJnOc0NTVBRJg/f77K7wnDhw+Hnp5erk/jY8aMgUgkktu/IS8+ffqE8ePHw9TUFBwOBwEBAbhw4UKBlTqGYTBkyBAQUZYn/F/58uULtLW1syg/kydPhr6+frb/c/fu3eHg4CCzMohEIpQuXRonT55USsbnz5+jUqVK0NLSwrZt25Qag6VkwCoDJZwDBw6AiPDs2TO1zmNvbw8ikj2Z/Ep8fDx0dHQwfvz4As2TkZGBevXqwczMTK5Y7Nz4/v076tevD6FQiC1bthRIpoIgFovh6+sLY2NjpfeS5eXHjx/Q1NTElClT1DpPfjAMg/v372PQoEEgIllkQpMmTbBy5Up8+vSpwHNER0dDKBRi5syZOZ5PTEyEtbV1rtYseXj06BF69OgBkUgELS0t9OvXDy9evFB6vJ+RSCTo27cviAiLFy/Os21oaCh0dHSyfPcaNmwIf3//bG1HjRols9Lcvn0bz549g4+PD4gIXbp0UWorMTExUeakOGDAADb88DeFVQZKON27d0f58uXVPo80FvngwYO5tgkODoaVlVWBzKZA5pOYlZUVatWqVaAbT1paGrp06QIiwpQpU4rEGerff/8Fl8tFeHi42ucqaJinqklPTweXy8XUqVMxb9481K1bN1tkwuvXr5Uev0ePHihVqhRSUlJyPL99+/Z8cy38CsMwOHnyJPz8/EBEsLCwwLRp0xAbG6u0nL8ikUjQo0cPcDgcrFq1Ks+2UqvAqFGjZMfS09OhpaWFWbNmZWs/f/58aGhogIiwdetW2TWtXr0aBgYGMDU1xdatWxX+LjAMg0WLFoHP56N27drF5jPGojpYZaAEI5FIYGZmplTSHkWROr8NGDAg1za3bt0CEeHAgQMFnu/KlSsqScrDMAwmTZoEIsI///yD9PT0AssmL/v27QMRYcaMGWqfS5oAqiBPwurA1tY2y0L2+fNnrF69Gv7+/rLIBFdXV0yYMAH37t1TaJF69uwZOBwOVqxYkeN5hmHg7e2N8uXL56tUpqWlYf369ahcubJMpg0bNqj8KVgsFqNz587gcrnYsGFDvu1HjhyZzSogTSiVU+iiNDGTubl5thwPHz9+RJs2bUBEaNKkCSIjIxWW/9KlS7C0tIS5ubnKskuyFA9YZaAEI00HnFOqYFXz8uVLEBEqVqyYZztPT080adJEJXMuXboURKSSVKkbN26EQCBAw4YNlfb6VoSnT59CV1cXgYGBhWKRuHbtGogIR48eVftciuDt7Y127drleC6nyITSpUtj6NCh2SITcqN169ZwdHTMte29e/fA5XIRFhaW4/nY2FhMnToVFhYWskXy9OnTavmfpaeno127duDxeNi+fXu+7T9//pzNKgBkhiDq6OjkaIE7deoUiAjVq1dH27Ztcxz3wIEDsLKygra2NubPn6+wf0lMTAx8fHzA4/EQFhbGhh/+JrDKQAlm1KhRMDY2LhRnMYZhoK2tDR6Pl6d3uDSNqir2xxmGQefOnaGpqYl79+4VeLyIiAgYGBigYsWKSj0VyUt8fDycnZ3h5OSkdN4ERSlorgd10aVLF1SvXj3fdqmpqTh27BiCg4Nhbm4ui0zo2bMnjh49mutn7saNG/nmFejXrx90dXWz5F14/vw5QkJCoKWlBZFIhJ49e+Lx48eKX6CcpKWlISAgAAKBAHv37pWrT05WAQBo3LhxrjUa7t+/DyJCQEAAXFxcch07Li4OISEh4HA4qFatmsJZGzMyMjB8+HAQEVq3bl1on3MW9cEqAyWYihUrokuXLoU2X506dUBEuHz5cq5tEhMToaenl2MtA2VISkqCq6srHB0d8f379wKP9/jxY9jb26NUqVK4efNmwQX8BYZhEBgYCF1dXaUyKipDXFwctLS0MGnSpEKZTxEmTJgAMzMzhfqIxWJcvHgxS2SCrq4u2rVrhx07dmRbeBo0aAAPD49cn1BjY2NhbGyMzp074/z582jRogU4HA5MTU0xYcIElTg05kVKSgr8/f0hFApx6NAhufrkZhXIyMiAjo5OrmGIMTExICKZ42N+yuGlS5fg7OwMPp+PMWPG5Op/kRu7d++Grq4unJyc1KpMsagfVhkooUjN9nv27Cm0OSdPngwiytFx6WdCQkJgYWGhsv35ly9fwsDAAM2aNVNJuuGYmBhUq1YNWlpaeTpEKsPMmTNBRHI//amCZcuWgcvlFij6Ql1s2LABRKR0rLs0MmHixIlwc3PLEpmwatUqfPr0CSdPngQR5eqkmZ6ejh49esgiG5ydnbFq1SqFFz5lSEpKQqNGjaChoaGQI6PUKvCr9780wVduCnlGRgY4HI4sRbc8oZWpqamYMGECBAIBypUrp7AvwNOnT1GhQgVoa2tjx44dCvVlKT6wykAJZd68eRAKhXJXQVMFZ86cARGhQYMGeba7d++eyhfEw4cPg4gKlG//Z5KSkhAQEAAul5tvaJe8nDx5ElwuF6NHj1bJePLAMAzc3NwKnPBJXUiT4zx69Egl471+/Rpz585FnTp1wOFwwOVy4eXlBWtra9SqVStL2x8/fiAsLAw2NjYy64Kjo2OBo13kJSEhAT4+PtDW1kZERITc/aRWgZw+R7Nnz4aWllaeirapqSmGDRumcFbQR48eyVKPBwcHK2SJS0hIQFBQkKyuQmE66rKoBlYZKKHUq1cPfn5+hTpnQkKC7Kaan9NQjRo1ct3XVJZx48aBw+Eo9ISVF2KxGIMHD5bdwAqy3/727VsYGxvD19e3UPftVZEKWp28e/cORITDhw+rfOxPnz7JIhP4fD6ICOXKlcOgQYPQsWNH6OrqQiAQoEuXLrh79y4uXrwIIso3nE8VxMXFoXbt2tDV1cXFixcV6jtixIgcrQIA4O/vj4YNG+bZv2LFiujfvz+0tLQUzuYpkUiwdOlS6OrqwsLCQiHLI8MwmD9/Pvh8PurUqaO2Qlws6oFVBkog3759A4/HU6oyWUGRZjfLL/nKunXrwOFwVJIBTopYLEbjxo1hZGSEN2/eqGzcxYsXg8vlIiAgQClzdnJyMjw8PODg4KDSeHR56NGjB2xsbIqd46AUsVgMgUCARYsWqXWe79+/w9jYWJb1kIhgYGCAXr164eLFi7LtpY4dO8LExEQl/ie58e3bN1SrVg0GBgYKVy78/PkztLS0crQKiMVi6Onp5VshtF69eggKCoKHhwd69Oih0PxSoqKi0Lx5c1kackW2oC5cuAALCwuUKlWqUCKdWFQDqwyUQLZs2QIiKpK64926dQMRYf369Xm2S0pKgr6+fq7545UlNjYW9vb2qFKlikr3fA8dOgQtLS1Uq1YNMTExcvdjGAZdu3aFhoYG7ty5ozJ55CEuLg7a2tqYOHFioc6rKI6Ojhg6dKhaxhaLxdizZw9q164tUwJGjx6NvXv3omfPnjAzM5PF3QcHB2Pz5s3Q1tbOM19GQfj69Svc3d1hZGSkVKGgvKwC0jwe58+fz3OMoKAg1KtXDx06dICXl5fCMkhhGAa7du1CqVKloKenh2XLlsnts/Px40fUrVsXfD4f8+bNY8MPSwCsMlACCQoKQpUqVYpk7vXr18tSm+ZH//79YWZmpvLELbdu3YJIJFL6qSc3bt68iVKlSsHe3l5uz2hpLoRNmzapVBZ5UFU9CHXTsGFDtGrVSqVjJiQkYOHChShdujSICHXq1JEtXN27d5e1k0YmDB06VNZWJBKBw+Fg9uzZKg2J+/TpE1xcXGBqaqpwqB6Qt1UAAObOnQsNDY18Cz/1798fFStWxKRJk2BiYqKwHL/y7ds3mQOml5eX3N+N9PR0We2FoKCgQvVvYlEcVhkoYaSlpUFPT6/IngafPXsGIoKdnV2+bR8+fJhvDLiyrF27Vi37v5GRkahYsSIMDAzydfq6dOmSSrIkKouHhweaNWtWJHMrQs+ePeHu7q6Ssd6/f4+RI0fCwMAAPB4P7dq1w/Xr12XnZ82aBYFAkKNZm2EY3Lt3D2PHjpVlPxSJRPD398fq1asLVPY6OjoaTk5OsLCwUDrEbsSIEdDV1c21fkCLFi3g4+OT7ziTJ0+Gqakpdu7cmWc9EUWJiIhA2bJlIRQKMXHiRLmV/J07d0JbWxvOzs6FFm7LojisMlDCkIZRFbZJWoo0+RAR4du3b/m2r127dr7RB8oSHBwMkUiEGzduqHTcHz9+oGHDhhAIBNi4cWOObT5+/AgLCwt4eXkVSeGWmzdvgojkjlsvSqZNmwZDQ8MCjXH79m107NgRfD4fenp6GDp0aI6Jo+Li4qCvr49hw4blOd6xY8dAROjcuXOWyIS6deti3rx5CvmkvHv3Do6OjrC2tsbz588VvTQAmVYFLS0tjBkzJsfzEokERkZGchUCW7lyJTgcDu7cuQMiUtiBMS+Sk5MxevRo8Pl8VKxYMc+cIz/z+PFjODk5QUdHB7t371aZPCyqg1UGShj9+/eHjY1Nke7BeXt7y+3BLq1poKpqbz+TmpoKT09P2NraquzpR0p6ejr++ecfEBEmTpyY5f1OT0+Hl5cXLCwsisxjumfPnrC2ti60MLmCsG3bNhCRwmmgJRIJDh06hHr16smsUXPnzs33/jJq1Cjo6Ojkq6w2a9YMNjY2SEpKwqdPn7Bq1So0adIEQqEQRAR3d3dMnDgR9+/fz/X79vr1a9jb28Pe3r5ARZeGDx+ep1VAGq575syZfMfav38/iAiRkZHgcrlYvXq10nLlxr179+Dp6QkOh4O+ffvKdc+Pj4+X1UYYNmxYifjs/kmwykAJgmEY2NnZoW/fvkUqx8SJE8HhcLJlR8uJlJQUGBkZqa2YUmRkJIyNjdGoUSOVe9QzDIMpU6bIfCSkFoABAwZAIBDg0qVLKp1PXuLj46GtrY0JEyYUyfyKIq2hIa81Kzk5GStWrICTkxOICNWqVcOOHTvkXjxiYmIgEonyLeX88uVLCIVCjB07NsvxuLg4bN++HUFBQdDV1QURoUyZMhg2bBguXbokc6J78eIFbGxs4OjoWKD01vlZBQBg4cKFEAqFSE5Oznc8aSGjBw8eoEyZMmp13pw3bx60tbVhbW0tl5WKYRjMmTMHPB4PPj4+CjnrsqgXVhkoQUifDlQVZ68s0q0KT09PudoPHjwYJiYm+To+FUQeLpershTIv7JlyxYIhULUq1cPy5cvBxFhyZIlaplLHlasWAEul4t3794VmQyKIE2Rm18SqpiYGIwbNw4mJibgcDho1aoVLl68qJQVrE+fPjA1Nc138Rw9ejREIlGuT/Wpqak4evRolsiEUqVKoW3btjAyMkL58uULXM5XahXIKyw1MDBQ7sgAaXbSU6dOwd/fH/7+/gWSLz/evn0rK/nctm1buRb4c+fOwdzcHJaWlkWmVLNkhVUGShCTJ0+Grq6u2hZVeZH+n4VCoVyZxp48eQIiwrZt29Qm07Rp00BEKk8vLOXcuXPQ09MDh8MptEqEuVGlShU0bdq0yOZXFIZhoKWlhblz5+Z4/uHDh/jnn38gFAqhra2N/v374+XLlwWa89WrV+ByufkqbYmJibCyspKr9LNYLMaFCxdkJYiJCDo6Omjfvj127typlLe81CqQlyLLMAxMTU3ztBz8THx8PIgIW7duxdChQ1GmTBmF5VIUhmGwZcsWmJiYwNDQEGvWrMn3OxIdHY3atWuDz+dj4cKFbPhhEcMqAyUIT09PtGnTpqjFAABZmNbPntx54e3tLZcntLJIJBK0aNEC+vr6avFPiI2NhZWVFYRCIczMzOS+blUjdRxUl9KjLipUqJAl6oJhGISHh6Nx48YgIlhaWmLGjBlyOaXKS7t27WBvb5/v9oLUp0Eei9vt27dhbGwMd3d3REREYMKECXB1dZVFJjRt2hRr1qyROzJh2LBh+VoFHj16lGfthV9hGAYaGhqYP38+Vq1aBS6XWyh1GADgy5cv6Ny5M4gI9evXz/e7mJ6ejkGDBoGI0L59eyQmJhaKnCzZYZWBEkJ0dHSRxbPnRLdu3cDhcDBv3jy52m/duhVEhKdPn6pNph8/fsDR0REuLi5KF8bJCbFYDF9fXxgbG+PWrVuoUaMGNDU1sX//fpXNIS+9evWClZVViXO+atKkCZo2bYrU1FSsW7cOLi4uICK4ublh06ZNaonIkHrTb9myJc92DMOgbt26cHJyylOOa9euwcDAANWqVcumtLx69Qpz5syBl5eXLDLB29sb8+bNy7Wc96dPn6CpqZnv9tbSpUvB5/MVWihtbW0xevRoWQrmBw8eyN1XFZw4cQIODg7Q0NDA9OnT87Ugbtu2Ddra2qhYsSKePXtWSFKy/AyrDJQQVqxYAR6PV+jpbnNjzZo1slSl8pCamgoTExMMGTJErXLdv38fWlpa6Nixo8rMjmPGjAGXy5U9mSUnJyMwMBAcDgfz589XyRzykJCQAB0dHYwbN67Q5lQV3bt3h5mZGUqVKgUigr+/P86cOaN203Djxo1RuXLlfOe5e/cuuFxurrn8L168CF1dXdSuXTvf+1tMTAxWrlwJPz+/LJEJkyZNwoMHD2SyyGMVADKTjNWoUSPPNr/i6emJHj164OvXr2rL9ZEfiYmJGDp0KLhcLlxdXfMNAX748CHKlSsHXV3dQq36yZIJqwyUEPz9/eHt7V3UYsiQmi6NjY3lvqEPGzYMRkZGajdZSq0QqqhGuG/fPhARZsyYkeW4RCLB8OHDQUQYMGBAodQGWLVqFTgcToE81wubZ8+eoU+fPhAIBLJqeIWZeObs2bMgIhw9ejTftn379oWuri4+fvyY5XhERAS0tbXh4+OjsF9ATpEJjo6OCAkJgUgkytcPgGEYlCpVCiNHjlRoXn9/f1klSxMTE0yaNEmh/qrk5s2bcHNzA5fLxZAhQ/K0cMTFxaFVq1YgIowcObLEWcBKMqwyUAJITEyESCRSuAKZOpFIJNDS0gIRyR1f/fz580Lb6hgwYAD4fH6BPJWfPn0KXV3dPB0Gly5dCi6Xi+bNm6t9v7Nq1apo0qSJWudQBQzD4OzZs2jevDk4HA7MzMxk5W0LkuVPWVmqV6+OunXr5ts2NjYWxsbGWVJth4eHQ1NTE3/99VeBt55SU1Nx5MgR9OjRQ1ZQyczMDL169cLx48dz3KKQZvyUR5n5mW7duqF69eoAAC8vL3To0KFAsheU9PR0zJw5ExoaGrC3t8fx48dzbcswDGbNmgUul4t69erh06dPhSjpnwurDJQApE+nymY3Uxc+Pj4KL+7169cvUPEUeUlLS0Pt2rVhaWmpVCxzfHw8nJ2d4eTklG/++iNHjkBbWxtVq1bN9lSpKqRFag4cOKCW8VVBeno6tm7diipVqoCIUKFCBaxevRopKSky+RWt4qcKpN8febLlSUNHr1y5gsOHD8vSFavSmiX1FejSpQsGDx4Me3t7EBH09fXRoUMH7Nq1S2aBWLlyJbhcrsL31JEjR8LBwQFAZmVLDw8PlclfEF68eIH69euDiNCxY8c8k4WdOXMGZmZmsLKywpUrVwpRyj8TVhkoAXTr1g3Ozs5FLUY2xo8fDx6Ph969e8vdZ8eOHSAiPHz4UI2SZRIdHQ1zc3N4e3srZG5kGAaBgYHQ1dWV2+Hx9u3bsLS0hJ2dnVqurXfv3rC0tCyWZtPv379j9uzZsLGxARHhr7/+wrFjx7JYU759+wYiwo4dOwpdPolEAicnJ7Ro0SLftmKxGO7u7ihTpgwEAgECAgJU7tw4dOhQ6OnpyXwFGIbB3bt3MX78eFSuXFkWmdCsWTPUqFEDbm5uCs8xZ84caGtry37X0tKSu+KgumEYBuvWrYOhoSFMTEywefPmXC1v79+/R82aNSEQCLB48WI2/FCNsMpAMUcsFsPU1FThPcPCQJrfvXz58nL3SUtLg5mZmdpKyP7KuXPnwOPx8s1V/zMzZ84EEWHfvn0KzfXu3Tu4uLhAX18fp0+fVlDS3ElISICurm62THlFzevXrzFw4EDo6OhAIBCga9euuHfvXq7t9fX1s/leFBbr1q0DEeHRo0f5tp04caIsqZY8eTQUISYmBpqamnn+L1++fImwsDDUqlVLVpbZ29sb8+fPzzUy4VekacATExNx5MgRWXri4kRMTAzatWsHIoKvr2+u9SDS0tLQv39/mTVBlZFCLP+HVQaKOZcuXQIRFcssXdKnPQ6Ho1De+dDQUBgYGMiVWlUVzJ07F0SEXbt25ds2PDwcXC5X7gQvvxIXFwdfX1/w+XysX79eqTF+ZfXq1eBwOHIvBOrmypUraNOmDbhcLoyMjDBmzBi5ajS4urqiV69ehSBhdtLS0mBtbZ1v6e2NGzeCy+XCwcEBJiYm+P79u0rl+NUqkBevXr0CEaFv377w8/OTOWF6eHhg8uTJePjwYa5PyuHh4SAivHnzRjZOUWcuzY3Dhw/DxsZGlpgqN2fcLVu2QEtLCy4uLmrJJfKnwyoDxZzQ0FCYmpoWire6Mjg4OICI8nQI+hXpzUlVi2V+MAyDoKAg6Ojo5Fle9s2bNzA2Noavr2+B3u/09HRZ/fdx48YV2LRZrVo1+Pn5FWiMgiIWi7F7927UrFkTRISyZcti6dKlCj2ltWzZEo0aNVKjlHkzd+5c8Pn8XJ+QpUpX9+7d8e7dO+jo6GDgwIEqm18eq8DPrF27FhwOR6aQxMXFYdu2bWjbti10dHRk/4cRI0bg8uXLWbYB7t69K/PREIvFEIlEWLBggcquRdXEx8ejf//+4HA4qFq1Ku7evZtju/v378PR0RH6+vrF2n+mJMIqA8WcChUqoFu3bkUtRq507doVfD5fYRN2o0aNULNmTTVJlZ2EhARUqFAhV4fA5ORkeHh4wMHBQSW5HBiGwfTp00FE6NSpk9IppKWJcxTdslAVCQkJWLBggUzpq1u3Lg4cOKDU/vPgwYNRrlw5NUgpHwkJCTA0NMSgQYOynVuyZAmICCEhIbJrmzlzJng8nsoS9kitAvJmWezSpUuu/gIpKSk4fPgwunfvDlNTUxARLCws0Lt3b5w4cQJv374F0f9LXLu4uKBPnz4quQ51cuXKFVSsWBE8Hg+hoaE5Wg9//PiBFi1agIgwevToYvugVNJglYFizIsXL4p0IZCHFStWgIgUTjW8Z88eEBHu37+vJsmyIw0VbN26dZandYZh0KVLF2hoaMhdWU9etm/fDpFIBG9vb6VS7YaEhMDCwkLle9f5ERUVhREjRkBfXx88Hg8dOnTIN2lMfkgr7xWlI9u4ceOgpaWVpVSwdBtp8ODBWT4XqampKFu2LOrXr19g687Hjx+hqampUMIoe3t7uSwTYrEY58+fzxaZQETo06cPEhIS0LZtW9SrV68AV1B4pKWlYfLkyRAKhXB0dMyxbLNEIsH06dPB5XLRsGHDQg9Z/R1hlYFizNy5cyESiYp1vu779++DiKChoaGQp3t6ejpKlSpV6OWY9+7dCyJCWFiY7NjSpUvVmv/gwoULMDIygpOTk0I17xMTE6Gnp6e0/4Iy3Lp1C3///Tf4fD709PQwbNgwlVVHPHjwIIgI79+/V8l4yvDlyxdoamrKyj9LrTehoaE5LvhHjx6V298kL4YMGaKQVSAyMlKuSo+/wjAM7ty5g3HjxoHH48m+m+XKlYO+vn6eoXzFjSdPnqBOnTogIvzzzz85vnenTp2CqakpbGxsiiRs9XeCVQaKMT4+PmovP1pQxGKxLIHKrVu3FOo7ZswY6OnpFbqyM3LkSPB4PERERODSpUsQCARZiuiog+fPn8PR0RFmZma4evWqXH3WrFkDDoeTq5e1qpBIJDh48KAsb4S9vT3mz5+fb34FRXnw4AGICBcuXFDpuIrSv39/GBoaYvTo0SAiTJgwIc8n/2bNmsHW1lZpL3ZlrAIbN24EEWWxYCiKk5MTunbtirCwMJQrV07m7Ovj44MFCxYUu+iCnJBIJFi+fDn09PRgbm6OHTt2ZPtfvXv3DtWrV4dQKMSyZcvY8EMlYZWBYkpsbCx4PB5WrFhR1KLki4+PD7hcLhYuXKhQv7dv34LD4WD16tVqkixnMjIyUL9+fZiYmMDMzAxeXl6FYob/8uULatWqBQ0NDezZsyff9tWrV0fjxo3VJk9SUhKWLVsmWyhq1KiBXbt2qS2XQUJCQrEotvXmzRtwOBwQEaZPn55v+xcvXkAoFCpdE2LIkCHQ19dXaJuoe/fucHFxUWo+Kd7e3rLMg7dv35ZZQBo3biyLTKhSpQqmTJmSZ2RCcSA6OlqWprhZs2bZrFWpqakICQkBEaFLly5s+KESsMpAMWXz5s0gIkRHRxe1KPkyZswYCAQCBAUFKdzXz88Pnp6eapAqb96/fw+hUAiBQFCoT0gpKSlo27YtOBwO5s6dm+sNWOoNro6CLR8/fsS///4LY2NjcLlcBAYGFlroalHnyWcYBoMHDwYRwcDAQG4lcPTo0RCJRApt8wD/twqMHz9eoX6Ojo7o16+fQn1+pU2bNmjYsCGAzC2nnyN4fvz4ga1bt6JNmzbZIhOuXLlSbBIU/crevXthYWEBHR0dLF68OJucGzduhKamJlxdXfHy5csikrJkwioDxZS2bdsWySKpDIcPH5Z5MyvK/v37QUS4ffu2GiTLnf79+4PH44HP5xf4pqsoEokEI0eOlMWQ5/Qk3rdvX5QqVUqlFosHDx6gW7duEAqF0NbWxoABA/Dq1SuVjS8Pnp6eRRYdI5FIZE+PY8aMARFhw4YNcvVNSEiAlZUVAgICFJpz8ODB0NfXVyhfwfv371Xip9C3b19UrlxZ9rednR1CQ0OztcspMsHS0hJ9+vRBeHh4oTuv5sf379/Rq1cvEBFq1aqVLZHUvXv3UKZMGRgYGMiiKVjyh1UGiiFpaWnQ1dXF5MmTi1oUufjy5YssU5qizmYZGRmwsrIq1GQ00v3YpUuXYtmyZUVmupaWpW7atGmWanhJSUnQ09PD6NGjCzwHwzA4ceIEGjVqBCKClZUVZs6cqfJkOvJSVF7tEokEPXr0AIfDwapVqwAATZs2RYUKFeR+Ct62bRuISFbKOj8+fvwIDQ0Nha0CW7ZsAREVuEDPxIkTYW5uLvvb19c335TMYrEY586dw6BBg2BnZyezoHTs2BG7d+8uVs7M58+fR/ny5SEQCDB+/Pgs4bvfv39Hs2bNQEQYO3YsG34oB6wyUAyRZg/LK7VrcUMah75t2zaF+44bNw46Ojoqd1jLidu3b0NDQwNdu3YFwzCysEJNTc0ieb+PHTsGHR0duLu7y7aEpKlzFTVJ/0xqairWrl2LSpUqgYjg7u6OzZs3F/lT3siRI2Fvb1+oc2ZkZKBTp07gcrnYuHGj7PjFixdBRDh48KBc4zAMg7p168LJyUmu91EZqwAABAcHq6QWybJly8DlcmXKzsCBAxVKHc4wDG7fvo2xY8fCxcVFFpnQvHlzrFu3rkDOjaoiJSUF//77L/h8PpydnXHx4kXZOYlEgqlTp4LD4aBRo0bFQt7iDKsMFEP69esHOzu7Yu3Q8yudOnWCSCRSyuT+7t07cLlctTtLxsbGwt7eHh4eHlmSmSQnJ8PNzQ1lypQpkifmu3fvwsrKCjY2Nrh//z5q1KihdKa+L1++YPLkyTA3N5c5W0VERBSbz9KyZcvA4/EKreBSeno6goKCwOPxsH379mznvby8ULNmTbnfn7t374LL5eZbTlxZqwAAlC9fXqHiX7khzeUhDSdctmwZ+Hy+0grhixcvMHv2bNSqVQscDgc8Hg/16tXDwoULVRZ+qiz3799H9erVZbkVfk6PHh4eDmNjY9ja2hY4V8bvDKsMFDMYhoGtrW2h72MXlKVLl4LD4cDV1VWp/s2aNVNrmVWxWAxfX18YGxvnmOP/1atXMDAwQLNmzYrEeer9+/dwdXWVOXPt3r1bof5Pnz5F7969oampCQ0NDfTq1UvuiouFyfHjxwts9ZCXtLQ0BAQEQCAQ5OqIeejQIRARzp8/L/e4ffv2ha6ubp7lqpW1Cnz8+FFpC9uvSC0f0j31iIgIEBGePHlS4LE/fvyI5cuXw9fXN1tkwqNHj4pE+RSLxVi4cCF0dHRgaWmJ/fv3y85FRkbC09MTQqFQtk3EkhVWGShmSL3I5d2XLC5IQ5e4XK5S5n6pE6K6NPcxY8aAy+Xm+b5Kq7tNmTJFLTLkR3x8PGxtbUFEWLlyZb7tGYZBRESEbG/U3NwckydPLtaJZZ49ewYiyjGrnCpJSUmBv78/RCIRDh8+nGs7iUSCSpUqoUmTJnKPHRsbC2NjY3Tt2jXH81KrgDSxkSJIS3zLU/gpP54/fw4iQkREBIDM2gjqyGj6c2SCtrY2iAjlypXDyJEjcfXq1UJXriMjI+Hv7w8iQmBgoOy9TE1NlTke/vPPP4VWKK2kwCoDxYxJkyZBV1dX5TXU1U1GRgY0NDRARDh58qTC/cViMWxtbdGjRw+Vy7Zv3z4QkVzlc8ePHw8Oh1MkFd6kjoPu7u4yj/ecnrDS09OxefNmeHh4gIhQqVIlrF27FikpKYUus6KkpqaCiLBmzRq1zZGUlIRGjRpBQ0NDrv+jtNyvIj4jy5cvBxHlmEBq0KBBSlkFgMz002XLllW4X078+PEDRIQdO3YAyFQeDQwMMG3aNJWMnxMpKSk4dOgQ/vnnH5iYmMgiE0JCQgo1MoFhGGzfvh1mZmbQ19fHypUrZUrJunXroKGhAXd390KxUJUUWGWgmFG1alW0bdu2qMVQirp160IgEGDixIlK9Z80aRK0tbVV+vmR1iMIDAyUy3QpkUjg5+cHIyMjtWf++5X169eDiPDy5UvMmjULRIT27dvLvKS/f/+OmTNnwsrKCkSERo0a4cSJE8XGH0BeLC0t8e+//6pl7ISEBPj4+EBbW1v2RJwf6enpsLOzw99//y33PGKxGO7u7vD09Mzy5PvhwwelrQIAULFiRZUpxAzDQCgUYtGiRbJjNWrUQOfOnVUyfn5kZGTg7NmzGDhwYLbIhD179hRKZEJsbCy6desmK7Il3Tq7c+cOHBwcYGhoiKNHj6pdjpIAqwwUI6TxxZs3by5qUZQiNDQUIpFIaee36Oho8Hg8LF26VCXyxMfHw9nZGc7OzgptXUgdDatUqVKoT9u1atXCX3/9Jft7586dEIlE8PT0RHBwMLS1tSEUCtGtWzeVVdIrCmrXro2OHTuqfNy4uDjUrl0burq6WbzK5WHhwoXg8XgKPSlK9+R/zqBZEKuANERXlWGu1tbWWRSvrl27olq1aiobX15+jkyQRrhoamqiRYsWWL9+vdo9/U+dOoUyZcpAJBJh6tSpSE9Px7dv39CkSRNwOByMHz++2CZaKixYZaAYsXz5cvB4PJWU0C0KpAmEdHR0lI7rbdmyJSpXrlzgp12GYdCqVSvo6uoq5UgnDUFUx7ZFTkjz9v+caOby5cuyegFcLhd9+/bN02mtpNCxY0fUrl1bpWN++/YN1apVg4GBgVIFa5KSkmBiYqJw4ay///4bpqam+P79e4GtAlLvf1V65nt4eCA4OFj294wZM6Cnp1fk1qQXL15g1qxZqFmzJoioUCITkpKSZHVJXFxccO3aNUgkEkyaNAkcDgd+fn4l9t6rClhloBjRpEkThUsBFyekDkpEhLt37yo1xrFjx0BEuHLlSoFkmTFjRoGdpaTx/oXhfTxgwACYmZkhKSkJu3btQo0aNWSOWJMmTUKZMmVgYmKCy5cvq10WdfPvv//C0tJSZeN9+fIF7u7uMDY2VrhY1s9MmjQJGhoaCiX7iY6Ohra2NgYOHIhBgwbBwMBA6fDUAQMGwMHBQam+ueHn54eWLVvK/j5w4IDKHBRVxYcPH7JFJlStWhVTp07F48ePVT7f7du34eHhAQ6Hg4EDByIhIQHHjx+HkZER7O3tC/QZKsmwykAxISEhASKRCHPnzi1qUQqEnZ0duFwulixZolR/iUQCe3v7XD215SE8PBxcLlclpX979eoFkUik1vjk5ORk6Ovro0GDBrJ69D4+Pjh48KDMdPn161d4eXlBJBIVOE1tUbNmzRoQkUq2YGJiYuDi4gIzMzPcv3+/QGPFxsZCW1tbYX+GGTNmgMvlQiQSKe0vAwCurq4F+tznRJcuXVCrVi3Z39JojtOnT6t0HlXx/ft3bNmyBa1bt5ZFJpQvXx6hoaGyJ3lVkJGRgbCwMGhqasLW1hZHjx7FmzdvUKVKFYhEIrU6uBZXWGWgmLB3716Z81hJpkOHDtDW1pZVS1OGqVOnQlNTU6knrDdv3sDY2Bi+vr4qSUGampoKT09P2NraqiVk7927d2jSpAmICHw+H3///Tdu3ryZY9uUlBS0b98eRIRZs2YVualXWc6cOQMiwrNnzwo0TnR0NJycnGBhYaGyJ8jBgwfDwMBAIR+T1NRUGBgYgM/nK1SZ8Ge+ffsGDoeDdevWKdU/N4YPHw5HR0fZ3+np6RAIBEor64VJcnIyDh48iG7dusHY2FiWTjskJAQnT55USWTCq1ev8Ndff4GI0KFDB0RGRqJHjx4gIvTs2bNEROioClYZKCZ07doVFSpUKGoxCszChQvB5XJhZ2en9BgfP34En89XuCRycnIyPDw84ODgoNK9v8jISJiYmKBRo0Yqy3F+8+ZNdOjQAXw+HzweD3Z2doiKisq3n0QikRXZ6d27d6Fl8lMlb968ARHh+PHjSo/x7t07ODo6wtraGs+fP1eZbFFRURAIBAgLC5O7z4cPHyAUCpVKFiVFar5Xdajb7Nmzoaenl+WYs7Mz+vfvr9J51M3PkQnSXByGhobo1KkT9u7dW6CSxQzDYMOGDTAyMoKRkRHWr1+PVatWQSQSoUqVKjkmKfsdYZWBYoBYLIaJiUmOFcVKGjdu3JD5DRSk/HLr1q1RsWJFuZ9+f64xcOfOHaXnzY1Tp06By+UWKCROIpHgwIED8Pb2BhHBwcEBoaGhICLs3LlTobFWr14NHo8HPz+/QqnpoEoyMjLA4/GwbNkypfq/fv0a9vb2sLe3V0uceLdu3WBpaZml8E1eDBw4EAYGBvD19YWtra1SC9OQIUNgY2OjcmvPhg0bsm3JBAQEZIlaKWkwDINbt27h33//RcWKFWWRCS1btsT69euVfhD4/Pkz/v77bxARGjZsiP3798Pe3h5GRkbyK65xccDmzcCAAUCtWkC5cpmvunWBoUOBHTuAAigu6oRVBooB0hCl38E5LC0tDSKRSKkF7mdOnjwJIpI7RGzp0qVqrz44ffp0hQrbSElKSsLSpUtRtmxZEBFq1qyJ3bt3QywWY+DAgTA1NVUqyVR4eDj09PTg5uaG9+/fK9y/KLG3t8eIESMU7vf8+XPY2NjA0dFRbV7njx8/BofDkWvfWBpBMGnSJLx48QJCoVCpegRVqlRRS7il1CE3MjJSdmz06NGwsbFR+VxFxfPnzzFz5swskQn169fHokWL5LK2/crRo0dhZ2cHTU1NTJgwAb6+vuBwOJg0aVLuPguRkUDv3oCGBkAECASZP39+SY/p6gKDBwMFrEqpalhloBgwYsQImJmZ/TZlNr28vGQe1soikUhQpkwZdOrUKd+2ly5dgkAgwIABA5SeTx4YhkHLli2hr6+PFy9e5Nv+48ePGDNmDIyMjMDlctG6dessCl9ycjIMDQ2VWhSl3L9/HzY2NrCysipRVS7r1auncHKtx48fw8LCAk5OTgWyOslDy5YtUb58+Xy/kwMGDICBgYGsMM6oUaOgoaGhUMKqHz9+gMvlqiVqRZom/GcHWGkJ75/LZv8ufPjwAcuWLUOjRo3A5/NBRPD09MS0adMUqsmQkJCAQYMGgcvlwt3dHcHBweBwOPD398/qF8IwwMqVgJYWwOdnVwBye/F4gIFBpqWgmMAqA8UAJycn/PPPP0UthsoYNmwYtLS0ULVq1QKNM3PmTIhEojzNfh8+fICFhQXq1KlTKKlOf/z4gbJly8LFxSVXc/D9+/fRtWtXCIVC6OjoYODAgTmas6VpcAu65x0dHQ13d3fo6uoWaB++MPnnn3/g6ekpd/v79+/DzMwMlSpVQkxMjBoly+TKlSsgIuzZsyfXNtHR0RCJRJg0aZLsWEJCAqysrBAQECD3XNKaGKr0fZAiTWR25MgR2bHr16+DiHJ1VP1d+P79OzZv3ozAwEBoaWlli0yQZ0vm2rVrcHFxAY/HQ2BgIAwNDVG6dOnMrUixGOjaVX4F4NcXh5P5c9iwTKWiiGGVgSJGGurzc4Wtko40eQqPxytQytFPnz5BIBBg3rx5OZ5PS0tD7dq1YWFhUajJeB48eAAtLS107NhRdkNhGAbHjx+XeSZbW1tj1qxZeUZEeHl5oX79+iqRKSEhAf7+/uDxeGovBa0KJk2aBBMTE7na3r59G8bGxnB3dy/UIkw+Pj6oVq1arovGr1YBKVu3boUixcZGjBgBCwsLtUSHpKWlgYiyRClI79MlNdOpMuQWmdC3b1+cOnUqzweJ9PR0TJs2DSKRSLZFpSES4VmdOv9f0Av6Kgb+YqwyUMSEhYVBQ0OjUPJ0FxbR0dEyJ0J588PnRlBQEMqXL5/jjbJ///4QCARF4mshveHPmzcPa9askTkyeXh4YMuWLflaKR49egQiwvbt21UmU0ZGBkJCQkBECA0NLdbpVaVWkfxM1deuXYOBgQGqVaumdNieskjLLedUYTEnq4AUhmFQp04dODs7y2Wtql69Otq1a6cSmXPCwMAAM2fOzHJMnfUhijsZGRmIiIjAgAEDYGNjI4tM6Ny5M/bt25erxe/Zs2cy599hZmZ5Lu4JRBhHBF8iGP53L1yXn0JQxDUSWGWgiKlbty6aNm1a1GKoHBsbG4hEogKXA5bGpJ89ezbLcem+p6rqGCjK58+fZVkCORwOmjdvjrNnz8r9dDdo0CCYmJjI7bEuLwzDYM6cOeBwOAgKCiq2cdJSp9m8aixcvHgRurq6qF27dpHcUxiGgZubW461NnKzCki5e/cuuFxuvknEEhISChRZIQ/lypXDkCFDshxr0KABWrdurbY5SwoMw+DmzZsYM2ZMtsiEDRs2ZNuilEgk2Dx7NuKJIMljYX/znwJgSwQfeZQBLhcwNwdy+TwVBqwyUIR8/foVXC5Xrtr1JY22bdvC0NAQfn5+BRqHYRiUK1cO7du3lx2T1g3o2rVroSfeefLkCYKDg6GhoQFNTU2UKlUKZmZmCu1jp6SkwNDQEMOHD1ebnHv27IGGhgZq165dqKZ1eZHuZecWmREREQFtbW34+PgUqaPbtm3bQERZUtRKrQKTJ0/Os29ISAj09PTy/GycOHECRKSWtLtSvLy8skUq9O3bFxUrVlTbnCUVaWSCVNHn8Xho0KABFi9e/P+InWHDwPB4eT7lpxLh43+/35DXMsDlArNnF9m1s8pAESJ9ui1OecJVxbx588Dn82FgYFBgc3VYWBiEQiG+fPkiqyjo4eGB5ORkFUmbNwzD4MyZM2jatCmICKVKlcKUKVPw5csXfPjwAaVKlYK3t7fcCYA2b94MVWTgy48rV67A1NQUjo6OanFOKwgSiQQikQgLFizIdu7EiRPQ0NDAX3/9VaBkMqogIyMDpUuXRlBQkOxY//79YWhomKtVQEpsbCyMjIzQrVu3XNuMHj0aZmZmalVqAwMDs1k3Fi1aBKFQWCKTVhUW0dHRWLp0Kf766y9ZZEKdqlWRIhIp5A8gtzJABNjaAkW0vccqA0VI69ati6ScaGEg9cbOzxQsD1++fIFQKMTMmTPh6+sLY2PjQskKlpaWhk2bNsHd3R1EBBcXF6xbty6baf/8+fPg8XgYNmyYXOPWrVsX9erVU4fI2Xj16hXKly8PY2Njhcv6qpty5cph8ODBWY4dPnwYQqEQ/v7+xWaLY9myZeByuXjx4gXev38vl1Xg575EhKtXr+Z4vnbt2mjTpo0qxc1Gnz594ObmluWYNI+HPCGyLJnpojdv3oxpNWsq7ByokDJABChRdVMVsMpAEZGamgodHZ0C76kXV1JTUyEQCMDlclXi3d6hQwcYGRmBw+Hg5MmTKpAwd759+4YZM2bAysoKRARfX1+Eh4fn+fQ2b948/FqCOCeePHkCIsK2bdtULXauxMbGwtvbGyKRSKUOiwXF19c3S0W9vXv3QiAQICAgQKkkTOoiOTkZZmZm6NWrl9xWASlisRhubm7w9PTMZiFLSkqCQCDA4sWL1SG2jPHjx2erEhkVFQUiwqFDh9Q692/HuHFgFMknoKgywOEARVQ3glUGigipp3JBK60VZ2rUqAEjIyN07ty5wGNNmTIF0uIh6uLVq1fo378/tLW1IRQK8c8//8ht1WAYBkFBQdDR0clz/3fIkCEwNjZWueNgfqSmpspSrc6YMaNYFDnq1asXXF1dAQDbt28Hj8dDUFBQoeSLUJRp06ZBKBQqZBWQcuHCBRBRtoyGp0+fVonlLD+WLFkCPp+f5X/OMAx0dHQwuwj3qEskzZopHE6okDLA5wM9ehTJpbHKQBEREhICe3v7YnFTVheDBw+Gnp4eypQpU6Bxnjx5Ah0dHejq6iqctS4/GIbBpUuX0KpVK3C5XBgbG2Ps2LFKJbZJSEhAhQoV4OTklGO9gJSUFBgZGWHo0KGqEF1hGIbB2LFjZUpVUS+6M2bMgJ6eHjZs2AAul4tOnToV2yyc379/h0AggIaGhlL3t7///humpqZZ8k6MHTsWxsbGag8B3bVrF4goW2hm1apVf6tkZ4VC7drq3SbgcIAiivJglYEigGEYWFtbqz19blGzY8cOmd+Aslnj4uPj4eTkBGdnZ8yYMQMCgQCfVJDTOyMjAzt37kT16tUhzUy2YsWKAjslPn36FLq6umjdunU2RW/Lli0gIjx9+rRAcxSUdevWgc/nw9fXt0i/q9LPB4fDQY8ePYqtIgBkRj/weDyIRCK5twh+7a+trY1BgwbJjtWtW1ehTIXKcu7cORBRtnS8HTt2RK1atdQ+/29FnTrqVQa4XEDFDzzyIu/6zSUWlXH37l16//49NW/evKhFUSs1a9aU/X7p0iWF+wOgrl27UnR0NO3bt4+Cg4OJx+PRunXrlJYpPj6e5s+fT2XLlqW2bduSlpYWHT58mB4/fkzBwcGkqamp9NhEROXLl6cNGzbQ7t27ae7cuVnOrVy5knx8fKh8+fIFmqOgdO3alY4fP05XrlwhLy8vev/+fZHIcevWLSIiat26Na1YsYJ4PF6RyCEPM2bMIF1dXWIYhpYvX65wfysrKxo7diwtWrSIHj16RKmpqXTt2jXy9vZWg7RZMTMzIyKiz58/Zznu5ORET548IQBql6EkI5FI6NmzZ7Rz50669/UrSdQ5GY9HZG6uzhkKjio1iz+dCRMmQF9fv8jNtOqGYRhYWlpCT08vW9ITeZgxYwaICPv27ZMd69y5M0qXLq2waTUyMhJDhw6Fnp4e+Hw+OnbsmCV2XNWMHDkSPB5PloHx6dOnICJs3bpVbXMqysOHD2FrawtLS0u1lH3Oi7lz58qsRvk5XRY179+/h1AoxJQpU9CzZ0+Ym5srFemQmpqKsmXLokGDBoiIiAARFcr7/u3btxzf5927d4OI8PnzZ7XLUFJISEjApUuXsHTpUgQHB6N69erQ1NSUfVZH8fkQq9MyQARs2FAk185uExQBHh4eak0/WpwIDAyEmZkZatSooVC/8PBwcLlcjBkzJsvxS5cugYhw4sQJuca5ceMG2rdvDx6PBwMDA4wcOVKpsqaKkpGRgfr168PU1BRRUVEYOnQojI2Ni024nJSPHz+iSpUq0NHRyVLMRp1IS0GHhoZCS0sLYWFhhTKvsvTr1w9GRkaIi4vD8+fPweFwlI6QkRYlCgoKgoGBQaFsjTAMAz6fjyW/eKlLU2KfP39e7TIUNxiGQWRkJA4ePIjJkycjMDAQjo6O4HA4IMpMNmRtbY3SpUvDwMAARAQul4ueTk5yKwGLiDCZCH3+UwZa/ff3ZCL8yKtvEW0jsspAISMN6SlOT4jqZMGkSQjm8bCGw4GkYkXAxAQwMgJKl87cG5s1C/il3OubN29gbGyMxo0bZ7tZMgyDSpUqoVWrVrnOKZFIsH//ftStWxdEhNKlS2PhwoWFnsnu06dPsLa2RvXq1WFkZKSUdaQwSExMRLNmzcDlctWaFpdhGEyYMAFEhAkTJsj+l3379lXbnAVFahWYOnWq7FibNm1QpkwZpRfypk2bQiQSoUmTJqoSM18sLS0xfvz4LMdSU1NLTGGrgpCamorbt29j3bp1GDhwIHx8fGBoaCh72jc0NEStWrXg5+cHb29vWb0CIkLlypUxaNAgHDx4MNP5UyIB7Ozkiiiw+2+MnF5vcvMXKMK8M6wyUMgsW7YMfD6/0IuuFDofPgC9ekEiFEJChPScPvw8XuYXgMMBmjQBrl9HcnIyPDw84ODgkGvp4kWLFoHH42XL3JiYmIglS5bA0dERRITatWtjz549ReqYdvXqVfB4vBwduIoTYrEY/fv3BxFh+PDhKvdwZxgGo0aNAhFh+vTpsuNNmzYt1EVRUfr27SuzCki5efMmiAg7lKxFL30i/+uvv1QlZr64ubmhT58+2Y6XLVs2W+Knksznz59x8uRJhIWFoWPHjnBxcZFlDyQiODo6IjAwEKNGjcKoUaPQpUsXVKhQQXbeyckJISEh2LVrV+5pvOfMAaOqaoW/vjZtKtw37CdYZaCQ8fPzU1nZ2mIJw2R+oHV1M2Nm5f0S8HhgOBwcqlQJ+hoauHv3bq5TfP/+HZqamrKETR8+fMDo0aNhZGQELpeLtm3b5prxrSgoW7YsiAgbN24salHyZf78+eBwOGjdurXK0j0zDIPBgweDiLIV7unfvz+cnZ1VMo+qiYqKymYVkNKwYUO4u7srFRosLdIkFArx5hermLpo1KhRjta0Zs2aFbh+SFEgFovx9OlTbN++HaNGjYKfnx8sLS1li7qWlhaqV6+O4OBgLF26FOHh4di5cyeGDBkCd3d32XZA6dKl0b17d2zZskXutPAfXr3Ce01NZKhSCeDzAU9PoAgfXFhloBBJSEiAUCjE/Pnzi1oU9cAwwLBhmR9uJTVnCRFiypcHcojT/5lu3brBwsICnTt3hkAggI6ODgYNGlRoN1d5efbsGYgIderUgaamZp5KTnFh37590NTURI0aNQrsXCaRSGRllX/dswYyHQk1NTWLZb6NnKwCUk6dOgUiQnh4uMLjTp06Fbq6urC0tMxzu0uVdOzYEV5eXtmODx8+HA4ODoUig7LEx8fj4sWLWLJkCYKDg1GtWrUsTn1WVlZo0qQJRo0ahR07duDp06eIj49HeHg4Ro0aherVq8usc1ZWVujUqRPWrVunVErznTt3Qk9PD7U4HEiIwKhCEeBwAIEAKGLLIasMFCJ79uwBEeHVq1dFLYp6+Pdf1WjJPB7g7Q3kkJKWYRgcO3YMnp6eICKYmpoiLCxMqdjvwmDYsGEwMjLCt2/f4ObmhtKlS5eILaLr16/DzMwMpUuXVjovglgsRo8ePcDhcLB69eoc2+zbtw9EyuehUBd5WQWAzM9h1apVlbLyNWrUCH5+fti6dSuISO3ptQFg6NChKFeuXLbja9asAYfDKbSiX3khdeo7cOAAJk2ahMDAQJQpU0a26PP5fFSuXBmdOnVCWFgYTp06JTPlp6am4ty5cxg/fjzq1q0LgUAguz8EBQVh+fLleP78udJK5/fv32UZPLlcLjQ0NNBfwYJFuSoCHA6we7cq30qlYJWBQqRLly6oVKlSUYuhHk6fzvNDn0qEEUSwIIIGEaoRITy/L8lPDk8pKSlYvXq1bH+vatWqsLW1RbNmzYrumvMhNTUVJiYmsj3ZV69ewcDAAE2bNlV71jlV8Pr1azg7O8PQ0BDnzp1TqG9GRgY6deoELpeb5/bInTt3QES4cuVKQcVVKXlZBaRIM/tdU6CwTHp6OrS1tWUpoevUqQNnZ2e1hxnPnDkTBgYG2Y5fvnwZRFToFiupU9/atWtzdeqrV68eBg0ahHXr1uHOnTtZUnhnZGTgypUrmDp1Kho2bCizFBgaGqJly5ZYuHAhHjx4oBKL0+nTp2FlZSVTMLS1tWFjY4NHjx4Bq1dnmvjzKWmc60OPSATs2VNgGVUBqwwUEmKxGMbGxhg9enRRi6J6EhMBK6tMZ8BcPvjtiMAnwjAirCBCzf/+vpDPlyX2zBlMmDABpqam4HA4aNGiBc6fPw+GYbBs2TLweLz/1xkvZmzfvh1EWWvVS0PLFM1vX1R8+/YN9erVg1AoxJYtW+Tqk56ejqCgIPB4vHwLI/348QPFLbpGahWYNm1anu3EYjHKli2rkKn/6tWrWZSfO3fugMvlZvOlUDXr1q0DEWUrABUbGwsiUmsBK6lT3+zZs9GxY0dUqlQpm1Nf69atMXnyZBw6dAjv3r3LtoiLxWLcunULYWFhaNKkCXR1dUFE0NHRQZMmTRAWFoZbt26p1Fk4OTkZgwYNkikAQqEQGhoacHd3z+pfcO8e4OKSec/K4x6YRQkgAmrVAopR1UhWGSgkpMVKipNjm8pYujRPH4Fr/33pZ/90LIUIZf5TCnLrJ+ZwsJPLhaamJkJCQvD8+fMs08bFxUFbWxsTJ04sogvPm/r166NOnTrZjo8fPx4cDgfHjx8vAqkUJy0tDZ07dwYRYcqUKXk+baWlpSEgIAACgQB79+6Va3xDQ8N8F97CJCQkBEZGRjnWl/iVVatWgcPhyL2VMnPmTGhra2exBPTp0wd6enpq3SqRKqE5Kc5mZmaYMGFCgecQi8V48uQJtm/fjtDQUPj5+cHCwkK26Eud+nr16oWlS5fi8uXLuYb7MgyDhw8fYuHChQgICJBZDTQ0NNCwYUNMnToVV65cUZtF5fbt26hQoQL4fD40NDRgbm4OHo8HPz+/nGVOTwe2bAFq1Pj/PUwg+P/rZ2fqevWAvXszwxSLEawyUEgMHz4c5ubmJcI8rBAMAzg55akMDCcCjwhxvxyf9t9N4l0eCoGEw0Hso0e5Tt+zZ0/Y2NgUu7z2z58/BxFhUw6hQhKJBH5+fjAyMip2Do+58XOOgH/++SfHm3BKSgr8/f0hEolw+PBhucd2d3dXazVKRXj37p1cVgEpqampsLCwQPfu3eVq36RJk2whhV+/foWRkRG6deumsLzycuPGDRARbt++ne1c3bp1FU6CJnXqW7x4MXr27JmjU5+/vz9Gjx6NHTt24NmzZ3l+RxmGwfPnz7FixQoEBQXBzMwMRASBQIA6depg/PjxOHfunNqrfWZkZGDq1Kng8XgyGZydnUFE6NGjBzIyMvIf5O3bTB+AMWOA3r2BPn2AceOA/fuB6Gi1yl8QWGWgkChfvjx6FFFpSrXy7Fm+ZrGGRHDO4fip/24cB/Pqz+EAeSRFkcZ8F7e67CNGjIChoWGujlmxsbGwt7eHh4dHsctKmBcbNmyAQCBAw4YNszhtJiUl4a+//oKmpqbc2SGltGrVCg0bNlS1qEqhiFVAyqxZsyAQCPLdrhKLxdDT05OFxP7MsmXLFPY/UITIyEgQEY4dO5btXHBwMNzc3HLsxzAM3r59iwMHDmDixIlo1aoVSpcuLVv0pU59nTt3xpw5c3D69Onc4/N/4e3bt1i3bh06deoEa2trSDP/Va9eHaNGjUJ4eDiSkpIKdN2K8PLlS9SsWRMcDge2trbg8XgyR+WpU6cWy4gXVcIqA4WANC/9wYMHi1oU1bNlS77KQEUi1M/h+KP/bijL8+ovEADBwXmKUKVKFfj7+xfSBedPWloaTE1NMXDgwDzb3b59GxoaGnI/VRYXzpw5A319fVSqVAmRkZFISEiAj48PtLW1ZbUYFGHo0KFwdHRUvaAKoqhVQEpcXBz09fXzLU0tVVwvXLiQ7ZxYLIabmxs8PT3VYj1MSUkBEWFDDnnv582bB01NTSQlJeHWrVtYu3YtBgwYAG9vb1kqXiKCkZER6tWrh8GDB2P9+vW4e/duNh+EvPjw4QO2bNmCHj16yBQKDocDd3d3DBkyBIcPHy6StYNhGKxYsQLa2tqwsLCAsbExSpUqhapVq0IgEORo3fsdYZWBQmD27NmyL9tvx8iRmQt2Hgt6aSL45XD81X83mXn5KBOoUiVPEVauXAkul4vIyMhCuui8kZbmffjwYb5tpY5dq1atKgTJVMfjx49hb28Pc3NzuLq6QldXFxcvXlRqrMWLF0MgEBT5Vk9ISAiMjY0VsgpIGT16NHR0dPIMG50zZw40NDRyNXVL/YrWrl2r8PzyoKenh9mzZwPITJUdHh6O2bNno169epCGzEkX6LJly6JNmzaYMmUKDh06hKioKIWfjL98+YLdu3cjJCQETk5OMqWiQoUK6NevH/bu3ZtrltHC4uPHj/D39wcRyfIR1KxZExUqVIC+vj7OnDlTpPIVJqwyUAjUqVMHzZs3L2ox1EPv3vkqAwWyDBABZcrkKUJCQgJ0dXUxduzYQrrovGnQoAFq164td/tevXpBKBTi+vXrapRK9Tx9+hTa2togIsyZM0fpcQ4fPpzpO/LunQqlUwypVeDnVMmKEBMTAw0NjRy3AKQ0b94c9erVy3OcDh06wMzMTGV5M8RiMR4/foxt27bBwMAADg4O2Zz63NzcQETo169fnk59+fHjxw8cPHgQgwYNgqurq2wOR0dHBAcHY9u2bfj48aNKrksV7NmzB8bGxjAxMUHNmjVl/jBWVlawsbHBgwcPilrEQoVVBtTMly9fwOVyS9yTn9z07ZuvMlAgnwEifDc3R3h4OJ49e5br/nrv3r1haWkpn4OPGnnx4gUUTT2cmpoKT09P2Nrayr3fWtR8+fIF7u7uMDIygo+PD7hcLhYvXqzUWNJc/YrmMlAlffr0Udoq8PMYpqamOVoAJRIJDA0N8/Xaf//+PbS1tZWqFxAXF4cLFy5g8eLF6NGjBzw9PbM49QmFQlhbW2PMmDHYuXOnzKlPIpFAQ0MD8+bNU2i+xMREHD9+HCNHjoSnp6fMsmBjY4MuXbpgw4YNRarg5caPHz/QpUsXEBHq168PBwcH6OvrY9KkSdDT04Obmxuii7Gjn7pglQE1s2HDBhBRsdKIVcq0afkm3BhGOUcTTCU5ogmIcIKyVvwyNzdHtWrV0KZNGwwbNgyLFy/GggULQERyx8Kri5EjR8LAwEDhjG6RkZEwMTHBX3/9VeTm8vyIiYmBi4sLzMzMcP/+fYjFYlk89pAhQxTe805KSsp1P7swePfuHQQCgdJWASmvXr3KVSm6e/cuiEgun4rp06eDz+dnJrXJAYZh8ObNG+zfvx8TJ05EQEBAFqc+gUAAV1dXdO7cGXPnzsXp06fx9etXtGzZMtc6BK6urujVq1eecqWkpCAiIgJjx45F7dq1ZUl4zM3N0b59e6xcuRIvX74s1o52Z8+ehZ2dHXR1ddGzZ09oamrC1dUVs2fPhkAggK+vb4EUwpIMqwyomcDAQFSvXr2oxVAfJ07k60B4lbLnGUglgiMRqufTN4PDwcyfEpSYmpqiYsWKqFq1Ktzc3ODg4CC7KUlfBgYGcHV1RfPmzdG/f3/MmTMHu3fvxo0bN/D582e13azS0tJgZmaGAQMGKNX/1KlT4HK5GDNmjIolUx3R0dFwcnKChYVFlmRKQGY1SS6Xi1atWinsH2Nubq6SWHdlUIVVQEr79u1hb2+fzUK1YMECCIVCuZTE1NRUODo6okGDBkhOTsbNmzexZs0aDBgwAHXr1s3i1GdsbIz69etj8ODB2LBhQ55OfcHBwfDw8MjxXLt27VC3bt0sx9LT03Hp0iVMnjwZ9evXh0gkgtSRMDAwEIsXL8bjx4+L9eIvJSUlBcOGDQOHw4GXlxfat28PIkLXrl0xfvx42RaBujNBFmdYZUCNpKSkQFtbO9f85r8FsbFypeJsQ5kZB4dTZgbCWv/9fS6ffiCCeP9+PH78GJs2bcKgQYNQt25d6OjoyG6I9vb28Pf3h4+PD4gIAwYMQJ8+feDn54cKFSrI9rV/3id1cnKCr68vgoODMW3aNGzZsgUXL15EVFSU0k/m0vS0BdlrnD59OogIBw4cUHoMdfHu3Ts4OjrCxsYGL3LJnHbw4EFoaWmhWrVqcifR+ZGRAaf27VF92jTMefcOi9+/x/HYWHxRwFNdWaRWgRkzZqhkPKkF4FcLVatWrXJMQPUznz59wokTJzBr1izZZ/lnp75y5crJnPoOHz6ssFPf2LFjYW1tneO5CRMmwMzMDDdu3MCsWbPQuHFj2fdGT08PTZs2xdy5c3Hnzp0Slyvl7t27qFSpEoRCIUaNGoUqVapAJBJhxYoV6NGjB4gIkyZNKhFKjTqRd/3mAADlQ3x8POnr61NcXBzp6enl1/y35/jx4+Tn50cPHjygSpUqFbU46qNtW6J9+4jE4lybpBLRWCLaTETfiagyEU0mIt/8xjYzI4qOJuLzsxxmGIZevHhBt27dotu3b9OtW7fo1q1blJCQQEREdnZ25OHhQVWqVCEPDw8qXbo0JSUlUWRkJEVGRtLbt29lv0dGRtK3b99kY/P5fLKxsSE7Ozuys7Mje3t72e92dnZkY2NDQqEwm6iNGjWipKQkunTpkhxvWs4AoMDAQDp9+jTdvHmTypYtq/RYquTNmzdUv359IiKKiIgge3v7XNveunWLmjZtSpqamnT06FFycnLK1iZVIqFdX77QouhouvHf/4wA4nE4xFCm1kZEVEFLi/pZWVFHc3PS/eUzoAr69OlDu3btordv35KOjo5KxvTz86Po6Gi6d+8ecTgcAkBmZmbUu3dvmjx5MonFYnr+/Dndu3eP7t27R3fv3qV79+5RTEwMERFpa2tT5cqVKTo6mhITE2nPnj3k6elJ2traBZJr8eLFNHToUEpNTSUOh0MMw9CjR4/ozJkztHnzZrp58yYREWlqalKdOnWoXr16VL9+ffLw8CC+Gt57dSORSCgsLIzGjh1Lzs7OFBwcTGPHjiUDAwPasGEDTZs2jU6dOkWrV6+mLl26FLW4RY7c67cqNYs/hT59+sDBweH31zjPncv36V6pF5cLKJBqWCKRoGPHjjAwMMCQIUNQv379LCZVa2trtGjRApMmTcLhw4ez+HHEx8fj4cOHOHLkCJYuXYoRI0YgKCgINWrUyOJ9Tf89pVlaWqJmzZpo164dRo4ciUmTJoEoMzlJYmJigd7OHz9+oFy5cnBxcSnwWKrg+fPnsLa2hqOjo9wOYW/fvkXFihVhYGCAs2fPZjl3PDYWFpcugSIiwI2IAOXx4vz3MrhwAdtiYlT6XYqMjFSpVUDK2bNnQUQ4cuQIfvz4IfMb8vPzQ9WqVaGhoSH7LNnY2KBp06YYM2YMdu3ahefPn8uevF+8eAGhUKiy7RNprYy5c+eiTZs2MDExAVGmY2HVqlVBRFi2bJlCuQOKK69evYKXlxc4HA6GDx+O0NBQEBGaNWuGR48ewc3NDbq6uoVSMbKkwFoG1AQAsrGxodatW9P8+fOLWhz107Yt0d69RBKJSoYTE1GSvj7pvHtHPAU+Sw8fPiQXFxfavXs3BQYGEgB68+aNzHIgtSRILQGWlpYy60GVKlWoSpUqZGlpmW3ctLQ0ioqKytWy8O7dO2IYRtbe2Ng4V8uCnZ0dGRoaEofDyfU6Hj16RNWqVaOWLVvS5s2b82yrTp48eUINGjQgfX19OnPmDFlYWMjd98ePH9S6dWs6f/48rV27ltr//TcNfPGClnz4QFwiYvId4f9wKHP1bGNqShudnEiDx1PwSrKjSqsAAIqMjKS7d+/S3bt3aeHChZScnExpaWmyNpUrVyZ3d3dydXUlNzc3qly5MhkbG+c57qhRo2j+/Pn05MmTPK0xufHmzRuKiIigM2fO0IkTJ+jr16/E4/GoWrVqVL9+fapXrx7VqlWLiDItEmvWrKFu3bopPE9xAQCtXbuWBg0aRCYmJrRw4UJauHAhnTlzhqZMmUJNmzalpk2bkkQioaNHj1LlypWLWuRig7zrN6sM/I+9sw6LauvC+JqCoVs6REFFwMRAbDFAUcTCFru7u7u79dpeuxtbsRUUxUQUFURQOua83x845zIyM8wMg6Afv+c5z72e2GefYebstdde611K8uDBA6pSpQpdvHiRda/+1cTGUpaTE9H376QOhyKIqD4RcevXp507d0odoGVRq1Yt0tHRoXPnzklv++eL+9clhq9fvxIRkYWFhYRxULlyZbKxsZE5IGdkZJCNjQ35+PhQr169chkK4i0tLY29RldXV66xYG5uTvv376fAwEBauXIlDRo0SOHnVxehoaHUsGFDsrCwoAsXLlCJEiWUbiMjI4P69etHW7dtI7c9eyjM3JzyfJHIgUtEdQ0N6ZSbW74Mgvfv31Pp0qVp5syZNHbsWKWuTUtLo6dPn7Lu/UePHtGTJ0/o+/fvRJRtCFpbW9OTJ09o8uTJFBISQomJiXTz5k2l+5mUlERlypShmjVr0oEDB/I8/+PHj+zgHxwcTO/evSMOh0OVK1cmd3d32rp1K507d468vb1zXevo6Eht27al+fPnK93PokBMTAz17t2bjh07RkFBQRQYGEg9evSg9PR02rt3L3E4HPL39yc7Ozs6deoU2djYFHaXixTFxkABMW3aNFq2bBnFxsaSQCAo7O4UONeuXaMpzZrRqdRUEnI4xMmvh2DtWrrk7EydO3emzMxM2rZtG/n6+ip06T///EPdunWjly9fUunSpRW6BgBFRUVJGAf379+nmJgYIiIyMzOTMA6qVKlCdnZ2xOFw6ODBg9SmTRt68uQJubm5yWw/NjZWqldBvIkHEyIiDQ0NsrOzo/T0dPrw4QP17NmTateuzRoLNjY2BbqO++DBA/L29iZ7e3s6f/58njNYeQCgBjt20GVbWyI1eDi4RNTNwoK2SIlFUJT+/fvTgQMH6O3bt3K9Al++fJFY13/06BG9ePGCRCIRcTgccnJyoooVK7Kz/QoVKpCVlRUBIFdXVypdujSFhIRQz549ac6cOSr1dffu3dSpUye6cOECNWzYUOJYTEwMXb58mTUAIiIiiIjI1dWVGjRoQA0aNKA6deqQkZERff36lczMzOjgwYPUunXrXPfx8fEhPp9Px44dU6mfhcnRo0epd+/eRES0YcMGev/+PY0cOZKqVatG+/fvpytXrlD37t2pbt26dODAATIwMCjkHhc9imMGCohKlSohMDCwsLvxWzh58iSEQiEaNGiApOBgwNRUoQyDXzeGx8su9bl5M9t2TEwMfHx8QEQYPny4QlXLUlJSYGRkhDFjxuTruRiGwYcPH3D06FFMmTIFvr6+EvEDJiYm8Pb2RsmSJeHs7Iw3b97ka007Pj4ejx49wtGjR7FixQqMHDkSrVu3hq6uLhtVLt64XC5sbW3h5eWFTp06YeLEidiwYQPOnj2L58+fK61zkJOQkBAYGhqiWrVqcuV1FeX+jx//xQacOgXq2hXk4QH6WZOexo7NHS+wZg3Izw/k5ATi8bLP++Wck1+/qtQfcazA/Pnz2X2ZmZl4+vQpdu/ejTFjxqBJkyYwNzdnP28dHR14enqif//+WLduHW7fvp1nPIdYapqI8lWummEYeHl5wcXFBTExMThy5AiGDBkCNzc3tn1nZ2f069cP+/btw5cvX6S2IxKJwOPxsHbtWqnHhw8fDicnJ5X7WRj8+PEDQUFBICL4+fnhzZs3aN++Pfu+SE9Px5w5c0BE6Nat218RD1FQFKcWFgDv378HEWHPnj2F3ZUCZ+/eveDz+fDz8/tPHTAuDujUKXuQz1nHW54RQIRXhoaAFKEVhmGwZMkSCAQCVK5cGREREXn2a+jQoTAzMyuQH390dDSOHz+O6dOno2HDhhKDtJGRERo2bIgxY8Zg3759ePnyZb6D3qKjo2FhYQEvLy88efIEZ86cwfr16zFhwgR06tQJXl5esLW1zWUwlChRAh4eHmjTpg1GjRqFlStX4tixY3j8+LFMudvr169DT08PtWrVUtvvuOq9e+CJB/E9e7L7Z24O+imDK9UY6NYNxOeDnJ1Btra5jAFucDBsbt5ElgqfbY8ePWBgYICFCxeiZ8+eUoP6WrRogUmTJuHff//Fy5cvVUqnS09Ph6GhITgcjsoaBomJiTh16hSrmMfhcEBEsLe3R48ePbBjx448qyXmxMLCAtNlBOWuX78ePB6vwMsEq4tr166hZMmS0NXVxaZNmxAWFoayZctCV1cX+/fvR2ZmJvr27QsiwpQpU/7+QO58UmwMFACrV68Gn89HfHx8YXelQNmwYQM4HA46d+4sXazj7l2ge3dAQyN74OdwAIEADJ+PzJwGQaNGuDRsGLhEuHXrlsz73bt3D6VLl4aurm6ecr/Pnj0DEWHv3r35fUy5TJgwAQYGBnjz5g1OnTqFmTNnolWrVrAVD2BEMDAwQP369TFq1Cjs3r0bL168UHpwuXbtGvh8vtzKeBkZGXjz5g2Cg4Oxbds2TJ8+HUFBQWjYsCFKly4NDQ0NCWPBwMAA7u7uaNGiBQYPHoz+/ftDU1MTlStXzreXQ8zd798lB/mzZ0EHD2b//7p1so2BgwdBZ85k/3+rVlI9AxQcjKNy5JsZhsGbN29w+PBhTJ06Fa1atWJL5RJlK/VVrFgR3bt3x9KlS3Hp0iW1F86pXLkyiEjhIlopKSm4cOECJk6ciJo1a4L/U3DL0tISTk5OEAqF+Spz7O7ujoEDB0o9duXKFRCRTOXDokJaWhrGjBnDCgi9fv0ae/bsgY6ODsqXL4/nz58jMTERPj4+4PF42JzD01iMbIqzCQqApk2bUlZWFl24cKGwu1JgLFy4kMaMGUMDBw6kFStWEJfLlX1yairRkydE9+8TfflCyMqiKUuW0H2RiBqOHk0jZ88mkUhElStXJkNDQ7p8+bLMYL3ExEQaOHAg7dixgzp37kxr1qwhPT09qefWqVOH+Hw+Xbp0SR2PnIvMzEyys7OjgIAAWrVqVa7jsbGxEjEIDx48oHfv3hERkb6+PlWqVEkiUNHJyYl4coLili9fTsOGDaP9+/dT27Ztle4vwzD0+fNnqfEKT58+pcjISInztbS0yM7OTmaQo5WVldz+EhH1e/GCNn/+TFnSXh8vXhD160c0dixR06ayG1m+nOjIEaLgYIndPCJqbGxMp9zdKTU1lZ4+fSqxvp8zqM/U1JQqVKhAsbGx9PbtWzp37hxVrlxZql6EugBA1tbW9O3bN+rXr5/UrKKMjAy6c+cOG/B38+ZNysjIIFNTU6pfvz6b6+/s7Ezfvn0jZ2dnatWqFW3evFmlPnl7e5ORkRHt378/17HY2FgqUaKEzJiCokBoaCh17tyZwsPDaebMmTRkyBAaM2YMrVq1ijp16kTr16+nxMREat68Ob148YIOHDhATZrkqWZSDBXHDKid79+/QyAQYPny5YXdlQKBYRhMmDABRISJEyeqPHts2rQpTExM0LJlS3bfyZMn2fzsvPjnn3+go6OD0qVL4969e1LP2blzJ4gIL168UKmPeXHw4EEQER49eqTwNV+/fsW5c+cwd+5ctG3bVkJTXldXF15eXhg6dCj++ecfhIWFSaghMgyDDh06QEdHJ5cUcH44ceIENDQ04OPjgw8fPuD+/fs4dOgQli5dimHDhsHf3x+VK1eGsbGxhGeBz+fDwcEBdevWRbdu3TBlyhRs3rwZFy5cwMuXL5GWlgbn27dl6wjI8wzk3OR4Bvhnz6Kciwt4P+MKOBwOypQpg3bt2mHOnDk4efIkPn78CIZh8O7du1yxAgWJuGhVhw4doK2tjdjYWGRmZiIkJATz5s1D48aNoa2tzXpp/Pz8sGzZMjx+/Fim52jNmjUgIpW9Ax07dkTdunWlHmMYBsbGxnIrLxYWWVlZWLhwITQ0NODq6oqHDx/i/fv3qFGjBgQCAdasWQOGYfDs2TPY29vD0tISDx8+LOxu/1EULxOoGbEk7Zs3bwq7K2pHJBJhwIABICK2LrqqTJs2DUKhEJaWluw+hmFQt25duLm5KSQJHBERgcqVK0MgEGDJkiW5DJPU1FSYmJjIda3nhyZNmqil7sS3b99w8eJFLFiwAO3bt0fp0qXZAVdbWxuenp4YPHgwtm7ditu3b6N8+fIoU6aMWn5nhw4dgkAggL+/v0LxFYmJiRLiTGPHjkWHDh2kijORUAi6eLFAjQEKDkan0aOxfv36PIP6+vbtC1NT098m5LRp0yZwuVwcP34cAoEATk5O0NfXZwMSmzZtigULFuDu3bsKS2BnZWWhQoUKqFatmkpxDMOGDUO5cuVkHvf09ETnzp2VbrcgeffuHerWrQsOh4ORI0ciNTUV586dg6mpKezs7FjD6MqVKzAyMkL58uUVXpYp5j+KjQE106VLF7i5uRV2N9RORkYGOnXqBA6Hgw0bNuS7vbNnz7KDRs4AqNu3b4NI8Qp2aWlpGD58OIgIPj4+iImJkTg+YsQImJiYyCx9rCpv3rwBh8MpsPXIhIQEBAcHY9GiRQgMDESZMmXY4DENDQ1wuVw4Ojpi06ZNePTokUoFVvbu3Qsej4f27durrUBLWloaXr58iQsXLmDO9u3yB3k1GQOXFMh4EHsFFixYoJbnlIV4drpq1SrY2dmxHgsejwc+n4/Jkyfjxo0b+fq8r169CiLCli1blL527ty5MDY2lnk8KCgIVatWVblv6oRhGGzduhV6enqws7PD5cuXIRKJMGPGDHA4HDRp0oQt+b1nzx5oaGigfv36f32sVkFRbAyokczMTBgbGxfpqnOqkJqaihYtWkAgEGDfvn1qaTM+Pp41Bg4fPixxLCAgAHZ2dkoN4CdPnoSpqSksLS1x8eJFdv/z589BpP7SxhMnToS+vv5vlQv+8eMHrly5giVLlqBOnToSs3BNTU14eHigX79+2LBhA+7fvy93pr99+3ZwuVx07dq1wEomP0tK+i3GwDkFgv769OlTIF4BhmHw6tUrbNy4EYGBgbCwsGCXUDQ1NVG9enVcunQJz58/B4/Hw7Jly9Ry344dO6JEiRIys0JksXnzZhCRTGNkwYIF0NXVLfTI+5iYGPj7+7MpgQkJCfj69SuaNWsGDoeDadOmISsrCwzDYMGCBSAidO7cuTh1MB8UGwNqRByNm59o36LGjx8/UL9+fWhpaeHUqVNqbdvFxQXa2tqYMGGCxH7xi3Px4sVKtffx40c0aNAAHA4HEyZMYF949evXz1WeNT9kZGTA0tISAwYMUFubqjBu3DhwuVwsX74cy5cvR9euXVG+fHk2xVBDQwNVqlRB7969sW7dOty9exdpaWnYuHEjOBwOevXqVaAV6KJSU3+LMXAzjwHx3bt34PP5avMKvH//Htu3b0f37t1hZ2fH6j54eHhgzJgxOHPmDMLCwkBEOHLkCHtdly5dYGtrq5YB68OHD9DR0cHw4cOVuu748eMgIkRHR8s9rky6oro5fvw4zM3NYWJigoMHDwIA7t69C3t7exgbG7OaDVlZWeyyZX7il4rJptgYUCMjR46EhYXFH1fiUxZfv36Fh4cH9PX1cfXqVbW3HxQUBH19fTRq1CjXsb59+8LY2FjpmU9WVhZmz54NHo+HmjVr4u3bt2yBFnWlTB0+fFjpwMGCIDMzEw0bNoSZmRmioqLY/cnJybh58yZWrlyJ7t27w93dnXVXiw2FcuXKYdWqVQgJCcmXQJE8GIaB3tWrBW4MfM/MlNuPPn36wMzMTGWvwOfPn7Fnzx706dNHIp6jQoUKGDZsGI4dO5bLNb1t2zZwOByJVMXQ0FAQEbZt26ZSP35l7ty54PP5Sn2vQ0JC5H53xUGPhVHAJzExEb179wYRwdfXF58+fQLDMFi3bh00NDRQrVo1NhYgKSkJLVq0AI/Hw/r16397X/9Gio0BNcEwDEqXLo3evXsXdlfUwsePH1G+fHmYmpri/v37BXIP8QzVwMAgl1UfHR0t1WugKDdu3IC9vT0MDAywe/dumJmZYejQoWroNdCsWTNUq1ZNLW3ll5iYGNjY2KBGjRpyZ5wpKSkYOnQoiAiurq6oUKECm8PO4/Hg7u6OHj16YNWqVbh58yaSk5PV0r+6Dx6AU4DGgPDQIaxatUpmNUWxV0CZgNe4uDgcOnQIgwYNQvny5dnBv2zZshgwYAAOHDjArlXLokePHnB3d8+1v0WLFnBxcVHLhCEtLQ2lS5dGo0aNFJ4Vv337FkSEc+fOST2emZkJDQ0NrFy5Mt/9U4YbN27A0dEROjo6WL9+PRiGQXJyMrp06QIiwoABA1gxpM+fP8PDwwM6OjoKZR4VoxjFxoCaCA8PBxHh+PHjhd2VfPP69WuULFkSNjY2CA8PL7D7iGdKRCRVVXDixInQ0tLCx48fVWo/Pj4ebdq0YWdxhoaG+Z4Fv337FhwOB5s2bcpXO+okJCQEGhoaMsVkALCSrOPHj2cHjtTUVNy5cwfr1q1D79692cwMsQfB1dUVXbt2xfLly3H9+nWVZtYroqJyGwNDhoCCgrLlholAtWtn/zsoCHT8ePY5e/b8t69cuezzxP8ePx4UHAzupUtwmDOHNWqqVKmCmTNnIjQ0lH3G3r175+kV+P79O06cOIGRI0eiUqVKbKCmo6MjevbsiV27dsl0q8vC0dERgwcPzrX/+vXrICIcPXpUuQ9SBidOnAARse70vEhOTgYRYefOnTLPKV++vNzvkjpJT0/HhAkTwOVyUbNmTbx8+RJAdqaQm5sbtLW1JeJ9nj9/jpIlS8LCwqLAJin/rxQbA2pi/vz50NLSKjCX6+8iLCwMlpaWKF26NN69e1eg9xKJRND7qU8v7eWUkJAAExMT9OnTR+V7MAyD9evXs+p7s2fPzk+XMWnSJOjp6SExMTFf7aibdT9n2b8qMzIMg6lTp4KIMH369DxnkOnp6bh//z42bNiAvn37wsPDA5qammwOf7ly5dC5c2csXboUV69ezVNmNyEzE8IrVySNgRya/7m2PXuyz1m6VPY5FSqAgoPBCQ7Gm5QUxMfHY/fu3WjXrh10dXVBRChVqhR69eoFHo+XS1cgOTkZ58+fx/jx41G9enV2CcXa2hpdunTB1q1b8/Xdj4qKAhHhwIEDUo97eXmhRo0aalvj9vX1hb29vcLvHl1dXbnxOAEBAWjYsKFa+iaPsLAwVKpUCXw+H7Nnz0bmz+WegwcPQl9fH2XKlEFYWBh7/vXr12FsbIxy5crh7du3Bd6//zeKjQE1UatWLQkBnT+RkJAQGBsbw93dHZ8/f/4t92zUqBG0tbVluvCXLFkCHo+Xbw9FWFgYdHR0wOFwsHbtWpVexJmZmbC0tES/fv3y1ZeCgGEYdO/eHVpaWux6MMMwGDduHIgIc+fOVbntjIwMPHz4EJs2bcKAAQNQvXp1VstfLPLTsWNHLFq0CMHBwbniPDpduSJfb0CFjRccjI5S1srT0tJw6tQp9O3bF1paWiDKLijl4+ODDh06wMvLizUMzczM0L59e6xbtw4RERFqG5zFYle/prmKEc/mr1y5opb7RUREQENDA9OmTVPofEdHR4wdO1bm8UmTJsHa2lotfZOGSCTCkiVLoKmpCRcXF3aGn5GRgZEjR4KI0LZtWwlD899//4Wmpibq1q2rluJZxeSm2BhQAzExMQWac/47uHTpEnR1dVGzZs3f+mObPHkyNDU1UbNmTanH09LSYG9vj9atW+f7Xrt27WJnlwEBAUo/55EjR0BEePDgQb77UhCkpKSgYsWKcHR0RFxcHKu/sGTJErXfKzMzE0+ePMHWrVsxaNAg1KxZkx18iQhOTk4ICAiAl5cXSFMTmv/++1+xonxunOBgGF+7hq8y0uMyMzNx6NAhcLlc2NjYsMsI4viIChUqYPbs2fiqYtXDvOjduzdcXFxkHmcYBq6urvDx8VHbPceNGwehUKiQR6NGjRro0aOHzONiY6Yg3uORkZGoX78+iAjDhg1jvRnR0dGoXbs2+Hw+li5dyhpmDMNg8eLF4HA46NChwx9TROlPpNgYUANbt24Fh8P5bbNpdXPs2DFoamrC29v7t+bNA/9JEGtoaMjMff7nn39AJL+IkSJkZGTA3NwczZo1g6GhIezs7HD9+nWFr/fx8YGHh0e++lDQvH79GkZGRrC3twcRYfXq1b/t3pmZmQgLC8P27dsREBAgUQmQnJ3BOXs2/x6CS5fACw7GmRxR+iKRCA8ePMCiRYvg4+PDLj1xOBw0btwYixYtwv379xEWFoZ58+ahRo0arGFQv359LF++XK1LYs7Ozujfv7/cc3bs2AEiwuPHj9Vyz8TERFhZWSEgICDPc/38/ODr6yvz+L1790BEuHPnjlr6BmQP6jt27IC+vj5sbW0ltEAuX74Mc3NzWFlZSfwes7KyMGTIEBARxo4d+9dkaRVVio0BNeDv7y9zZlvU2blzJ3g8Hlq3bl0oVvfXr1/ZAUOWlnhWVhbc3d1Rp06dfLtyx48fDwMDA4SHh8PT0xM8Hg+zZs3KU3gnMjISHA4HGzduzNf9C5qsrCw0adIERIRWrVr99vsnJSVhyJAh4HA48PT0xNOnT/Hs2TPs2LEDbWfNAvfsWdCFCyoZAtxLl0Dnz6PxrFkIDQ3FihUr4O/vDyMjIxARhEIhGjVqhFGjRkmNFchJdHQ01q1bh6ZNm7JBk5UqVcL06dPx+PFjlb9n0dHRIMq7WmZGRgbs7e3RsWNHle4jDbHn68KFC3LP69Wrl1yjNjExUWr8iap8/fqVDeTt3Lkzm4bJMAzmz58PHo+HBg0a4MuXL+w1ycnJ8Pf3B5fLxdq1a9XSj2LkU2wM5JPU1FRoa2vna022sFi9ejU4HA66d+/OBu8UBk5OTuBwOHLzhU+dOgUixYoYyUMsI7xlyxZkZmZi4sSJ4HA4qF+/vtyshSlTpkBXV7fIBQ7mJDMzE126dAGXy4W/vz84HA4r0PI7uHLlCkqVKgWhUIglS5ZINbBCExPhfueO7HRDOUsDpmfPomxAAGs8CgQC1K5dG1OnTsWVK1dYY7ZXr14oUaKEwl6u79+/Y+/evQgMDGRrBzg4OGDYsGG4fPmyUr8NsabFp0+f8jx35cqV4HK5aqtjwjAMvLy84OLiIlfueMKECbC3t5fblo2NjcppvTk5deoULCwsYGxsjP3797P74+Pj0bJlSxARJkyYIPFdiYmJQfXq1aGtrf1XZGf9KRQbA/lE7OYu6jXAc8IwDJtqNnTo0EJ3v3Xr1g1aWlro1auXzHMYhkG9evUULmIkj6ZNm0oUGLp48SIsLS1hYmIi9eWTmZkJKysr9O3bN1/3LUgyMjLQvn178Hg87Nu3DyKRCD4+PjA2Ni7wyOvExEQMGjQIRAQvLy+paaISfRWJsCAyEmbXrmXP+GUtHZw/n/3f48ezUwqFQtjY2KDcz1TDrVu35mr7zZs34PP5WLRokUrPkp6ejrNnz6J///6wsrJiAxC7d++OI0eO5Km/0L9/fzg7Oyt0r+TkZJiamqo1je/hw4fgcrlyZY+XL18OLS0tud4Pb2/vfMXpJCUloV+/fiAiNG3aVMLQfvToEUqVKgVDQ0McO3ZM4rqIiAiUKlUKJUqUwN27d1W+fzHKU2wM5JN+/fqhVKlSf4wUJsMwGDNmDIgI06ZNKxL9Xrt2LTgcTp4FnsTqaYoWMZKFWEEw57JETEwMfH19WQMp55LJ0aNHQURFNq85LS0NrVq1gkAgkKjzEBcXh5IlS6Jy5cpqL9QkJjg4GCVLloSWlhaWLVumlGG5eft2UJ066HT/Plxu3oTg0iXQpUugc+dAW7eCxoyBQZs2aNayJdq0aYP69evnKqNcs2ZNTJkyBUePHsWHDx/Qs2dPpbwC8hCJRAgJCcGECRPg4uICIoKWlhZatmyJrVu3ShUecnFxUUp4bMaMGRAKhRIu8vzSr18/GBgYyGxzz549ICK5aaGDBw+WW91QHrdv34aTkxO0tbVzZe5s3boVQqEQlSpVwuvXryWuu3nzJkxMTFCmTJm/suprUafYGMgHDMPAyspKaX3wwiIrKwt9+vQBEamtYIo6ePToESt0k9fMS5UiRr8inun/miLIMAyWLl0KgUCASpUq4cWLFwCy87irVKmi8v0KktTUVPj4+EBTUxMnTpzIdfzBgwcQCoXo2bOnWu+bmJiIgQMHgohQu3ZtVixGUb5+/YpKlSrB0tKSnekTEVxcXDBo0CAcOnQIXl5e8PPzk7iOYRhWYtrBwQF8Ph+GhoYSBkLZsmUxadIkHD58GJGRkWozeF+8eIEFCxbA09MTHA4HXC4XdevWxdKlS/HmzRvExMTkKejzK3FxcdDR0VFrcbOvX7/C2NhY5t/84sWLICK8evVKZhurV6+GQCBQqrpiRkYGJk+eDB6Ph2rVqrG/HyD7e9qrVy8QEXr16pXr93vw4EEIhUJ4eXlJSDgX8/soNgbygTjqNjg4uLC7kifp6elo3749uFyuVPdqYZKZmcmmpeUV3a9qEaNfmTx5skzxoPv378PJyQk6OjpYsmQJuFxukdQ/T05Ohre3N7S0tGTKywLZOvlEpLbgx4sXL8LBwQHa2tpYsWKFQt6AhIQEHDt2DMOHD0eFChXYgdvMzAx9+vTBnj17cq2zz5w5E/r6+jLX7BMSEuDm5gY7OzvcuXMHjRo1go6ODpo0aQLzHMJGpqamaNKkCSZMmIADBw7g7du3+TYQPn36hA0bNsDX15fVLRBncJw+fVqp9keMGAFDQ8M8BZyUYc2aNeBwOFIzAsTKnzdv3pR5vdhgyDmgy+PZs2eoUqUK+Hw+ZsyYIfE3e/36NSpVqgShUCi17PKyZcvA4XDQrl27AvNgFZM3xcZAPpgyZQqMjIzUVgu+oEhOTkazZs2goaGhsGzp76ZevXrgcrlYunRpnueKixjlp255ZGQkuFwuNmzYIPX4jx8/0LVrVxBll6NVVRK5oEhMTES9evWgo6OjkDHar18/aGho5Ctd7MePH+jfvz+ICHXr1pU7s0xKSsLZs2cxduxYeHh4sAWSbG1t0a1bN/To0QNcLleue/zGjRt5prhFRUXB2toa5cqVA5/PZ41EhmHw4cMHHD16FFOnTkXz5s1haWnJGgjGxsZo1KgRxo4di/379+P169cqGwg/fvzAv//+izJlyrDPaWdnhyFDhuDSpUt5BiBGRUVBIBCoHOcgjaysLFSoUAHVqlXLZax9+fIFRIQjv5QOz8nHjx9BlLdsskgkwvLlyyEUClG2bNlc6/zHjx+HoaEhSpUqlStbSCQSYdiwYSAijB49utBjl/7fKTYG8kHFihXRqVOnwu6GXBISElC7dm1oa2vLnT0WNuPHj4dAIECHDh3yPFdcxGj8+PH5umde7v/MzEwYGRlBIBCgdOnSuHfvXr7upy4SEhLg6ekJPT09hXUS0tLSUK1aNdjZ2eVZZEcaFy5cgL29PXR0dLBq1apcL+7U1FQEBwdj8uTJ8PLyYtP1zM3NERgYiI0bN+LVq1fsgNugQQOp1SpzkpGRAR0dnTwzdR4/fgyBQAANDY08q1xGR0fjxIkTmD59Ovz8/GBtbc0aCIaGhmjQoAFGjx6NvXv3IiIiQqkByt3dHd27d8f58+cxcOBAtm0jIyN06dIFBw8elBnL0KNHD1hZWak1vffq1av/BVoyDBAcDAwZAqZaNSQRAUQAlwtYWwOtWwNLlwI/vxsMw0BfX19uemZUVBQaNWoEIsKQIUMk5JCzsrIwYcIEEBFatmyZy3BPSUlBQEAAuFwuVq1apbZnLkZ1io0BFYmMjAQRYd++fYXdFZnExMSgcuXKMDQ0xI0bNwq7O3I5duwY62pVhPwWMcp5T1mDvLi2+6FDh1ClShUIBAIsXry4UGcw3759g4eHBwwNDRESEqLUte/fv4epqSm8vb0Vzsj4/v07+vbtCyJC/fr12aCvjIwM3LhxA7NmzUKDBg1YgSFjY2MEBARg1apVePbsmdTZ9qdPn8DlchUq9tSsWTN4e3vLPef169fg8Xjgcrno2bOn0jP8z58/49SpU5g5cyb8/f1hZ2fHGgj6+vqoV68eRo4ciV27duH58+dS//5ivYycwa0Mw+DevXuYNGkSXF1dWS2EFi1aYPPmzRJekWfPnhVIAazADh3QT18fWaVKZQ/+fH72f3/deLxsw0AgALp2BT5+RLVq1dC9e3ep7e7evRuGhoawtrbONcn48uULGjRoAC6Xi/nz5+f6e8TGxsLT0xNaWlo4cuSIWp+3GNUpNgZUZNWqVRAIBHnORAqLqKgolC1bFiVKlJBZu7woIXZdEpFCAUTqKGKUmZkJGxsbmdHfLVq0QOXKlQFkx1yMGDECRIRmzZqpNfpbUWJjY1GpUiWYmJioLIl84cIFcLlchQLWzp07Bzs7O9YbcOfOHSxYsABNmzaFjo4OO1g2b94cS5YswcOHDxUylFauXAmBQKDQ33nRokXQ0tKSO2Pu2bMnzM3NsWHDBhARZsyYkWe7eRETE4MzZ85gzpw5CAgIgIODA/v91NPTQ506dTBs2DDs2LEDz549w8GDB0FEcpUMX758iUWLFsHLywscDgccDgdeXl5YtGgRXr16BX9/fzg7O+c7dZbl82ekNGoEEEEkzQCQtfH5gJ4e1tWqhRo1akg0GRcXh/bt24OIEBgYmEvS+/r167CysoK5ubnU5atXr17ByckJZmZmuH37tnqesxi1UGwMqEjjxo3znLEUFhEREbC3t4ednV2eOd9FCfGM7OzZswqdv3Tp0nwXMZo2bRp0dHRyfWffv38PLpeLdevWSew/efIkzMzMYGFhkafSmzr5/PkzXF1dUaJECTx58iRfbc2bN0/uevD379/ZyG8nJyd4e3uzEftaWlpo3Lgx5s6di5CQEJXEqmrVqiVXDjcnDx48AJHsoj6vX78Gn89n6y/MnDkTRIRt27Yp3a+8+Pr1K86fP4958+ahbdu2cHR0ZA0EPp8PTU1NDBkyBNu3b0doaKjcz+bLly/YvHkzWrRowVaFFLe3YMGC/GdAvH4N2Nhkz/iVMQTEG4cDEGGBpiaYnwbe2bNnYWVlBUNDQ+zZs0fiduJMHD6fj9q1a0st+Xz79m2YmZnByclJbrxJMYVDsTGgAt+/f4dAIMDKlSsLuyu5ePz4MczNzVGmTBm8f/++sLujFB07dmTlgRVBHUWMoqKipEqeyjISgOx154YNG4LD4WD8+PEFHkD68eNHlC1bFpaWlvmu3ghkv7j9/f2hr6/PGosMw+D58+cYPHgwtLS0wOFwIFb5q1evHqZPn45r164hPT09X/d+//49iAg7duxQ6HyRSAQjIyNMnTpV6vGgoCCYm5uzKakMw6BXr17g8/m/JUbm27dvuHjxIqysrODg4AAnJyfWQNDS0kLNmjUxaNAgbNmyBY8fP5ZqICQmJuLgwYPo0qULW1TJ2toaAwcOxPnz55X/fn35Atjayl4SUHKLGz2aTSP19vbGhw8fJG7348cPtG3bFkSEUaNGSe3vkSNHoKWlBU9PT5ViVoopeIqNARXYv39/ni7BwuDmzZswNDREpUqVZJZPLcqsWrUKHA4HzZs3V/gadRQx8vPzQ8WKFdnZWFZWFmxsbOQqImZlZWHOnDng8XioUaNGgan8vX//HqVLl4atra3SufzySEhIQMmSJWFjY4P27dvDwsKCHcQMDAwwaNAgXLhwQSIoTB0sWrQIQqFQqXdE69at4eXllWu/OFbg16qMGRkZaNq0KfT09NRWCEge8fHxElVLExISEBwcjMWLF6Njx44oU6YMa1wJhUJUq1YN/fv3x6ZNm/Dw4UMJA0tc3jhn7IKhoSE6deqEf//9N+/0Q4YBWrZU2CMw6+ffvLycc0RE8NLUxMqVK3MtA4WFhaFMmTLQ09OTmam0cuVKcDgcBAQEqP37VIz6KDYGVKBz586oUKFCYXdDgvPnz0NbWxteXl5FNo4hL8S6DSYmJgpfIy5iVLt2bZVdq+K6B+KAPPELWZE0vJs3b8Le3h4GBgYS2uvq4M2bN3BwcICDg4NajI0PHz5gx44dCAoKklgD19XVha6uLrS0tLBixYoCVaWsWrWq0p6cVatWgc/n54rE/9UrkJMfP36gUqVKsLa2RlRUVL76nBfiQFN5ru8fP37g6tWrWLp0KTp37oxy5cqxBoKGhgaqVq2Kvn37Yt26dXB2dkbDhg3BMAwePHiAKVOmwN3dnT3Xx8cHGzZskF7/YN8+hWf8UUTQJoJOHsZAJhHSHByAX2b8O3fuhLa2Ntzc3KTqEYhEIowaNQpEhOHDhxenDhZxio0BJRGnm02aNKmwu8Jy6NAhaGhooFmzZnkq+BVlMjIyWAGXX12R8hAP5tIU+BQhKysL9vb2CAoKApDtKahUqZLCg2J8fDzrJu3du7da/gYRERGwsbFB6dKlVV7uiYmJwf79+9GvXz+UKVOGHfzd3NwwZMgQ7Ny5E56enhCr9kVGRua73/J4+fIliEhpoyk8PBxEJFF0SZZXICfR0dGwt7eHq6trgRrIo0aNgrW1tdJGVGJiIq5fv47ly5eja9eucHV1ZXUKxH+TXr16Ye3atbhz5w7Cw8OxdOlS1K1bF1wul60MuWDBguzlHoYBXFzY9f68tvZEaECEunkYA+x24ACA7OW5AQMGgIjQtWtXqd/31NRUtGvXDhwOp0ipnRYjm2JjQEkuX76s8Kzxd7Bt2zZwuVy0a9cu3+u5RYHq1auDiCQ09vNCXMTI1dVV5UjsWbNmQUtLC0+fPlWpbCrDMNiwYQO0tLTg4uKC0NBQlfoBZKeZiWV6pQViySI+Ph5HjhzB0KFD4ebmxg4qzs7O6NevH/bt28dmQZw4cQJWVlbQ19dHo0aNwOfzFdYsUJXZs2dDR0dHaWOJYRhYWlpizJgx7D55XoGcPH36FIaGhmjYsGGB/T48PDzUVoo4OTkZV69ehampKRwcHODu7g4ejwdxkGKFChUQFBSE+fPnY9KkSWjevDmr3hlob6+wV+AKEXhEeKKoMcDjAXXqIDIyEtWqVYOGhgbWr18v1QCKi4uDl5cXhEJhkRU5KyY3xcaAkowYMQKWlpZFwuW1fPlydjaqtnSkQmbMmDHgcrlKCwqJixipGkUeHR0NPp8PX19faGtrq/wdfvr0KVxdXSEUCnMVaVGEx48fw8zMDG5ubnmmLyYmJuL06dMYPXo0qlSpws4q7e3t0aNHD+zYsSOXh+Xbt2/o1q0biLKryb1//x4ZGRnw8vKCpaWlQqV3VcXNzQ2BgYEqXdupUydUrVoVwH9eAUXUKoFsA15DQwNdunRR+xLIjx8/wOPx1C5XvXbtWnC5XERERCAlJQUhISFYs2YNevbsiYoVK7KBhjweD+XLl0eDBg3wj6UlMhQwBLKI4E6Evj//rbBngAgORkawt7eXWVHwzZs3KFOmDExMTOTKHRdT9Cg2BpSAYRiUKlUqX7nt6urH9OnTIY7eLQqVB9XFoUOHQERSA8byok2bNvkqYuTv7w+BQMAuF6hKSkoKW761devWuXKxZXH//n0YGxujcuXK+Pr1q9R2L168iIkTJ8LT05MdECwtLdGpUyds3rxZbrW3Y8eOwdLSEgYGBtiyZYvE9yY6OhoWFhaoU6dOgWRHPH36FIrI28pi8+bN4HA4+PbtG3r06AELCwulgtHElfrUvbx3+vRpEBGeP3+u1nZTU1Nhbm4u812TlpaGu3fvYt26dejduzeqVKmCyxyOQnoCq4hgQIQYFYyBMdWqydSHuHv3LkqUKIFSpUr9USnNxWRTbAwowbNnz/K1Nq0OGIbB8OHDQUSYPXv2X2UIANmDEhFBW1tbae/Lixcv8lXESJyjrq6CPgcOHIChoSFsbW1x7do1uefevn0bhoaGqFatGivdmp6ejmvXrmHGjBmoV68em49uamqKtm3bYs2aNXj+/Hme34G4uDh06dIFRAQfHx+ZAXXXrl0Dn8/HiBEjVHpeeUyZMgUGBgYqy+2+ffsWRIQ1a9Yo5RXIyfz580FEMutRqMK4ceNgbm5eIL/DuXPnQkNDQ+GlIsbIKM/B/CsRjImwKMc+RY0BEYcD0fLlUu99/PhxaGtro3r16n9kJlMxxcaAUsybNw/a2tqFlh6TmZmJHj16gIiwevXqQunD70BccU7Rimk5yU8RIz8/P2hoaKBr165KXyuLd+/eoVatWuByuZg5c6bU5Zxr165BT08Pnp6euHTpEubNm4fGjRtDW1sb4lQ/Pz8/LFu2DI8fP1bKSDp69CgsLCxgYGCAbdu25TloLVu2DOqW2WYYBs7OzjKlbRWlZMmSKFeunNJegZz9GDBgAHg8Hk6dOpWvvoipWbMm2rVrp5a2fiU+Ph56enoYO3asYhcIhXkO6P2IUJoI6SoYA+DzgTlzct1WvKTRqlWrPzqA+f+dYmNACTw9PdGqVatCuXdaWhoCAgLA4/EUFmz5U2ndujWIlKsLL0bVIkYfPnwAj8dDy5YtIRQKFXbtK0JmZiYmT54MDoeDevXqsev4IpEIGzduhIaGBkxMTKCnpwcigo6ODpo2bYoFCxbg7t27KsWDfP36FZ06dQIRwdfXV+HsDIZh0KFDB+jo6ODp06dK31caYhXBnNkAqtCuXTsQkUpeATFZWVlo0aIFdHR08l14KikpCXw+v0AN8zFjxkBfX19uNsS3b99w7949ZGpqyh3MI4jAJcIKIrzNsVUngvPP/4+TZwzweMCCBex9RSIRxo4dCyLC4MGD/5q4pf9Xio0BBfny5Qs4HI7UetwFTVJSEho3bgxNTU2V11z/JMT1zQcOHKjS9eIiRsqkJ86cORPa2tqIiIgAn88vkHSoixcvokSJEtDR0WGrDhIROBwO6tati5kzZ+LGjRv5XrM/fPgwzM3NYWhoiH/++UellLfy5cujTJkyavktjx07FiYmJvl+rrp164KI8q25kJSUBA8PD5ibm+errfPnz4OIEBYWlq/+yCM6OhoaGhoYM2YMLl68iI0bN2LcuHFo164dqlSpAiMjI4izRsLzmNkH/zxP3jY0L+/AT49RWloaAgMDQURYvHjxX7dc+f9IsTGgIFu2bAGHw/ntBWri4+Ph6ekJHR0dXLx48bfeu7AQZwa4urqqdL24iJGsAkS/8qvOQNu2bVGuXLl8v+AYhsGrV6+wceNGBAYGsip/YrEZDocjESOQX2JjY9kXdIsWLZRKS/yVFy9eQE9PD61bt87X58AwDOzt7dG3b1+V2wCyNQrEKXa7d+/OV1tAtnHv6OiIsmXLquwFmjRpEkxNTdUyECYmJuLx48c4fPgwFi1ahAEDBqBJkyZwcnKS0B7gcrmwt7dH/fr10atXL8yZMwf79u3D3bt3kRYYKFeCOJYIh6Vs5Ylg9/P/n+RlDLx6hW/fvqFu3brQ1NRUu9BWMYVHsTGgIK1atYKnp+dvvefnz59RoUIFGBsbK12u9k8mPT0dfD4ffD5f5dnk0qVLweVyFdLyF0eEi6uoXbhwAUSEq1evKn3fqKgobN++Hd27d2flZLlcLjw8PDB27FicOXMGO3fuBJfLBZfLRcWKFVWKjfiVgwcPokSJEjAyMsLOnTvVMkCJMzsW5HANK8utW7dARFIr2ClD9+7dYWFhwQrxqIMXL17AxMQEderUUSmwsXbt2gqrKYpEInz8+BFXr17Ftm3bMHnyZHTq1Ak1atRAiRIlJGbnOjo6cHNzQ6tWrTBixAhMnToVHA4HM2bMkK+VsGmTwoJDOTdFYwYYMzO8e/sW5cqVg7GxcZ5BscX8WRQbAwqQkpICbW1tzJs377fdMzIyEk5OTrC0tMyXgM2filg0R9VSveIiRv7+/nme6+/vD3d3d3YAFYlEKF26NDp16pTntZ8/f8bevXvRp08flC5dmn2hV6hQAcOGDcOxY8ck1nv37t0LHo+HDh06ICQkBE5OTtDR0VEouE8aMTExbEnZli1bql0nYNy4ceByuSp7pYYNGwYLC4t8rSeLvQLLli3DoEGD4OjoqHJbv3Ljxg0IhUK0b99eqcDMlJQUaGhoYHmO6PqUlBQ8e/YMJ06cwPLlyzF06FA0b94cLi4uEAqFEgO+lZUVvLy80K1bN0yfPh07d+7EzZs38eXLF6nfA3GVRLlVIn/8ALS1C8QYyCRC+M8aFiVLllR7KmUxhU+xMaAAYq36Z8+e/Zb7PX/+HLa2tihZsuT/banPwYMHg4jyJeayY8cOEJFc8ZOPHz+Cx+Nh1apVEvsXLlwITU3NXBXW4uLicOjQIQwaNAjly5dnX+5ly5bFgAEDcODAAZlV2bZv3w4ul4uuXbuyg2NiYiIrAtSpU6e8C9Hk4N9//4WZmRmMjY2xe/fuAlm3zczMRMOGDWFmZqa0xn9WVhYsLS0xZMiQfPWhe/fusLS0REpKCg4fPqyWuIGcHDx4EBwOB6NHj5Z7HsMwiImJwa1btzBx4kQQEfz8/FC7dm1YW1tLDPaampooW7YsfH19MXjwYCxbtgzHjh3D06dPVYq4F9ft2Lt3r/wTBw9WvWyxnC2DCI4aGvDw8MDnz5+V7n8xRZ9iY0ABxLO+3xEk8+DBA5iZmcHFxQUfP34s8PsVVf79918QUb5kXkUiESpUqCC3iJFYhvjXdfvY2FhoaGhg1qxZOHHiBEaOHIlKlSqx6/2Ojo7o2bMndu3apdDa/MaNG8HhcNCrVy+pM9CdO3dCV1cXpUqVkqnuJubLly9sLQR/f/8CfznHxMTAxsYG1atXV8qdLpbuzo8SndgrIJ6Bf/v2rUACecUplcuXL8fLly9x9uxZrFmzBqNGjYK/vz8qVKjABnyKN3HMR8eOHTFp0iRs3boVV65cwYcPHwpEodTb2zvvmhlxcWBMTRUSH1J0Y4gwgQguLi65ikUV8/dQbAzkgUgkgqWlZYEIsfzKtWvXoK+vj6pVq0pVoPt/IioqCmJp3fwgr4iRSCSCvb29RP57cnIyzp8/j/Hjx8PExIR98VtbW6NLly7YunWr0qWrV61aBSLCwIED5Q4SL1++RJUqVSAQCLBo0SKp5+7btw+mpqYwMTHB3r17f1sUd0hICDQ0NDBgwACFr+nfvz/s7Ozy1cdu3bqxXgExVapUUWgJRxbx8fG4d+8e9u/fj7lz56J3795o2LAh9PX1JQZ7Pp+PUqVKoXHjxujXrx8WLlyIgwcP4tGjR6hduzb8/PxU7oMqiGNZzp49K/Oc2NhYjCtfXm2GQBaHg/tEsDQ1VVusRjFFk2JjIA/u3LkDIsLly5cL9D6nT5+GlpYW6tWr91d9fvnByMgIHA4nX0Im8ooYnTlzBmIBp6lTp6JOnTps1UQzMzPUr18fRKRSep6YxYsXg4gwYsQIhdpIT0/HyJEjIa4dIM5e+fz5MwICAkBECAgI+O1ZLQCwbt06EBG2b9+e57mZmZkwMzPL0/Uuj1+9AmJGjx4NS0tLmZ9nVlYW3r17h0uXLmHjxo0YP3482rVrh6pVq0qk4okFnSpXroy2bdtizJgxqFy5MjQ1NXHo0CGZ6/NpaWkQCoUqK12qCsMwqFq1KurXry/1+OPHj+Hg4AAzMzM8CQpSiyHwhgirJ01Cx44dVZIIL+bPodgYyINJkybByMhIfuBOPtm/fz8EAgFatGhRaOqGRZFGjRqBiPJdTS9nEaPMzEzcunULc+bMgZmZGev2NzIygr+/P1asWIGwsDAwDAOGYVC2bFm0b99epfvOmTMHRIQJEyYobUycOnUKZmZmsLCwwIQJE2BiYgJTU9NCTeViGAbdu3eHUCjEw4cP5Z577tw5EBHu37+v8v2keQWA/7I/jhw5IpGK17RpUzg5OUEgEEi48u3s7FC/fn307NkTc+bMwd69e3H37l2pGvspKSnw9PSEmZmZzHida9eugYjyLVqkCgcOHAAR5couOnz4MHR0dFChQgU8ffoUVapUwSgDAzB8vtx0Q3lLA/c4HBz5Wb1zxowZMDU1/e3PW8zvo9gYyAN3d3d07ty5wNrftGkTuFwuOnbsWCAFYv5kFixYACLCwoULVW5DJBLhwYMHcHd3h1AohK6uLsS1DzgcDlq1aoX79+/LjHZfsmQJBAKBUjNxhmEwdepUEBGmT5+uslfh0aNHMDMzgzhAsSjEkKSkpKBixYpwdHSUm58fFBSUrzibiIgI8Hg8DB06FNu2bcOUKVPQqVMn1KxZk/1MZKXirVq1CqdPn8aLFy9UKlv89etXODs7w8nJSWow6KxZs6Cvr18ointZWVlwdnZmUxoZhmFragQEBCA+Ph7NmjWDnp5etsH27BlifpY2zlTAAGC4XGQQYZqWFq5eusTed//+/SAimcGxxfz5FBsDchAXRymo2diiRYtAROjfv3+RKIlc1Lhx4waICE2aNFH4GoZhEBYWhpUrV8Lf3591C2toaIDD4aBZs2a4desWZs6cCaFQmKfgT1xcHDQ1NTF//nyF7z9u3DgQkcqpqAzDYNeuXTA2NoapqSk6duwIHo+HGjVqyK1K+Lt4/fo1jIyM4OvrK/V7m56eDkNDwzwrBKampiI8PBwnTpzAihUrMHToULRo0QIuLi6swJB4s7S0hJeXF7p27Yrp06fD2dkZ9erVw+fPnwskbuL169cwMzNDzZo1c3kmvL294evrq/Z7KsqmTZvA4XBw//59NpB0+vTpyMrKQlBQEPh8Ps6dO4eUlBT06NEDHCIs8/VFlq+vpJeAy5XQJUjQ1cVcXV1UtbHJlTn15MkTtXjpiim6FBsDclixYgUEAoHan4dhGEyaNAlEhPHjxxdLecogNTUVXC5XrnuSYRhERERg/fr1aN++PVvkSCAQoHbt2pg6dSquXLmCtLQ09OvXD0ZGRoiLi0PJkiXRrVs3hfrRuXNnlCpVKk+DjWEYDBs2DESq6+dHR0ejZcuWICJ06NCBrQB369YtODg4QF9fX61FhFTl1KlTrBDOrxw/fhxEhNDQUMTExOD27dvYtWsXZs6cie7du6NOnTpyU/G6dOkCLpeLPn36ICwsTGrMyJQpU2BsbFygRnRISAi0tLTg7+/PegEyMjKgo6OTLyGm/JKWlgZzc3MYGxtDW1sbBw8eBADWG/XPP//g5cuXqFChArS0tCRjPNLSgLt3gc2bgWXLgFWrgKNH0bBsWfB5PFSpUkWqVoX4t7hp06bf9ZjF/GaKjQE5NGrUCI0bN1ZrmyKRCIMGDQIRKTzb/H+mVKlSICKJ9d3IyEhs3boVXbt2hY2NDYgIPB4P1atXx/jx43Hu3DmpA4i4iJFYpOfGjRsK9UG8Rnz+/HmZ54hEIvTv3x9E2WV2lYVhGOzYsQNGRkYoUaIE+4LPSXx8PFusp3fv3oVeIW7atGngcDjYvHkzzp49i7Vr12LUqFGwtbWFUCjMlYpnamqK6tWrIzAwEJMmTcKWLVtw5coVREVFSQzqXbt2haWlJVJTU2XeW5y2qKoolaIcO3YMXC4XQ4cOBfCfomJhKoJev36dXe4SZxZs3LgRRNllzY8cOQIDAwOULl0ajx8/zrM9sachr4lPqVKlMHLkSLU9RzFFi2JjQAYJCQng8/m5xGjyQ2ZmJrp06QIOh5MvMZ3/J7p06QIiwrhx49CrVy84OjqygWGVKlXCiBEjcOLECYW/c5MmTQKPx4Ozs7PCHhmGYeDi4oI2bdpIPZ6VlYWePXuCw+GoNHP6+PEjWrRoAbGugrx1WYZhsHHjRmhpaaFcuXJ48uSJ0vdTlvj4eNy/fx/79+/HvHnz2FQ8e3t7icGez+ejZMmS4PF48PDwwIIFC3Dw4EE8fPhQ4b9PREQEuFwuVqxYIfe8tLQ0aGlpYdGiRep4RLmsWbMGRIQlS5Zg7ty50NXVLdCAYnls3rwZAoEAnp6eMDAwwIgRI3Dy5EnweDz06dMHo0ePhlh/Ql6lQyD7uzR58mQQEfv9k2c8+Pr6FurySDEFS7ExIIO9e/eCiBAZGamW9lJTU9GyZUvw+Xzs2bNHLW3+rXz9+hUHDhzAgAEDYGVlxQ42Li4uGDRoEA4dOiQ1ElwRIiIiQESoWbOmUtctX74cfD4/lwtVbOBxuVylS0szDIPt27fD0NAQ5ubmOHz4sMLXPn36FK6urtDU1MSaNWvytdSUlZWFyMhIXLp0CZs2bcL48ePRvn17VK1aFcbGxlJT8dq0aYOxY8diyZIlsLS0hKurK378+MFGu0dERKjUF0W8AmK8vb3h4+Oj0n2UZezYseBwOKhYsaJSMSzqIjMzE0OHDgURoU+fPkhPT8fEiROhra0NLS0tNG7cGHXr1gWPx8OiRYvy/D6kp6eja9euICLMnTsXKSkp0NTUzJXGmZORI0eiVKlS6n60YooIxcaADDp27IiKFSuqpa0fP36gQYMGEAqFOHnypFra/JtISEjAsWPHMHz4cFSoUIEdeEqXLs1W4atUqZJa7jV37lzw+XyFixiJ+fbtG7S0tDB79mx2X0ZGBtq1awcej6f0Ov7Hjx/RvHlzEBE6d+6skshUSkoKBgwYwM4E5RlIiYmJePLkCQ4fPozFixezqXjOzs6stkLOVLx69eqhZ8+emD17Nvbu3Ys7d+4gLi5O6iDz8OFDCIVC9OjRAwEBAahcubLSzwIo7hUQI56l/44sHJFIxC4v9enTp8Dvl5O4uDg0atQIPB4Pq1evZv8G4pRZcQqqhYUFrly5kmd7CQkJaNSoEQQCAXbt2sXur1evHlq1aiXzuo0bN4LL5SpkqBXz51FsDEghIyMDhoaGmDJlSr7biouLQ/Xq1aGnp6fQD/X/gaSkJJw9exZjx45FtWrV2BKttra26NatG7Zv3473798DyJ496+joQEdHJ9/3FYlEcHR0RMeOHRUuYpST7t27w8HBASKRCGlpaWjVqhUEAoFSM3qGYbBt2zYYGhrCwsICR48eVfIpcnPo0CEYGhrCysoKq1evxvbt2zFlyhR07twZNWvWZIMqxZu2tjbc3NzQsmXLXKl4qlTvA7LrLoiXClQNruvatSusrKwUHmzEg6GisR/55fr16yAi6Onp/bZCPc+ePUPp0qVhbGwsUSwqJiYGpUuXZgsg1apVS6EiVVFRUXBzc4OBgUGuSpLTpk2DkZGRzKBM8fP/PxZO+3+g2BiQwqVLl9QiKhIdHQ1XV1eYmJgUikBJUSE1NRXBwcGYPHkyvLy8WFEYc3NzBAYGYuPGjXj16pVM12b16tVBRPjw4UO++nH+/Hk2PUqRIka/Ig4eO3r0KHx8fKCpqSlV5lgWHz58gI+PD4gIXbt2VXqp49dUvGHDhqFFixYoX748NDU1JQZ8CwsL1KpVC127dsW0adOwY8cO3Lhxo8BS8YD/RKJUMXBevHgBLpeLlStXKnxNZmYm9PX1MXPmTKXvpwoLFy5kYzVKlixZ4DUhTpw4AT09Pbi4uEgIICUnJ6NKlSrs35zD4WDZsmV5tvf48WNYW1vDzs4OYWFhuY6LgzIfPXok9fqvX78WaKp1MYVLsTEghWHDhsHKyipfL803b96gVKlSsLa2/m3VDosKGRkZuHHjBmbNmsUujxARjI2NERAQgFWrVuHZs2cKf74TJkwAEeHff//NV7/atm0LFxcXMAyjUBGjX2EYBq6urjAzM4OWlhbOnTun8HVbtmyBgYEBLC0tcfz4cZnnxcbG4vbt29i9ezdmzpyJHj16oE6dOrCxsWHVEnOm4vn4+GDw4MFYunQpDh06hH79+oHD4aBevXr5Np6UxcfHB7q6urC1tVVanKZLly5KeQXEtGjRQqY8r7pp3rw5GjZsiHfv3sHCwgJVq1YtkMI9DMNg/vz54HA4aNGihcT7NDMzE/Xq1QOHw4GOjg4OHz7MerrkLZecO3cOenp6qFSpkkzxqtTUVAiFQrlpsaamplLTSYv58yk2Bn6BYRiULFkS/fr1U7mNp0+fwsrKCqVKlVJrqdWiSlZWFu7du4cFCxagWbNm0NHRARFBX18fzZs3x5IlS/Dw4UOVc8KvXLkCIkJQUJDKffz8+TP4fL7EDEosaytrcP6VxMRElC5dWinD5P3792jatCmICN27d8eXL1/w6tUrNhVv9OjRaN26NSpWrCg1Fa9atWoIDAzExIkTsWXLFly+fDlXKt6vBAcHw8rKCiYmJjh27JhC/cwv3759g0AgwPTp02FmZoZGjRoprNCnildAzLJly6CpqVngMt5ZWVkwMDBgB8IHDx5AV1cXzZs3V2tmQUpKCjp16gSibBnrnH9nhmHQoEEDEBFKliyJly9fAshWqiQi7Ny5U2qbW7duBZ/PR9OmTfMskV2/fn20bNlS5nEvL698VRItpuhSbAz8QlhYGIgIp06dUun6u3fvwsTEBG5ubgqt4f2JiEQiPHnyBMuXL0fLli1haGgIImKjmufNm4eQkBC1vSSTk5PB4XBQpkwZlduYN28eNDU1JVzzDMOgfv36KF++fJ4DV0JCAjw9PaGnpwehUCh3dpSQkIB79+6hX79+0NTUhLa2NipUqMCm3YkHex6Ph1KlSsHb2xt9+/bFggULcODAAaVS8WQRGxvLposNGTJE5VgARdmyZQs4HA6io6Nx8eJFcLlcTJgwQaFru3TpAmtra5UC08TKeDnX0wuCBw8egIgk4n5Onz4NHo+Hfv36qWXp5ePHj/Dw8IBQKMTu3bsljqWmpqJatWogInh6eubSmGjWrBlcXV0l+sEwDKZPnw4iQq9evRQKtJw+fbrcuIFevXqpHCBaTNGm2Bj4hblz50JHR0elF9Ply5ehp6eHGjVqqJz6VhRhGAYvXrzA2rVr0bZtW1YbXkNDA/Xq1cP06dNx7do1lXTgFcXKygoCgUAl74JIJEKpUqWk1pgQV6Xctm2bzOu/ffsGDw8PGBoa4s6dOwgKCoKVlRUuXLiATZs2YcKECWjfvj08PDxypeIJBAK4ubmhTZs2GDNmDNavX4/z58/jzZs3BZ6rzjAMli9fDg0NDVSsWLFAg94aN26MevXqsf+eP38+iLKLCclD7BVQVc9DJBLBzMxMYcNDVZYuXQpNTc1c74VNmzax6Xn5ISQkBJaWlrC2tsbdu3cljr19+xYODg6sHoA0w0PsPRPHsGRkZCAoKAhEhFmzZilsrIjbkVWIatGiRdDW1i6WT/8LKTYGfqFmzZpsERBlOHHiBIRCIRo2bIjExMQC6Nnv5e3bt9i8eTM6d+7M5vrzeDzUrFkTEydOxIULF35rhUU/Pz8QEV68eKH0teI68FevXpV6vE2bNrC1tZV40SclJeHJkyf4559/YGVlBaFQCE9PTzg7O4PP50tNxevRowdatWoFLS0tlChRAvv27SsSUtMPHjyAs7MzdHR0sHXrVrX3KSYmBjweD+vWrWP3MQwDf39/6Ovry9Uc6Ny5s8peATHt2rVDjRo1VL5eEVq1aoW6detKPSYW7smZpqcMO3bsgKamJmrUqIHo6GiJYydPnmSXj1q2bCnzb8cwDGrWrInatWvj+/fvaNy4Mfh8Pv755x+l+iIuz7xkyRKpx0+ePKlW/ZViig7FxkAOPn/+DA6HI3eWKI3du3eDz+ejVatWf2wO7sePH7Fz504EBQWxsxAOh4MqVapg9OjROHXqVJ7rjQXJunXrQERY+7OkqjK0a9cO5cqVy+VCjY6OxvXr19lgrcqVK8PT0zNXKp5Y86Bly5YYPnw4Vq5ciVKlSqF+/fqs+/3du3dsNH3Pnj3zVH/73SQmJqJ79+6syqE6f6Nr164Fj8fLFTT4/ft3ODs7w9XVVWqg3fPnz/PlFRCzbt068Hi8AnvviEQiGBsby0w1ZhgG3bp1g0AgyJWuJ4+srCyMGTMGRIRu3bpJvDuysrJYI4PH46FRo0Z5uvmPHDnCflf19fVx4cIFhfuSkwYNGsDPz0/qsdevX4PoPxnkYv4eio2BHGzevBlcLpctDqMIa9euBYfDQdeuXQtNolQVYmJisH//fvTr1w9lypRhBz03NzcMGTIER44ckVui9nfz6tUrEJHMl5Q00tLScP36dfD5fPj7+0uk4mlpaUkM9lpaWuDz+Wjfvj2mTZuG5cuXw97eHubm5lKzQdatWwcul4vIyEisW7cOurq6sLGxwZkzZ9T52Gpn165d0NPTQ6lSpXDnzh21tFm3bl2ZqnxhYWHQ0dFBx44dc81q1eEVAICXL19KuMjVjSJxCenp6WjUqBEMDAykpu39SkJCAnx8fMDlcrF48WKJzyY2Nhbe3t7gcrnQ1dVF5cqVFfI2Pn78GHw+H0KhMF8y1TNmzIChoaHUOJqsrKw8lQqL+TMpNgZy0LJlS3h5eSl8/ty5c0FEGDx4cJFfQ4uPj8eRI0cwdOhQuLm5sYOgs7Mz+vXrh3379uHLly+F3U2ZMAwDTU1NWFtbS+yLjY1FSEgIdu/ejVmzZqFHjx6oW7durlQ8gUCAMmXKwMfHB4MGDcLSpUtx9OhRhIWFISkpiS1iNG7cOERGRqJUqVKwtbVlI7Z/5cePH9DR0WG9KL179y5y3gBZvHr1ClWrVgWfz8fChQvz9d39+PEjOBwOtm7dKvMcsbR3TmVBdXkFgOzvga2tLYYPH57vtqSxcuVKCASCPAtDff/+He7u7rC1tZWZvgdkKy2WLVsWBgYGOH36tMSxW7duwcbGBqamprC1tVVYz+DixYswMDBgC3flRxjo6tWrIJJdBMrNzQ39+/dXuf1iiibFxsBPUlJSoKWlpZB6GsMwGDt2LIgIU6ZMKRLrwr+SmJiI06dPY/To0ahatSqr8mdvb48ePXpgx44dvz0PXRUyMjLw6tUrnDt3DpaWluBwOPD390fFihWhr68vMbs3MTFBtWrV0KFDB0ycOBGbNm2CtbU1/P39FRrwJk2aBE1NTdjY2KBkyZIy00JFIhHWrFkDPp8PHo+ncuZJYZKeno5Ro0aBiNC0aVOVBXSWLVsGDQ0NxMfHyz1v+PDh4PP5uH79OgD1eQXEdOvWDRUqVFBLW7/Spk0b1KpVS6Fzo6KiYG1tjYoVK0pdVjt37hwMDQ3h7OwsEdDJMAxrdNSoUQMeHh4wMTFRKEZmx44dEAgE8Pb2RmxsLGxtbdG1a1fFH/AXxHEDixcvlnq8bdu2v03boZjfR7Ex8BNxDfa8Iq5FIhH69esHIpIZZFMYpKSk4OLFi5g4cSI8PT3ZIDdLS0t06tQJmzdvxps3bwq7m1JJSEjAgwcP8O+//2L+/Pno06cPGjVqlCsVTzzTr1atWq5UPGmz8osXL+ZKB5PHgwcPwOVyoa+vz8oh/8qbN29Qv359EBECAgIUipgvypw+fRpmZmYwNzdXWEQpJzVq1FBo6SYjIwO1a9eGpaUlrl27Bi6Xi9WrV6vSZamI5ZCVFTvKC4ZhUKJECaWyFZ48eQJ9fX00adKEXecXZ3bweDw0adJEwnhKTExEhw4dQEQYOnQoWrduDaFQmKc6JsMwmDVrFogIPXr0YO+1dOlS8Pl8vHv3TvkH/knDhg3RokULqcemTJkCCwsLldsupmhSbAz8pHfv3nB2dpZ7TkZGBgIDA8HlcrF58+bf1DPppKen49q1a5gxYwbq1avHSpOampqibdu2WLNmDZ4/f14kvBbiqnjBwcFsKl6HDh3Y2U/O2b2+vj4qVaqEgIAAjBkzBuvWrcP58+fx+vVr1mCbOnWqQvdt3749ypQpo9Bn8OzZM1hYWMDc3BxcLjdXnIBIJMKqVaugo6MDe3t7nD9/HgDg4eGBZs2aKf2ZFCU+ffqERo0agcPhYNy4cQoX/nn79i2IKFdOvLz7WFpaokSJErC2tlar9kFUVJRaVCp/5dmzZyoFzF24cAECgQBBQUFITU1Fz549QUQYOXKkxFr8s2fPUK5cOejq6mLv3r0YOnQouFxungZmRkYGevXqBSLCtGnTJL7jiYmJMDY2xpAhQ5R72BzMnDkTBgYGUuMGdu/eDSLK0xtUzJ/F/40xkJqVhUMxMRj3+jUaPXwI15AQlA8JQb2HDzHy5UsYtGqFIWPHyrw+JSUFvr6+EAgEan/hKEJmZibu3LmDefPmoUmTJtDW1gZRdklZPz8/LFu2DE+ePCm02IWkpCSEhobiyJEjWLJkCQYOHIhmzZpJrYpna2uLevXqISgoCLNnz8aePXsQEhKCr1+/yh24ExMTQUQKxXXExMRAIBDIdHXm5PHjxzAzM4Obmxvev38PBwcHiSJGr169Qt26dUFE6N+/v4T7d9OmTeBwOH+80qRIJMK8efPA5/NRvXp1hbxI8+fPh5aWllKptDt37gQRoUGDBvnprlScnZ3VvpYtzpRQJV34n3/+AVF2AS4NDY1cWUp79+6Fjo4OXFxcEB4ejkWLFoGIsGbNGrnt/vjxA02bNgWfz5cZqzF16lRoaWmp7Cm5du0aiAj379/PdUwswHT79m2V2i6maPLXGwOx6ekY8+oVDK5eBQUHQ3D5MjjBwaAcG//nf4XBwRgSEYEPv8xYvn//jrp160JLS+u3RYuLRCI8evQIS5cuRYsWLdj1cR0dHTRt2hQLFizA3bt3FZZ8zS8Mw+DTp0+4fv06/vnnH0ydOhVdunSBp6cnLCwsJGb32tracHV1hZ+fH5uKd+rUKTx//jzfs0FjY2MYGRnled7ChQuhoaGR58vw/v37MDY2RuXKldkywuIiRtevX8eKFSugra0NBwcHqdHkSUlJ0NfXx8SJE1V7oCLGrVu34ODgAH19fezdu1fuuZUqVULbtm2Var9Tp04wMDAAESld9jkv+vXrl6d3T1k6dOiA6tWrq3TtgwcP2GedNGkSuz89PR1Dhgxh0zwTExOxZ88eEBHGjRsnt83o6GhUqlQJenp6cr0VsbGx0NbWVtiL9itpaWnQ0tLCokWLch1LSkrKU6irmD+Pv9oYOBQTA+Nr18D7ZfCXt/GDg6F79Sq2ffrERqtXqVIFBgYGbPBTQcAwDMLDw7F69WoEBASw7nNNTU00aNAAM2fOxI0bNwq0dntaWhqeP3+OkydPYuXKlRg2bBj8/PykpuKJq+J16dIFU6dOxT///IPr16/j08/PraCoU6cOiEhugRiGYeDk5ITAwEC5bd2+fRuGhoaoXr26hMtTJBKhbNmyrAE2cOBAuTPDAQMGwMLCokD/Nr+ThIQEtG/fnpWxlRZF/+LFCxARDh48qHC74eHhbAZBYGAgdHR08PTpU7X1e//+/SAiREVFqaU9hmFgaWmJMWPGqNQXLS0tVK5cGYGBgeDz+Th79iyioqJQs2ZNCAQCrF69GgzDIDg4GBoaGujcubPc387Tp09hZ2cHKysrmZUFczJkyBAYGxurLILWqFEjNG/eXOoxOzu7PA2XYv4s/kpjgGEYjH/9GhQcnMsLoMgmvqbT/fso6+ICMzMzmfKc+enj69evsXHjRnTs2JGdXfP5fNSqVQuTJ0/GpUuX1CpixDAMvn79ipCQEOzZswezZs1CUFAQ6tatC1tbW4lUPA0NDZQpUwbNmjXDoEGDsGTJEhw9ehShoaEFUqlNUcRa6/Ii+IODg0FEuHz5ssxzrl27Bj09PXh5eUl8X0UiERshT0SYM2dOnn16/Pix0gNjUYdhGGzatIkt2fv48WOJ4zNmzICenp5SKpSdOnWCjY0N0tLSkJSUBFdXV5QpU0Zt74uYmBgQkdKqe7KIiIgAEeHkyZMKXyMSiVixoMDAQKSkpCAzMxPNmjWDtrY2DA0NYWtry7rYQ0NDYWBggEaNGsmV8w4ODoaBgQFcXV1lBrf+yrt378Dn8+VWIZTHrFmzoK+vL9X72KRJE7Rq1UqldospmvyVxsCkN2+UNgCkbpcuQWfSJLVpukdFReGff/5B9+7dYWdnByICl8uFh4cHxo4dizNnzuRbyjgzMxOvX7/GuXPnsG7dOowePRoBAQF5puJNmDABmzdvRnBwMN6/f//blh+UJTQ0FESEvn37yjwnMDAQzs7OMmdZly5dgra2NurXry/xeUdERMDLywtEhEGDBqFOnToKFTECsqPqGzdurPwDFXGePXsGd3d3aGpqsjNZhmFQrlw5qbUeZCH2CuRcD3/x4gX09fXRunVrtXmT3N3d0b17d7W0tXHjRnC5XIXfZ4mJiWjVqhU4HA7mzp3LPlNOA0FTU5Od1UdFRcHGxgYVKlSQe49du3ZBQ0MDDRs2VFrLomvXrrCxsVGpbsj169dBRLh3716uY0OHDs1X4bBiih5/nTFwNi5OPYZAjm23ijnYnz9/xt69e9GnTx84OTmxg3CFChUwbNgwHDt2TCWhmu/fv+PBgwc4cOAA5s+fj759+6JRo0ZwdHTMVRXP0dERjRo1Qt++fTF//nwcOHAADx48+GMEcn6FYRgY8Hjo6ugIrF8PLF0KrF4NnDkDxMYiNjYWGhoaUtc6AeDMmTMQCoVo3Lgx6/7OysrCkiVLIBQKUapUKdajIC5iJE9QR8zWrVtBRHj9+rW6HrXIkJqaioEDB4KI4O/vzwaXKaP417FjR9YrkBOxhK4i+h6KMHz4cNjZ2anFuOjcuTOqVKmi0Llv3ryBm5sbdHV1JcpGx8XFwdfXFxwOByNHjoS9vT1cXV3x7t07uLm5yRUoYhiGFTbr2rWrSgO6uAqrKuv76enp0NbWxsKFC3MdW7t2Lfh8/l+zNFbMX2YMfM/MhOWNG+DKG9zXrQN5eIC0tUFaWqCqVUEbN8pdMjC4ehWfFAh8i4uLw6FDhzB48GCUL1+eHZTLli2LAQMG4MCBAwpF94pEIrx//x7BwcHYvHmz3FQ8PT09VKxYEQEBARg9ejTWrVuHc+fO4fXr13/XDzU9Hdi3D/DygogIEG9cLsDhsP+OMzPDUB4PX6UMysePH4eGhgaaN2/OLr88f/4cnp6e4HA4GDp0aK4lkLZt28LGxiZPd3hycjIMDAz+6nXUQ4cOwcjICPr6+tDV1VV4cAoPDweHw5EZJT9+/HhwuVy1lCEWp5/KUo5UFLGq4YgRI/I8Nzg4GCYmJnB0dJSQIr537x4cHBxgbGzMKg0+e/YMRkZGMDQ0hIGBgcyYiczMTFbPZPLkyfkyblq0aIFy5cqplGnk7e0NX1/fXPvFS3Hh4eEq96uYosVfZQwsev9eviGwfj1IQwNkYwPq3x/Uty/IwgKkowPavl3mdbzgYIx99SrX/X78+IGTJ09i5MiRqFy5Mrvm7ujoiF69emHXrl25qpCJSU5ORmhoKI4ePYolS5Zg0KBBaNasGcqUKSM1Fa9u3boICgrCrFmz2FS82NjYIqEjUOBcvQo4OGQP+Dzef4aAlE1EBIYI0NMDtm8Hfn4+Bw8ehEAgQOvWrZGeno6srCwsWrQIQqEQpUuXllnRMCIiAjweT+rs6FcGDx6MEiVKFGgp58Lm3bt3EAqF4HA4mD59ukJLKB07doStra3MTJKsrCw0atQIZmZm+Q7++/79O3g8HtavX5+vdt68eQMikpjlS0M8Q27QoAGbjcIwDNavXw8NDQ14eHhIiP+IRCI0bNgQRARvb2+pv9/ExET4+vqCx+Nh06ZN+XoOALhx44bK4lizZ8+Gvr5+rrornz59AhHh8OHD+e5fMUWDv8YYEDEM7G/elO/yr14dpKcHOnLkv30HDmR7CGrXlnut4bVriEtMxPnz5zF+/HjUqFGDdclbW1ujS5cu2Lp1K/vD/zUVb9q0aejSpQtq1aqVKxVPS0sL5cuXh5+fH4YNG4aVK1fi5MmTeP78+R9bBVEtMAwwfnz2zD8PIyDXJvYW+Plh/9at4PF46NChAzIyMhAeHo4aNWqAw+Fg+PDheWrO9+/fH0ZGRnmKrIhdsupOmStK3L17F0SEzp07g8vlom7dunIHcLFXIK9qkzExMbC1tUX16tXznX5avXp1tG/fPl9tbN26FRwOR+bfPCMjA/379wdRdm0SsRcuOTkZ3bp1AxFhwIABuZ5l9OjRrBeKiHIpG3769AlVqlSBrq6uWtOYa9eujRo1aig9eRAbEnfv3pXYzzAMDA0NMXfuXLX1sZjC5a8xBkK+f897/V9bG1S3bu79NWqABALQqVPy0w5/BpeZmZmhffv2WLVqFc6cOcOm4g0fPhx+fn5wdXVlRYFypuJ5enrmSsWLjo7+/5jdKwvDAH37KmcASPMUcDi4ToReHTsiPT0dCxYsgKamJpycnBROFf306RNbxCgvvLy8CkRQp6gwatQolChRApmZmbh8+TKsra1hbGyMo0ePSj0/MDBQrlcgJyEhIdDQ0MCAAQPy1cfx48fDzMwsX7+r7t27o2LFilKPxcbGol69ehAIBNiwYQO7PyIiAu7u7tDW1sbOnTtzXbdixQoQERvdv2DBAhAR68UIDw+Hg4MDLC0tZRYJUpWTJ09CGWluMeK4AWkxHTVq1MhXDYRiihZ/jTGw+sOHvNMIBQJQ48a59/9Ul6PVq2Vfe+ECnGfPhr+/v9RUPIFAAGdnZzRr1gwDBw7EkiVLcOTIkUJPxftjWbQo34ZAToMgoWlTVK9enQ3kyssb8CuTJk2CUCjMs7iTWLAoIiIiP09fJBGJRLC1tZUYrL9+/YoWLVqwM+Scnqxnz54p5BXIyfr160FE2L59u8r9PH/+PIjyV7nPwcEBQ4cOzbX/yZMncHBwgKmpqcTS0qFDh6Cvrw9nZ2ep9z148CA4HI5EDALDMBg4cCB4PB7mz58PIyMjlC9fHpGRkSr3WxYMw8DNzU0l6ezGjRvDx8cn1/7u3bujWrVq6uheMUWAv8YY6PX8OfiXL8s3BhwdQba2oAsX/tt37hzI3Dx7UJ82Tfa1Fy9CMH8+PDw82FS8TZs2ITg4GJGRkUU2Fe+PJDwcEAhkDu7BOTwuv2635BgFgy0tcePGDZW69P37d5iYmKBXr15yz0tNTYWxsTFGjRql0n2KMuJUs1/jKxiGwYoVK6ChoYGKFSuyqbjKeAVyttWjRw8IhUKVtT1SUlKgoaGBZcuWqXR9ZGQkiAiHDh2S2H/48GHo6OjA3d2dXQ7MzMxkqz+2adNG6rvv+vXrEAqFaNeuXa4gvqysLFStWhVEhCpVqhSo3r9YCloRwaKczJkzB3p6erniBubNmwd9ff1iz+Zfwl9jDLQJC8vbMzB8ePag0aQJaOtW0JYtoPr1QT8r/NGECXKvr3DlCp49e4b3798jPj7+74rWL0o0bAjw+XkaA0OIsOOXLVaWd4AIjIkJkI/16GXLlkktYvQrw4cPh6mpqVoL8RQFBg8eDGtra5lR6Q8fPkSZMmWgra2NWbNmKe0VEJOSkoJKlSrB0dER3759U6mv9erVU6iaojTENQXEmT8Mw2DmzJkgIrRu3ZrVpoiOjkadOnVYYR9pg2J4eDiMjIxQp06dXPE/DMNg4cKFEGt+mJubF2hl0czMTDg4OOSpzPkrN2/eBBHhzp07EvvFaaGygqSL+bNQdPzmAADlwY8fP8jAwIC+f/9O+vr6eZ2uVto9fUoHYmMpz05u2kS0bx9RVlb2v8uUIfLwINq5k2jmTCIvL9nXPn5MNGyYxC5NTU3S1dXNtenp6Undr8hxDQ2N/HwUfzYvXhCVLSv3lMtEVJ+I/iWiNsq2v2sXUceOKnUtPT2dypYtSxUrVqTDhw/LPO/58+dUrlw52r17NwUGBqp0r6KGSCQia2tr6tixIy1ZskTmecnJyTR48GDaunUraWtr07t378jMzEzp+719+5aqVKlCnp6edOzYMeJyuUpdP3PmTFq0aBHFxcURn89X6tpevXpRSEgIhYaGUkpKCvXo0YP2799PU6dOpSlTphCXy6UrV65Q+/bticfj0f79+6lWrVq52vn06RPVrFmTdHV16dq1a2RkZMQeE4lENHToUFq9ejVNmDCBhgwZQp6eniQQCOjmzZtkbGysVJ8VZfXq1TRkyBB6+fIlOTo6KnRNZmYmGRkZ0ZQpU2jMmDHs/oiICCpTpgxdunSJ6tevXyD9Leb3oej4XeSNgcEvX9L66GjKzLubRImJRO/eEenoEDk6Em3cSLR7N9HWrUQODtKvEYmIrlzJNhiIiMvlkrGxMRkaGpKenh5pa2uTpqYm8fl84nK5xDAMpaamUlJSUq4tr49SIBDky5iQdlxDQ4M4HI5yH2phMHo00bJl/xlrUrhM/xkDTYhIi4gUet1zuUSenkTXrqncvV27dlHnzp3pxo0b5OnpKfO8evXqZff18mWV71WUuHTpEjVs2JBCQkKoWrVqcs8NDw+n8uXLk4aGBllbW9PevXvJw8ND6XuePn2afH19afr06TR58mSlrr1x4wZ5eXnRnTt3lL63k5MTNWnShMaOHUstW7akFy9e0Pbt26lNmzYEgBYtWkTjx4+nOnXq0J49e8jc3DxXG4mJiVS3bl368uUL3b59m2xtbdljKSkpFBgYSCdPnqQ1a9ZQnz59iIjo5cuXVLNmTSpXrhydP3+ehEKhUv1WhJSUFLK3t6d27drR6tWrFb6uadOmxOVy6dSpU+y+zMxM0tHRoWXLltGAAQPU3tdifi+Kjt/KmdaFQBVdXcUMASIiPT0iN7f//v3gAZGZGZGdnexrOBwyiYujbxwOIXvZhEQiEaWnp1N6ejqlpKTQt2/fJAZ6Y2NjsrOzo3LlypGdnR3Z2dmRra0tWVhYkLGxMWlpaVFKSopUgyEpKYkSExNz7fv48aPU4wzDyH1kPp+vNs+F+Limpqb6DYzgYLmGQE56EFESEfGIqDYRLSSiqvIuYBiikBCizEwigUCl7gUGBtLChQtp7NixdPXqVZnP37dvX+rYsSM9f/6cyubh6fgT2LdvH5UsWVKhgXXGjBlkY2NDZ8+epW7dupGnpyfNnTuXRowYodQMv1mzZjRt2jSaOnUqeXh4UNOmTRW+1sPDg3R0dOjSpUtKGQPR0dH06tUr6tatG1WtWpWEQiHduHGDKlasSN+/f6fu3bvTkSNHaPz48TRjxgypXofMzExq06YNvX79mq5duyZhCMTExFCLFi3o6dOndOzYMfLx8WGPOTk50fHjx6lBgwbUrVs32rNnj9IekbzQ1tamoUOH0uzZs2nKlClSDRlp1KtXj2bPnk1ZWVnsMwsEAipdujQ9f/5crX0spmhT5D0D4cnJ5HL3rvIXXrqUPdvv35+oXTu5pwa7u1M1oZCePn1KT548kdi+fftGRES6urrk4OBAJUqUIF1dXeJwOJScnEyfPn2iyMhISkpKYtsTCARkY2PDGgrSNl1d3TwfAQClpaUpZEwoejwxMZFEIpHc+/J4PLV5LnR1dUlXKCQtMzPiZGTIve9NIlpCRD5EZEpEz4hoEREl/zxWKa8P7NEjogoV8vxcZXH27Flq2rQpHT9+nJo3by71nPT0dLKxsaEuXbrIdav/CWRmZpKFhQX16dOH5s6dK/fcZ8+ekaurK61du5b69u1LGRkZNGnSJFq4cCE1adKEtm/frvAARETEMAy1aNGCbt26Rffv36eSJUsqfK2Pjw9lZWXRuXPnFL5mz5491LFjRxIIBFS9enU6ePAglShRgh4/fkxt2rSh2NhY2rFjB7Vo0ULq9QCoR48etHv3bjpz5gw1aNCAPRYREUHNmjWj5ORkOnnyJFWpUkVqG4cPH6aAgAAaOXIkLVy4UOG+K0p8fDzZ2dnRkCFDaPbs2Qpdc/v2bapZs2Yuz1Dr1q0pKSlJqc+4mKLJX7NMQERU5d49epSURDLnyI8fE/3zD1HVqkT6+kTh4USnT2f/e84cIh5P+nUAUUwMOUyYQH169aIePXqQhYVFjsOg6OjoXAbC8+fPKevnLNfBwYHc3d3J2dmZzM3NSUdHh7KysujDhw/0/v17douOjpaY5RsZGZG9vb1MY8HCwoJ4svqdDwBQenq6ysaEtOOJiYns5yENCyL6pGJ/XxGROxHVIaIzeZ187BiRjJe5IgCghg0bUkxMDD1+/Fjm5z969GjasmULffz4sUBcvr+L06dPk4+PDz169Igq5GFEBQYG0o0bN+jVq1cSsS9nz56lrl27EofDoR07dpC3t7fC94+Pj6eqVauSoaEhXb9+nbS0tBS6btGiRTRlyhSKj48nTU3NPM/PysqiypUrU2hoKPXq1YtWr15NGhoatG3bNurfvz+VK1eODhw4IHetffLkyTRr1izatWsXdcwRm3Ljxg3y8/OjEiVK0OnTp8lB1nLkT1asWEFDhw6llStX0qBBgxR6XmUYNWoUbd68mSIjIxV6V4vjBiZPnkxjx45l90+YMIF27txJ79+/V3sfi/m9KDx+qzMasaDY9umT/GyCnTuzaxEYGGRrDtjZgXr3zk4vlHMdNzgYA69eRbdu3SAUCsHn8xEQEICzZ8/K1ftOS0vDo0eP8M8//2DUqFFo3LixhPqglpYWqlatiqCgICxbtgyXLl3Cp0+f8O7dO1y9ehU7d+7EnDlz0LdvXzRr1gzly5eHrq6uRCodn8+Hg4MD6tSpg86dO2PixIlYv349Tp8+jadPn+a7CqK6SU9PR1xcHCIjIxEWFobbt2/jwoULOHLkCA4tX54vPYEORNAgQlZe56qh1LAiRYzEJXB37NiR7/sVJt26dUPZsmXzTCF7+vQpOBwO1q1bJ/X4p0+f4O3tDSLC2LFjlcrGefjwIYRCIXr06KFwKtv9+/cVFtr59u0bGjduDCJCrVq1wDAMUlNT0bt3bxARevbsmWd9inXr1oGIMG/ePIn9Bw4cgKamJurUqaNUdsTw4cPB4XAKRPL3w4cPEAgECslsi2natCmaNm0qsU+ceVHU3jPFKM9fk1oIAJkiESrdvQt+XimGSmy84GCUvHULyT91BL59+4aVK1fC1dUVRISSJUti9uzZ+PTpk8L9/PLlCy5cuIAlS5age/fuqFy5MjQ1NdkB3traGs2aNcPYsWOxc+dOPHnyhNW7ZxgG8fHxePz4MY4fP47Vq1dj7NixCAwMRK1atWBjYwMulythMBgZGaFChQpo0aIFBg4ciPnz52PPnj24efMmPnz4UHQ0Er59y5cxMPrn837P47yXa9eqReZZkSJGDRo0QK1atfJ9r8IiNTUV+vr6mDp1ap7ndujQAXZ2dnJrM4hEIsyfPx98Ph/Vq1dXKpVu+/btICIJ1T95ZGVlwcjIKM++h4eHw8nJCQYGBiAi7N69G2/evEHlypUhFAqxZcuWPO917NgxcLlcDBw4UMJYWbJkCTgcDjp06KB0qqlIJEKbNm0gFApx69Ytpa5VhKCgIFhaWircr3nz5kFXV1fCiBMbxdLKHBfzZ/FXGQMAEJaUBP7ly3lrDii4cYKDcV1KuV+GYXDz5k10794dWlpa4PP5aN26Nc6cOaNSdbDMzEw8e/YMe/fuxYQJE9C8eXPY2dmxA7pAIIC7uzu6dOmChQsX4uzZs/j06ZPUWVJGRkYu70K/fv3g4+MDV1dX6OnpyfUuTJgwAevWrcOpU6cQFhaGHz9+qPS3UAkzM5WNgQAiCH9qCsg7z4IIXC4XZcuWRZs2bTB9+nQcPHgQERERShlGihQx2r9/P4hIoprdn8Thw4dBRHlqK4SFhYHD4ShcIOj27dsoWbIk9PX1sXfvXoX7079/f2hoaCAkJESh8/39/VG7dm2Zx0+dOgV9fX24uLiwcsHbt2+HoaEhHB0dFRI+un37NrS0tODv789+f7KysjBkyBDWC6LKOwHINsZq1aoFU1PTfFdi/BVx3YiNGzcqdP7t27dBRBKGifidL01+uZg/i79GZyAn+2JiKPDZMyKivHUH8mC1kxMNsLaWe05CQgLt3LmT1q9fT2FhYeTg4EC9e/emHj16kKWlZb7un5CQQKGhoRKxCKGhoZScnExERGZmZuTu7i6xubi45LlG/f37d4qMjJSIV8i5ffz4MVfsgrxAR0tLS/XELvj5EZ08mR35L4NYIvo1c/0xEXkQUTMiOiqn+a8cDpkBxOFwyNTUlDQ1Nen79++UmJhIRERaWlrk4uJCrq6u5OrqSm5ubuTq6kpWVlZSMwcGDBhAe/fupdevX0vkkYvJyMggW1tbat++Pa1YsSKvpy9yBAYGUnh4OD169EjueR06dKBbt27Ry5cvFdbJ+P79O/Xt25f27dtHPXv2pOXLl5OOjo7ca9LT06lu3boUHR1N9+/fz1PDYPXq1TR8+HCKj4+XaBsALV68mMaMGUO+vr60a9cuGj9+PO3Zs4fi4+PJz8+Ptm/fToaGhnLbf/nyJXl6epKzszNduHCBzRDq3LkzHT16lFauXJnvtLu4uDiqVasWiUQiunnzpkq6DbIICAigsLAwevbsWZ6/38zMTDI2NqaJEyfSuHHj2P3W1tYUFBREM3+mXRfzZ/JXBRDmZF9MDHUJDycGIPkx8bnhUbYRsdrJifrlYQjkBACFhITQ+vXrad++fZSRkUF+fn7Ut29f8vb2VluaEMMw9Pbt21wBi69fvyYAxOVyqUyZMrmMBFtbW4VTAbOysig6OlrCQMhpPERGRrIDKFF26qK1tTXZ2dnJDHjU09PL+8ZbtxIFBck9pQFlawt4ElEJys4m2EBEAiK6RUTlZF3I5xN69qRXI0fSlStX6OrVq3TlyhU2+MnBwYGsra1JQ0OD4uPj6eXLl6zRZWRkJGEciLf09HQqVaoUDR48mObNmyf1tuPHj6e1a9dSdHQ0aWtr5/0ZFBGSk5OpRIkSNGnSJBo/frzM854+fUpubm60bt06NmdeUQDQ1q1bafDgwWRnZ0f79u0jd3d3udd8+PCBKleuTO7u7nT27Fm5g1h4eDi5uLjQmTNnqEmTJkRElJaWRn369KEdO3bQ+PHjaebMmRQXF0eOjo6UnJxM8+bNo9GjR+f5e42JiSFPT0/i8/l048YNMjExodjYWPLz86MnT57Q3r17ZWYdKMubN2+oZs2a5OjoSBcvXlTb9+jOnTtUvXp1OnDgAAUEBOR5vo+PDzEMQ2fO/Bem27BhQzI2NqZ///1XLX0qpnD4a40BIqLnycnU9flzupuYSDyiPI0CLhExRFROW5t2litHlRUZvGSQkJBAu3btovXr11NoaCg5ODhQr5+ZCFZWViq3K4+kpCSpaY8JCQlERGRgYJDLQHB1dVUofVEa379/l+lZiIyMzOVdMDQ0zGUgKg0j4gAAQ1xJREFU5DQcLC0tiZeeTmRpSfTjh8z7riCiXZSdQfCDsr0EDYloKhGVzqvTT55IakwQUWRkJGsYXL16lV6+fElERM7OzlSxYkWytrYmHo9HHz58oLCwMIksEWtraxIKhRQZGUkLFy6kOnXqULly5SQi3t+8eUOlSpWirVu3Uvfu3RX7cIsA+/btow4dOtDr16/lRtB36NCBbt++TRERESqrZ4aHh1OHDh3oxYsXtHjxYhowYIBcw/XSpUvk7e1NY8eOpTlz5sg8DwBZWVlR165daf78+RQdHU3+/v705MkT2rJlCwUGBtLNmzcpICCAPn/+TOPHj5fbnpjk5GSqX78+vX//nm7dukUlS5akly9fUrNmzSgxMZFOnDihktCSPO7evUv16tWjxo0b04EDB9SWRdSgQQNKTEykO3fu5DlZWLBgAc2YMYPi4+NJ8FOrY9CgQXTlyhUKDQ1VS3+KKRz+qmwCaWQxDPZ9+QKv+/fZOADB5cvg/9wEOYobVbl7F9s+fUK6iut70mAYBrdu3UKPHj2gpaUFHo8Hf39/nD59+rcE7jEMg/fv3+PEiROYM2cOOnToABcXF/B4PDZmoFSpUvD398fUqVNx8OBBvHz5UuU1zpxkZmYiMjIS165dw65duzB37lz0798fvr6+cHNzYwO2xBuPx4O9vT022tvnue6v9MbnA82bK9Tvjx8/Yu/evejfvz/Kly/P9s/e3h5du3bFunXrcPLkSezatQsTJkxA06ZNJYI2uVwunJ2d0bp1a0ydOhX//vsvatWqherVq+f7M/2d+Pv751mVThwroGhQnzxSU1MxcOBAEBFatWqFuLg4uefPnz8fRJRntH3Hjh1RtWpV3LlzB1ZWVrC2tsbdu3fBMAyWLVsGPp+PsmXLgogUqhiYmZkJX19f6OjosIFzN2/ehKmpKZydnfH69WuFn1lZjh8/Di6Xi8GDB6utQNDZs2dBRLhw4UKe54aEhICIcPPmTXbfypUroaGhkauQUTF/Fn9dAKE83qWm4t8vXzD+9Wv0ev4cQeHhGP3qFfZ8/oyXSpa0VYWEhASsXr0a7u7u7OAyc+ZMfPz4scDv/Supqal48OABtm3bhhEjRqBRo0YwMzNjBzRtbW1Ur14dvXv3xsqVK3HlyhWVi8bIIyEhAaGhoThx4gTWrFmDcePGoUv79nitrY1MNRkCDIcD6OkBKn7OMTExOHToEIYOHYpKlSqxpautrKzQoUMHtt9cLhd79uzBpk2bMHToUDRs2BAlSpSQMHjKlCmDLl26YP78+Th16hTev39fJKu+JSQkQFNTE4sXL5Z7Xrt27WBvby83g0BZDh8+DCMjI9jY2OSqkJgThmHg7+8PfX19vHjxQuZ5mzZtAofDgYaGBqpXr47o6Gj8+PED7dq1AxFhxIgRGDx4MBwcHPLsG8Mw6N27N3g8Hk6fPg0gu3yxUChErVq18PXrV+UfWEnWrl0LIsrzb6MoDMOgUqVK8Pb2zvPczMxM6OnpYc6cOew+cclodQc4FvN7+b8yBooKDMPg9u3bCAoKgra2Nng8Hlq1aoVTp04Veprf58+fce7cOSxatAhdu3ZFxYoVoaGhwQ5mtra28PX1xfjx47Fnzx48ffq0YGYEoaGAri4YLjd/hsDP7IIbo0YhNDRULd/N+Ph4nDhxAqNHj0b16tVZLwuXy4WlpSWWLVuGhw8fsn/LL1++4Ny5c2zUeo0aNST0IgwMDFCrVi307dsXq1atwuXLl/OcFRc04jS+qKgomeeEhoaqzSvwK+/fv0ft2rXB5XIxbdo0mb+L79+/w9nZGeXLl0dSUlKu41lZWejXrx+ICPXq1UNqairCwsJQpkwZ6Onp4d9//wUAVKxYEd26dcuzXzNmzADRf/oSy5cvB4fDQdu2bdWSrqoo48aNAxFh//79amlv7969IFIsRdDHxweNGzdm/x0VFQUiwvHjx9XSl2IKh2JjoJBJSEjAmjVrUKFChUL3FsgiIyMDYWFh2L17N8aNGwcfHx/Y2Niwg5mmpiYqVaqEbt26YfHixTh//jy+fPmS/xvfupU9o5dTzljelvXTEOiaY2YuHnzd3Nzg6+uL/v37Y+7cudi1axeuX7+O9+/fK23cJCYm4ty5c2jZsiWIslM1iQiGhoZo3rw5FixYgJCQEIwbNw76+vpISkoCwzB4+/Ytjh8/jjlz5qBjx45wd3eHQCBg+2lpaQlvb2+MGDECW7Zswd27d5H8GzxYQPYL38vLS+45BeEVyElmZiamTZsGLpeLOnXqyDRMwsLCoKOjg8DAQAkvy/fv3+Hr6wsulwtjY2MMGjQIu3btgra2NlxdXVlvwrdv38DhcPLUE9iyZQuICDNmzIBIJMLwnyXRR44cqZZlNWUQiUTo2LEjNDU1ce3atXy3l5mZiVKlSqFt27Z5nrtgwQJoa2uzegMMw0BXV1cpAaNiih7FxkARgWEYhISEoGfPnqy3oGXLljh58mShewtkERcXh8uXL2PFihXo1asXqlWrBi0tLXYwMzc3h7e3N0aOHInt27fj4cOHSguv4PlzoGpV5Y0BLhewsgIuXMCNGzegp6cHV1dXbN68GfPmzcOAAQPQvHlzuLu7w9DQUMJY4PF4sLOzg5eXFzp27Ihx48ZhzZo1OHHiBJ48eYIEKboTQPYLukKFCvD09ERwcDBmzJiBhg0bsp+J+L+tWrXCtWvXpH4WGRkZePr0Kfbu3YtJkyahZcuWKFWqFLs0weFwULp0abRq1QqTJk3Cvn378PTpU6XU/PLi69ev4PP5WLVqlcxzCtIr8CtXrlyBtbU1jI2NcfToUanniGe2y5cvBwC8fPkS5cqVg4GBAU6fPo3u3bvD2NgYRITOnTtLeBGOHTsGIpK71n/mzBnweDz07t0bycnJCAgIAIfDwYoVK9T7sEqQlpaGevXqwcjICOHh4flub926deBwOIiIiJB7nlho6MaNG+y+qlWromfPnvnuQzGFR7ExUAT5/v27hLfAzs4OM2bMwIcPHwq7a3mSlZWFiIgIHDhwAFOmTEGrVq3g6OgoMdCWL18egYGBmDt3Lk6ePImoqCj56+ZZWcDSpYCFxX/BgNIMAB4P4HAAHR1gxAggh1jSnTt3YGBggJo1a0r9fn7//h2hoaE4efIk1q5di/Hjx6NTp06oXbs27O3tJQIu5XkXFi1alCuoLT09HTdv3sS8efNgZmbGBhsKhULUq1cPU6ZMwcWLF+XO+pOSknDnzh1s2bIFw4cPh7e3t4S0tYaGBtzd3dGpUyfMnTsXx48fx7t371SKR9iwYQO4XC4+f/4s85yC9gr8ytevX+Hn5wciwqBBg6S65IcPHw4+n4+lS5fCyMgIzs7OeP78OSIjI9nv4Pz583N9JiNHjoSNjY3Mz+r+/fvQ0dGBr68vPn36BE9PTwiFwgKRCVaW+Ph4uLi4wMHBQe7fSxFSU1Nhbm6OPn36yD1PHDcwe/Zsdl/nzp3h6emZr/sXU7j8laJDfwsA6N69e7Rhwwbas2cPpaamUvPmzalPnz7UtGnTAilQVFAkJiZSWFhYrrTHHz9TCI2MjHKlPZYvX15ShCYri+jECaIzZ7JLEYeHE6WnZ5cjtrcnqlGDqF49og4diKSI19y9e5e8vb3ZvHNlvqMikYg+ffokU3fh/fv3bAqnGBsbG7K3t5dIn4yOjqZZs2bRhg0bKCkpia5cuULXrl2jb9++kUAgIA8PD6pTpw7VrVuXPD098+zj169f6enTpxQaGkphYWHsf8Wfq56eXi4BJVdXV7nCNY0aNSIiogsXLkg9HhYWRu7u7rRhwwbq1auXwp9hfgFAq1evplGjRlHZsmVp7969EuWhMzIyyMXFhV6/fk316tWjQ4cO0d27d6ljx46kqadH0RYWFDBxImXZ21N8VhZxORyy0dSkyxs3UnmATi9Zkiu17u3bt1SzZk2ys7OjzZs3U0BAAMXHx9Px48epRo0av+3Z5fH+/XuqUaMGWVtb0+XLl/MUbpLHvHnzaOrUqfTu3Tu5gmnNmzenjIwMtlrh7NmzafHixRQXF6f+subF/Bb+ap2Bv4kfP37Q7t27af369fTo0SOytbWlXr16UVBQENnY2BR291QCAEVGRuYyEF6+fEkMwxCHw6HSpUvnMhIcHBz+E4QBiJR4+eTHIMiLHz9+UFRUFF24cIGGDRtGvr6+ZGRkxBoOHz58kCgLra+vT3Z2dmRra0u6urqUlpZGMTExFBERQfHx8cThcKhy5cpUt25dqlOnDtWuXZuMjY3z7AcAioqKorCwMAkD4dmzZ5Txszy0ubm5hIHg5uZGLi4ulJSURNbW1rR+/XqZA327du3o7t279OLFC5V1BfLD48ePqX379hQVFUWrVq2i7t27U0ZGBg0cOJA2b95MOjo6VKlSJWrQoAHNWLuWHEaNorgaNSiRYYjDMERcLqtMyiMi0c99TlpaNMTamnpbWZEml8sq/2VlZdGqVauoa9euZGBgQKdPn6bSpfNUtPitPHr0iGrXrk1169alI0eOEJ/PV6md79+/k52dHfXr14/mz58v87xFixbR1KlTKT4+njQ0NOjgwYPUpk0biomJUatCYjG/j79eZ+Bvg2EY3L17F7169YKOjg64XC5atGiBEydOFNnYAmVJTk7G3bt3sXnzZgwdOhT169eHiYkJ6xLX1dVFzZo10bdvX6xevRrXrl2TuY4vDfGSQY0aNQrsu9quXbtcRYyysrIQFRWFoKAgCIVCzJgxAwMHDkSLFi1QoUIFGBkZSSxFcDgcaGtrS2RzWFlZwdfXFwsXLsxzbfdXMjMzER4ejv3792PKlClo3bo1nJyc2HgEIoKJiQk4HA6GDx+OPXv2IDQ0VCIeITQ0FESksJ59QZGUlISgoCAQEfz9/VG9enVoaGhg69atOHHiBIjDATVtCo0LF8BTog4JJzgYZUNCcD02FjVr1oSpqSnWrVsHLS0t1KxZE7GxsYX63PIQxzX07ds3X+mqY8eOhZ6eHuLj42Wec/fuXRARrl+/DiA7iJOI5KaCFlO0KV4m+IP58eMH7dmzh9avX08PHz4kW1tb6tmzJ/Xs2fOP9RbIAgB9+vQplxchPDycVQO0t7fP5UVwcnKSupxy7949atSoEZUrV47OnDlDBgYGau3vy5cvycXFhebOnUujRo2SOPbhwweyt7enNWvWUN++fSWOJSYmSlV0jIiIoDdv3lBcXBzl/ClyuVwyMDAgOzs7dnafU+HRysqKVYqTRUpKCoWHh1NYWBhNnDiR0tPTSVNTkz5+/EhERAKBgMqUKUNubm4UGhpKMTExdPXqVXJyclKbxLaqzJs3jyZMmEBcLpfWr19P7u7uFNCuHUV37kyihg2V9hwR/ectECxZQkPLlaMlS5ZQy5YtadeuXRLKkkWRLVu2UM+ePWnOnDlyJaTl8enTJypZsiRNmzZNogZBTrKyssjExITGjBnDfmd0dHRo7dq11Lt37/w8QjGFRPEywV+COLZg9+7dlJqaSr6+vtSnTx9q1qzZHxVboCwZGRn0/PnzXEbCp0+fiIhIKBRS+fLlcxkJpqamdO/ePfL29qayZcsWiEEgr4iRn58fffjwge7fv6/UGqtIJKLPnz/T/fv36cKFC3Tnzh12WYEo2zjIKQHN5XLJyspKqvyzeDMwMCAOh0NRUVFkZ2dH//zzD3Xp0oW+ffsmEY8QEhJCDx48YNvW1dWl8uXL54pHMDc3z+cnpxj//vsvde/enRwdHYnP59OTJ0+IuFwymj+fvlWunL8iZQyTbUTMnk1DXV1p8eLFf8zvaOrUqTRjxgzauXMnderUSaU2+vbtS0ePHqW3b9/KNIBatGhBaWlpdP78eSLKlu9u3rw5LVmyROW+F1N4FBsDfxmJiYlsbMHDhw/JxsaG9RbY2toWdvd+G7GxsbmqPT59+pTS0tKIiMjS0pLc3d3J3NycDhw4QKVLl6YLFy6odb3z8+fPMosYnTx5kpo3b0537txRi4Z9TEwMXbt2ja5evUqXLl2isLAwIsquB2FtbU26urrEMAzFxsbShw8fWG8KUXaQoZ2dHYlEIoqIiKCJEyeSs7MzaziIvQviWIHg4GB6/vx5rngE8WdrZmaWKx6hfPnyihWqUgCGYWj69Ok0Y8YM6tChA61YsYKGDh1Ke/bsIWrZkmjYMLXchxiGeET0tEYNKvMHFZgCQEFBQbRr1y46e/Ys1a9fX+k2Xr16RWXKlKHVq1dTv379pJ6zePFimjx5MiUkJJCGhgb5+flRVlYWnTp1Kr+PUEwhUGwM/MXcv3+f9RakpKSQj48P6y1QNcDoTyYrK4tevXqVy4sQGRlJREQcDodcXFyoUqVKEl4ECwsLlSOkp0yZQgsXLqSXL19KLN2IRCJydHQkb29v2rRpk1qeLyfx8fF0/fp1tgDTgwcPSCQSkZmZGdWuXZsqVqxIDg4OxOfz6cOHD/T+/XvauXMnASAej0ffvn1j2+JyuWRmZkZfvnwhDw8Pql+/vtSKlG/evJEwEEJDQ9lgUKLsZZycBoKrqyuVLVtWqSDEpKQk6tq1Kx0+fJhmz55NrVu3pjZt2tDbt29pztatNMbMjDKIZC8NfPhAtGULUWgoUWIiUYkSRA0bErVvTySl7Defw6FKurp0q3Jl4v1BUfKZmZnk6+tLd+7coevXr5Orq6vSbbRv357u3btHL168kPq+uH//PlWtWpWuXbtGXl5eNGbMGDpw4AC9efNGHY9QzG+m2Bj4PyAxMZH27NlDGzZsoPv37//fegtkkZCQQAcPHqTBgweTnp4eOTg40LNnzygpKYmIiExNTXMtM7i4uCi0fvzjxw8qVaoUtWzZMtegP3PmTJo3bx5FR0erfYniVxITE+nmzZuscXDnzh3KzMwkIyMjql27Nrm4uNC8efNo9+7dFBgYSElJSRIxC0uXLqWoqCiqXLkyffjwgaKioqR6F37dLCwsKCMjg758+ULPnz9nDYWoqCgiyi597ezsnMuTULJkyVzxCO/evSM/Pz96+/Yt7dy5kzIzMykoKIisra3p4MGDtJjLpX++fKEsWa+qmBiinj2z0079/Ij09IiePctOVfX0JJo9W+bnd7B8eWr9h0XJ//jxg+rUqUPfvn2j27dvK10t9cGDB1SlShXau3cvtW/fPtdxkUhEJiYmNGrUKJo0aRJt2bKFevXqRcnJyUU+tqKY3BQbA/9n/OotaNasGfXt2/f/1luQk/v375O3tzc5OzvT6dOnKT4+PpcX4dWrVwSAuFwuOTs75zIS7OzscnkRVqxYQcOHD6fQ0FBycXFh90dHR5OdnR2tWLGCBgwY8FufNTU1lW7fvs0aB9euXaOsrCzS0dEhLy8vNp3Rw8ODXrx4Qe7u7rRp0ybq2bMnEWUPBF++fJGru5DTu8DhcNjYBXt7eypRogTxeDxKS0ujb9++UVRUFIWHh7OxD9ra2uTi4sIaCABozpw5pK+vT4cOHaIdO3bQ0qVLqV27drRp0ybKEgrJ8uZNSpf3mtq5k2jz5mzPQMmS/+2fO5fo3DmiY8eyDYRf4BFRHUNDulSxojo++t/Kx48fqUaNGmRiYkJXr15V+r3cuHFjio2NpQcPHkj1jvn5+VFKSgpduHCBbt26RZ6envT48WNyd3dX1yMU85soNgb+T0lMTKS9e/fShg0b6N69e2Rtbc16C+zs7Aq7e4XGgwcPqFGjRuTk5ETnzp3LNWNPTk6mp0+f5jISxIOYvr6+1IyGatWqkbu7Ox05ckSiPX9/f3r9+jU9fvy4UMVa3N3dqUSJEtSwYUO6cuUK3bhxg5KSkkhLS4t0dXUpMzOT9u/fT15eXgrP+pKSkigqKkpqdkRkZGQu74Kuri5ZWVmRvr4+8fl8Sk9Pp4SEBHr//j2rz2BoaEgMw1BiYiK1bduWBg8eTG5ubnQwJYV6vXghP2hwwwaiPXuIjhwhyvl33bCBaN++bEErOc/2qWZNstDUVOjZixKhoaHk5eVF1atXp5MnT+aZXZKTS5cuUcOGDenMmTPUpEmTXMeXLFlCkyZNovj4eEpOTiYTExOZnoRiijbFxkAx9ODBA9qwYQPt2rWL9Rb06dOHfHx8/i+9BTkNgrNnz5KhoaHc8wHQx48fcxkIz58/ZwexEiVKUExMDPXo0YN8fX3J3d2dHB0d6fz589SsWTO6efMm1axZ8zc8XW7Cw8PJxcWFjhw5Qi1btiSi7PiKhw8f0r59+2jx4sWkpaVFqampJBAIqFq1aqznwNPTU+XAQGnehV+3uLg4iWs4HA5xOBwSCoWUmprKpllqTZhAaQ0aEORF/N+5QzR2bPaSQI8eRPr6RGFhREuWEDVrRjRwoNz+Hnd1peampio9a2Fz6dIlatq0KXXu3Jk2b96ssOEJgKpXr046OjoUHByc67h4KeHq1atUu3ZtMjc3pwEDBtDUqVPV/QjFFDDFxkAxLElJSbR3715av3493bt3j6ysrKhnz57Uq1ev/ztvgbIGgTTS09MpPDycnjx5Qo8fP6aNGzdSWloaZWZmElG2K9zV1ZWePXtGLi4utGDBAnJzc1NIZVCdTJs2jZYtW0ZfvnwhzV9mvm3atKEHDx5QeHg4PX/+nF1WuHr1KsXGxhKPx5NQSfTy8sqVRqkKcXFx1LZtW7p69SpNmDCBPnz4QNu2bSN7e3uqVq0axcTESHoX1q8ncnbOu+EdO4h27cqWsRbTuXN2LIEc+EQ0xcGBJjs45Ou5CpOdO3dSly5daNq0aUoN1ocOHaKAgAC6ffs2Va9eXeKYSCQiU1NTGjFiBE2ePJnq1q1LVlZW2ZkdxfxRFBsDxUjlwYMHtHHjRtq1axclJSWx3gJfX9//G2+BOgyCnJw9e5aaNm1K27dvJysrK9aDcO7cOVYXgSi7psGvSw3Ozs5KuXcVBQCVK1eOatSoQdu2bZM49uTJE6pQoQJt3ryZgoKCcl334sUL1jC4cuUKffz4kTgcDrm7u0tIKJcoUUKpPoWFhZGfnx8lJibStm3baP369XT8+HGaOHEiTZ8+XSLfn2EY+vLlC1V68YK+KNL4+fPZW5062Z6B27ezAwgHDyby95d5mYDDoQFWVrTMyUmpZylqzJkzhyZOnEhbtmyhHj16KHSNSCQiFxeX/7V373E5n/8fwF/3oXPKOhE5n1ZEjCmM0IoJOQ85zHEbfi2HTE772gyzkdkQk8aMmNMMX+eco1GKVEzMKYelo3S6X78/bn2+Wqe7uit0PR+P+0H34fO57jvu6/V5f67r+qB58+bYuXNnvsf79u2L1NRUHD16FBMnTsSFCxcQFham7aYL5UyEAaFIqampCAoKgr+/P0JDQ6VqwdixY1GvXr3Kbl65yw0EjRs3xqFDh8oUCEjCxcUF8fHxiIiIkDq1+Ph42NjYwMfHBy1btsxzqiF31L2uri7s7OzyhYSyLvATHh6O1q1b48CBA+jRo0eex3KrAjExMcUGEZKIi4vLEw7i4uIAALa2ttLFlzp37ozatWsXup3ff/8dw4cPR8OGDfH1119jypQpSExMxKZNm9CrV69CX1fv3Dn8/fLRfkGOHQO++UZdHXh5ZsCSJUBwMLB1a96xBC/RkckwqXZtLH/FrklQUiTx8ccfIyAgAPv27YOrq6tGr1u/fj3GjRuHqKgo2Nra5nls+fLl8PX1RWJiIlavXg1fX1+kpqZW+uqUQsmIMCBoLCwsDOvWrcMvv/yC1NRU9OjRAxMmTIC7u/sbXS0ICwtD9+7dtRIIQkND8e677+Y7Mhs0aBCioqJw5cqVPOdznz59mm/xpMjISDx79gyAeizCvwOCra0t9AuYM1+QWbNmYd26dXjw4EGeDr+oqoCm7ty5g5MnT0rhICYmBgDQqFGjPOGg/ovS+6JFizBnzhx4eHjAxcUFU6dORfPmzfHbb7+hwcuj/wvw7sWLCE1JKbpBXl5ATg7www957z91Cpg3D/j2W+Cddwp8qQLAfxo0wOw3IABnZ2ejb9++OHnyJE6dOgUHDWZJZGRkoGHDhnBzc0NAQECex8LCwtCmTRucOHFCGnMUFxcn/V6F14MIA0KJ5VYL1q5diwsXLsDa2lqqFrypXwBhYWFwcXFBo0aNyhwIhgwZgrNnzyI2NlYamX/kyBG8//770gIuRVGpVLh582a+AYt//fUXAEChUKBZs2b5QoKNjU2eoEESDRs2hKurK/z9/fPsY+DAgQgLC0N0dLTWTk88fPgwTziIjIwEoD4tolAocPv2bUycOBEZGRkIDAzEhAkTsGLFCo2CzaTYWKx78ABZRX1NjRwJGBsDq1blvf/4cWDBAnWF4N13C335fnt79DQ31+i9vupSU1Ph7OyM+/fvIyQkRKMxQd999x1mzZqFmzdv5ltAy8LCAt7e3hg5ciQaNGhQYKVJeLWJMCCUSXh4uFQtSElJgZubGyZOnIhevXqVyznuypQbCHJnAZQ2EORexOjrr7/GjBkzAKg7+KZNm8LJyQmbNm0q1XZTUlIKnPaYlJQEQD0t7+VwIJfLMW7cOBw7dizPkrW5VYGSnFcujYSEBOzatQu+vr548uQJSEqzA9q1a4dRo0ahc+fOaN68ebEl543x8RgVHV30Dn19gT//VK818PJiW3PnAmfPqqcXFjZbgMQvaWkY5OpaKZdtLg/x8fFwcnKCkZERTp8+Xey/55SUFNStWxdjxozBd999l+cxDw8PJCcn48iRIzAyMsKiRYvwmbaWhRYqhAgDglakpaVJ1YLz58/D2toaY8aMwbhx496oakF4eDi6d++Ohg0b4tChQ6UeOT9p0iT8+uuvuHnzprSNb775BvPmzcO9e/dgrqUjUJK4c+eOFAwuX76MiIgIxMbGSssEN27cOE9IWLNmDa5fv67RWIGyOHfuHPr16wc9PT14e3tj/vz5MDIyQs+ePREdHY3Q0FBkZWXBzMwM7733nnRawcHBId9Fg5Kzs1Hz7Fmkv3SRpnwuXwamTlWPC/Dw+N8AwvPngV69gH9dXTKXjIRhVBTSJk+Gubk5Bg0ahGHDhqFjx46v/Xnx6OhodOjQAQ4ODjhw4EC+2ST/NmfOHPj5+eHvv//OM+vFz88Ps2bNwtOnT+Ho6AhHR0esWbOmvJsvaJEIA4LWXb58GWvXrpWqBa6urpg4cSLc3d3fiGqBNgJBfHw8GjdujEmTJmHJkiUA1BcbsrGxwZIlS+Dt7a3tZueRlpaG+vXro1WrVrC3t5eCQu68fj09vXzXaLC3ty/zjIpcgYGBmDhxItq2bYt33nkHK1euhIeHBwIDA6WFnp49e4aQkBBpUGJISAieP38OExMTdOzYUQoHbdu2xfPnz+G8ezcuWVsDRY1fuXYN+Pln4Pp1IDkZsLYGXF2BoUOBItYo2NuiBerev4/Nmzdjy5Yt0hUehw0bhmHDhsHe3l4rn0tlOHXqFFxcXDBo0CBs2rSpyDUIHj16hHr16sHX1xdz586V7s8diBocHIw1a9bgwYMHCA4OroDWC9oiwoBQbtLS0rBt2zb4+/vj/PnzqFmzplQtKG5A2KsuNxA0aNAAhw8fLlUgKOgiRh9++CHCw8Nx7dq1cl2R8OTJk+jSpQvOnDmDDh06AFBXEXr16oWwsDB4eXlJpxyuXbsmrY1Qt27dAldY1HQAaXZ2Nnx8fLB8+XIMGzYM9+/fx6lTp7B48WJMmzatyPeckZGB0NBQKRycOXMGaWlpUsBUmZlBtmkTcnR0ynb54pcoAXQ0NcUxBwfIX7RNpVLh9OnT2Lx5M7Zv346nT5/C3t4ew4YNw9ChQ1/LWTZBQUH48MMPMWvWLHz99ddFPnfy5MkICgrC7du3Yfjiao4qlQoWFhbw8vICAKxatQoPH2o02VN4RWjcf1MDSUlJBMCkpCRNni5UIeHh4Zw0aRJNTEwok8no5ubGHTt2MDMzs7KbVmrh4eE0MzPjO++8w4SEhBK/PikpiRYWFhw7dqx037FjxwiAwcHB2mxqPp9++inr1q3LnJwc6b7w8HACYEBAQJ7nZmRkMCIigr/88gt9fHzYo0cP1qpViwAIgHp6emzTpg1Hjx7NZcuW8ejRo3z06FG+fSYkJNDV1ZUKhYJeXl60trZmzZo1eeLEiRK3X6VScffu3axfvz5lMhltbGxYrVo1ws2NOH5cKzfZ8eM0OHGCcc+eFdqOjIwM7tmzh0OGDKG+vj4BsFOnTly9ejWfPHlS4vdVmZYuXUoAXLNmTZHPu3nzJhUKBVeuXJnnfg8PDzo7O3Pr1q0EwH/++ac8mytomab9twgDglakpqYyICCAjo6OBMCaNWvS19eXN2/erOymlUpZA8GKFSsol8t59epVkupOrmnTpvzwww+13VRJVlYWLS0tOX369Dz39+/fn40aNWJWVpZG23n8+DGPHTtGPz8/jhkzhm3btpU6RAC0tramm5sbZ8yYwW+++Yb16tWjqakpP/74YyoUCnbu3Jn3798vcfsvXbrEbt26EQC7devGS5cukSSzs7N56dIldtq+nTh2rMxBQH78OPc8fqxxu5KTk7lx40a6ublRLpdTqVTS3d2dW7ZsYVpaWonfZ0VTqVScPHky5XI5//jjjyKfO2zYMNarVy9PmPfz86Oenh7Pnz9PADx79mx5N1nQIhEGhEpz+fJlTp48maamppTJZHR1dX0tqwXh4eE0NzcvVSB4/vw5GzRowL59+0r3ffvtt9TR0Snw6FobDh06RAD8888/pfvCwsIIgBs2bCjTtrOzsxkdHc1t27Zxzpw57NOnD2vUqCEFBJlMRgC0tbXlokWLeODAAd67d48qlarYbd+5c4cjR46kTCajra0t//jjjwJfl6NS0Ss2VurUSxoElMHB1A0O5u4SBIF/i4+P5/fff8/27dsTAI2MjOjp6cn9+/drHLYqQ3Z2Nj08PGhoaMjQ0NBCn3f58mUC4KZNm6T7citL//3vfymTyfJVmIRXmwgDQqVLS0vjhg0b6OTkRACsUaMGZ82axb/++quym6ax3EDQpk2bEgeCzZs3EwBPnz5NUn3Eraury2+++aY8msqxY8eycePGeTrSfv36lagqoAmVSsVvv/2WcrmcHTp0YO3atamvr083Nzd26NCBxsbGUkgwNzdn165d6eXlxfXr1zM0NFQ6mk5OTubs2bOpr69PS0tLrl69WqN27nr0iOanTlGuaTXg6FHi+HE6nDvHaC0eyd+4cYMLFixgs2bNCICWlpacPHkyz549q1EIqmhpaWls3749raysiqzYffDBB2zRooX0HnJycmhmZsb58+ezQYMG9PHxqagmC1ogwoDwSomIiJCqBQD4/vvv87fffnstqgUvB4KSnC/Nycmhg4MDO3bsKH2xDh8+nI0bN85zTl8bMjIyWL16dc6ePVu6T1tVgZelp6dz5MiRBEB3d3caGhqyZcuWjI2NlZ6Tk5PDmzdvcvfu3VywYAEHDhzIpk2bStUDuVzOGjVqUE9Pj0qlkoMGDWJERESJOtB/MjP51a1btD5zhnhR+lcGB1P2omqgPH5cOqWgFxBAuLgQcjmbNGnCsWPHcuPGjbx165ZWPhOVSsWLFy9y2rRp0piLBg0acPbs2YyKitLKPrTl0aNHbNSoEZs1a1bo2IcTJ04QQJ5TCv369WOXLl3Ys2dP9u7du6KaK2iBCAPCKyktLY2BgYHs0KGDVC34/PPPeePGjcpuWpEuX75cqkBw8OBBAuCePXtIkidPniQAHjlyRKvt27t3LwEwMjJSuk/bVYH79++zffv21NPTo4uLCwFw1KhRGp83T01N5bJly2htbS397nPDIQBWq1aNHTt25CeffMLVq1fzzJkzxX7nZOXk8HRiIv3u3OFH166xX2QkB165wsmxsdxw/z6vpaZKbQ8KCuKnn37KFi1aSPusW7cuR4wYwXXr1jE2NrbMR/TZ2dk8evQox44dK703BwcHLl26lHfv3i3TtrUlNjaWFhYW7NSpE9PT0/M9rlKp6OTkxE6dOkn3rVixgrq6upwyZQqbNGlSkc0VykiEAeGVFxERwSlTpuSpFmzfvp0ZGRmV3bQCXb58mRYWFmzdurXGgUClUrFbt260s7NjdnY2VSoVbW1tOWjQIK22zdPTk82bN5d+zq0KBAYGamX7Fy5cYK1atWhlZUU7Ozvq6elx7dq1GneeYWFh7N69OwGwa9euvHjxIkn153P37l3u37+fixcv5rBhw9iiRQsqlUqpw84dezF37lxu376dMTExzM7OLtP7efz4MXft2sXPPvuMbdq0oVwulwZHDhkyhD/++COvXLlSpnCQnp7OnTt3csCAAdTT06NMJqOzszPXrVtXqkGp2nTu3Dnq6+tz8ODBBVap9uzZQwA8deoUyf+NJZg6dSoVCgWfP39e0U0WSkmEAeG1kZaWxp9//lmqFlhZWXHmzJmvZLWgNIHgwoULeab2+fn5UalUMj4+XittevbsGY2NjblgwQLpPg8PD61VBTZv3kx9fX02a9aMb731FuvXr59nkGJR7ty5w1GjRlEmk/Htt9/m3r17Nepgnz9/zvDwcG7cuJHTp0+nq6sra9asKQUEAwMDtmvXjmPHjuWKFSt4/PjxMk35S0xM5L59++jj40NHR0cpjFhYWLBfv35cvnw5L126VOoQkpiYyICAAHbv3p0ymYy6urr08PDg9u3b+ayIKY7laefOnZTJZJw2bVq+x3JycmhnZ0d3d3fpZ3Nzc44aNYoApFkywqtPhAHhtRQZGcn/+7//Y/Xq1QmALi4u3LZt2ytVLYiIiChxIBg8eDBtbGz47NkzJiQkUF9fn4sWLdJKe3777TcCYExMDEn1FD1tVAWys7P5+eefEwBbtmxJmUzGXr16afSecwcHGhgYlGhwYHEePnzII0eOcNmyZRw9ejTbtGlDPT09KSTUrl2bPXv25MyZM7l582ZGRkaWalxKamoqDx8+zDlz5rBz587SPkxNTdmrVy8uWbKEISEhpdr2/fv3uWzZMrZt25YAaGJiwtGjR/PQoUNlrniU1Pfff08A/P777/M9FhgYmOfUU//+/aWpwzt27KjQdgqlJ8KA8Fp79uwZN27cyI4dO+apFly/fr2ym0ay5IEgNjaWSqVSmkkwcuRINmzYUCsDCQcNGsQ2bdpIP2ujKpCUlER3d3fKZDI2bdqUcrmcCxcuLLa9WVlZXLNmDa2srKivr09fX99y/97IyspiVFQUt27dSl9fX7q7u7Nu3bpSQNDR0WGrVq04YsQILl26lAcPHuSDBw9KdAogPT2dJ06c4IIFC+ji4kJDQ0NpauH777/PL7/8kidPnizwHHxRoqOjOX/+fDZu3Fhan8PLy4sXLlyosBkJU6dOpUwm486dO/Pcn5GRwTp16nDEiBEk1cFBR0eHZmZm/OqrryqkbULZiTAgvDGuXLlCLy8vqVrQvXt3BgUFVXq1oKSB4NNPP2X16tWZkJDAM2fOEAAPHjxYpjYkJyfTwMCAS5YsIamdqsD169dpa2tLQ0NDWlpa0tLSstgBjyqVivv27aOdnR0BcMSIEfz7779L3QZtSEhI4MmTJ/nDDz9wwoQJdHR0pJGRkRQSLC0t2b17d3p7e3PDhg28ePGixp15RkYGz507x8WLF/ODDz6giYmJtGpjly5dOHfuXB45coSpLwYwFkelUvH8+fP08vKS1m9o0qQJ58+fn2emRnnIycnhoEGDqK+vz3PnzuV5zM/PjwqFgrdu3WJERAQBsHnz5vT09CzXNgnaI8KA8MbJrRZ06tRJ+jL38fGp1GpBZGQkLSws6ODgUOw56wcPHtDIyIg+Pj5UqVRs0aIF+/fvX6b9565lEBcXR1JdFWjcuHGpqwJHjhxh9erVaWlpSR0dHTo5OfHOnTtFvublwYHOzs7S4MBXUU5ODm/cuMGdO3fyiy++YP/+/aWjcgBUKBS0tbXlkCFDuHDhQu7du5e3b98u9ig9OzubFy9e5PLly+nh4UEzMzMCoFKppJOTE2fOnMn9+/dr9B2alZXFQ4cOcdSoUeqlmAG2bduWy5cvL9XKjppIT09np06daGFhkef/U2pqKs3MzDhlyhRp3ICDgwPbtm1bLu0QtE+EAeGNdvXqVX722Wd86623pOVrK6taUJJAMG/ePOrp6fHvv//mypUrqVAoeO/evVLvu0+fPnRyciL5v6rAzz//XOLtqFQqfv/995TL5dJAPS8vryI/zzt37nD06NGUyWRs1qwZf//991dysR1NpKSkMCQkhGvXruXkyZPZuXPnPNMeTU1N+d5773HSpEn09/fnuXPnmJKSUuj2cnJyGBkZyR9//JGDBw+WjvblcjnbtGlDb29v7tq1q9h/L8+ePeO2bdvo4eFBHR0dyuVyuri4cMOGDUxMTNTqZ/DPP/+wWbNmbNSoUZ5VMufPn08DAwM+fvyYAwYMYJu6ddlXX5+qtWvJ1avJTZvI8HDyNVgzpCoSYUCoEp49e8ZNmzblqRbMmDGj3Eur/xYZGUlLS8tiA0FSUhItLS05ZswYPn36lAYGBvzyyy9Ltc+EhATq6OjQz8+PJNm3b99SVQUyMjI4btw4AqCZmRmNjY0ZFBRU6POTk5M5Z84caXDgqlWrXovFo0pKpVLx9u3b3Lt3LxcuXMghQ4bQ1tZWmoYIgI0aNWK/fv04f/587tixg9evXy9wXIVKpWJMTAzXrVtHT09P1qlTR9pGixYtOGnSJAYFBfHBgweFtichIYFr166ls7MzZTIZ9fT0OHDgQO7cuVNrU/1u3rzJGjVqsH379tL6EY8fP6aNgQH/6+LCRAsLEvjfTSb73991dckBA8hjx8jXNBS+iUQYEKqcf1cLunbtyq1bt1bYnOjcQNCqVasiA8HLFzH66KOPWLdu3VKNIg8ICKBMJuO9e/dKXRV4+PAhO3XqRIVCQT09PdrZ2fHatWsFPjcrK4v+/v6sUaNGhQ0OfBWlp6fz4sWL3LBhA729vdm9e3daWFhInbuRkRHbt2/P8ePHc+XKlTxx4kSB6wrExcXx559/5pgxY/KcqmjatCnHjx/PTZs2FTru4s6dO1y6dCkdHBykysXYsWN57NixMg9KDQ0NpaGhIfv27cvszEzSz4+ZCgVzAKpeDgIF3ZRK9Z+OjuSL2S1C5RJhQKiy0tPT+csvv/C9996T5opPnz69QqoFmgSCly9iFBISQgDct29fiffl5uZGZ2dnkqWrCoSFhbFOnTrSyPihQ4cWWPouaHDg7du3S9zeN5lKpeKDBw948OBBLl26lCNGjGCrVq2oo6MjdfJ16tRhr169OGvWLG7ZsoVXr17N8/u6e/cut2zZwo8//lj6rAGwfv36HDVqFNevX88bN27kOxVz9epVzp49mw0aNJCmV06bNo2XLl0q9WmbvXv30lIm4w1r66I7/6JCga4u+dNPZfpchbITYUAQSEZFRdHb21sa0NW1a1du2bKlXKsFV65ckQLB40KukJc78O/UqVN0cHBgnz59SrSPR48eUaFQcPXq1aWqCvz222/U19enkZERdXR0+MMPPxTYcYSFhUlLDzs7O2u82JCglpmZycjISG7evJkzZ85kz549Wbt2bamj19PTY+vWrTlq1Ch+9913PHz4MB8+fEhS/TvesWMHvby86ODgIF3boVatWhw6dChXr17NqKgo6femUql49uxZTpo0SapUvP322/zyyy9LvoDXo0d8amXFzNIEgX/fVqzQ9scqlIAIA4LwktxqQefOnfNUC2LKqZR55coVWllZFRoIXr6I0apVqyiXy4sdtf+y1atXU6FQ8NGjR+zbty+bNGmiUVUgJyeH8+fPlzoiGxsbhoSE5Hve3bt335jBga+iJ0+e8Pjx41yxYgXHjh3Ldu3a0cDAQAoJNWrUoKurK6dPn86NGzcyPDyc8fHx3Lt3L2fMmMF3332XCoVCGiczYMAArlixguHh4czJyWFmZib3799PT09PaTqlo6MjV65cKYWNQmVnk05OpEJR9iCQe9u7t2I+WCEfEQYEoRDXrl3j1KlTpWqBs7NzuVQLcgNBy5YtCwwEuRcx2rJlC42MjPjFF19ovG1nZ2e6ubnx4sWLBMCNGzcW+5qUlBT269ePACiTyejq6pqvXcnJyZw7dy4NDAxoYWHBH3/88Y0cHPgqys7OZkxMDLdv3865c+eyb9++Uuk/d5piixYtOGzYMC5evJg7duzg5s2b6evry06dOlFXV5cAWL16dfbu3ZtLly7lhQsXmJiYyC1bttDd3Z1KpZIKhYI9evTgxo0bmZycnL8h335baKd+AeAkgHYADQHWATgIYExRQUAuJy0tyUq+HkNVpWn/LSNJFCM5ORmmpqZISkqCiYlJcU8XhNfC8+fPsXPnTqxduxYnTpyAubk5Ro8ejfHjx6NZs2Za2UdUVBS6du2KmjVr4ujRo7CwsJAeI4n3338fDx48gJOTEw4ePIi4uDgolcoit3n//n3Y2Nhg/fr12L17N65du4aoqKgiX3fr1i306tULMTExUKlUmDt3LubNmweFQgEAyM7ORkBAAObNm4fExERMnToVM2fOhKmpqVY+B6H0kpOTceXKFUREROS5paSkAADMzMzQsmVL2NnZwdDQEMnJyYiJicGFCxeQnp4OY2NjdOjQAV26dEHLli1x69YtBAUF4fTp0zAwMECfPn0wfPhwuLm5QffpU6BuXSAzs8C2DARwBsAgAC0BxAP4AUAqgBAALQp7EwoF8MknwMqV2v1whGJp3H9rM1kIwusqt1pgbm5OAOzSpQt//fVXrVQLrl69WmiFIDQ0lAA4d+5cAuDvv/9e7Pb8/Pyoo6PD4OBgjaoCJ0+eZPXq1alUKmlqasoDBw5Ij6lUKu7fv5/NmzcnAHp6eorBga8BlUrFuLg47tmzh19++SUHDRrEZs2aSdMeZTIZmzRpwq5du9LFxYWtW7eWThfo6+vT2dmZXl5eHDdunPS7NzMz46527aiSyws9yj8DMONf98UC1AM4vLhTBQYGZEGVCKFcidMEglAK6enp/PXXX+ns7EwANDc359SpUwudbqep3EBgb2+fLxAMGTKEtWvXZuvWrdmrV69it+Xk5MQ+ffqwT58+xY4V8Pf3p1wup0wmo4ODA2/duiU9Fh4eLg0O7NKlixgc+AZIS0tjaGgo169fTy8vL3bt2lU6HQaopz3Wr1+f9erVk2aRKJVKtmrVik6Ojrwnlxc/fbCAW5sXtyKfJ5ORa9dW9kdU5YgwIAhlFB0dzWnTpuWpFmzevLnEF6PJdfXqVdaoUYP29vZ5Vni7fv06lUol+/fvT5lMxj9iYrjs7785/OpVvvvnn3QIDWWnixf5SUwMF0dEEBYW/OqrrwiAmzZtKnBfmZmZnDhxotQJTJw4Uapy3L17lx999JE0OHDPnj1icOAbTKVS8d69ezxw4ACXLFnC4cOH097eXrpMMwAaGhqykY5OqQYHqgDWBuha3HMVCvLFRY+EiiPGDAiClmRkZGDXrl3w9/dHcHAwzMzMMGrUKEyYMAFvv/12ibYVFRWFbt26wcrKCkePHoWlpSUA4NNJkxB49y4y+vSBqlEjyAHIAOS89FodmQxZKvVxm9WNG9DbuRM3//gj31iBf/75B+7u7ggJCYGOjg4CAgLg6emJ1NRULF26FN9++y0MDQ3xn//8B+PHj4eOjk7ZPiDhtZSZmYno6GhpDILx4cOYFx5e4u38AmAEgPUAxhT35CZNgNjYEu9DKD1N+28RBgShBGJjY7Fu3ToEBgbiyZMn6Ny5MyZMmIABAwZAX19fo21cu3YNXbt2lQJBqrExhkVEICQ9HVCpALm8+I1kZwMKBT6rUwcLGzSA4YuBgFevXkX37t3x6NEj1K5dG/v374etrS02bNiAuXPnIjExEd7e3vj888/F4EAhLz8/YNo09b9BDUUDaA+gOYBTABTFvUBfH0hPL20LhVIQYUAQylFGRgZ2794Nf39/HD9+XKoWjB8/Hra2tsW+PjcQGDk6It7bG5kkskvRDjkAW0NDHHVwwLn9+zF48GBkZWXBzc0NQUFBOHv2LGbMmIGrV6/C09MTX331FerVq1eKPQmvo8zMTCQlJSE5ORlJSUnSraCf3zt/HkMjIqAovksAoJ5J0BFAFtQzCWpp8iKlEsjKKvX7EUpOhAFBqCCxsbH46aefsGHDBjx58gTvvfceJkyYgIEDBxZZLdgaEYGh8fHqL0hNqgGFUMpkME1JwT/DhkGWmoqFCxeiZ8+e8PHxweHDh9G5c2d89913aNu2ban3IVQsknj27FmBHbemnXtSUhKeP39e6D709PRgamoKU1NTmJiYwDMlBV6xsZBp0L4kAM4A/oa6ImCn6RurVg1ITtb02YIWiDAgCBUst1qwdu1aHDt2DG+99ZZULbCzy/t1mZydjbcvXMDDzExoXpQtQk4OFGfPIsjODvv27UNgYCCaNGmCpUuXonfv3pDJNPmKF7QhJycHKSkpJe64//1zTk5OofswNjaWOvLczrykP+vp6eXd6MmTQJcuxb6/5wBcAVwEcASAU0k+nA4dgDNnSvIKoYxEGBCESvTvakGnTp0wceJEDBgwAAYGBpgQE4OABw/UAwTT04GtW4Fr14DoaCAlBZg5E+jRI/+Gb98GfvwRiIwEdHQAR0fg00+B6tUBALoLF8IkPBxffPEFJkyYIAYHllBuWb2wjlqTzjw1NbXQ7SsUimI76uI682rVqkmLRWlVSgpgaqoe+1+IHAD9AewHsAfAByXZvlIJTJ4MLF9epmYKJSPCgCC8AjIyMrBnzx74+/tL1YK+H3+Mn11dIf3Hi48Hhg4FatQArK2B8PCCw8Djx8D48YCREdC/vzpEbNsGWFkBq1cDCgWqp6cjrmNHVH8RDqoKkkhLSyv1UXjuLSMjo9B96Ovrl/ooPPfvhoaGr3aVpmtX4NQpoJCqxGcAVgDoDWBwAY97Frf9o0eBbt3K0kKhhDTtv4te91QQhDLR09PD4MGDMXjwYFy/fh0//fQTVqangzk56iVaAcDMDNixQ/1nTAzw8ccFb+yXX4DnzwF/f3VwAABbW2D6dOC//wV690aikREukXidvm5zcnKQnJxcbEddVGeenJxcZFm9WrVq+TpmS0tLNGrUSOOjcl1d3Qr8VCrJlClAcHChD4e/+HPvi9u/FRoGZDKgUSN12BBeSSIMCEIFadKkCZYsWYKNZ84g/eUR1bq66iBQnFOn1KcFcoMAALzzDlCnjvoLvHdvKGUy/PrwIbq99ZbW21+QjIyMMp8bL66sXlDHXK9ePY2PysutrP4m6tMHaNoU+OuvAqsDwaXdLgnMm6cOBcIrSYQBQahADzMzEV+aqVWPHwNPnwIFXUDp7beB8+cBANkkzmkwWju3rK5px13YczQpq/+7o65Vq5bGJXYDA4NXu6z+plEq1RWo9u21u00XF8Cz2JMIQiUSYUAQKlB4EUfBRUpIUP9pbp7/MTMz9XStzExAVxfX0tLg4+uL1MTEIjtyVRGLy5iYmOTrmC0tLdG4cWONOnITE5OqUVZ/E7VrByxcCPj6ln1bCgVgYQH89JOoCrziRBgQhAqUUNoFV3KPwAuaHZDb6b4IA5TJELR3L8yUSqlzzi2razKCvVq1apCXYd0D4Q3w+efq2QWLFpV+G0qlOrwGBwO1a2utaUL5EGFAECpQqY+NcueEFxQmcq89/9KRePilS3hLTCsUSksmA77+Wj1+YPJk9cDVIgZoFqhLFyAwELCxKZcmCtol4r8gVKAapS2d5w4w/Oef/I8lJAAmJlIY0JHJUE0MmBO0YfRo9doXgwf/b6XMwqpGuRfMqltXfVrg8GERBF4jojIgCBWotbFx6V5oaaleWCgmJv9j0dHqaVsv2BsZQSnK/IK22NgAv/4KLFsGbNwInD6tHrD66JH6cR0doHlz9aDDvn0BN7cyLa8tVA4RBgShAlXX0UFDfX3cLGLN+EJ17gwcPKj+ErayUt938SJw5w4wcCAA9XUKOoqrEQrloWZNwMdHfQPUVzfMzlaHATE48LUnwoAgVLBx1taYExeX95oEu3YBqanAkyfqn8+eVU8nBIB+/QBjY2D4cPVgLG9vYMAA9QqEQUFAw4bSaoXZJEbXrFmRb0eoquTyPONUhNebWI5YECrYo8xM1D53Dtkv/9f78EPg4cOCX7Bli/qoDADi4oBVq4ArV9TnaB0dgU8+AczMoADQytgYF8XVCQVBeEFcm0AQXmHz4+Lw5e3b0OzK8ZqRATjp4IBOVey6BIIgFE7T/luM8hCESjC7Xj3YGRpCW2P+5QC8bGxEEBAEoVREGBCESqArl+N3e3uY6eiUeeCOHECX6tWxuGFDbTRNEIQqSIQBQagkDQ0McKZ1a1jr6ZWpQtDDzAz77O2hJ6ZzCYJQSuLbQxAqURNDQ1xp1w5jrK0BaD69RwFAXy7HqiZNsNfeHgZikSFBEMpAhAFBqGQmSiXWNmuGkDZtMNjKCsoXc7YVUIcDBdTrB+T+Z31LqYRP3bqIffddfFK7NuRijrcgCGUk1hkQhFdEexMTbLazw8qsLIQkJ+NiSgpuPn+OLJUKhgoFmhsZ4R1jY7QzMRGnBARB0CoRBgThFWOmo4MPzM3xQUGXKxYEQSgH4vBCEARBEKo4EQYEQRAEoYoTYUAQBEEQqjgRBgRBEAShihNhQBAEQRCqOBEGBEEQBKGKE2FAEARBEKo4EQYEQRAEoYoTYUAQBEEQqjgRBgRBEAShihNhQBAEQRCqOBEGBEEQBKGKE2FAEARBEKo4EQYEQRAEoYoTYUAQBEEQqjgRBgRBEAShihNhQBAEQRCqOKUmTyIJAEhOTi7XxgiCIAiCoD25/XZuP14YjcJASkoKAKBOnTplbJYgCIIgCBUtJSUFpqamhT4uY3FxAYBKpcL9+/dRrVo1yGQyrTZQEARBEITyQRIpKSmoVasW5PLCRwZoFAYEQRAEQXhziQGEgiAIglDFiTAgCIIgCFWcCAOCIAiCUMWJMCAIgiAIVZwIA4IgCIJQxYkwIAiCIAhVnAgDgiAIglDF/T8oSEx/WvxzewAAAABJRU5ErkJggg==" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# print BF results\n", + "bf_best_cases, bf_best = brutal_force(hard_graph)\n", + "print(f\"cost: {bf_best:.3f}\\nbit string: {bf_best_cases}\")\n", + "\n", + "# plot NetworkX graph\n", + "colors = [\"r\" if bf_best_cases[0][i] == \"0\" else \"c\" for i in hard_graph.nodes]\n", + "nx.draw_networkx(hard_graph, with_labels=True, node_color=colors, pos=pos_hard)\n", + "ax = plt.gca()\n", + "ax.set_facecolor(\"w\")" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "9df75fbc", + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + }, + "ExecuteTime": { + "end_time": "2023-07-03T11:48:35.050434800Z", + "start_time": "2023-07-03T11:48:31.518734800Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "cost: 0.000\n", + "prob: 0.070\n", + "bit string: ['000000111111', '111111000000']\n" + ] + } + ], + "source": [ + "# print SA results\n", + "sa_best_cases, sa_best, n_exp = [], float(\"inf\"), 100\n", + "for _ in range(n_exp):\n", + " sa_case, sa_cost = sim_annealing(hard_graph, 200, 1)\n", + " gap = sa_best - sa_cost\n", + " if gap > 1e-6:\n", + " sa_best = sa_cost\n", + " sa_best_cases = [sa_case]\n", + " elif abs(gap) < 1e-6:\n", + " sa_best_cases.append(sa_case)\n", + "sa_prob = len(sa_best_cases) / n_exp\n", + "sa_best_cases = list(set(sa_best_cases))\n", + "print(f\"cost: {sa_best:.3f}\\nprob: {sa_prob:.3f}\\nbit string: {sa_best_cases}\")" + ] + }, + { + "cell_type": "markdown", + "id": "c4f3a812", + "metadata": {}, + "source": [ + "We found that the probability of SA getting the correct solution on the hard problem is much lower than that on the easy problem. This is because the energy landscape is different for the easy and hard problem, as shown in the following figure.\n", + "\n", + "\n", + "\n", + "The global minimum is located in a large and smooth neighborhood for a simpler problem and a narrow region for a harder problem. It is worth noting that when the system size is relatively small, most of the randomly generated problems are easy, and hard problems need to be constructed with special methods, please refer to [Wang, Zheng, Wu, and Zhang (2023)](https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.5.023171)." + ] + }, + { + "cell_type": "markdown", + "id": "99ee9bf8", + "metadata": {}, + "source": [ + "Now we use QAOA to solve this hard problem." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "1f6ba479", + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + } + }, + "outputs": [ + { + "data": { + "text/plain": "
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" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# use vvag to get the losses and gradients with different random circuit instances\n", + "QAOA_vvag = K.jit(\n", + " K.vvag(QAOAansatz, argnums=0, vectorized_argnums=0), static_argnums=(1, 2, 3)\n", + ")\n", + "\n", + "params_hard = K.implicit_randn(\n", + " shape=[ncircuits, 2 * nlayers], stddev=0.1\n", + ") # initial parameters\n", + "if type(K).__name__ == \"JaxBackend\":\n", + " opt = K.optimizer(optax.adam(1e-2))\n", + "else:\n", + " opt = K.optimizer(tf.keras.optimizers.Adam(1e-2))\n", + "\n", + "list_of_loss = [[] for i in range(ncircuits)]\n", + "\n", + "for i in range(2000):\n", + " loss, grads = QAOA_vvag(params_hard, hard_graph)\n", + " params_hard = opt.update(grads, params_hard) # gradient descent\n", + "\n", + " # visualise the progress\n", + " clear_output(wait=True)\n", + " list_of_loss = np.hstack((list_of_loss, K.numpy(loss)[:, np.newaxis]))\n", + " plt.xlabel(\"Iteration\")\n", + " plt.ylabel(\"Cost\")\n", + " for index in range(ncircuits):\n", + " plt.plot(range(i + 1), list_of_loss[index])\n", + " legend = [f\"circuit {leg}\" for leg in range(ncircuits)]\n", + " plt.legend(legend)\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "a6b7606f", + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + }, + "ExecuteTime": { + "end_time": "2023-07-03T14:01:09.731783100Z", + "start_time": "2023-07-03T14:00:36.495805100Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Circuit #0\n", + "cost: 0.02998761646449566\n", + "max prob: 0.04241819679737091\n", + "bit strings: ['111111000000']\n", + "\n", + "Circuit #1\n", + "cost: 0.034460458904504776\n", + "max prob: 0.03702807426452637\n", + "bit strings: ['000000111111']\n", + "\n", + "Circuit #2\n", + "cost: 0.04517427086830139\n", + "max prob: 0.027316443622112274\n", + "bit strings: ['111111000000']\n", + "\n", + "Circuit #3\n", + "cost: 0.02961093559861183\n", + "max prob: 0.04281751438975334\n", + "bit strings: ['111111000000']\n", + "\n", + "Circuit #4\n", + "cost: 0.030255526304244995\n", + "max prob: 0.042135994881391525\n", + "bit strings: ['111111000000']\n", + "\n", + "Circuit #5\n", + "cost: 0.029639022424817085\n", + "max prob: 0.04278436675667763\n", + "bit strings: ['000000111111']\n", + "\n" + ] + } + ], + "source": [ + "# print QAOA results\n", + "for num_circuit in range(ncircuits):\n", + " print(f\"Circuit #{num_circuit}\")\n", + " c = QAOAansatz(params=params_hard[num_circuit], g=hard_graph, return_circuit=True)\n", + " loss = QAOAansatz(params=params_hard[num_circuit], g=hard_graph)\n", + "\n", + " # find the states with max probabilities\n", + " probs = K.numpy(c.probability())\n", + " max_prob = max(probs)\n", + " index = np.where(probs == max_prob)[0]\n", + " states = []\n", + " for i in index:\n", + " states.append(f\"{bin(i)[2:]:0>{c._nqubits}}\")\n", + " print(f\"cost: {K.numpy(loss)}\\nmax prob: {max_prob}\\nbit strings: {states}\\n\")" + ] + }, + { + "cell_type": "markdown", + "id": "565dd4a7", + "metadata": {}, + "source": [ + "The probability of QAOA getting the correct solution is also very low. A very simple trick can be adopted to improve the performance of QAOA, namely quantum dropout, please refer to [following tutorials](qaoa_quantum_dropout.ipynb) or [Wang, Zheng, Wu, and Zhang (2023)](https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.5.023171)." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "89ed16e3", + "metadata": { + "collapsed": false, + "jupyter": { + "outputs_hidden": false + }, + "ExecuteTime": { + "end_time": "2023-07-03T14:02:46.556219900Z", + "start_time": "2023-07-03T14:02:46.519177800Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "OS info: Linux-5.4.119-1-tlinux4-0010.2-x86_64-with-glibc2.28\n", + "Python version: 3.10.11\n", + "Numpy version: 1.23.5\n", + "Scipy version: 1.11.0\n", + "Pandas version: 2.0.2\n", + "TensorNetwork version: 0.4.6\n", + "Cotengra is not installed\n", + "TensorFlow version: 2.12.0\n", + "TensorFlow GPU: []\n", + "TensorFlow CUDA infos: {'cpu_compiler': '/dt9/usr/bin/gcc', 'cuda_compute_capabilities': ['sm_35', 'sm_50', 'sm_60', 'sm_70', 'sm_75', 'compute_80'], 'cuda_version': '11.8', 'cudnn_version': '8', 'is_cuda_build': True, 'is_rocm_build': False, 'is_tensorrt_build': True}\n", + "Jax version: 0.4.13\n", + "Jax installation doesn't support GPU\n", + "JaxLib version: 0.4.13\n", + "PyTorch version: 2.0.1\n", + "PyTorch GPU support: False\n", + "PyTorch GPUs: []\n", + "Cupy is not installed\n", + "Qiskit version: 0.24.1\n", + "Cirq version: 1.1.0\n", + "TensorCircuit version 0.10.0\n" + ] + } + ], + "source": [ + "tc.about()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.9" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/source/tutorials/qaoa_portfolio_optimization.ipynb b/docs/source/tutorials/qaoa_portfolio_optimization.ipynb deleted file mode 100644 index 7f390853..00000000 --- a/docs/source/tutorials/qaoa_portfolio_optimization.ipynb +++ /dev/null @@ -1,602 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "6ddb8a88-779a-43f7-ae14-115463bd87f5", - "metadata": {}, - "source": [ - "# Solving QUBO problems using QAOA\n", - "\n", - "## Overview\n", - "\n", - "Here we show how to solve a quadratic unconstrained binary optimization (QUBO) problem using QAOA. Later on below we will extend this to show how to solve binary Markowitz portfolio optimization problems.\n", - "\n", - "Consider minimizing the following 2x2 QUBO objective function:\n", - "\n", - "$\\begin{pmatrix}x_1 & x_2\\end{pmatrix}\\begin{pmatrix}-5& -2 \\\\-2 & 6\\end{pmatrix}\\begin{pmatrix}x_1\\\\x_2\\end{pmatrix} = -5x_1^2 -4x_1x_2 +6x_2^2$\n", - "\n", - "Clearly this is minimized at $(x_1,x_2) = (1,0)$, with corresponding objective function value of $-5$\n", - "\n", - "We first convert this to an Ising Hamiltonian by mapping $x_i\\rightarrow \\frac{I-Z_i}{2}$\n", - "\n", - "This gives\n", - "\n", - "$$-\\frac{5}{4}(I-Z_1)^2 -\\frac{4}{4}(I-Z_1)(I-Z_2) + \\frac{6}{4}(I-Z_2)^2 $$\n", - "\n", - "which simplifies to\n", - "\n", - "$$-\\frac{1}{2}I +\\frac{7}{2}Z_1 -2Z_2 -Z_1Z_2$$ \n", - "\n", - "The $-I/2$ term is simply a constant offset, so we can solve the problem by finding the minimum of \n", - "\n", - "$$\\langle \\psi | \\frac{7}{2}Z_1 -2Z_2 -Z_1Z_2 |\\psi\\rangle$$ \n", - "\n", - "Note that the minimum should correspond to the computational basis state $|10\\rangle$, and the corresponding true objective function value should be $-4.5$ (ignoring the offset value of $-1/2$)" - ] - }, - { - "cell_type": "markdown", - "id": "8176aa81", - "metadata": {}, - "source": [ - "## Setup" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "45964c1f", - "metadata": {}, - "outputs": [], - "source": [ - "import tensorcircuit as tc\n", - "import numpy as np\n", - "import tensorflow as tf\n", - "import matplotlib.pyplot as plt\n", - "from functools import partial" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "4006848a-1a2f-407a-9f80-63e75ea0d3a4", - "metadata": {}, - "outputs": [], - "source": [ - "# we first manually encode the terms (-7/2) Z_1 - 2 Z_2 - Z_1Z_2 as:\n", - "pauli_terms = [\n", - " [1, 0],\n", - " [0, 1],\n", - " [1, 1],\n", - "] # see the TensorCircuit whitepaper for 'pauli structures'\n", - "weights = [7 / 2, -2, -1]\n", - "\n", - "# see below for a function to generate the pauli terms and weights from the QUBO matrix" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "d197cf4a-1bad-4470-a846-998bfe68ba3c", - "metadata": {}, - "outputs": [], - "source": [ - "# Now we define the QAOA ansatz of depth nlayers\n", - "def QAOA_from_Ising(params, nlayers, pauli_terms, weights):\n", - " nqubits = len(pauli_terms[0])\n", - " c = tc.Circuit(nqubits)\n", - " for i in range(nqubits):\n", - " c.h(i)\n", - " for j in range(nlayers):\n", - " for k in range(len(pauli_terms)):\n", - " term = pauli_terms[k]\n", - " index_of_ones = []\n", - " for l in range(len(term)):\n", - " if term[l] == 1:\n", - " index_of_ones.append(l)\n", - " if len(index_of_ones) == 1:\n", - " c.rz(index_of_ones[0], theta=2 * weights[k] * params[2 * j])\n", - " elif len(index_of_ones) == 2:\n", - " c.exp1(\n", - " index_of_ones[0],\n", - " index_of_ones[1],\n", - " unitary=tc.gates._zz_matrix,\n", - " theta=weights[k] * params[2 * j],\n", - " )\n", - " else:\n", - " raise ValueError(\"Invalid number of Z terms\")\n", - "\n", - " for i in range(nqubits):\n", - " c.rx(i, theta=params[2 * j + 1]) # mixing terms\n", - " return c" - ] - }, - { - "cell_type": "markdown", - "id": "cb38c120-500a-44cc-96ec-fb5ceb11032d", - "metadata": {}, - "source": [ - "For a general state that is the output of a quantum circuit c, we first define the corresponding loss with respect to the Ising Hamiltonian." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "88cec9cf-3ab6-4a4c-b743-ed95ee8c3817", - "metadata": {}, - "outputs": [], - "source": [ - "def Ising_loss(c, pauli_terms, weights):\n", - " loss = 0.0\n", - " for k in range(len(pauli_terms)):\n", - " term = pauli_terms[k]\n", - " index_of_ones = []\n", - "\n", - " for l in range(len(term)):\n", - " if term[l] == 1:\n", - " index_of_ones.append(l)\n", - "\n", - " if len(index_of_ones) == 1:\n", - " delta_loss = weights[k] * c.expectation_ps(z=[index_of_ones[0]])\n", - "\n", - " else:\n", - " delta_loss = weights[k] * c.expectation_ps(\n", - " z=[index_of_ones[0], index_of_ones[1]]\n", - " )\n", - "\n", - " loss += delta_loss\n", - "\n", - " return K.real(loss)" - ] - }, - { - "cell_type": "markdown", - "id": "30a3aa96-7823-4337-9b2f-5170502bb893", - "metadata": {}, - "source": [ - "For the particular case of a circuit corresponding to a QAOA ansatz this is:" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "26e4bec2-ce5b-4d0d-9e06-c80fda20619f", - "metadata": {}, - "outputs": [], - "source": [ - "def QAOA_loss(nlayers, pauli_terms, weights, params):\n", - " c = QAOA_from_Ising(params, nlayers, pauli_terms, weights)\n", - " return Ising_loss(c, pauli_terms, weights)" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "ca8b7a76-5c4f-4ad8-9173-90126b8bb93b", - "metadata": {}, - "outputs": [], - "source": [ - "K = tc.set_backend(\"tensorflow\")" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "d5b1897f-cd77-4cd3-bd3b-ece64e6004fc", - "metadata": {}, - "outputs": [], - "source": [ - "def QAOA_solve(pauli_terms, weights, nlayers, iterations):\n", - " print_every = 100\n", - " learning_rate = 1e-2\n", - "\n", - " loss_val_grad = K.value_and_grad(partial(QAOA_loss, nlayers, pauli_terms, weights))\n", - " loss_val_grad_jit = K.jit(loss_val_grad)\n", - "\n", - " opt = K.optimizer(tf.keras.optimizers.Adam(learning_rate))\n", - "\n", - " params = K.implicit_randn(shape=[2 * nlayers], stddev=0.5)\n", - " print(f\"initial params: {params}\")\n", - " for i in range(iterations):\n", - " loss, grads = loss_val_grad_jit(params)\n", - " if i % print_every == 0:\n", - " print(K.numpy(loss))\n", - " params = opt.update(grads, params)\n", - "\n", - " return params" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "id": "2bc533da-b4f2-4ffb-b486-c65880a30a6d", - "metadata": { - "tags": [] - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "initial params: [ 0.39931756 -0.49578992 -0.22545011 -0.40585193]\n", - "-2.1728685\n", - "-4.177884\n", - "-4.2291102\n", - "-4.2291365\n", - "-4.229136\n" - ] - } - ], - "source": [ - "iterations = 500\n", - "nlayers = 2\n", - "final_params = QAOA_solve(pauli_terms, weights, nlayers, iterations)" - ] - }, - { - "cell_type": "markdown", - "id": "e93d8cbe-2884-4f0a-80f8-3b600194927b", - "metadata": {}, - "source": [ - "We note that for nlayers=2 and 500 iterations, the objective function does not in this case (although it depends on the initial parameters)converge to the true value of $-4.5$. However, the we see below that the final wavefunction does have large overlap with the desired state $|10\\rangle$, so measuring the output of the QAOA algorithm will, with high probability, output the correct answer." - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "id": "294ea9ce-5064-4176-94d0-8dbb7d1707f8", - "metadata": {}, - "outputs": [], - "source": [ - "def print_output(c):\n", - " n = c._nqubits\n", - " N = 2**n\n", - " x_label = r\"$\\left|{0:0\" + str(n) + r\"b}\\right>$\"\n", - " labels = [x_label.format(i) for i in range(N)]\n", - " plt.bar(range(N), c.probability())\n", - " plt.xticks(range(N), labels, rotation=70);" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "id": "fc1353ab-7a7a-4cdc-931c-3b90417c4961", - "metadata": { - "tags": [] - }, - "outputs": [ - { - "data": { - "image/png": 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qWbYp9RJOWXvunpt6CeSRo/35ndOVkf7+/mhtbY36+vo3P0BxcdTX18f27duP6mO88cYb8d///d/xnve854j79PX1RXd397A3AKAw5RQj+/fvj8HBwaisrBy2vbKyMtrb24/qY3zta1+LSZMmDQua/6+5uTkqKiqG3qqrq3NZJgCQR97VZ9PcfffdsWHDhnjooYeirKzsiPs1NjZGV1fX0FtbW9u7uEoA4N00KpedJ0yYECUlJdHR0TFse0dHR1RVVb3lsX/5l38Zd999dzz66KMxbdq0t9y3tLQ0SktLc1kaAJCncroyMmbMmJgxY0a0tLQMbctkMtHS0hKzZs064nHf/OY346677ootW7bEzJkzj321AEDByenKSEREQ0NDLFmyJGbOnBmXXHJJrFmzJnp7e2Pp0qUREbF48eKYPHlyNDc3R0TEPffcEytWrIgHH3wwampqhu4tGT9+fIwfP/44fikAQD7KOUYWLlwYnZ2dsWLFimhvb4/p06fHli1bhm5q3bt3bxQXv3nB5bvf/W709/fHZz/72WEfp6mpKVauXPnOVg8A5L2cX2ckBa8zAvxfXmckHa8zQi5OyOuMAAAcb2IEAEhKjAAASYkRACApMQIAJCVGAICkxAgAkJQYAQCSEiMAQFJiBABISowAAEmJEQAgKTECACQlRgCApMQIAJCUGAEAkhIjAEBSYgQASEqMAABJiREAICkxAgAkJUYAgKTECACQlBgBAJIalXoBABARUbNsU+olnLL23D036ed3ZQQASEqMAABJiREAICkxAgAkJUYAgKTECACQlBgBAJISIwBAUmIEAEhKjAAASYkRACApMQIAJCVGAICkxAgAkJQYAQCSEiMAQFJiBABISowAAEmJEQAgKTECACQlRgCApMQIAJCUGAEAkhIjAEBSYgQASEqMAABJiREAICkxAgAkJUYAgKTECACQlBgBAJISIwBAUmIEAEhKjAAASYkRACApMQIAJCVGAICkxAgAkJQYAQCSEiMAQFJiBABISowAAEmJEQAgKTECACQlRgCApI4pRtauXRs1NTVRVlYWdXV1sWPHjrfc/4c//GGcf/75UVZWFhdddFFs3rz5mBYLABSenGNk48aN0dDQEE1NTbFz586ora2NOXPmxL59+0bcf9u2bXH11VfHF7/4xXjiiSdi/vz5MX/+/Hjqqafe8eIBgPyXc4ysXr06rr322li6dGlceOGFsW7duhg3blysX79+xP2//e1vx5VXXhl/9md/FhdccEHcdddd8ZGPfCTuvffed7x4ACD/jcpl5/7+/mhtbY3GxsahbcXFxVFfXx/bt28f8Zjt27dHQ0PDsG1z5syJhx9++Iifp6+vL/r6+ob+3dXVFRER3d3duSz3qExt+slx/5gcnafumJN6CeSpTN8bqZdwyjoR/w8fYq7pnKi5Hvq42Wz2LffLKUb2798fg4ODUVlZOWx7ZWVlPPvssyMe097ePuL+7e3tR/w8zc3Ncccddxy2vbq6OpflcpKrWJN6BUCunLeF6UTPtaenJyoqKo74/pxi5N3S2Ng47GpKJpOJ1157Lc4666woKipKuLKTS3d3d1RXV0dbW1uUl5enXg7HibkWLrMtXGY7smw2Gz09PTFp0qS33C+nGJkwYUKUlJRER0fHsO0dHR1RVVU14jFVVVU57R8RUVpaGqWlpcO2nXHGGbks9ZRSXl7um78AmWvhMtvCZbaHe6srIofkdAPrmDFjYsaMGdHS0jK0LZPJREtLS8yaNWvEY2bNmjVs/4iIn/70p0fcHwA4teT8ME1DQ0MsWbIkZs6cGZdcckmsWbMment7Y+nSpRERsXjx4pg8eXI0NzdHRMRNN90Ul19+eXzrW9+KuXPnxoYNG+Lxxx+P733ve8f3KwEA8lLOMbJw4cLo7OyMFStWRHt7e0yfPj22bNkydJPq3r17o7j4zQsus2fPjgcffDCWL18et912W5x33nnx8MMPx9SpU4/fV3GKKi0tjaampsMe0iK/mWvhMtvCZbbvTFH27Z5vAwBwAvnbNABAUmIEAEhKjAAASYkRACApMQIAJCVG8lQmk0m9BE4Qsy1cZluYzPWd89TeApLNZv3tngJltoXLbAuTuebmpPxDeYysq6srWltb48knn4yampr4wAc+EC+99FKcddZZMW3atBg7dmzqJXKMzLZwmW1hMtfjy5WRPNLa2hr33XdfdHZ2xq5duyKbzcZFF10Uu3fvjueffz6++tWvxi233BITJ06MTCYz7JVwObmZbeEy28JkrseXGMkzPT090d/fH2eddVbs27cv2tvbY8qUKfHzn/88vvvd78aUKVPitttui7POOiv1UsmR2RYusy1M5nr8iJE8cqTHIA9t37p1a9x5553R1tYWq1atij/6oz+KkpKSBCslV/93tiPN2Wzzl/O2MDlnjy8xkod6enqitLQ0xowZM+L777nnnnj00UdjwYIF8aUvfeldXh3H6mhueDPb/OW8LTzO2ePHDax5or+/P7Zu3Rrf/OY3Y8yYMTF27NioqamJz3zmM/GJT3wiIt48MW655ZYYHByMvXv3DtvOye2tZnToMeebb77ZbPOI87awOWePH1dGTnKHvqH/4i/+ItavXx8XXHBBVFVVRX9/f7zwwgvR2dkZtbW1ceONN0ZdXd2wYwcGBmLUqFG++U9Sh2a7devWePXVV+NjH/tYTJw4MUaPHn3YvoODg8Mu8Zrtyc15W5icsyeOGMkTkydPjqamprjuuusiIqK3tzeee+65+MUvfhEbNmyIbDYbDzzwQJx77rlxaKS+4fPDpEmTor29PS688ML49Kc/HXPnzo0Pf/jDceaZZw79Z/bDH/4wXnzxxbj11lv9Z5ZHnLeFyTl7/HmuUR546aWXory8PKZNmza07bTTTouLL744/vRP/zQeeuiheP311+M73/lORPzuPzPf+Pnh6aefjnHjxsUPfvCD+IM/+IP467/+67j88stj/vz58Vd/9Vexa9eu6OzsjKamphgYGIiICL8/5AfnbWFyzp4gWU56b7zxRnbu3LnZ2bNnZ9va2rKZTOawfe6///7sRRddlH3jjTcSrJBj9cgjj2Q//elPZ5944omhbb/61a+yixYtyp522mnZ8ePHZy+//PJsUVFRtrOzM5vNZkecPycf521hcs6eGK6M5IGxY8fG8uXL4+DBg/GVr3wlfvrTn0ZXV9dQdUdE7NmzJ8aNGxdjx471dxLySG1tbdxwww3x/ve/PyJ+95h0XV1dPPDAA3HgwIF44IEHYteuXTFnzpyYMGFCDA4O+u05TzhvC5Nz9sRwz0geOHTT1KOPPhorV66Mbdu2xXnnnRdXXHFFTJo0KbZs2RKvvvpq3HHHHbFgwYLDbpwiP2T/93HlTCYTmUwmRo363ZPdqqqq4p577oklS5aYbR762c9+FitXroxf/OIXztsC5Zx958RIHvqP//iP+Nu//dvYvHlzlJeXxznnnBOLFy+OT33qU6mXxnHwf//zevLJJ2PBggWxe/duv13luaeffjo2bNgQ//RP/xTjx4933uap7NvcjOqcPTZi5CT3+uuvxxNPPBG//e1vo7+/P2bPnh0f+tCHht7f09MT48eP902fhw7Ntr29PTKZTHzsYx+Lc889d9g+fX190dnZGe973/v8fYs8NTAwECUlJcPO0Z6enhg3bpzfmAvQf/3Xf8X+/fujurraOZsDMXISOvQN/Nhjj8Xq1atj8+bN8f73vz+qqqriwIEDcf7558fChQtj7ty5MW7cON/weeStZtvb2xvnn39+LFq0KH7v934vSktLUy+XHBz6jbmzszMGBwdj4sSJw87LbDYbg4ODUVxc7HzNI283V44PMXISOvQD6yMf+UhMnz49Vq5cGaWlpdHa2hq7du2Kf/3Xf42XX345vvCFL8RXvvKV1MslB2ZbuA7N9g//8A+jq6srFi5cGJdddlmcc845MX78+GH7Pv300zEwMDDsab+cnHKZ6zPPPBP9/f1RW1ubaLV5LMEzeDgKr7zySvaMM87I/uY3vznsfc8991y2sbExW1RUlH3ggQfe/cXxjpht4XrppZeyo0ePzs6ePTtbWlqaraioyF511VXZH/zgB9nnn38+e/DgwWwmk8nOnz8/+41vfCObzXraZz4w1xPPtaaT1MGDB+ODH/xg/PjHPz7sfeedd16sWrUqrrvuunjkkUeiv78/wQo5VmZbeLL/e4F527ZtMWvWrHj44Yfj4MGDce+998ZLL70UCxcujE9+8pNx6623xt/8zd/E3//938dnPvOZxKvm7Zjru0eMnIQymUx84AMfiCuvvDK+//3vx49//OM4cODAYftNmTIldu3adcS/AsrJx2wL06GbU2tqauLKK68cmunnP//5+OUvfxn79++PG2+8MR599NFYunRp1NbWxtSpU71M+EnOXN897hk5ibW1tcUtt9wSDz30UMyePTuuueaa+OhHPxqjR4+O3bt3x5133hlXXXVVNDY2Dv0RJvKD2RamgYGB2LdvX0yaNGno30VFRcOeNTNlypS44YYb4qtf/arZ5glzfRekfIyIw23cuDH79NNPD9v2y1/+MrtgwYLsaaedlj3ttNOyF198cfb000/P3nTTTdkDBw5ks1mPT+YDsy1cI812cHAwOzAwkM1mfzfDgYGB7L/9279li4qKsvv27RvazsnLXN89roycRLLZbCxYsCAef/zxOOecc2LBggWxaNGieO973zu0z2OPPRa//e1vY+bMmTFlyhSvU5AnzLZw/f/ZXnXVVbFo0aJ4z3veM7TPoZcEb2tri61bt3plzjxgru8uMXKSee211+I3v/lNPPLII7Fly5Z48cUXY9q0afH5z38+PvvZzx72/Hbf+PnDbAvXSLOtra2Na665JhYsWDDs/oH+/n73AuUJc333iJGT1MDAQLz66qvx1FNPxebNm6OlpSUOHDgQn/jEJ+KP//iP47LLLhva99AI3TCVH8y2cP3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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "c = QAOA_from_Ising(final_params, nlayers, pauli_terms, weights)\n", - "\n", - "print_output(c)" - ] - }, - { - "cell_type": "markdown", - "id": "d155c5e5-5843-4bba-9edc-595a18cb0c9a", - "metadata": {}, - "source": [ - "## General Case\n", - "\n", - "For the general QUBO case, we wish to minimize\n", - "\n", - "$$ x^T Q x$$\n", - "\n", - "where $x\\in\\{0,1\\}^n$ and $Q\\in\\mathbb{R}^{n\\times n}$ is a real symmetric matrix.\n", - "\n", - "This maps to an Ising Hamiltonian \n", - "\n", - "$$\\frac{1}{2}\\left(\\sum_{i=1}^n C_{ii} + \\sum_{i 0 $: risk-appetite\n", - "* $\\Sigma \\in \\mathbb{R}^{n\\times n}$: covariance matrix of the assets\n", - "* $\\mu\\in\\mathbb{R}^n$: mean return of the assets\n", - "* $B$: budget (i.e., total number of assets out of $n$ that can be selected)\n", - "\n", - "Our first step is to convert this constrained quadratic programming problem into a QUBO. We do this by adding a penalty factor $t$ and consider the alternative problem:\n", - "\n", - "$$ \\min_{x\\in\\{0,1\\}^n}\\quad q x^T \\Sigma x - \\mu^Tx + t(1^Tx-B)^2$$\n", - "\n", - "The variables in the linear terms $\\mu^Tx = \\mu_1 x_1 + \\mu_2 x_2+\\ldots$ can all be squared (since they are boolean variables), i.e. we can consider\n", - "\n", - "$$\\min_{x\\in\\{0,1\\}^n}\\quad q x^T \\Sigma x - \\sum_{i=1}^n\\mu_i x_i^2 + t(1^Tx-B)^2$$\n", - "\n", - "which is a QUBO defined by the matrix $Q$ \n", - "\n", - "$$ Q = q\\Sigma -\\mu\\begin{pmatrix}1 & \\\\ & 1\\\\ & & \\ddots\\end{pmatrix} + t\\begin{pmatrix}1 -2B & 1 & \\ldots & 1 \\\\\n", - "1 & 1-2B & 1 & \\ldots \\\\1 & 1 & 1-2B \\\\\n", - "\\vdots\\end{pmatrix}$$\n", - "\n", - "i.e., we wish to mimimize\n", - "\n", - "$$ x^T Q X + tB$$\n", - "\n", - "and we ignore the constant term $t B$.\n", - "We can now solve this by QAOA as above.\n", - "\n", - "Let us first define a function to convert portfolio data into a QUBO matrix:" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "id": "3080b901-fb6c-4bda-8348-c96540cbc39a", - "metadata": {}, - "outputs": [], - "source": [ - "def QUBO_from_portfolio(cov, mean, q, B, t):\n", - " # cov: n x n covariance numpy array\n", - " # mean: numpy array of means\n", - " n = cov.shape[0]\n", - " R = np.diag(mean)\n", - " S = np.ones((n, n)) - 2 * B * np.diag(np.ones(n))\n", - "\n", - " Q = q * cov - R + t * S\n", - " return Q" - ] - }, - { - "cell_type": "markdown", - "id": "b4cdcb0e-15a2-461c-b487-084488486c67", - "metadata": {}, - "source": [ - "We can test this using the qiskit_finance package to generate some stock covariance and mean data:\n", - "\n", - "*Note that this was tested with qiskit version 0.39.3 and qiskit-finance version 0.3.4.*" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "id": "2168c69e-73ce-4306-8a39-4ddc475acc8f", - "metadata": {}, - "outputs": [], - "source": [ - "import datetime\n", - "from qiskit_finance.data_providers import RandomDataProvider" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "id": "6a7bc671-a496-4cd8-b954-50a280b5dd85", - "metadata": {}, - "outputs": [], - "source": [ - "num_assets = 4\n", - "seed = 123\n", - "\n", - "# Generate expected return and covariance matrix from (random) time-series\n", - "stocks = [(\"TICKER%s\" % i) for i in range(num_assets)]\n", - "data = RandomDataProvider(\n", - " tickers=stocks,\n", - " start=datetime.datetime(2016, 1, 1),\n", - " end=datetime.datetime(2016, 1, 30),\n", - " seed=seed,\n", - ")\n", - "data.run()\n", - "\n", - "mu = data.get_period_return_mean_vector()\n", - "sigma = data.get_period_return_covariance_matrix()" - ] - }, - { - "cell_type": "markdown", - "id": "f6dc53d4-7ed0-436d-aa1f-8674c56e756e", - "metadata": {}, - "source": [ - "Using this mean and covariance data, we can now define our portfolio optimization problem, convert it to a QUBO matrix, and then extract the pauli terms and weights" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "id": "3f6edcd5-3c10-49fc-86ea-160fc6d3187e", - "metadata": {}, - "outputs": [], - "source": [ - "q = 0.5\n", - "budget = 3 # Note that in this example, there are 4 assets, but a budget of only 3\n", - "penalty = 3\n", - "\n", - "Q = QUBO_from_portfolio(sigma, mu, q, budget, penalty)\n", - "portfolio_pauli_terms, portfolio_weights, portfolio_offset = QUBO_to_Ising(Q)" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "id": "809b90fa-7047-4c88-b862-355da4f58a50", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0000: 21.006979417669037\n", - "0001: 6.006208358124514\n", - "0010: 6.006857249462996\n", - "0011: -2.994037697463167\n", - "0100: 6.007889613170697\n", - "0101: -2.992836964752989\n", - "0110: -2.992179512275861\n", - "0111: -5.9930299775811875\n", - "1000: 5.992965725313347\n", - "1001: -3.007905195444355\n", - "1010: -3.0070278423618397\n", - "1011: -6.008022650501182\n", - "1100: -3.0060506769683\n", - "1101: -6.006877116105166\n", - "1110: -6.005991201884008\n", - "1111: -3.006941528402507\n" - ] - } - ], - "source": [ - "# Brute force search over classical results for comparison before we run QAOA\n", - "for i in range(2):\n", - " for j in range(2):\n", - " for k in range(2):\n", - " for l in range(2):\n", - " x = np.array([i, j, k, l])\n", - " print(f\"{i}{j}{k}{l}: {np.dot(x,np.dot(Q,x))- portfolio_offset}\")" - ] - }, - { - "cell_type": "markdown", - "id": "b5e69a34-87dc-47b4-aeb2-3b9a03fd0974", - "metadata": {}, - "source": [ - "We see that, due to the penalty, the lowest energy solutions correspond to 0111, 1011, 1101, 1110, i.e. the portfolios with only 3 assets." - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "id": "80c1de6c-d3a4-4ea5-922a-bffb59dd1ea3", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "initial params: [ 0.13778198 -0.75357753 -0.01271329 -0.5461785 -0.1501883 0.36323363]\n", - "-4.204754\n", - "-5.681799\n", - "-5.6837077\n", - "-5.6837044\n", - "-5.6837053\n", - "-5.683704\n", - "-5.6837063\n", - "-5.683709\n", - "-5.6837063\n", - "-5.683705\n" - ] - } - ], - "source": [ - "iterations = 1000\n", - "nlayers = 3\n", - "final_params = QAOA_solve(portfolio_pauli_terms, portfolio_weights, nlayers, iterations)" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "id": "8a9064e3-0c61-4d2d-baf9-bdf120c0331d", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "c_final = QAOA_from_Ising(\n", - " final_params, nlayers, portfolio_pauli_terms, portfolio_weights\n", - ")\n", - "print_output(c_final)" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.8.0" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/docs/source/tutorials/qaoa_quantum_dropout.ipynb b/docs/source/tutorials/qaoa_quantum_dropout.ipynb new file mode 100644 index 00000000..e856d151 --- /dev/null +++ b/docs/source/tutorials/qaoa_quantum_dropout.ipynb @@ -0,0 +1,1064 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# Quantum Dropout for QAOA" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "## Overview" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "Quantum Approximation Optimization Algorithm (QAOA) is a hybrid classical-quantum algorithm used for solving the combinatorial optimization problem, which is proposed by [Farhi, Goldstone, and Gutmann (2014)](https://arxiv.org/abs/1411.4028). In the [previous tutorial](qaoa_nae3sat.ipynb), we introduced solving the [Not-all-equal 3-satisfiability (NAE3SAT)](https://en.wikipedia.org/wiki/Not-all-equal_3-satisfiability) by QAOA and the dilemma of QAOA on the hard problem. In this tutorial, we will introduce a simple trick to alleviate this dilemma, namely quantum dropout, please refer to [Wang, Zheng, Wu, and Zhang (2023)](https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.5.023171) for more details." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "## NAE3SAT and Hard Problem" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "Let's briefly review the NAE3SAT and the difference between the easy and hard problem.\n", + "\n", + "Let the set of clauses in the NAE3SAT be $\\mathcal{C}$. In each clause, there are three literals and each literal is represented by a spin. Spins up ($s=1$, $\\text{bit}=0$) and down ($s=-1$, $\\text{bit}=1$) represent false and true respectively. NAE3SAT requires the three spins in each clause are not all equal to each other, in other words, at least one is up, and at least one is down. The Hamiltonian of the NAE3SAT is as follows\n", + "$$\n", + "\\begin{split}\n", + " \\hat{H}_C&=\\sum_{(i,j,k)\\in\\mathcal{C}}\\left[(s_i+s_j+s_k)^2-1\\right]/2\\\\\n", + " &=\\sum_{(i,j,k)\\in\\mathcal{C}}(s_i s_j+s_j s_k+s_k s_i)+|\\mathcal{C}|,\n", + "\\end{split}\n", + "$$\n", + "where $|\\mathcal{C}|$ is the number of clauses in $\\mathcal{C}$. When all clauses are true, $\\hat{H}_C$ takes the minimum value 0, and the corresponding bit string is the solution of the NAE3SAT.\n", + "\n", + "The difference between the easy and hard problem is the energy landscape, as shown in the following figure.\n", + "\n", + "\n", + "\n", + "The global minimum is located in a large and smooth neighborhood for a simpler problem and a narrow region for a harder problem. It is worth noting that when the system size is relatively small, most of the randomly generated problems are easy, and hard problems need to be constructed with special methods, please refer to [Wang, Zheng, Wu, and Zhang (2023)](https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.5.023171)." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "## Quantum Dropout" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "The algorithm is shown in the following figure.\n", + "\n", + "\n", + "\n", + "We first implement the classical algorithm that can be done in polynomial time, such as simulated annealing method (SA). If the result is satisfactory, we stop the procedure since there is no point in a quantum solver. Otherwise, these failed classical results, typically low-lying excited states (local minima), offer insights as we prepare quantum dropout for QAOA: whether a clause should be kept or available for quantum dropout to underweight the distracting local minima and enhance the chances to locate the true ground state. Specifically, the clauses violated by low-lying excited states should be all kept, and the other clauses can be randomly discarded at the ratio $R$.\n", + "\n", + "Finally, we optimize the PQC with respect to the original cost function $H_C$ with a complete set of clauses to ensure the uniqueness of the global minimum. The current procedure does not incur obvious overhead to the conventional QAOA since the preliminary approaches and the quantum-dropout controls are both inexpensive on a classical computer." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "### Setup" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": null, + "outputs": [], + "source": [ + "import tensorcircuit as tc\n", + "import optax\n", + "import jax.numpy as jnp\n", + "import tensorflow as tf\n", + "import networkx as nx\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "from functools import partial\n", + "from IPython.display import clear_output\n", + "import random\n", + "\n", + "K = tc.set_backend(\"jax\")\n", + "\n", + "nlayers = 30 # the number of layers\n", + "ncircuits = 6 # six circuits with different initial parameters are going to be optimized at the same time\n", + "R = 0.5 # dropout ratio, 0 means no dropout, 1 means all dropout" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "We use the same NAE3SAT as the [previous tutorial](qaoa_nae3sat.ipynb)." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 2, + "outputs": [], + "source": [ + "# a hard graph instance\n", + "hard_clauses = [\n", + " [4, 1, 7],\n", + " [5, 11, 8],\n", + " [4, 1, 8],\n", + " [4, 11, 8],\n", + " [4, 1, 10],\n", + " [5, 11, 8],\n", + " [4, 1, 8],\n", + " [1, 11, 8],\n", + " [4, 1, 7],\n", + " [0, 11, 8],\n", + " [4, 1, 10],\n", + " [4, 11, 8],\n", + " [5, 0, 10],\n", + " [0, 6, 7],\n", + " [5, 0, 11],\n", + " [0, 6, 7],\n", + " [5, 0, 9],\n", + " [3, 6, 7],\n", + " [5, 0, 8],\n", + " [5, 6, 7],\n", + " [5, 0, 10],\n", + " [3, 6, 7],\n", + " [5, 0, 10],\n", + " [1, 6, 7],\n", + " [2, 4, 6],\n", + " [1, 8, 11],\n", + " [2, 4, 6],\n", + " [2, 8, 11],\n", + " [2, 4, 9],\n", + " [5, 8, 11],\n", + " [2, 4, 10],\n", + " [2, 8, 11],\n", + " [2, 4, 10],\n", + " [4, 8, 11],\n", + " [2, 4, 8],\n", + " [4, 8, 11],\n", + " [3, 0, 9],\n", + " [5, 11, 7],\n", + " [3, 0, 10],\n", + " [2, 11, 7],\n", + " [3, 0, 9],\n", + " [0, 11, 7],\n", + " [3, 0, 9],\n", + " [5, 11, 7],\n", + " [3, 0, 10],\n", + " [3, 11, 7],\n", + " [3, 0, 7],\n", + " [4, 11, 7],\n", + " [5, 0, 10],\n", + " [4, 0, 10],\n", + " [2, 5, 6],\n", + " [2, 11, 10],\n", + " [2, 6, 10],\n", + " [2, 4, 9],\n", + " [0, 9, 10],\n", + " [3, 0, 7],\n", + " [2, 5, 6],\n", + " [1, 10, 9],\n", + " [1, 4, 11],\n", + " [5, 10, 11],\n", + " [0, 4, 8],\n", + " [0, 9, 8],\n", + " [2, 11, 10],\n", + " [2, 8, 6],\n", + " [3, 6, 7],\n", + " [0, 8, 10],\n", + " [4, 0, 9],\n", + " [3, 5, 8],\n", + " [5, 11, 10],\n", + " [2, 11, 10],\n", + " [4, 11, 8],\n", + " [1, 3, 11],\n", + "]\n", + "cost_factor = 1 / len(hard_clauses) / 4" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-03T11:45:08.202605500Z", + "start_time": "2023-07-03T11:45:08.202029100Z" + } + } + }, + { + "cell_type": "code", + "execution_count": 3, + "outputs": [], + "source": [ + "# convert to a NetworkX graph\n", + "def construct_graph(clauses):\n", + " graph = nx.Graph()\n", + " for i, j, k in clauses:\n", + " graph.add_edge(i, j, weight=0)\n", + " graph.add_edge(j, k, weight=0)\n", + " graph.add_edge(k, i, weight=0)\n", + " for i, j, k in clauses:\n", + " graph[i][j][\"weight\"] += 1\n", + " graph[j][k][\"weight\"] += 1\n", + " graph[k][i][\"weight\"] += 1\n", + " return graph" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-03T11:45:08.206621400Z", + "start_time": "2023-07-03T11:45:08.203172500Z" + } + } + }, + { + "cell_type": "code", + "execution_count": 4, + "outputs": [ + { + "data": { + "text/plain": "
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" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# plot original hard graph\n", + "hard_graph = construct_graph(hard_clauses)\n", + "pos = nx.spring_layout(hard_graph)\n", + "nx.draw_networkx(hard_graph, with_labels=True, pos=pos)\n", + "ax = plt.gca()\n", + "ax.set_facecolor(\"w\")" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-03T11:45:08.390560600Z", + "start_time": "2023-07-03T11:45:08.210412300Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "We first use the brutal force method (BF) to obtain the true solution." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 5, + "outputs": [], + "source": [ + "def b2s(bit):\n", + " return 1 - 2 * int(bit)\n", + "\n", + "\n", + "def energy(cfg, graph, n_cls, normalize=True):\n", + " factor = 1 / n_cls / 4\n", + " E = 0.25\n", + " for a, b in graph.edges:\n", + " E += cfg[a] * cfg[b] * graph[a][b][\"weight\"] * factor\n", + " return E if normalize else E / factor\n", + "\n", + "\n", + "def brutal_force(graph):\n", + " num_nodes, n_cls = graph.number_of_nodes(), len(hard_clauses)\n", + " min_cost, best_case = 1.0, []\n", + " for i in range(2**num_nodes):\n", + " case = f\"{bin(i)[2:]:0>{num_nodes}}\"\n", + "\n", + " cost = energy(list(map(b2s, case)), graph, n_cls)\n", + "\n", + " gap = min_cost - cost\n", + " if gap > 1e-6:\n", + " min_cost = cost\n", + " best_case = [case]\n", + " elif abs(gap) < 1e-6:\n", + " best_case.append(case)\n", + "\n", + " return best_case, min_cost" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-03T11:45:08.390560600Z", + "start_time": "2023-07-03T11:45:08.390046300Z" + } + } + }, + { + "cell_type": "code", + "execution_count": 6, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "cost: 0.000\n", + "bit string: ['000000111111', '111111000000']\n" + ] + }, + { + "data": { + "text/plain": "
", + "image/png": 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" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# print BF results\n", + "bf_best_cases, bf_best = brutal_force(hard_graph)\n", + "print(f\"cost: {bf_best:.3f}\\nbit string: {bf_best_cases}\")\n", + "\n", + "# plot NetworkX graph\n", + "colors = [\"r\" if bf_best_cases[0][i] == \"0\" else \"c\" for i in hard_graph.nodes]\n", + "nx.draw_networkx(hard_graph, with_labels=True, node_color=colors, pos=pos)\n", + "ax = plt.gca()\n", + "ax.set_facecolor(\"w\")" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-03T11:45:08.708112400Z", + "start_time": "2023-07-03T11:45:08.390560600Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "Then we start to execute the algorithm loop shown in the figure above. The algorithm starts from the classical method - SA." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 7, + "outputs": [], + "source": [ + "def sim_annealing(graph, t_max: int, T: float):\n", + " num_nodes, num_cls = graph.number_of_nodes(), len(hard_clauses)\n", + " state = np.random.randint(0, 2, num_nodes)\n", + " next_state = state.copy()\n", + " E = energy(1 - 2 * state, graph, num_cls, normalize=False)\n", + " t = 0\n", + " while t < t_max:\n", + " temper = (1 - t / t_max) * T\n", + " flip_idx = np.random.randint(num_nodes)\n", + " next_state[flip_idx] = 1 - next_state[flip_idx]\n", + " next_E = energy(1 - 2 * next_state, graph, num_cls, normalize=False)\n", + " if next_E <= E or np.exp(-(next_E - E) / temper) > np.random.rand():\n", + " state[flip_idx] = 1 - state[flip_idx]\n", + " E = next_E\n", + " else:\n", + " next_state[flip_idx] = 1 - next_state[flip_idx]\n", + " t += 1\n", + " return tuple(state), E" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-03T11:45:08.711814200Z", + "start_time": "2023-07-03T11:45:08.709702400Z" + } + } + }, + { + "cell_type": "code", + "execution_count": 8, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "number of low-lying excited states: 23\n" + ] + } + ], + "source": [ + "# obtain the low-lying excited states\n", + "ll_excited, n_exp = set(), 100\n", + "for _ in range(n_exp):\n", + " sa_case, sa_cost = sim_annealing(hard_graph, 200, 1)\n", + " if sa_cost > 1e-6:\n", + " ll_excited.add(sa_case)\n", + "print(f\"number of low-lying excited states: {len(ll_excited)}\")" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-03T11:45:12.123684300Z", + "start_time": "2023-07-03T11:45:08.709702400Z" + } + } + }, + { + "cell_type": "code", + "execution_count": 9, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "number of clauses should be kept: 12\n", + "number of clauses can be discarded: 60\n", + "number of clauses after dropout: 42\n" + ] + } + ], + "source": [ + "# obtain the clauses violated by low-lying excited states and the clauses can be discarded\n", + "def get_clauses(ll_exc_st, clauses):\n", + " kept, drop = [], []\n", + " for cls in clauses:\n", + " violated = False\n", + " for state in ll_exc_st:\n", + " if sum(state[i] for i in cls) in [0, 3]:\n", + " kept.append(cls)\n", + " violated = True\n", + " break\n", + " if not violated:\n", + " drop.append(cls)\n", + " return kept, drop\n", + "\n", + "\n", + "kept_clauses, drop_clauses = get_clauses(ll_excited, hard_clauses)\n", + "num_selected = int((1 - R) * len(drop_clauses))\n", + "num_after_drop = len(kept_clauses) + num_selected\n", + "driving_factor = 1 / num_after_drop / 4\n", + "print(f\"number of clauses should be kept: {len(kept_clauses)}\")\n", + "print(f\"number of clauses can be discarded: {len(drop_clauses)}\")\n", + "print(f\"number of clauses after dropout: {num_after_drop}\")" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-03T11:45:12.128858800Z", + "start_time": "2023-07-03T11:45:12.128083Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "There are two ways of quantum dropout. One isotropic or uniform, i.e., $\\hat H_{C_1} = \\hat H_{C_2} = \\cdots = \\hat H_{C_p}$. The other is random or different, i.e., $\\hat H_{C_i}\\neq\\hat H_{C_j}$ if $i\\neq j$." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "### Isotropic Quantum Dropout" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 10, + "outputs": [ + { + "data": { + "text/plain": "
", + "image/png": 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" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# get the graph after dropout\n", + "iso_clauses = kept_clauses + random.sample(drop_clauses, num_selected)\n", + "iso_graph = construct_graph(iso_clauses)\n", + "nx.draw_networkx(iso_graph, with_labels=True, pos=pos)\n", + "ax = plt.gca()\n", + "ax.set_facecolor(\"w\")" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-03T11:45:12.461569500Z", + "start_time": "2023-07-03T11:45:12.132507800Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "The PQC is similar to the regular QAOA, but the cost Hamiltonian is the original Hamiltonian but the driving Hamiltonian is the one after dropout." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 11, + "outputs": [], + "source": [ + "def QAOAansatz_iso(params, g, each=1, return_circuit=False):\n", + " n = g.number_of_nodes() # the number of nodes\n", + "\n", + " # PQC loop\n", + " def pqc_loop(s_, params_):\n", + " c_ = tc.Circuit(n, inputs=s_)\n", + " for j in range(each):\n", + " # driving layer\n", + " for a, b in g.edges:\n", + " c_.RZZ(a, b, theta=g[a][b][\"weight\"] * params_[2 * j] * driving_factor)\n", + " # mixing layer\n", + " for i in range(n):\n", + " c_.RX(i, theta=params_[2 * j + 1])\n", + " s_ = c_.state()\n", + " return s_\n", + "\n", + " c0 = tc.Circuit(n)\n", + " for i in range(n):\n", + " c0.H(i)\n", + " s0 = c0.state()\n", + " s = K.scan(pqc_loop, K.reshape(params, [nlayers // each, 2 * each]), s0)\n", + " c = tc.Circuit(n, inputs=s)\n", + "\n", + " # whether to return the circuit\n", + " if return_circuit is True:\n", + " return c\n", + "\n", + " # calculate the loss function\n", + " loss = 0.25\n", + " for a, b in hard_graph.edges:\n", + " loss += c.expectation_ps(z=[a, b]) * hard_graph[a][b][\"weight\"] * cost_factor\n", + "\n", + " return K.real(loss)" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-03T11:45:12.464821600Z", + "start_time": "2023-07-03T11:45:12.462095700Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "Here, several circuits with different initial parameters are optimized/trained at the same time." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 12, + "outputs": [ + { + "data": { + "text/plain": "
", + "image/png": 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" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# use vvag to get the losses and gradients with different random circuit instances\n", + "QAOA_vvag = K.jit(\n", + " K.vvag(QAOAansatz_iso, argnums=0, vectorized_argnums=0), static_argnums=(1, 2, 3)\n", + ")\n", + "\n", + "params_iso = K.implicit_randn(\n", + " shape=[ncircuits, 2 * nlayers], stddev=0.1\n", + ") # initial parameters\n", + "if type(K).__name__ == \"JaxBackend\":\n", + " opt = K.optimizer(optax.adam(1e-2))\n", + "else:\n", + " opt = K.optimizer(tf.keras.optimizers.Adam(1e-2))\n", + "\n", + "list_of_loss = [[] for i in range(ncircuits)]\n", + "\n", + "for i in range(2000):\n", + " loss, grads = QAOA_vvag(params_iso, iso_graph)\n", + " params_iso = opt.update(grads, params_iso) # gradient descent\n", + "\n", + " # visualise the progress\n", + " clear_output(wait=True)\n", + " list_of_loss = np.hstack((list_of_loss, K.numpy(loss)[:, np.newaxis]))\n", + " plt.xlabel(\"Iteration\")\n", + " plt.ylabel(\"Cost\")\n", + " for index in range(ncircuits):\n", + " plt.plot(range(i + 1), list_of_loss[index])\n", + " legend = [f\"circuit {leg}\" for leg in range(ncircuits)]\n", + " plt.legend(legend)\n", + " plt.show()" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "After inputting the optimized parameters back to the ansatz circuit, we can perform the projective measurement on the output quantum state to get the solution. Here we directly use the bit string with the maximum probability as the solution since we know all information of the probability distribution of the output quantum state, but which is not feasible in the experiment." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 13, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Circuit #0\n", + "cost: 0.042537812143564224\n", + "max prob: 0.047906018793582916\n", + "bit strings: ['000000111111']\n", + "\n", + "Circuit #1\n", + "cost: 0.033970173448324203\n", + "max prob: 0.054868899285793304\n", + "bit strings: ['000000111111']\n", + "\n", + "Circuit #2\n", + "cost: 0.033648744225502014\n", + "max prob: 0.055139534175395966\n", + "bit strings: ['111111000000']\n", + "\n", + "Circuit #3\n", + "cost: 0.03602508455514908\n", + "max prob: 0.05475332960486412\n", + "bit strings: ['111111000000']\n", + "\n", + "Circuit #4\n", + "cost: 0.03601868823170662\n", + "max prob: 0.05406792089343071\n", + "bit strings: ['111111000000']\n", + "\n", + "Circuit #5\n", + "cost: 0.03338256850838661\n", + "max prob: 0.05537496879696846\n", + "bit strings: ['000000111111']\n", + "\n" + ] + } + ], + "source": [ + "# print QAOA results\n", + "for num_circuit in range(ncircuits):\n", + " print(f\"Circuit #{num_circuit}\")\n", + " c = QAOAansatz_iso(params=params_iso[num_circuit], g=iso_graph, return_circuit=True)\n", + " loss = QAOAansatz_iso(params=params_iso[num_circuit], g=iso_graph)\n", + "\n", + " # find the states with max probabilities\n", + " probs = K.numpy(c.probability())\n", + " max_prob = max(probs)\n", + " index = np.where(probs == max_prob)[0]\n", + " states = []\n", + " for i in index:\n", + " states.append(f\"{bin(i)[2:]:0>{c._nqubits}}\")\n", + " print(f\"cost: {K.numpy(loss)}\\nmax prob: {max_prob}\\nbit strings: {states}\\n\")" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-03T12:07:03.904854400Z", + "start_time": "2023-07-03T12:06:31.721659700Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "On average, QAOA with isotropic quantum dropout improves the probability of correct solution (max prob) by nearly 0.015 compared to regular QAOA.\n", + "\n", + "It should be noted that isotropic quantum dropout will lead to more ground state degeneracy, so it does not necessarily lead to better results than conventional QAOA. However, it has a high upper limit, which means that it is possible to get much better results, please refer to [Wang, Zheng, Wu, and Zhang (2023)](https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.5.023171) for more analysis and details." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "### Random Quantum Dropout" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "markdown", + "source": [ + "Because the dropout of each layer is different, we need to generate $\\text{nlayers}$ graphs after dropout. In order to perform just-in-time (JIT) compilation more conveniently, here we only save the weights in the order of the edges of the original hard graph, instead of saving each graph after dropout." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 21, + "outputs": [], + "source": [ + "def graph_weights(graph):\n", + " gw = []\n", + " for a, b in hard_graph.edges:\n", + " gw.append(graph[a].get(b, default={\"weight\": 0})[\"weight\"])\n", + " return jnp.asarray(gw)" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-03T13:23:26.871885Z", + "start_time": "2023-07-03T13:23:26.858216600Z" + } + } + }, + { + "cell_type": "code", + "execution_count": 22, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Here is the graph of the H_C of the last driving layer:\n" + ] + }, + { + "data": { + "text/plain": "
", + "image/png": 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" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# get the graph after dropout\n", + "rnd_graphs_w = []\n", + "for _ in range(nlayers):\n", + " rnd_clauses = kept_clauses + random.sample(drop_clauses, num_selected)\n", + " rnd_graph = construct_graph(rnd_clauses)\n", + " rnd_graphs_w.append(graph_weights(rnd_graph))\n", + "print(\"Here is the graph of the H_C of the last driving layer:\")\n", + "rnd_graphs_w = jnp.stack(rnd_graphs_w, axis=0)\n", + "nx.draw_networkx(rnd_graph, with_labels=True, pos=pos)\n", + "ax = plt.gca()\n", + "ax.set_facecolor(\"w\")" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-03T13:23:28.437985100Z", + "start_time": "2023-07-03T13:23:28.262064700Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "The ansatz needs to accept $\\text{nlayers}$ weights of graphs as inputs." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 23, + "outputs": [], + "source": [ + "def QAOAansatz_rnd(params, g, each=1, return_circuit=False):\n", + " n = hard_graph.number_of_nodes() # the number of nodes\n", + " rep = nlayers // each\n", + " g = g.reshape(rep, each, g.shape[-1]) * driving_factor\n", + "\n", + " # PQC loop\n", + " def pqc_loop(s_, pkg):\n", + " params_, g_ = pkg\n", + " c_ = tc.Circuit(n, inputs=s_)\n", + " for j in range(each):\n", + " # driving layer\n", + " for i, (a, b) in enumerate(hard_graph.edges):\n", + " c_.RZZ(a, b, theta=g_[j][i] * params_[2 * j])\n", + " # mixing layer\n", + " for i in range(n):\n", + " c_.RX(i, theta=params_[2 * j + 1])\n", + " s_ = c_.state()\n", + " return s_\n", + "\n", + " c0 = tc.Circuit(n)\n", + " for i in range(n):\n", + " c0.H(i)\n", + " s0 = c0.state()\n", + " s = K.scan(pqc_loop, [K.reshape(params, [rep, 2 * each]), g], s0)\n", + " c = tc.Circuit(n, inputs=s)\n", + "\n", + " # whether to return the circuit\n", + " if return_circuit is True:\n", + " return c\n", + "\n", + " # calculate the loss function\n", + " loss = 0.25\n", + " for a, b in hard_graph.edges:\n", + " loss += c.expectation_ps(z=[a, b]) * hard_graph[a][b][\"weight\"] * cost_factor\n", + "\n", + " return K.real(loss)" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-03T13:23:41.855222600Z", + "start_time": "2023-07-03T13:23:41.802298100Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "Then, we perform the optimization step, and also optimize several circuits in parallel. Since graph weights Jax arrays are non-hashable static arguments and not supported when using vmap, we use $\\text{partial}$ to wrap the ansatz and accept the graph weights input." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 28, + "outputs": [ + { + "data": { + "text/plain": "
", + "image/png": 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" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# use vvag to get the losses and gradients with different random circuit instances\n", + "QAOA_vvag = K.jit(\n", + " K.vvag(partial(QAOAansatz_rnd, g=rnd_graphs_w), argnums=0, vectorized_argnums=0)\n", + ")\n", + "\n", + "params_rnd = K.implicit_randn(\n", + " shape=[ncircuits, 2 * nlayers], stddev=0.1\n", + ") # initial parameters\n", + "if type(K).__name__ == \"JaxBackend\":\n", + " opt = K.optimizer(optax.adam(1e-2))\n", + "else:\n", + " opt = K.optimizer(tf.keras.optimizers.Adam(1e-2))\n", + "\n", + "list_of_loss = [[] for i in range(ncircuits)]\n", + "\n", + "for i in range(2000):\n", + " loss, grads = QAOA_vvag(params_rnd)\n", + " params_rnd = opt.update(grads, params_rnd) # gradient descent\n", + "\n", + " # visualise the progress\n", + " clear_output(wait=True)\n", + " list_of_loss = np.hstack((list_of_loss, K.numpy(loss)[:, np.newaxis]))\n", + " plt.xlabel(\"Iteration\")\n", + " plt.ylabel(\"Cost\")\n", + " for index in range(ncircuits):\n", + " plt.plot(range(i + 1), list_of_loss[index])\n", + " legend = [f\"circuit {leg}\" for leg in range(ncircuits)]\n", + " plt.legend(legend)\n", + " plt.show()" + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 29, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Circuit #0\n", + "cost: 0.034298673272132874\n", + "max prob: 0.061373475939035416\n", + "bit strings: ['000000111111']\n", + "\n", + "Circuit #1\n", + "cost: 0.034172173589468\n", + "max prob: 0.06166590005159378\n", + "bit strings: ['000000111111', '111111000000']\n", + "\n", + "Circuit #2\n", + "cost: 0.03370116278529167\n", + "max prob: 0.06229700148105621\n", + "bit strings: ['000000111111']\n", + "\n", + "Circuit #3\n", + "cost: 0.035995520651340485\n", + "max prob: 0.0600101463496685\n", + "bit strings: ['111111000000']\n", + "\n", + "Circuit #4\n", + "cost: 0.03770057111978531\n", + "max prob: 0.05639055743813515\n", + "bit strings: ['000000111111']\n", + "\n", + "Circuit #5\n", + "cost: 0.042536795139312744\n", + "max prob: 0.047668762505054474\n", + "bit strings: ['111111000000']\n", + "\n" + ] + } + ], + "source": [ + "# print QAOA results\n", + "for num_circuit in range(ncircuits):\n", + " print(f\"Circuit #{num_circuit}\")\n", + " c = QAOAansatz_rnd(\n", + " params=params_rnd[num_circuit], g=rnd_graphs_w, return_circuit=True\n", + " )\n", + " loss = QAOAansatz_rnd(params=params_rnd[num_circuit], g=rnd_graphs_w)\n", + "\n", + " # find the states with max probabilities\n", + " probs = K.numpy(c.probability())\n", + " max_prob = max(probs)\n", + " index = np.where(probs == max_prob)[0]\n", + " states = []\n", + " for i in index:\n", + " states.append(f\"{bin(i)[2:]:0>{c._nqubits}}\")\n", + " print(f\"cost: {K.numpy(loss)}\\nmax prob: {max_prob}\\nbit strings: {states}\\n\")" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-04T01:38:27.853435600Z", + "start_time": "2023-07-04T01:37:48.381823700Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "On average, QAOA with random quantum dropout improves the probability of correct solution (max prob) by nearly 0.02 compared to regular QAOA.\n", + "\n", + "Compared with isotropic quantum dropout, the standard deviation of the probability of correct solution obtained by random quantum dropout is smaller, but the upper limit is lower. From the physical picture, QAOA after random quantum dropout works like a quantum interferometer. QAOA circuits with different dropouts over driving layers may work through a focusing effect on the true ground state: different clause sets lead to different energy landscapes and minima, whose configurations receive constructive interference and enhanced amplitudes. Being the only common minimum of all $\\hat{H}_{C_i}$ irrespective of the dropouts, the true ground state remains stand-out through all driving layers. Please refer to [Wang, Zheng, Wu, and Zhang (2023)](https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.5.023171) for more analysis and details." + ], + "metadata": { + "collapsed": false + } + }, + { + "cell_type": "code", + "execution_count": 30, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "OS info: Linux-5.4.119-1-tlinux4-0010.2-x86_64-with-glibc2.28\n", + "Python version: 3.10.11\n", + "Numpy version: 1.23.5\n", + "Scipy version: 1.11.0\n", + "Pandas version: 2.0.2\n", + "TensorNetwork version: 0.4.6\n", + "Cotengra is not installed\n", + "TensorFlow version: 2.12.0\n", + "TensorFlow GPU: []\n", + "TensorFlow CUDA infos: {'cpu_compiler': '/dt9/usr/bin/gcc', 'cuda_compute_capabilities': ['sm_35', 'sm_50', 'sm_60', 'sm_70', 'sm_75', 'compute_80'], 'cuda_version': '11.8', 'cudnn_version': '8', 'is_cuda_build': True, 'is_rocm_build': False, 'is_tensorrt_build': True}\n", + "Jax version: 0.4.13\n", + "Jax installation doesn't support GPU\n", + "JaxLib version: 0.4.13\n", + "PyTorch version: 2.0.1\n", + "PyTorch GPU support: False\n", + "PyTorch GPUs: []\n", + "Cupy is not installed\n", + "Qiskit version: 0.24.1\n", + "Cirq version: 1.1.0\n", + "TensorCircuit version 0.10.0\n" + ] + } + ], + "source": [ + "tc.about()" + ], + "metadata": { + "collapsed": false, + "ExecuteTime": { + "end_time": "2023-07-04T01:40:31.531945400Z", + "start_time": "2023-07-04T01:40:31.478214100Z" + } + } + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/source/tutorials/tc_qcloud_sdk.ipynb b/docs/source/tutorials/qcloud_sdk.ipynb similarity index 100% rename from docs/source/tutorials/tc_qcloud_sdk.ipynb rename to docs/source/tutorials/qcloud_sdk.ipynb diff --git a/docs/source/tutorials/qcloud_sdk_demo.ipynb b/docs/source/tutorials/qcloud_sdk_demo.ipynb new file mode 100644 index 00000000..8f0a97a5 --- /dev/null +++ b/docs/source/tutorials/qcloud_sdk_demo.ipynb @@ -0,0 +1,1648 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "a246d497", + "metadata": {}, + "source": [ + "# Demo on TensorCircuit SDK for Tencent Quantum Cloud\n", + "\n", + "This notebook is not served as a full user manual for TC SDK for QCLOUD. Instead，it only highlighted a limited subset of features that TC enabled, mainly for live demo and tutorials.\n", + "\n", + "## Import and Setup" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "ff5cc3c8", + "metadata": {}, + "outputs": [], + "source": [ + "import tensorcircuit as tc" + ] + }, + { + "cell_type": "markdown", + "id": "e66850fe", + "metadata": {}, + "source": [ + "The following two line are by default and no need to run explicitly, \n", + "unless you activate tencent cloud service for the first time when you have to set up the token copied from the web" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "4352cc25", + "metadata": {}, + "outputs": [], + "source": [ + "# tc.cloud.apis.set_token(\"123456isnotgoodpassword\")\n", + "# tc.cloud.apis.set_provider(\"tencent\")" + ] + }, + { + "cell_type": "markdown", + "id": "2aa760be", + "metadata": {}, + "source": [ + "## Devices and properties" + ] + }, + { + "cell_type": "markdown", + "id": "735c2d63", + "metadata": {}, + "source": [ + "**Provider agnostic**: The SDK architecture is designed to be provider agnostic so that we have the potential to support multiple QPU providers in the future. And from the user's pespective, no code will change to deploy the quantum program on different QPU providers. We also support some third party and local providers now internally, and the list will be expanding...\n" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "72106e97", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[tencent, local]" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tc.cloud.apis.list_providers()" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "e35e1518", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[tencent::simulator:tc,\n", + " tencent::simulator:aer,\n", + " tencent::simulator:tcn1,\n", + " tencent::tianshu_s1,\n", + " tencent::tianxuan_s1]" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tc.cloud.apis.list_devices()" + ] + }, + { + "cell_type": "markdown", + "id": "4f5ce14e", + "metadata": {}, + "source": [ + "list only devices online that are currently available with `state` argument" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "b8456acc", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[tencent::simulator:tc,\n", + " tencent::simulator:aer,\n", + " tencent::tianshu_s1,\n", + " tencent::tianxuan_s1]" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tc.cloud.apis.list_devices(\"tencent\", state=\"on\")" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "7ced9cc6", + "metadata": {}, + "outputs": [], + "source": [ + "device_name = \"tianxuan_s1\" # 9 qubits chip\n", + "\n", + "# get the device object\n", + "\n", + "d = tc.cloud.apis.get_device(device_name)" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "id": "0e0633c5", + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "execution_count": 46, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from IPython.display import Image\n", + "\n", + "Image(filename=\"../statics/tianxuan_s1.png\")" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "0461fc24", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'id': 'tianxuan_s1',\n", + " 'type': 'CHIP',\n", + " 'qubits': 9,\n", + " 'T1': 30.593555450439453,\n", + " 'T2': 12.94344425201416,\n", + " 'Err': {'SQ': 0.0008366666666666665,\n", + " 'CZ': 0.01615125,\n", + " 'Readout': {'F0': 0.0209, 'F1': 0.0849111111111111}},\n", + " 'report': {'at': 1683908208,\n", + " 'consumed': 181292436838,\n", + " 'done': 32164,\n", + " 'total': 32175,\n", + " 'waiting': 5039},\n", + " 'at': 1685496713,\n", + " 'state': 'on',\n", + " 'links': {(0, 1): {'A': 0, 'B': 1, 'CZErrRate': 0.0135, 'GateLenInNs': 75.56},\n", + " (0, 2): {'A': 0, 'B': 2, 'CZErrRate': 0.02358, 'GateLenInNs': 78.74},\n", + " (0, 3): {'A': 0, 'B': 3, 'CZErrRate': 0.01899, 'GateLenInNs': 79.94},\n", + " (0, 4): {'A': 0, 'B': 4, 'CZErrRate': 0.03357, 'GateLenInNs': 79.93},\n", + " (1, 5): {'A': 1, 'B': 5, 'CZErrRate': 0.00552, 'GateLenInNs': 74.94},\n", + " (2, 6): {'A': 2, 'B': 6, 'CZErrRate': 0.01951, 'GateLenInNs': 79.71},\n", + " (3, 7): {'A': 3, 'B': 7, 'CZErrRate': 0.00422, 'GateLenInNs': 65.04},\n", + " (4, 8): {'A': 4, 'B': 8, 'CZErrRate': 0.01032, 'GateLenInNs': 76.07}},\n", + " 'bits': {0: {'Freqency': 3974.78,\n", + " 'Qubit': 0,\n", + " 'ReadoutF0Err': 0.035,\n", + " 'ReadoutF1Err': 0.0876,\n", + " 'SingleQubitErrRate': 0.00079,\n", + " 'SingleQubitGateLenInNs': 40,\n", + " 'T1': 34.524,\n", + " 'T2': 9.62},\n", + " 1: {'Freqency': 4180.96,\n", + " 'Qubit': 1,\n", + " 'ReadoutF0Err': 0.0308,\n", + " 'ReadoutF1Err': 0.0732,\n", + " 'SingleQubitErrRate': 0.00064,\n", + " 'SingleQubitGateLenInNs': 40,\n", + " 'T1': 34.459,\n", + " 'T2': 8.321},\n", + " 2: {'Freqency': 4106.44,\n", + " 'Qubit': 2,\n", + " 'ReadoutF0Err': 0.0192,\n", + " 'ReadoutF1Err': 0.0728,\n", + " 'SingleQubitErrRate': 0.00085,\n", + " 'SingleQubitGateLenInNs': 40,\n", + " 'T1': 18.917,\n", + " 'T2': 5.222},\n", + " 3: {'Freqency': 4657.5,\n", + " 'Qubit': 3,\n", + " 'ReadoutF0Err': 0.0073,\n", + " 'ReadoutF1Err': 0.1156,\n", + " 'SingleQubitErrRate': 0.00124,\n", + " 'SingleQubitGateLenInNs': 40,\n", + " 'T1': 31.079,\n", + " 'T2': 42.79},\n", + " 4: {'Freqency': 4405.96,\n", + " 'Qubit': 4,\n", + " 'ReadoutF0Err': 0.0117,\n", + " 'ReadoutF1Err': 0.0483,\n", + " 'SingleQubitErrRate': 0.0006,\n", + " 'SingleQubitGateLenInNs': 40,\n", + " 'T1': 32.353,\n", + " 'T2': 9.3},\n", + " 5: {'Freqency': 4371.74,\n", + " 'Qubit': 5,\n", + " 'ReadoutF0Err': 0.0125,\n", + " 'ReadoutF1Err': 0.0604,\n", + " 'SingleQubitErrRate': 0.00058,\n", + " 'SingleQubitGateLenInNs': 40,\n", + " 'T1': 30.132,\n", + " 'T2': 6.954},\n", + " 6: {'Freqency': 4247.08,\n", + " 'Qubit': 6,\n", + " 'ReadoutF0Err': 0.0465,\n", + " 'ReadoutF1Err': 0.1351,\n", + " 'SingleQubitErrRate': 0.00102,\n", + " 'SingleQubitGateLenInNs': 40,\n", + " 'T1': 34.827,\n", + " 'T2': 4.462},\n", + " 7: {'Freqency': 4462.26,\n", + " 'Qubit': 7,\n", + " 'ReadoutF0Err': 0.0096,\n", + " 'ReadoutF1Err': 0.0525,\n", + " 'SingleQubitErrRate': 0.0006,\n", + " 'SingleQubitGateLenInNs': 40,\n", + " 'T1': 28.269,\n", + " 'T2': 13.429},\n", + " 8: {'Freqency': 4335.34,\n", + " 'Qubit': 8,\n", + " 'ReadoutF0Err': 0.0155,\n", + " 'ReadoutF1Err': 0.1187,\n", + " 'SingleQubitErrRate': 0.00121,\n", + " 'SingleQubitGateLenInNs': 40,\n", + " 'T1': 30.782,\n", + " 'T2': 16.393}},\n", + " 'langs': ['tQASM', 'eQASM'],\n", + " 'memo': 'tQLab 9Gmon',\n", + " 'usage': '9gmon?o=0 \\nthe o(ptimized) to specify optimization level bits: both = 3 (bits 11) = gate decomposition = 2 (bit 10) | qubit mapping = 1 (bit 01)',\n", + " 'native_gates': ['h', 'rz', 'x', 'y', 'z', 'cz', 'cx']}" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "d.list_properties()" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "b44f1844", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'Freqency': 4106.44,\n", + " 'Qubit': 2,\n", + " 'ReadoutF0Err': 0.0192,\n", + " 'ReadoutF1Err': 0.0728,\n", + " 'SingleQubitErrRate': 0.00085,\n", + " 'SingleQubitGateLenInNs': 40,\n", + " 'T1': 18.917,\n", + " 'T2': 5.222}" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "d.list_properties()[\"bits\"][2]" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "ae4798dc", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(['h', 'rz', 'x', 'y', 'z', 'cz', 'cx'],\n", + " 'tianxuan_s1',\n", + " tencent,\n", + " [[0, 1],\n", + " [6, 2],\n", + " [4, 0],\n", + " [0, 4],\n", + " [8, 4],\n", + " [1, 5],\n", + " [3, 7],\n", + " [0, 3],\n", + " [2, 0],\n", + " [5, 1],\n", + " [3, 0],\n", + " [7, 3],\n", + " [0, 2],\n", + " [2, 6],\n", + " [4, 8],\n", + " [1, 0]])" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# some meta data for the device\n", + "\n", + "d.native_gates(), d.name, d.provider, d.topology()" + ] + }, + { + "cell_type": "markdown", + "id": "ccd597ae", + "metadata": {}, + "source": [ + "The native gate set and the coupling map information is essential for TC to transpile the circuits so that they conform the standard of the corresponding devices." + ] + }, + { + "cell_type": "markdown", + "id": "dcea5cfe", + "metadata": {}, + "source": [ + "## Tasks" + ] + }, + { + "cell_type": "markdown", + "id": "3ad38549", + "metadata": {}, + "source": [ + "Submit a simple two-qubit task.\n", + "\n", + "Note that there is no need to explicitly add any measurement operations to the circuit. By default, t.results will return the number of (Z-basis) measurement outcomes for all (in this case 2) qubits in the specified circuit" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "01a0fb92", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'00': 494, '11': 391, '10': 80, '01': 59}" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c = tc.Circuit(2)\n", + "c.H(0)\n", + "c.cx(0, 1)\n", + "\n", + "t = tc.cloud.apis.submit_task(device=d, circuit=c, shots=1024)\n", + "\n", + "t.results() # this will wait until the result is return" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "33b9eb5a", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
     ┌───┐     \n",
+       "q_0: ┤ H ├──■──\n",
+       "     └───┘┌─┴─┐\n",
+       "q_1: ─────┤ X ├\n",
+       "          └───┘
" + ], + "text/plain": [ + " ┌───┐ \n", + "q_0: ┤ H ├──■──\n", + " └───┘┌─┴─┐\n", + "q_1: ─────┤ X ├\n", + " └───┘" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c.draw()" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "88cfc4ad", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tc.results.counts.plot_histogram(t.results())" + ] + }, + { + "cell_type": "markdown", + "id": "0596e9f1", + "metadata": {}, + "source": [ + "Check with the analytical exact result is easy, just use tensorcircuit's sota tensornetwork based simulation engine. The answer is a quantum state as $\\vert 00\\rangle + \\vert 11\\rangle$" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "dd798dd7", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.49999997 0. 0. 0.49999997]\n", + "{'00': 0.4999999701976776, '11': 0.4999999701976776}\n" + ] + } + ], + "source": [ + "p = c.probability()\n", + "print(p)\n", + "exact_result = tc.results.counts.vec2count(p, prune=True)\n", + "print(exact_result)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "0d5ca58d", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tc.results.counts.plot_histogram([t.results(), exact_result])\n", + "# experiment vs exact" + ] + }, + { + "cell_type": "markdown", + "id": "d48cb1c1", + "metadata": {}, + "source": [ + "Let us further investigate the Task object ``t`` returned by ``submit_task``, it contains enriched information on manager, compiling, etc." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "598448da", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'id': '3a8840fa-1831-48c3-85fd-67a66523ed8f',\n", + " 'queue': 'txq.low',\n", + " 'device': 'tianxuan_s1?o=3',\n", + " 'qubits': 2,\n", + " 'depth': 3,\n", + " 'state': 'completed',\n", + " 'shots': 1024,\n", + " 'prior': 1,\n", + " 'at': datetime.datetime(2023, 5, 31, 11, 45, 7, 695261),\n", + " 'ts': {'completed': datetime.datetime(2023, 5, 31, 11, 45, 7, 695261),\n", + " 'pending': datetime.datetime(2023, 5, 31, 11, 45, 6, 364959),\n", + " 'scheduled': datetime.datetime(2023, 5, 31, 11, 45, 6, 359719)},\n", + " 'md5': '9cb407b41938a256ec15dfec163dca1d',\n", + " 'runAt': 1685504730279662,\n", + " 'runDur': 1016276,\n", + " 'source': 'OPENQASM 2.0;\\ninclude \"qelib1.inc\";\\nqreg q[2];\\nh q[0];\\ncx q[0],q[1];',\n", + " 'version': '1',\n", + " 'lang': 'OPENQASM',\n", + " 'result': {'00': 494, '01': 59, '10': 80, '11': 391},\n", + " 'optimization': {'progs': [{'code': 'Tencent Quantum Program\\nversion 1.0\\nqubit involved: q0,q1,q2,q3,q4,q5,q6,q7,q8\\n# section: eqasm\\n# section lines 3\\neqasm program\\nbs 1 H q0\\nbs 1 CX (q0, q1)\\nMEASZ q0,q1\\n# section: end\\n',\n", + " 'lang': 'QEXE'},\n", + " {'code': 'Tencent Quantum Program\\nversion 1.0\\nqubit involved: q0,q1,q2,q3,q4,q5,q6,q7,q8\\n# section: eqasm\\n# section lines 3\\neqasm program\\nbs 1 H q0\\nbs 1 CX (q0, q1)\\nMEASZ q0,q1\\n# section: end\\n',\n", + " 'lang': 'QEXE_COMPACT'}],\n", + " 'pairs': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7, 8: 8}},\n", + " 'results': {'00': 494, '01': 59, '10': 80, '11': 391},\n", + " 'frontend': ,\n", + " 'backend': }" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "t.details(prettify=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "c6a539ab", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'completed'" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "t.status()" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "b3fcd4ec", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'3a8840fa-1831-48c3-85fd-67a66523ed8f'" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "t.id_" + ] + }, + { + "cell_type": "markdown", + "id": "f951f18c", + "metadata": {}, + "source": [ + "The task can be retrieved from cloud with the id without task object `t`" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "00e6c83d", + "metadata": {}, + "outputs": [], + "source": [ + "t1 = tc.cloud.apis.get_task(t.id_)" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "19a5e66b", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
     ┌───┐     \n",
+       "q_0: ┤ H ├──■──\n",
+       "     └───┘┌─┴─┐\n",
+       "q_1: ─────┤ X ├\n",
+       "          └───┘
" + ], + "text/plain": [ + " ┌───┐ \n", + "q_0: ┤ H ├──■──\n", + " └───┘┌─┴─┐\n", + "q_1: ─────┤ X ├\n", + " └───┘" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "t1.details(prettify=True)[\"frontend\"].draw()\n", + "# exactly the task we submitted" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "1e7520af", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'00': 494, '11': 391, '10': 80, '01': 59}" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "t1.results()" + ] + }, + { + "cell_type": "markdown", + "id": "303cf6c3", + "metadata": {}, + "source": [ + "Task group management is also possible but not shown here. Try using ``group`` argument when ``submit_task`` and ``list_task`` when retrieving." + ] + }, + { + "cell_type": "markdown", + "id": "ce9f8313", + "metadata": {}, + "source": [ + "## Cloud simulator\n", + "\n", + "We can also submit tasks to run on tc simulators on the cloud, the only thing you need to change is the device name, and now the result becomes exact." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "adadefd1", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'11': 546, '00': 478}" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c = tc.Circuit(2)\n", + "c.H(0)\n", + "c.cx(0, 1)\n", + "\n", + "t = tc.cloud.apis.submit_task(device=\"simulator:tc\", circuit=c, shots=1024)\n", + "\n", + "t.results() # this will wait until the result is return\n", + "# instead, using wait=False for t.results(wait=False), the task objects can be returned in async mode" + ] + }, + { + "cell_type": "markdown", + "id": "c00c7dde", + "metadata": {}, + "source": [ + "**Batch submission:** Tasks can also submitted in batch, either on real devices or on simulators, a list of task object is returned by ``submit_task``, if the circuit submitted is in a list. In this way, the joint tasks are executed on the QPU at the same time so that the noise profile remains consistent." + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "7f57f4e2", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'10': 524, '00': 500}\n", + "{'00': 519, '01': 505}\n" + ] + } + ], + "source": [ + "c1 = tc.Circuit(2)\n", + "c1.h(0)\n", + "\n", + "c2 = tc.Circuit(2)\n", + "c2.h(1)\n", + "\n", + "ts = tc.cloud.apis.submit_task(device=\"simulator:tc\", circuit=[c1, c2], shots=1024)\n", + "for t in ts:\n", + " print(t.results())" + ] + }, + { + "cell_type": "markdown", + "id": "1e72f1ab", + "metadata": {}, + "source": [ + "## Compling: gate decomposition and qubit mapping" + ] + }, + { + "cell_type": "markdown", + "id": "7bea5aba", + "metadata": {}, + "source": [ + "Say we want to simulate the following logic circuit, however, the gate set and the coupling for two-qubit gates are both incompatible with our real device" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "2fc080c9", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c = tc.Circuit(5)\n", + "c.rx(0, theta=1.5708)\n", + "for i in range(4):\n", + " c.cx(i, i + 1)\n", + "c.measure_instruction(*range(5))\n", + "# note for tasks involving qubit mapping, we recommend you add the measure instruction explicitly\n", + "c.draw(output=\"mpl\")" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "ea2b3692", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'00000': 4014, '11111': 4178}" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# the ideal answer with shot noise\n", + "c.sample(allow_state=True, batch=8192, format=\"count_dict_bin\")" + ] + }, + { + "cell_type": "markdown", + "id": "79349e8e", + "metadata": {}, + "source": [ + "The target state we prepare is the so called GHZ state (here is GHZ-5), which is also famuous as Schordinger cat state, as it is a superposition of two very different (macroscopic) quantum states: $\\vert 00000\\rangle + \\vert 11111\\rangle$. GHZ state is also a great measure to determine the quality of the quantum hardware.\n", + "\n", + "\n", + "By default the **backend compiler** options are both enabled which we write expicitly below" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "f381a9f7", + "metadata": {}, + "outputs": [], + "source": [ + "t = tc.cloud.apis.submit_task(\n", + " circuit=c,\n", + " shots=8192,\n", + " device=d,\n", + " enable_qos_gate_decomposition=True,\n", + " enable_qos_qubit_mapping=True,\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "0704b37f", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'00000': 3794,\n", + " '11111': 862,\n", + " '00010': 584,\n", + " '10000': 311,\n", + " '00011': 258,\n", + " '01111': 254,\n", + " '00110': 221,\n", + " '10111': 188,\n", + " '00111': 176,\n", + " '11101': 169,\n", + " '11000': 128,\n", + " '00100': 113,\n", + " '11100': 104,\n", + " '10010': 102,\n", + " '01010': 89,\n", + " '00001': 87,\n", + " '10100': 84,\n", + " '11110': 79,\n", + " '11011': 78,\n", + " '01011': 71,\n", + " '01000': 66,\n", + " '01101': 63,\n", + " '01110': 63,\n", + " '10110': 49,\n", + " '01100': 43,\n", + " '10011': 42,\n", + " '00101': 26,\n", + " '10101': 25,\n", + " '10001': 18,\n", + " '01001': 15,\n", + " '11001': 15,\n", + " '11010': 15}" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "rb = t.results()\n", + "rb" + ] + }, + { + "cell_type": "markdown", + "id": "9847ccaa", + "metadata": {}, + "source": [ + "We can inspect the circuit compiled after the backend server compiling:" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "id": "24748fe7", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "t.details(prettify=True)[\"backend\"].draw(idle_wires=False, output=\"mpl\")" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "5f0ad718", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{0: 1, 1: 3, 2: 2, 3: 0, 4: 4, 5: 5, 6: 6, 7: 7, 8: 8}" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "t.get_logical_physical_mapping() # the logical qubit - physical qubit mapping is also returned by the server" + ] + }, + { + "cell_type": "markdown", + "id": "98b2b053", + "metadata": {}, + "source": [ + "To better customize and use the advanced compiling system, we strongly recommend the users to compile the circuit before task submission as **frontend compiling**" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "4debc9ad", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'logical_physical_mapping': {0: 6, 1: 2, 2: 0, 3: 4, 4: 8}, 'positional_logical_mapping': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4}}\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c1, info = tc.compiler.default_compile(\n", + " c, compiled_options={\"coupling_map\": d.topology()}\n", + ")\n", + "print(info)\n", + "c1.draw(idle_wires=False, output=\"mpl\")" + ] + }, + { + "cell_type": "markdown", + "id": "258236df", + "metadata": {}, + "source": [ + "We now submit the compiled circuit ``c1`` for the qcloud, with now the ``logical_physical_mapping`` in ``info``, the result is improved with tc built in compiler" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "id": "3a165a8c", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'00000': 3506,\n", + " '11111': 1962,\n", + " '01111': 523,\n", + " '11011': 279,\n", + " '10000': 262,\n", + " '11110': 257,\n", + " '10111': 174,\n", + " '11000': 167,\n", + " '00111': 148,\n", + " '11101': 109,\n", + " '01000': 92,\n", + " '01011': 90,\n", + " '00001': 87,\n", + " '01110': 85,\n", + " '00011': 80,\n", + " '11100': 72,\n", + " '11010': 45,\n", + " '00100': 42,\n", + " '10011': 31,\n", + " '00110': 24,\n", + " '01101': 24,\n", + " '00010': 22,\n", + " '10110': 18,\n", + " '11001': 17,\n", + " '01100': 16,\n", + " '01010': 15,\n", + " '10100': 11,\n", + " '00101': 10,\n", + " '10001': 10,\n", + " '10101': 8,\n", + " '01001': 4,\n", + " '10010': 2}" + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "t = tc.cloud.apis.submit_task(\n", + " circuit=c1,\n", + " shots=8192,\n", + " device=d,\n", + " enable_qos_gate_decomposition=False,\n", + " enable_qos_qubit_mapping=False,\n", + ")\n", + "rf = t.results()\n", + "rf" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "22d46c41", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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h50TNrKmZ/RpoAbwHdAUygCkVbcIQnA4cGC7KBTaF7Su8C3xXpc2M8LUVXgcygS61viMiItKoxe1IFILzlUABkEIQiMe5+ydmVhGCq6q8ZBXQIXyeAayJPZp0dzez1eG6ijZF1WyjYt2SamoaDYwGyMzMZOrUqQB069aNli1bMmfOHAD22msvsrKymD59OgBJSUnk5eUxe/ZsNm7cCEBOTg6rVq0Cuu/afxCJrDbep6+++gqAnj17kpyczNy5cwFo27YtvXr1Ij8/H4Dk5GRyc3MpLCxk06ZNAAwdOpSioiKWL18OQO/evWnatCnz588HICMjg65du1JQUABAamoqQ4cOZebMmZSUBN/xcnNzWbJkCStXrgSgX79+bNu2jYULFwLQoUMHOnbsyMyZMwFo0aIFOTk5FBQUUFpaCkBeXh6LFi1i9erVAPTv35/S0lI+++wzADp16kS7du0oLCwEID09nezsbPLz8ykrKwNg2LBhzJs3j2+//RaAQYMGUVxczOLFiwHo0qULbdq0Yfbs2QC0bt2aQYMGMW3aNNwdM2P48OHMmTOHdevWAZCdnc3atWtZunSp3qcdvE+wN/VNfn7+Lr1P33zzDWeeeSbr1q0jKSmJCy+8kOzsbG666SaWL19OWloaq1evJi0tjQcffJBNmzYxduxYNm/eTFJSErfccgvDhw/f7n264oormDdvHg8//HDc/3/6MRbPHk4zaw7sC+wJ/Ao4DzgYSCc4quzs7l/GtH8I6ODuI83sWuBcd+9WZZuLgQfc/VYzmwIUufvZMev3BZYBB1Z0A+9ITk6OV3zY/BTn3fWTNxFXY/86LtEl1Fj3heMSXYLIT1LfPicAHhiza+1WrFjBihUryM7Opri4mP3224/nnnuOfv36Vba5/PLL2XPPPbnhhhv48MMPadeuHZmZmcydO5eRI0dWfvEB+Pe//83TTz/Nxx9/XPklKp7MbJa751S3Lq7due6+1d0/d/dZ7n4N8BFwKbAybNKuykvaxaxbCewTO9I2fN62SpvqtkFMGxER2Y3at29PdnY2AC1btqRv377bhaK78+STT3LKKacAMGTIEDIzMwHIysqipKSk8ghw06ZNTJgwgeuvvz7Oe7FrEn2daBMgmaCbdSUwomKFmaUAB/Gfc6AFBOdQc2NenwvsUaXNQeFrK4wAvgaW1n75IiLyY5YuXcqHH37I0KFDK5fNmDGDdu3a0bNnzx+0f+aZZ8jOziY5ORmA3//+91x++eWkpaXFreaaiOd1oreZ2UFm1iW8lvNWgq7cx8PznHcBV5vZ8WbWH3iE4LzpPwDcfQHwGsFI3VwzywUmAS+FI3MJ224GHjGz/mZ2PDAW0MhcEZE427RpEyeccAJ33XUX6enplcufeOKJyqPQWPPmzePqq69m0qRJAHz00Ud88cUXHHfccXGruabiObAoA/jf8N8NwMfAL9z99XD9H4FU4F6gNTATONzdi2O2cSowkWDELcALwEUVK919g5mNCLdRCKwD7gQm7KZ9EhGRanz//feccMIJnHbaaRx//PGVy8vKyvj3v//NrFmztmtfVFTEcccdx2OPPUb37sHgzIKCAgoLC+nSpQtlZWWsXr2agw8+uHJgYV0Qz+tEz9zJegfGhY8dtVkHjNrJdj4BhtW4QBERqRXuzjnnnEPfvn257LLt57p588036dOnDx07dqxctn79eo466ihuu+02fv7zn1cuv+CCC7jggguAoFv46KOPrlMBCok/JyoiIg3Mu+++y+TJk3n77bcZPHgwgwcP5pVXXgHgn//85w+6cu+55x4+//xzxo8fX9m+4jKTui6u14mKiEjDl5eXx46GoTzyyCM/WHb99dfvdPRtly5dEnJ5y87oSFRERCQihaiIiEhEClEREZGIFKIiIiIRKURFREQiUoiKiIhEpBAVERGJSCEqIiISkUJUREQkIs1YJCIiu+SL3uMSXUKNdF84brf/Dh2JioiIRKQQFRERiUghKiIiEpFCVEREJCKFqIiISEQKURERkYgUoiIiIhEpREVERCJSiIqIiESkEBUREYlIISoiIhKRQlRERCQihaiIiEhEClEREZGIFKIiIiIRKURFREQiUoiKiIhEpBAVERGJSCEqIiISkUJUREQkIoWoiIhIRApRERGRiHY5RM1smJklVbM8ycyG1W5ZIiIidV9NjkTfAdpUs3zPcJ2IiEijUpMQNcCrWb4X8F3tlCMiIlJ//KB7tiozeyF86sD/mllpzOqmQH/gvd1Qm4iISJ220xAFvg3/NWAdUBKzbiuQDzxQy3WJiIjUeTsNUXc/C8DMlgJ3uLu6bkVERNi1I1EA3P2m3VmIiIhIfbPLIWpmbYBbgMOAtlQZlOTu6bVbmoiISN22yyEK/B0YAvwN+JrqR+qKiIg0GjUJ0cOAEe4+c3cVIyIiUp/U5DrR1cCm3VWIiIhIfVOTEL0OGG9mLXZXMSJS/5x99tm0bduW/v37Vy6bM2cOubm5DBgwgGOOOYaNGzdWrvv444/Jzc0lKyuLAQMGsGXLFjZv3sxRRx1Fnz59yMrKYuzYsYnYFZEaq0mIXg8cDqw2swVm9nHsYzfVJyJ13Jlnnslrr7223bJzzz2X2267jU8++YTjjjuOP/3pTwCUlZUxatQo7r//fubNm8fUqVNp1qwZAFdccQWffvopH374Ie+++y6vvvpq3PdFpKZqck706d1WhYjUW8OGDWPp0qXbLVu0aBHDhgX3pRgxYgQjR47k5ptvZsqUKQwcOJBBgwYBsNdeewGQlpbGIYccAkDz5s3Jzs6mqKgofjshEpGuExWRWpeVlcXzzz/Psccey1NPPcVXX30FBOFqZowcOZI1a9bw61//mquuumq7165fv54XX3yR3/3ud4koXaRGdD9REal1Dz30EPfddx/77bcfxcXFNG/eHAi6c/Pz83n88cfJz8/n2Wef5a233qp8XVlZGaeccgqXXHIJ3bp1S1T5IrusJpMtFPMj14ZqsgURqdCnTx+mTJkCBEefL7/8MgAdO3Zk2LBh7L333gAceeSRzJ49m8MOOwyA0aNH07NnT8aMGZOQukVqqiZHohcBF8c8LgMmA5sJRu6KiACwevVqAMrLy/nDH/7Ab3/7WwBGjhzJJ598wubNmykrK2PatGn069cPgOuvv54NGzZw1113JapskRqryTnRR6tbbmazCSZimFhbRYlI/XHKKacwdepUvvnmGzp27MhNN93Epk2buPfeewE4/vjjOeusswBo3bo1l112Gfvvvz9mxpFHHslRRx1FUVERt9xyC3369CE7OxuAiy66iHPPPTdh+yWyK2oyOndH3gHuqoXtiEg99MQTT1S7fEcDg0aNGsWoUaO2W9axY0fcNZOo1D+1MbDo18A3O2tkZteY2QdmttHM1pjZi2bWv0obM7NxZva1mZWY2VQzy6rSprWZTTazDeFjspm1qtJmgJlNC7ex3MxuMDOrhX0VERGpVJOBRZ+w/cAiA9oBbYALdmETBwP3AR+Erx0PvGlm/dx9bdjmKuBy4ExgIXAD8IaZ9Xb34rDNP4B9gSPCnx8kODd7TFhnOvAGMB3YH+gDPAx8B9y5q/srIiKyMz9lsoVyYA0w1d0/3dmL3X1k7M9m9htgA/Bz4MXwSHEMcJu7PxO2OYNgzt5TgUlm1pcgPPPcvSBscz4wIwzahcBpQBpwhruXAHPNrA9wmZlNcPUZiYhILUnkZAstCbqT14U/dwUygCkxv7PEzKYDBwKTgFyCSfDfi9nOuwRHmQcSHL3mAjPCAK3wOnAz0AVYUsv7ISIijVSNBxaZ2aFAP4Ku3XnuPjXi7/4L8BFQEP6cEf67qkq7VUCHmDZrYo8m3d3NbHXM6zOAqvOFrYpZt12ImtloYDRAZmYmU6dOBaBbt260bNmSOXPmAMH0ZFlZWUyfPh2ApKQk8vLymD17duXk2jk5OaxatQrovmv/BSSy2nifKmbR6dmzJ8nJycydOxeAtm3b0qtXL/Lz8wFITk4mNzeXwsJCNm0KbmQ0dOhQioqKWL58OQC9e/emadOmzJ8/H4CMjAy6du1KQUHw552amsrQoUOZOXMmJSXB97vc3FyWLFnCypUrAejXrx/btm1j4cKFAHTo0IGOHTsyc2Zw98EWLVqQk5NDQUEBpaWlAOTl5bFo0aLKS0r69+9PaWkpn332GQCdOnWiXbt2FBYWApCenk52djb5+fmUlZUBwbR98+bN49tvvwVg0KBBFBcXs3jxYgC6dOlCmzZtmD17NhCMsB00aBDTpk3D3TEzhg8fzpw5c1i3LvhOnJ2dzdq1ayunA9T79MP3CYJrZWX3WbFiRa38//RjbFd7N82sA/AssB/BTbkBMoFC4Dh3/3pHr61mWxMIBiTlufvicNmBBEeVnd39y5i2DwEd3H2kmV0LnOvu3apsbzHwgLvfamZTgCJ3Pztm/b7AMuDAim7g6uTk5HjFh81Pcd5dP3kTcTX2r+MSXUKNdV84LtEliPwk9e1zAurfZ0VtfU6Y2Sx3z6luXU1G594NbAN6uHsnd+8E9AyX3V2DYv4MnAIcWhGgoZXhv+2qvKRdzLqVwD6xI23D522rtKluG7G/Q0RE5CerSXfuCOBgd6/sDnX3xWZ2CfDWjl/2H2b2F+Bk4JBqBiMtIQi5EQQjeDGzFOAg4MqwTQHQguC8Z8V50Vxgj5ifC4DbzSzF3bfE1P41sHSX9lRE+KL3uESXUCPqnZBEqOl1otX1/e5Sf7CZ3QucRTDSdp2ZZYSPFhCc2ySYtOFqMzs+vIb0EYKBRP8I2ywAXiMYqZtrZrkEA45eCkfmErbdDDxiZv3N7HhgLKCRuSIiUqtqEqJvARPNrFPFgvBc413s2pHohQQjct8CVsQ8rohp80fgz8C9BOda2wOHx1wjCkEIzyEYcft6+Pw3FSvdfQPBkWfF+dp7Ca4PnbDLeyoiIrILatKdewnwArDYzGIHFn1CcI7zR7n7TmcMCo8Ux4WPHbVZB4za0fqwzSfAsJ39PhERkZ+iJteJfmVm2cD/I5gFCGCBu7+5WyoTERGp43banWtmvzCzpWaW7oE33H2iu08EPgjXjYhDrSIiInXKrpwTvQj4k7tvrLoiPP94O8F0fSIiIo3KroToQODHumzfBgbVTjkiIiL1x66E6D4Ek83viAN71U45IiIi9ceuhGgRwdHojgwEltdOOSIiIvXHroToy8DNZpZadYWZpRHcF/Tl2i5MRESkrtuVS1xuAX4FLDKze4CK6fr6Egw6MuB/dk95IiIidddOQ9TdV4d3WPkrQVhWTJrgBDMG/be7V719mYiISIO3S5MtuPsy4Egzaw30IAjSz8LZg0RERBqlGt2UOwzND3ZTLSIiIvVKTe/iIiIiIiGFqIiISEQKURERkYgUoiIiIhEpREVERCJSiIqIiESkEBUREYlIISoiIhKRQlRERCQihaiIiEhEClEREZGIFKIiIiIRKURFREQiUoiKiIhEpBAVERGJSCEqIiISkUJUREQkIoWoiIhIRApRERGRiBSiIiIiESlERUREIlKIioiIRKQQFRERiUghKiIiEpFCVEREJCKFqIiISEQKURERkYgUoiIiIhEpREVERCJSiIqIiESkEBUREYlIISoiIhKRQlRERCQihaiIiEhEClEREZGIFKIiIiIRKURFREQiUoiKiIhEpBAVERGJSCEqIiISkUJUREQkIoWoiIhIRApRERGRiOIaomY2zMxeMLPlZuZmdmaV9WZm48zsazMrMbOpZpZVpU1rM5tsZhvCx2Qza1WlzQAzmxZuY7mZ3WBmtvv3UEREGpN4H4m2AOYCvwNKqll/FXA5cDGwP7AaeMPMWsa0+QeQDRwRPrKByRUrzSwdeANYFW7jd8CVwGW1vC8icXHssceSkpJCSkoKnTt3Zv369ZSXl/Pzn/+c5s2bk5yczAknnADAhRdeSGpqKikpKbRs2ZInn3wywdWLNGxJ8fxl7v4K8AqAmT0Suy48UhwD3Obuz4TLziAI0lOBSWbWlyA489y9IGxzPjDDzHq7+0LgNCANOMPdS4C5ZtYHuMzMJri77/49FakdhYWFvPzyy6xatYo2bdrQqVMnrrjiCsrLy1m5ciWbN28mKSmJefPmATBo0CDmz59P165dGT9+PGeffTYnnXRSgvdCpOGqS+dEuwIZwJSKBWEITgcODBflApuA92Je9y7wXZU2M8LXVngdyAS67I7CRXYnd2fdunVs2bKFrVu30r17d5588kn+9re/kZQUfA/OygrOepx//vl07doVgN/85jeUlFTX4SMitSWuR6I7kRH+u6rK8lVAh5g2a2KPJt3dzWx1zOszgKJqtlGxbknsCjMbDYwGyMzMZOrUqQB069aNli1bMmfOHAD22msvsrKymD59OgBJSUnk5eUxe/ZsNm7cCEBOTg6rVq0Cutdsz6XGauN9+uqrrwDo2bMnycnJzJ07F4C2bdvSq1cv8vPzAUhOTiY3N5fCwkI2bdoEwNChQykqKmL58uUA9O7dm6ZNmzJ//nwAMjIy6Nq1KwUFBQCkpqYydOhQZs6cWRlsubm5LFmyhJUrVwLQr18/tm3bxsKFCwHo0KEDWVlZ5Obm0qNHD8yMfffdl4MPPpjrrruOq6++mgULFpCcnMy1115LTk4O/fv3p7S0lM8++4xrrrmGzp07s2nTJgoLCwFIT08nOzub/Px8ysrKABg2bBjz5s3j22+/BYKj2eLi4tp9w+KgoKAgYe9Tx44dmTlzJgAtWrQgJyeHgoICSktLAcjLy2PRokWsXr0agP79+wN7x+G/SuO2YsWKn/w+VazbEUtU76aZbQIucvdHwp8PJDiq7OzuX8a0ewjo4O4jzexa4Fx371ZlW4uBB9z9VjObAhS5+9kx6/cFlgEHVnQDVycnJ8crPmx+ivPu+smbiKuxfx2X6BJqrPvCcYkuIS6WLFlCdnY27733Hp07d6Z79+4ce+yx3H///Rx99NG8+OKLXHXVVUyaNIkNGzZUvm7ChAlcc801zJ07l549e0b63V/0HldLexEf9e1vor59TkD9+6yorb8JM5vl7jnVratL3bkrw3/bVVneLmbdSmCf2JG24fO2VdpUt43Y3yFSL0ycOJF99tmHvn37kpaWxjHHHMOMGTNo3rw5V155JQC33XZb5VE2wNNPP83VV1/NCy+8EDlARWTX1KUQXUIQciMqFphZCnAQ/zkHWkAwwjc35nW5wB5V2hwUvrbCCOBrYOnuKFxkd8nKyuLLL7/km2++oby8nLfeeos+ffowZMgQHn74YQDuvvtu0tLSgKBL85RTTuGee+5h5MiRiSxdpFGI6zlRM2sB9Ah/bALsa2aDgbXu/qWZ3QVca2afAouA6wkGEv0DwN0XmNlrBCN1R4fbmQS8FI7MJWx7I/CImf0B6AWMBW7SyFypb8455xwee+wxOnTogJmRmZnJQw89xLp169h///1JSUmhWbNmlYF65plnsm3bNsaMGcOYMWNo0qQJ3333XYL3QqThivfAohzgnZifbwofjwJnAn8EUoF7gdbATOBwd48d5XAqMJFgxC3AC8BFFSvdfYOZjQi3UQisA+4EJtT+7ojsftOmTfvBsvT09MrBD7EqBlGISHzE+zrRqcAOZw4KjxTHhY8dtVkHjNrJ7/kEGBalRhERkV1Vl86JioiI1CsKURERkYjq0mQLIg1WvbwmMNEFiNQDOhIVERGJSCEqIiISkUJUREQkIoWoiIhIRApRERGRiBSiIiIiESlERUREIlKIioiIRKQQFRERiUghKiIiEpFCVEREJCKFqIiISEQKURERkYgUoiIiIhEpREVERCJSiIqIiESkEBUREYlIISoiIhKRQlRERCQihaiIiEhEClEREZGIFKIiIiIRKURFREQiUoiKiIhEpBAVERGJSCEqIiISkUJUREQkIoWoiIhIRApRERGRiBSiIiIiESlERUREIlKIioiIRKQQFRERiUghKiIiEpFCVEREJCKFqIiISEQKURERkYgUoiIiIhEpREVERCJSiIqIiESkEBUREYlIISoiIhKRQlRERCQihaiIiEhEClEREZGIFKIiIiIRKURFREQiUoiKiIhEpBAVERGJSCEqIiISkUJUREQkogYbomZ2oZktMbMtZjbLzA5KdE0iItKwNMgQNbOTgb8A/wMMAd4DXjWzfRNamIiINCgNMkSBy4BH3P0Bd1/g7hcDK4ALElyXiIg0IA0uRM2sObAfMKXKqinAgfGvSEREGipz90TXUKvMLBNYDgx39+kxy28ATnP33lXajwZGhz/2BhbGq9Y6ZG/gm0QXIXWO/i6kqsb6N9HZ3fepbkVSvCupa9z9b8DfEl1HIplZobvnJLoOqVv0dyFV6W/ihxpcdy7Bt6RtQLsqy9sBK+NfjoiINFQNLkTdfSswCxhRZdUIglG6IiIitaKhdudOACab2fvAu8BvgUzg/oRWVXc16u5s2SH9XUhV+puoosENLKpgZhcCVwHtgbnApbEDjURERH6qBhuiIiIiu1uDOycqIiISLwpRERGRiBSiIiIiESlEZTtmZjHPm8T+LCIi21OISlVNzKwbgLuXezjyTGEqImZ2QKJrqGs0OlcAMLMBwBXA/sAGoAyYCfyvu3+UwNIkAczMYr5ANQUqv1BJ42RmxwMXuHvViWwaNR2JSoV/A62BycArwBwgD/inmf3FzNomsjiJL3d3M+sbPt8W/mxhoEojYmYnhU8vBQrDZU2rnPpJSURtdUFDnbFIasDMTiX4QjXK3TeGy1oS3NXmCOAsINXMLgqnVZQGzsxOBP5lZu8BLwBPuPtXBPNSY2ZNgDSgq7t/krhKZXcKvzw/ZmaPhoseh+CLVbi+afj8RjN7191fSlCpCaMjUQHYF/gUKK5Y4O7F7l7o7n8guMn5fwGDE1OeJMDJwPvAAmAUUGBmr5jZ6WaW5u7lwDDgw0QWKbvdWqAt8CKQDEwws7Vm9oCZHeDu28ysC3A1MC+BdSaMzokKZvYz4B1gHHCfuxdXWW/AdOBVd/+f+Fco8WRmqcDL4eMxoDvBufJhwBCgKTAN6Acsc/cTE1SqxImZ5RL0PHwOnEjwJWswsB74Cljl7r9IVH2JpBAVAMzsOuA84FXgEYIjkFJ3LzWzzgTnSI90d90Jp4ELu/JHA8Xh/XYrlncgCM6hwGHAcGB/d5+VkEJlt6oYXBae78wEvnX3DeGX6jSgL3Bo2PwZd/8iUbUmkkK0kTOzJu5ebmbNCD44LyPo3p1LcAecTkAv4At3PzpxlUq8xXyIVpz3qlwO3AiMdvfMxFUou5OZJbl7mZmNAQYCE9x9bvj+7+3uaxJbYd2gc6KNXBigKe7+vbvf6+7dCY4y3iPowlsP3AOcm8AyJY7CUbiVl7jEDCKx8GcHDgT+lbgqZXdz97Lw6RhgNkHvFMAtwDNmNsXMshJRW12i0bmNmJllAL8CssPLGd4H/hXeMm562CbF3bcksEyJv6YxH6CVYq4bbQY8BzwT57okTmJ6IfYH9nD3e8LllwBnAg8RDDb8BY10QFEFHYk2bn8HLgbaEIyyPBiYbmaLzOy8sDtnS3g5gzQSFQEaXgv4g+tCw16L+9x9Vfyrk3iImVijF7DEzDLM7FfAMcCN7n49QZAekaga6wp9ODZSZnYocABwmLsfS3AudFj4mAZcA1wCQZdvgsqUODKzn5vZHDM718yah5MsVHTlJlXMpWxme2vShUbjDaA58E+C0zr/x3+68fcDvk5QXXWGQrTxGgZ84u5FAO6+xd03hKNvLyc4Sh1vZtmJLFLiajTQH7gZ2Gxmr5nZ0RAcnYZfpg4E/hfQXMoNXNilu5rgy/TnwB+Ace6+0cwGE4zOvjeBJdYJGp3bSJlZHvAs8Bt3f62a9UkE0/+96u5/jnd9En9mNg14DXiJoJfiRIIPyu+Bp4C7CQaYDXf3gYmqU3a/2IFl1azrDPyFoNf3uPhWVvdoYFHjNYvgmtB7zOxBgm6bT939u3B9C4JrAu9PUH0SR2aWCXwGrHX3T8xsPsF8yj0IRmufQDDwrBnBgBJp2CycYOH3BDMWvQvc5u5fu/syMzsfSE1ohXWEjkQbMTPrRHDu8/8B64APgJUE86PmAr3dvXfiKpR4MrO9gLRwjtzY5UkENye4GLjE3VsloDyJg4prgsP5tK8l6JnIAI4CugIbge7u/lkCy6xTFKKCmQ0kmB/1QILeidYE14lO0OTiUsHMngO2ufsJia5Fdo+YyVc+Bh519zvN7I/Avu7+azPrA9wFPOjuTye02DpC3bmNjJklE8w+cjzBhPMfA4XuflW4vjewFNiq+0dKBTNrQdBb8ZdE1yK7TxigGUA7grmTAc4BTg2fLwXSAX02hBSijc+fCAJ0BcH1oV2AlWb2PHC7uy9MYG1SR7n7JjP7rbuXJroW2e3WAjOADma2J8GX7anhuh7AIILxFIIucWlUzKwfwWwjZwNHhFP8ZQATCWYe+dTMzo+92a40bGbWzsx+Y2ZtdtIuJbwZgf42Gr4rw39vBR4FpofvfRfgemCqu29OVHF1jUK0cTkW+Mjdp7j7t+GMRGvc/TZ37wr8meDu9e0TWqXE0/UEH5Sfm9lTZnZk2OVfycz2BS4ys2R18TdMFV+Owtsi/o7gjk7vAXsAvcLLn94nGJF7Q6LqrIsUoo3LAqC9mfWA4AL6cCaalHD9A8Bmgvl0pXHIAW4nmGCjNcG1w0vMbGLMRBvnAerKbRw6Elwbvo7g/sKXEYzafx+4DThNt77bns6JNi7TgTLgJTO7AXg+/GAsA3D3JeF0bvqwbATCa0OLgCXu/rCZTSY45/VfwCnAheH1ot0ILneQBiqmh6Ef0NfMBrn7HIJJNp6quC1a4iqsu3SJSyMTfnD+GRhA8AH6PvB2+Py/CUbhdYmZdEEaKDPbg+CmyqvdfWaVdWkEUwBeQTAQraW7l8S/SokXMxtAMCK3LfAF8DDBPNofufv3iaytLlOINkLhRfVHAyMIjjJ6E3TlTQMmufs/E1ieJEh1U72Z2SMEF9cflJiqJJ7MLJ1gopWLgE4EI3U/IbjL0zvuviyB5dVJCtFGwsw6EnTVAXwHzAdKCEK0BcG50G/cfW1iKpR4C29x5z8yR2oq8DzwV3d/Nq7FScKZWXuCwYgnEtwS7TJ3fzKhRdVBCtFGwMwuILisZRBBWC4m6L59B3i66jRvIlB58+0cdy9IdC2SOOGXrd5AkbsXJ7qeukYh2sCFXbefA3cCfwX2IZgr92CCQQRfE8yHOv/H7twgDUcYjl2BZRpxK/LTKEQbODO7GBjl7kOrWZdHcEF1B+AAd/8m3vVJ/JnZGOAW4EmCO7V8AKypuAF32CYdOAh4w923JqJOkfpA14k2fFuBlmbWH4K5c82sOYC75wOnAVuAwxNXosTZyQSjsnsAzwEFwJ/MLC+c5g2CUdq/V4CK/DiFaMP3NFAOjDGzlu5e6u5bw/McuPuXwHqCi6ylgTOzfQhusv1AOOK2M/B3gtHa04G3zexqYAwwc0fbEZGAunMbsJh5Tv+L4O4bbQi68O4jGLLeERhGcK50gLsvTUCZEkfhiMtfA/Pd/fUq64YA54brWwOd3H15/KsUqT8Uoo2AmbUC9iW4X+hxwM/DVSsBAya7+7iEFCdxF1664u6+JXZC+YpBZWZ2C3Ckuw9JVI0i9YWm/WugzKwt8BuCOVG/IbgmdD2QD9wBNCM4J/aauy9KUJmSAO5eUhGe1UyukAacQDBbjYjshI5EG6hwppks4EWCWUfaEEz11wtYDVxfdao3adjCEbfFP3YZU3gzgpOBJzSoSGTnFKINUHiUUUzQJTc9Ztm+wFCC817dgJPcfXbCCpW4MrNJBKNy3ye4RnRjNW1aufv6eNcmUl9pdG7D1A9YQnB5CxDO7ea+LJy26xiCrt0TE1OexJuZnUJwS7M7Caby+5OZHWdm3cNzpBXnSh+tuBxKRHZOR6INUPhh+BKQBpwOfOHu5VXaXAyc4+6D41+hxJuZPQBsA/5IcFeWM4DuwELgFeAtgqnd/uLuzRNVp0h9oyPRBii8ZdV1BHehfww43cw6mVkLqBw8MhyYm7gqJV7MLImgZ2K9uy929zvcfQCwP8Gde84guPRpIjA5cZWK1D86Em3Awm653wO/JLhzSwGwhmDu3BXAue7+SeIqlHgxs9ZAO3f/NJyx6vvYAUZmdjLwBJDt7h8lqEyRekch2giEl7scRXBboy0ER6BPufuniaxLEiuctcrcfZuZnUfQlZuW6LpE6hOFaCNjZk2qnh8VMbPLgKbu/qdE1yJSnyhERaTi9mjb9AVLpGYUoiIiIhFpdK6IiEhEClEREZGIFKIiIiIRKURFREQiUoiKiIhEpBAVERGJ6P8D1MBU6xZ39A4AAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tc.results.counts.plot_histogram([rb, rf], number_to_keep=2)\n", + "# backend compiling vs frontend compiling" + ] + }, + { + "cell_type": "markdown", + "id": "60ba2314", + "metadata": {}, + "source": [ + "## Readout Error Mitigation" + ] + }, + { + "cell_type": "markdown", + "id": "acc9f9ab", + "metadata": {}, + "source": [ + "The above results can be further improved via readout error mitigation (a classical algorithmic postprocessing on the measurement results)" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "id": "da287ca9", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'00000': 3931.5654653719635,\n", + " '11111': 3736.9302177814375,\n", + " '11000': 156.2388037789295,\n", + " '00111': 139.79207327296174,\n", + " '10000': 82.70413218088015,\n", + " '10111': 62.54914892519676,\n", + " '11100': 40.2309011836783,\n", + " '00011': 34.01063384376864,\n", + " '01111': 5.923071025515406,\n", + " '00001': 2.0555526356691276}" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "mit = tc.results.rem.ReadoutMit(d.name + \"?o=0\")\n", + "mit.cals_from_system(9)\n", + "mr = mit.apply_correction(t.results(), qubits=5, **info)\n", + "mr" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "id": "1cbf19de", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "execution_count": 36, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tc.results.counts.plot_histogram([t.results(), mr], number_to_keep=2)\n", + "# raw vs mitigated" + ] + }, + { + "cell_type": "markdown", + "id": "73a6c287", + "metadata": {}, + "source": [ + "We can also collect the readout calibriation from the API, but the results can be wrose since it is not up to date" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "id": "43ea80ec", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "mit1 = tc.results.rem.ReadoutMit(d.name + \"?o=0\")\n", + "mit1.cals_from_api(9)\n", + "mr1 = mit1.apply_correction(t.results(), qubits=5, **info)\n", + "tc.results.counts.plot_histogram([mr, mr1], number_to_keep=2)\n", + "\n", + "# mitigated via real time calibriation vs. mitigated via api calibriation data" + ] + }, + { + "cell_type": "markdown", + "id": "8ec8d9c8", + "metadata": {}, + "source": [ + "Readout error mitigation in tc supports many other options for subset measurement, scalable mitigation for hundereds of qubits, customized calibriation in local and global mode and native error mitigated expectations, please refer to the API documentation for more interesting usages. For example, we can directly compute the expectation $$ (ideal value should be 1) as" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "id": "77e7d8e1", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(array(1.+0.j, dtype=complex64), 0.9584156264735034)" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "c.expectation_ps(z=[0, 1]), mit.expectation(t.results(), [0, 1])" + ] + }, + { + "cell_type": "markdown", + "id": "7b156c6f", + "metadata": {}, + "source": [ + "## High level API\n", + "\n", + "Ultimately, for near term quantum computing tasks, the users only want to evaluate some given observable expectation for a circuit without worrying too much details above: compilation, error mitigation, subset measruement, positional/logical/physical mapping etc. Therefore, for most of the applications, `batch_expectation_ps` method is all you need." + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "id": "f07070b5", + "metadata": {}, + "outputs": [], + "source": [ + "import logging\n", + "\n", + "logger = logging.getLogger(\"tensorcircuit.cloud\")\n", + "logger.setLevel(logging.INFO)\n", + "# ch = logging.StreamHandler()\n", + "# ch.setLevel(logging.INFO)\n", + "# logger.addHandler(ch)\n", + "\n", + "# we enable log for the high level API to see what happen behind the scene" + ] + }, + { + "cell_type": "markdown", + "id": "4f50a8f1", + "metadata": {}, + "source": [ + "$\\langle Z_0Z_1\\rangle$" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "id": "2100ff5d", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "INFO:tensorcircuit.cloud.wrapper:submit task on tencent::tianxuan_s1 for 1 circuits\n", + "INFO:tensorcircuit.cloud.wrapper:finished collecting count results of 1 tasks in 4.873 seconds\n", + "INFO:tensorcircuit.cloud.wrapper:submit task on tencent::tianxuan_s1 for 2 circuits\n", + "INFO:tensorcircuit.cloud.wrapper:finished collecting count results of 2 tasks in 7.6044 seconds\n" + ] + }, + { + "data": { + "text/plain": [ + "array([0.82589585])" + ] + }, + "execution_count": 40, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tc.cloud.wrapper.batch_expectation_ps(c, pss=[[3, 3, 0, 0, 0]], device=d)\n", + "# compute Z0Z1" + ] + }, + { + "cell_type": "markdown", + "id": "630b8791", + "metadata": {}, + "source": [ + "$\\langle Z_0Z_1\\rangle+0.5\\langle Z_1Z_2\\rangle$" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "id": "c405123f", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "INFO:tensorcircuit.cloud.wrapper:submit task on tencent::tianxuan_s1 for 1 circuits\n", + "INFO:tensorcircuit.cloud.wrapper:finished collecting count results of 1 tasks in 4.9699 seconds\n" + ] + }, + { + "data": { + "text/plain": [ + "array(1.54442738)" + ] + }, + "execution_count": 41, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tc.cloud.wrapper.batch_expectation_ps(\n", + " c, pss=[[3, 3, 0, 0, 0], [0, 3, 3, 0, 0]], device=d, ws=[1, 0.5]\n", + ")\n", + "# compute Z0Z1 + 0.5*Z1Z2" + ] + }, + { + "cell_type": "markdown", + "id": "0965380b", + "metadata": {}, + "source": [ + "The interface is also unifying the numerical simulation (exact) interface with QPU experiments, by spcifying the device as ``None``, we can obtain the expected result from tc simulator" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "id": "5744293b", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array(1.5+0.j)" + ] + }, + "execution_count": 42, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tc.cloud.wrapper.batch_expectation_ps(\n", + " c, pss=[[3, 3, 0, 0, 0], [0, 3, 3, 0, 0]], device=None, ws=[1, 0.5]\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "300cff3a", + "metadata": {}, + "source": [ + "The results with readout error mitigation disabled can become worse. Note how we cache the readout error calibriation within tc, so that REM is effcient to use." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "0e49467d", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "INFO:tensorcircuit.cloud.wrapper:submit task on tencent::tianxuan_s1 for 1 circuits\n", + "INFO:tensorcircuit.cloud.wrapper:finished collecting count results of 1 tasks in 3.6587 seconds\n" + ] + }, + { + "data": { + "text/plain": [ + "array(0.8828125)" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tc.cloud.wrapper.batch_expectation_ps(\n", + " c,\n", + " pss=[[3, 3, 0, 0, 0], [0, 3, 3, 0, 0]],\n", + " device=d,\n", + " ws=[1, 0.5],\n", + " with_rem=False,\n", + " shots=1024,\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "da002ef1", + "metadata": {}, + "source": [ + "**QPU support for tf/torch ML:** Above this API, we also have corresponding keras and torch layers for hybrid deployment" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "718d7215", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Z_i: [[3, 0, 0, 0, 0], [0, 3, 0, 0, 0], [0, 0, 3, 0, 0], [0, 0, 0, 3, 0], [0, 0, 0, 0, 3]]\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import tensorflow as tf\n", + "from functools import partial\n", + "\n", + "tc.set_backend(\"tensorflow\")\n", + "\n", + "pss = []\n", + "for i in range(5):\n", + " ps = [0 for _ in range(5)]\n", + " ps[i] = 3 # Z_i\n", + " pss.append(ps)\n", + "print(\"Z_i:\", pss)\n", + "\n", + "\n", + "def quantum_func(inputs, weights, device=None):\n", + " c = tc.Circuit(5)\n", + " for i in range(5):\n", + " c.rx(i, theta=inputs[i])\n", + " for i in range(5):\n", + " c.rz(i, theta=weights[0, i])\n", + " for i in range(5):\n", + " c.rx(i, theta=weights[1, i])\n", + " return tc.cloud.wrapper.batch_expectation_ps(c, pss=pss, device=device)\n", + "\n", + "\n", + "qlayer = tc.KerasLayer(quantum_func, [2, 5])\n", + "model = tf.keras.Sequential([qlayer, tf.keras.layers.Dense(1)])\n", + "inputs = tf.stack([0.1 * tf.ones([5]), 0.2 * tf.ones([5])])\n", + "model(inputs)" + ] + }, + { + "cell_type": "markdown", + "id": "f2b675fa", + "metadata": {}, + "source": [ + "``model`` is a model with quantum layer simulated using CPU/GPU and a classical layer on CPU/GPU while ``model1`` shares exactly the same architecture but is with quantum layer on real QPU while classical layer still live on CPU/GPU, namely, TC is powerful enough to handle these quantum-classical hybrid tasks with an interface familiar to any ML engineers." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "0ec02dac", + "metadata": { + "collapsed": true + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "INFO:tensorcircuit.cloud.wrapper:submit task on tencent::tianxuan_s1 for 1 circuits\n", + "INFO:tensorcircuit.cloud.wrapper:finished collecting count results of 1 tasks in 5.2411 seconds\n", + "INFO:tensorcircuit.cloud.wrapper:submit task on tencent::tianxuan_s1 for 1 circuits\n", + "INFO:tensorcircuit.cloud.wrapper:finished collecting count results of 1 tasks in 5.3121 seconds\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qlayer1 = tc.KerasHardwareLayer(partial(quantum_func, device=d), [2, 5])\n", + "model1 = tf.keras.Sequential([qlayer1, tf.keras.layers.Dense(1)])\n", + "model1(inputs)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "51620507", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Model: \"sequential\"\n", + "_________________________________________________________________\n", + " Layer (type) Output Shape Param # \n", + "=================================================================\n", + " quantum_layer (QuantumLayer (2, 5) 10 \n", + " ) \n", + " \n", + " dense (Dense) (2, 1) 6 \n", + " \n", + "=================================================================\n", + "Total params: 16\n", + "Trainable params: 16\n", + "Non-trainable params: 0\n", + "_________________________________________________________________\n", + "\n", + "\n", + "Model: \"sequential_1\"\n", + "_________________________________________________________________\n", + " Layer (type) Output Shape Param # \n", + "=================================================================\n", + " hardware_layer (HardwareLay multiple 10 \n", + " er) \n", + " \n", + " dense_1 (Dense) multiple 6 \n", + " \n", + "=================================================================\n", + "Total params: 16\n", + "Trainable params: 16\n", + "Non-trainable params: 0\n", + "_________________________________________________________________\n" + ] + } + ], + "source": [ + "model.summary()\n", + "print(\"\\n\")\n", + "model1.summary()" + ] + }, + { + "cell_type": "markdown", + "id": "3b5423ca", + "metadata": {}, + "source": [ + "we align the weights between the two models (numerical one vs hybrid one)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "ab5ca8a5", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "INFO:tensorcircuit.cloud.wrapper:submit task on tencent::tianxuan_s1 for 1 circuits\n", + "INFO:tensorcircuit.cloud.wrapper:finished collecting count results of 1 tasks in 5.5113 seconds\n", + "INFO:tensorcircuit.cloud.wrapper:submit task on tencent::tianxuan_s1 for 1 circuits\n", + "INFO:tensorcircuit.cloud.wrapper:finished collecting count results of 1 tasks in 5.2209 seconds\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model1.set_weights(model.get_weights())\n", + "model1(inputs)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.0" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/source/tutorials/qubo_problem.ipynb b/docs/source/tutorials/qubo_problem.ipynb new file mode 100644 index 00000000..a4779366 --- /dev/null +++ b/docs/source/tutorials/qubo_problem.ipynb @@ -0,0 +1,580 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "id": "6ddb8a88-779a-43f7-ae14-115463bd87f5", + "metadata": {}, + "source": [ + "# Solving QUBO Problem using QAOA\n", + "\n", + "## Overview\n", + "\n", + "In this tutorial, we will demonstrate how to solve quadratic unconstrained binary optimization (QUBO) problems using QAOA. There is a specific application for portfolio optimization and we will introduce it in another [tutorial](https://tensorcircuit.readthedocs.io/en/latest/tutorials/portfolio_optimization.html).\n", + "\n", + "## QUBO problem\n", + "\n", + "### What is QUBO?\n", + "\n", + "Quadratic unconstrained binary optimization (QUBO) is a type of problem that aims to optimize a quadratic objective function using binary variables. The primary goal of a QUBO problem is to determine the assignments of binary variables that minimize or maximize the quadratic objective function. These variables represent choices or decision variables that can be either selected (1) or not selected (0). The objective function captures the associated costs, benefits, or constraints related to these decisions.\n", + "\n", + "From a computational perspective, solving a QUBO problem is NP-hard. This classification implies that solving the optimal solution to a QUBO instance is believed to be computationally challenging, and no known polynomial-time algorithm that can efficiently solve all QUBO problems.\n", + "\n", + "However, a promising approach called Quantum Approximate Optimization Algorithm (QAOA), introduced in [this tutorial](https://tensorcircuit.readthedocs.io/en/latest/tutorials/qaoa.html), has the potential to offer significant advantages when applied to QUBO problem-solving. QAOA leverages inherent quantum parallelism and interference effects to explore the solution space more efficiently compared to classical methods. This efficiency can lead to faster and more optimal solutions. In QAOA, each qubit represents a binary variable, and the objective function is calculated as the expected value of a quantum state generated by the ansatz (a quantum circuit with parameters to be decided). The parameters in the ansatz are iteratively optimized by a classical algorithm to improve the solution quality.\n", + "\n", + "### General Case\n", + "\n", + "For the general QUBO case, we wish to minimize a cost function of the form\n", + "\n", + "$$ \n", + "x^T Q x\n", + "$$\n", + "\n", + "where $x\\in\\{0,1\\}^n$ and $Q\\in\\mathbb{R}^{n\\times n}$ is a real symmetric matrix.\n", + "\n", + "This function maps to an Ising Hamiltonian \n", + "\n", + "$$\n", + "\\frac{1}{2}\\left(\\sum_{i=1}^n C_{ii} + \\sum_{i{n_qubits}}\"\n", + " states.append(a)\n", + "\n", + " # Calculate the probabilities of each state using the circuit's probability method\n", + " probs = K.numpy(c.probability()).round(decimals=4)\n", + "\n", + " # Sort the states and probabilities in descending order based on the probabilities\n", + " sorted_indices = np.argsort(probs)[::-1]\n", + " if reverse == True:\n", + " sorted_indices = sorted_indices[::-1]\n", + " state_sorted = np.array(states)[sorted_indices]\n", + " prob_sorted = np.array(probs)[sorted_indices]\n", + "\n", + " print(\"\\n-------------------------------------\")\n", + " print(\" selection\\t |\\tprobability\")\n", + " print(\"-------------------------------------\")\n", + " if wrap == False:\n", + " for i in range(len(states)):\n", + " print(\"%10s\\t |\\t %.4f\" % (state_sorted[i], prob_sorted[i]))\n", + " # Print the sorted states and their corresponding probabilities\n", + " elif wrap == True:\n", + " for i in range(4):\n", + " print(\"%10s\\t |\\t %.4f\" % (state_sorted[i], prob_sorted[i]))\n", + " print(\" ... ...\")\n", + " for i in range(-4, -1):\n", + " print(\"%10s\\t |\\t %.4f\" % (state_sorted[i], prob_sorted[i]))\n", + " print(\"-------------------------------------\")" + ] + }, + { + "cell_type": "code", + "execution_count": 83, + "id": "da315228", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "-------------------------------------\n", + " selection\t |\tprobability\n", + "-------------------------------------\n", + " 10\t |\t 0.8848\n", + " 11\t |\t 0.1051\n", + " 01\t |\t 0.0093\n", + " 00\t |\t 0.0008\n", + "-------------------------------------\n" + ] + } + ], + "source": [ + "c = QAOA_ansatz_for_Ising(final_params, nlayers, pauli_terms, weights)\n", + "\n", + "print_result_prob(c)" + ] + }, + { + "cell_type": "code", + "execution_count": 84, + "id": "294ea9ce-5064-4176-94d0-8dbb7d1707f8", + "metadata": {}, + "outputs": [], + "source": [ + "def print_output(c):\n", + " n = c._nqubits\n", + " N = 2**n\n", + "\n", + " # Generate labels for the x-axis representing the binary states\n", + " x_label = r\"$\\left|{0:0\" + str(n) + r\"b}\\right>$\"\n", + " labels = [x_label.format(i) for i in range(N)]\n", + "\n", + " # Create a bar plot with the probabilities of each state\n", + " plt.bar(range(N), c.probability())\n", + "\n", + " # Set the x-axis ticks to the generated labels and rotate them for better visibility\n", + " plt.xticks(range(N), labels, rotation=70)" + ] + }, + { + "cell_type": "code", + "execution_count": 85, + "id": "fc1353ab-7a7a-4cdc-931c-3b90417c4961", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "print_output(c)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "c48e4a38", + "metadata": {}, + "source": [ + "## Improve the performance with CVaR\n", + "\n", + "Conditional Value-at-Risk (CVaR) is a risk measure that quantifies the potential loss beyond a certain threshold (alpha), considering the tail end of the distribution. As proposed by [Barkoutsos et al. (2020)](https://arxiv.org/abs/1907.04769), incorporating CVaR as an objective function in QAOA allows for addressing risk-averse optimization problems effectively. By optimizing for CVaR, the algorithm focuses on minimizing the expected value of the worst-case scenario, rather than solely optimizing for the mean or expected value, which usually leads to faster convergence to a more accurate result.\n", + "\n", + "To showcase the performance of CVaR, a more complicated QUBO problem is used. This QUBO problem is described as a randomly generated symmetric Q matrix. The Q matrix is:" + ] + }, + { + "cell_type": "code", + "execution_count": 86, + "id": "02ec55b6", + "metadata": {}, + "outputs": [], + "source": [ + "Q = np.array(\n", + " [\n", + " [-60.3657, 11.68835, 12.23445, 11.7274, 11.9959, 11.80955],\n", + " [11.68835, -59.7527, 11.6231, 13.23295, 11.96335, 12.44725],\n", + " [12.23445, 11.6231, -59.69535, 11.29525, 12.00035, 11.78495],\n", + " [11.7274, 13.23295, 11.29525, -59.12165, 12.1006, 12.5461],\n", + " [11.9959, 11.96335, 12.00035, 12.1006, -60.45515, 12.07545],\n", + " [11.80955, 12.44725, 11.78495, 12.5461, 12.07545, -59.9126],\n", + " ]\n", + ")\n", + "pauli_terms, weights, offset = QUBO_to_Ising(Q)" + ] + }, + { + "cell_type": "markdown", + "id": "76879a55", + "metadata": {}, + "source": [ + "Then let's define a function to classically brute-force calculate all feasible combinations of stocks and their associated cost. The results are printed below." + ] + }, + { + "cell_type": "code", + "execution_count": 87, + "id": "46e9cbd9", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "-------------------------------------\n", + " selection\t |\t cost\n", + "-------------------------------------\n", + " 110010\t |\t-109.2784\n", + " 100011\t |\t-108.9717\n", + " 011010\t |\t-108.7296\n", + " 111000\t |\t-108.7219\n", + " 101100\t |\t-108.6685\n", + " 001110\t |\t-108.4798\n", + " 001011\t |\t-108.3416\n", + " 101001\t |\t-108.3157\n", + " ...\t |\t ...\n", + "-------------------------------------\n" + ] + } + ], + "source": [ + "def print_Q_cost(Q, wrap=False, reverse=False):\n", + " n_stocks = len(Q)\n", + " states = []\n", + " for i in range(2**n_stocks):\n", + " a = f\"{bin(i)[2:]:0>{n_stocks}}\"\n", + " n_ones = 0\n", + " for j in a:\n", + " if j == \"1\":\n", + " n_ones += 1\n", + " states.append(a)\n", + "\n", + " cost_dict = {}\n", + " for selection in states:\n", + " x = np.array([int(bit) for bit in selection])\n", + " cost_dict[selection] = np.dot(x, np.dot(Q, x))\n", + " cost_sorted = dict(sorted(cost_dict.items(), key=lambda item: item[1]))\n", + " if reverse == True:\n", + " cost_sorted = dict(\n", + " sorted(cost_dict.items(), key=lambda item: item[1], reverse=True)\n", + " )\n", + " num = 0\n", + " print(\"\\n-------------------------------------\")\n", + " print(\" selection\\t |\\t cost\")\n", + " print(\"-------------------------------------\")\n", + " for k, v in cost_sorted.items():\n", + " print(\"%10s\\t |\\t%.4f\" % (k, v))\n", + " num += 1\n", + " if (num >= 8) & (wrap == True):\n", + " break\n", + " print(\" ...\\t |\\t ...\")\n", + " print(\"-------------------------------------\")\n", + "\n", + "\n", + "print_Q_cost(Q, wrap=True)" + ] + }, + { + "cell_type": "markdown", + "id": "04d4ea38", + "metadata": {}, + "source": [ + "The QAOA with CVaR and three different alpha (1, 0.25, 0.1) will be run and a callback function will be used to record the parameters during the solving procedure. When alpha is $1$, the complete measurement results are accepted and the model changes to the standard QAOA." + ] + }, + { + "cell_type": "code", + "execution_count": 88, + "id": "d3b386d6", + "metadata": {}, + "outputs": [], + "source": [ + "# Set the number of layers to 2\n", + "nlayers = 2\n", + "\n", + "# Define a list of alpha values\n", + "alpha_list = [0.1, 0.25, 1]\n", + "\n", + "\n", + "# Define the callback function to record parameter values\n", + "def record_param(xk):\n", + " xk_list.append(xk)\n", + "\n", + "\n", + "# Generate initial parameters randomly for all alpha\n", + "init_params = K.implicit_randn(shape=[2 * nlayers], stddev=0.5)\n", + "\n", + "# Create an empty list to store parameter values for each alpha\n", + "params_list = []\n", + "\n", + "# Iterate over each alpha value\n", + "for alpha in alpha_list:\n", + " # Create a new empty list for callback function\n", + " xk_list = []\n", + "\n", + " # Run the QUBO_QAOA_cvar function with the specified parameters\n", + " final_params = QUBO_QAOA_cvar(\n", + " Q,\n", + " nlayers,\n", + " alpha=alpha,\n", + " callback=record_param,\n", + " maxiter=100,\n", + " init_params=init_params,\n", + " )\n", + "\n", + " # Append the parameter values for the current alpha to the params_list\n", + " params_list.append(xk_list)" + ] + }, + { + "cell_type": "code", + "execution_count": 89, + "id": "b3da7c48", + "metadata": {}, + "outputs": [], + "source": [ + "best = 50 # Represents the binary number 110010\n", + "prob_list = [] # Create an empty list to store probabilities\n", + "loss_list = [] # Create an empty list to store loss values\n", + "\n", + "# Iterate three times\n", + "for i in range(3):\n", + " c = QAOA_ansatz_for_Ising(init_params, nlayers, pauli_terms, weights)\n", + " loss = [cvar_loss(nlayers, Q, 1000, alpha_list[i], True, init_params)]\n", + " prob = [c.probability()[best].numpy()]\n", + "\n", + " # Iterate 100 times\n", + " for j in range(100):\n", + " if j < len(params_list[i]) - 1:\n", + " params = params_list[i][j]\n", + " else:\n", + " pass\n", + " c = QAOA_ansatz_for_Ising(params, nlayers, pauli_terms, weights)\n", + " loss.append(cvar_loss(nlayers, Q, 1000, alpha_list[i], True, params))\n", + " prob.append(c.probability()[best].numpy())\n", + "\n", + " loss_list.append(loss) # Append the loss values to the loss_list\n", + " prob_list.append(prob) # Append the probability values to the prob_list" + ] + }, + { + "cell_type": "code", + "execution_count": 92, + "id": "d1f375ce", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "for loss in loss_list:\n", + " plt.plot(loss)\n", + "plt.legend([\"alpha = 0.1\", \"alpha = 0.25\", \"alpha = 1\"])\n", + "plt.xlabel(\"iterations\")\n", + "p = plt.ylabel(\"cost\")" + ] + }, + { + "cell_type": "markdown", + "id": "6a88dda3", + "metadata": {}, + "source": [ + "The depicted figure illustrates that utilizing CVaR results in quicker convergence towards a lower loss." + ] + }, + { + "cell_type": "code", + "execution_count": 93, + "id": "f81fdeae", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "for prob in prob_list:\n", + " plt.plot(prob)\n", + "plt.legend([\"alpha = 0.1\", \"alpha = 0.25\", \"alpha = 1\"])\n", + "plt.xlabel(\"iterations\")\n", + "p = plt.ylabel(\"probability of the best answer\")" + ] + }, + { + "cell_type": "markdown", + "id": "0ae45348", + "metadata": {}, + "source": [ + "The data presented in this figure indicates that QAOA with CVaR typically shows a higher probability of obtaining the correct measurement outcome." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "tc_dev", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/source/tutorials/sklearn_svc.ipynb b/docs/source/tutorials/sklearn_svc.ipynb new file mode 100644 index 00000000..5226eb08 --- /dev/null +++ b/docs/source/tutorials/sklearn_svc.ipynb @@ -0,0 +1,299 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Support Vector Classification with SKLearn\n", + "\n", + "Authored by [_Mark (Zixuan) Song_](https://marksong.tech)\n", + "\n", + "We use the `SKLearn` library to implement `SVC` in the following tutorial." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Overview\n", + "\n", + "The aim of this tutorial is to implant a quantum machine learning (QML) transformer into SVC pipeline. And this is a general introduction to connect `tensorcircuit` with `scikit-learn`." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Setup\n", + "\n", + "Install `scikit-learn` and `requests`. The data that is going to be used is [German Credit Data by UCI](http://home.cse.ust.hk/~qyang/221/Assignments/German/GermanData.csv)\n", + "\n", + "```bash\n", + "pip install scikit-learn requests\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "import tensorcircuit as tc\n", + "import tensorflow as tf\n", + "from sklearn.svm import SVC\n", + "from sklearn import metrics\n", + "from time import time\n", + "import requests\n", + "\n", + "K = tc.set_backend(\"tensorflow\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Data Preprocessing\n", + "\n", + "The data has 20 variables and each is a integer value. In order for the model to use the data, we need to normalize the data to between 0 and 1." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "def load_GCN_data():\n", + " link2gcn = \"http://home.cse.ust.hk/~qyang/221/Assignments/German/GermanData.csv\"\n", + " data = requests.get(link2gcn)\n", + " data = data.text\n", + " data = data.split(\"\\n\")[:-1]\n", + " x = None\n", + " y = None\n", + "\n", + " def destring(string):\n", + " string = string.split(\",\")\n", + " return_array = []\n", + " for i, v in enumerate(string):\n", + " if v[0] == \"A\":\n", + " return_array.append(int(v[1 + len(str(i)) :]))\n", + " else:\n", + " return_array.append(int(v))\n", + " return K.cast([return_array[:-1]], dtype=\"float32\"), K.cast(\n", + " [return_array[-1] - 1], dtype=\"int32\"\n", + " )\n", + "\n", + " for i in data:\n", + " if x is None:\n", + " temp_x, temp_y = destring(i)\n", + " x = K.cast(temp_x, dtype=\"float32\")\n", + " y = K.cast(temp_y, dtype=\"int32\")\n", + " else:\n", + " temp_x, temp_y = destring(i)\n", + " x = K.concat([x, temp_x], axis=0)\n", + " y = K.concat([y, temp_y], axis=0)\n", + " x = K.transpose(x)\n", + " nx = None\n", + " for i in x:\n", + " max_i = K.cast(K.max(i), dtype=\"float32\")\n", + " temp_nx = [K.divide(i, max_i)]\n", + " nx = K.concat([nx, temp_nx], axis=0) if nx is not None else temp_nx\n", + " x = K.transpose(nx)\n", + " return (x[:800], y[:800]), (x[800:], y[800:])\n", + "\n", + "\n", + "(x_train, y_train), (x_test, y_test) = load_GCN_data()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Quantum Model\n", + "\n", + "This quantum model takes in 1x20 matrices as input and output the state of 5 qbits. The model is shown below:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "def quantumTran(inputs):\n", + " c = tc.Circuit(5)\n", + " for i in range(4):\n", + " if i % 2 == 0:\n", + " for j in range(5):\n", + " c.rx(j, theta=(0 if i * 5 + j >= 20 else inputs[i * 5 + j]))\n", + " else:\n", + " for j in range(5):\n", + " c.rz(j, theta=(0 if i * 5 + j >= 20 else inputs[i * 5 + j]))\n", + " for j in range(4):\n", + " c.cnot(j, j + 1)\n", + " return c.state()\n", + "\n", + "\n", + "func_qt = tc.interfaces.tensorflow_interface(quantumTran, ydtype=tf.complex64, jit=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Wrapping Quantum Model into a SVC\n", + "\n", + "Convert quantum model into svc that can be trained." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "def quantum_kernel(quantumTran, data_x, data_y):\n", + " def kernel(x, y):\n", + " x = K.convert_to_tensor(x)\n", + " y = K.convert_to_tensor(y)\n", + " x_qt = None\n", + " for i, x1 in enumerate(x):\n", + " if i == 0:\n", + " x_qt = K.convert_to_tensor([quantumTran(x1)])\n", + " else:\n", + " x_qt = K.concat([x_qt, [quantumTran(x1)]], 0)\n", + " y_qt = None\n", + " for i, x1 in enumerate(y):\n", + " if i == 0:\n", + " y_qt = K.convert_to_tensor([quantumTran(x1)])\n", + " else:\n", + " y_qt = K.concat([y_qt, [quantumTran(x1)]], 0)\n", + " data_ret = K.cast(K.power(K.abs(x_qt @ K.transpose(y_qt)), 2), \"float32\")\n", + " return data_ret\n", + "\n", + " clf = SVC(kernel=kernel)\n", + " clf.fit(data_x, data_y)\n", + " return clf" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Create Traditional SVC" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "def standard_kernel(data_x, data_y, method):\n", + " methods = [\"linear\", \"poly\", \"rbf\", \"sigmoid\"]\n", + " if method not in methods:\n", + " raise ValueError(\"method must be one of %r.\" % methods)\n", + " clf = SVC(kernel=method)\n", + " clf.fit(data_x, data_y)\n", + " return clf" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Test\n", + "\n", + "Test the accuracy of the quantum model SVC with the test data and compare it with traditional SVC." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Accuracy:(linear as kernel) 0.78\n", + "time: 0.007764101028442383 seconds\n", + "\n", + "Accuracy:(poly as kernel) 0.75\n", + "time: 0.024492979049682617 seconds\n", + "\n", + "Accuracy:(rbf as kernel) 0.765\n", + "time: 0.011505126953125 seconds\n", + "\n", + "Accuracy:(sigmoid as kernel) 0.695\n", + "time: 0.010205984115600586 seconds\n", + "\n", + "Accuracy:(qml as kernel) 0.66\n", + "time: 3.0243749618530273 seconds\n" + ] + } + ], + "source": [ + "methods = [\"linear\", \"poly\", \"rbf\", \"sigmoid\"]\n", + "\n", + "for method in methods:\n", + " print()\n", + " t = time()\n", + "\n", + " k = standard_kernel(data_x=x_train, data_y=y_train, method=method)\n", + " y_pred = k.predict(x_test)\n", + " print(\"Accuracy:(%s as kernel)\" % method, metrics.accuracy_score(y_test, y_pred))\n", + "\n", + " print(\"time:\", time() - t, \"seconds\")\n", + "\n", + "print()\n", + "t = time()\n", + "\n", + "k = quantum_kernel(quantumTran=func_qt, data_x=x_train, data_y=y_train)\n", + "y_pred = k.predict(x_test)\n", + "print(\"Accuracy:(qml as kernel)\", metrics.accuracy_score(y_test, y_pred))\n", + "\n", + "print(\"time:\", time() - t, \"seconds\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Issue with `SKLearn`\n", + "\n", + "Due to the limitation of `SKLearn`, `SKLearn`'s `SVC` is not fully compatible with quantum machine model (QML). \n", + "\n", + "This is because QML outputs a result as complex number (coordinate on the bloch sphere) whereas SKLearn only accept float. This is causing the result output by QML must be converted into float before it can be used in SVC, leading to a potential loss of accuracy.\n", + "\n", + "## Conclusion\n", + "\n", + "Due to the present limitation of SKLearn, quantum SVC is worse than traditional SVC in both accuracy and speed. However, if the limitation is removed, quantum SVC might be able to outperform traditional SVC in both accuracy." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "tc2", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.11" + }, + "orig_nbformat": 4 + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/docs/source/tutorials/sklearn_svc_cn.ipynb b/docs/source/tutorials/sklearn_svc_cn.ipynb new file mode 100644 index 00000000..c737dc72 --- /dev/null +++ b/docs/source/tutorials/sklearn_svc_cn.ipynb @@ -0,0 +1,299 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 结合SKLearn实现的支持向量分类\n", + "\n", + "[_Mark (Zixuan) Song_](https://marksong.tech) 撰写\n", + "\n", + "本示例结合了`sklearn`库中的`SVC`类，实现了支持向量分类。" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 概述\n", + "\n", + "本示例的目的是将量子机器学习（QML）转换器嵌入到SVC管道中并且介绍`tensorcircuit`与`scikit-learn`的一种连接方式。" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 设置\n", + "\n", + "安装 `scikit-learn` 和 `requests`. 本模型测试数据为 [德国信用]The data that is going to be used is [German Credit Data by UCI](http://home.cse.ust.hk/~qyang/221/Assignments/German/GermanData.csv)\n", + "\n", + "```bash\n", + "pip install scikit-learn requests\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import tensorcircuit as tc\n", + "import tensorflow as tf\n", + "from sklearn.svm import SVC\n", + "from sklearn import metrics\n", + "from time import time\n", + "import requests\n", + "\n", + "K = tc.set_backend(\"tensorflow\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 数据处理\n", + "\n", + "数据集包含20个变量，每个变量都是整数值。为了使模型能够使用数据，我们需要将数据归一化为0到1之间。" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "def load_GCN_data():\n", + " link2gcn = \"http://home.cse.ust.hk/~qyang/221/Assignments/German/GermanData.csv\"\n", + " data = requests.get(link2gcn)\n", + " data = data.text\n", + " data = data.split(\"\\n\")[:-1]\n", + " x = None\n", + " y = None\n", + "\n", + " def destring(string):\n", + " string = string.split(\",\")\n", + " return_array = []\n", + " for i, v in enumerate(string):\n", + " if v[0] == \"A\":\n", + " return_array.append(int(v[1 + len(str(i)) :]))\n", + " else:\n", + " return_array.append(int(v))\n", + " return K.cast([return_array[:-1]], dtype=\"float32\"), K.cast(\n", + " [return_array[-1] - 1], dtype=\"int32\"\n", + " )\n", + "\n", + " for i in data:\n", + " if x is None:\n", + " temp_x, temp_y = destring(i)\n", + " x = K.cast(temp_x, dtype=\"float32\")\n", + " y = K.cast(temp_y, dtype=\"int32\")\n", + " else:\n", + " temp_x, temp_y = destring(i)\n", + " x = K.concat([x, temp_x], axis=0)\n", + " y = K.concat([y, temp_y], axis=0)\n", + " x = K.transpose(x)\n", + " nx = None\n", + " for i in x:\n", + " max_i = K.cast(K.max(i), dtype=\"float32\")\n", + " temp_nx = [K.divide(i, max_i)]\n", + " nx = K.concat([nx, temp_nx], axis=0) if nx is not None else temp_nx\n", + " x = K.transpose(nx)\n", + " return (x[:800], y[:800]), (x[800:], y[800:])\n", + "\n", + "\n", + "(x_train, y_train), (x_test, y_test) = load_GCN_data()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 量子模型\n", + "\n", + "这个量子模型是输入为1x20的矩阵，并输出为5个量子比特的状态。模型如下所示：" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "def quantumTran(inputs):\n", + " c = tc.Circuit(5)\n", + " for i in range(4):\n", + " if i % 2 == 0:\n", + " for j in range(5):\n", + " c.rx(j, theta=(0 if i * 5 + j >= 20 else inputs[i * 5 + j]))\n", + " else:\n", + " for j in range(5):\n", + " c.rz(j, theta=(0 if i * 5 + j >= 20 else inputs[i * 5 + j]))\n", + " for j in range(4):\n", + " c.cnot(j, j + 1)\n", + " return c.state()\n", + "\n", + "\n", + "func_qt = tc.interfaces.tensorflow_interface(quantumTran, ydtype=tf.complex64, jit=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 将量子模型打包成SVC\n", + "\n", + "将量子模型打包成`SKLearn`能使用的SVC模型。" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "def quantum_kernel(quantumTran, data_x, data_y):\n", + " def kernel(x, y):\n", + " x = K.convert_to_tensor(x)\n", + " y = K.convert_to_tensor(y)\n", + " x_qt = None\n", + " for i, x1 in enumerate(x):\n", + " if i == 0:\n", + " x_qt = K.convert_to_tensor([quantumTran(x1)])\n", + " else:\n", + " x_qt = K.concat([x_qt, [quantumTran(x1)]], 0)\n", + " y_qt = None\n", + " for i, x1 in enumerate(y):\n", + " if i == 0:\n", + " y_qt = K.convert_to_tensor([quantumTran(x1)])\n", + " else:\n", + " y_qt = K.concat([y_qt, [quantumTran(x1)]], 0)\n", + " data_ret = K.cast(K.power(K.abs(x_qt @ K.transpose(y_qt)), 2), \"float32\")\n", + " return data_ret\n", + "\n", + " clf = SVC(kernel=kernel)\n", + " clf.fit(data_x, data_y)\n", + " return clf" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 创建传统SVC模型" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "def standard_kernel(data_x, data_y, method):\n", + " methods = [\"linear\", \"poly\", \"rbf\", \"sigmoid\"]\n", + " if method not in methods:\n", + " raise ValueError(\"method must be one of %r.\" % methods)\n", + " clf = SVC(kernel=method)\n", + " clf.fit(data_x, data_y)\n", + " return clf" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 测试对比\n", + "\n", + "测试量子SVC模型并于传统SVC模型进行对比。" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Accuracy:(linear as kernel) 0.78\n", + "time: 0.00810384750366211 seconds\n", + "\n", + "Accuracy:(poly as kernel) 0.75\n", + "time: 0.024804115295410156 seconds\n", + "\n", + "Accuracy:(rbf as kernel) 0.765\n", + "time: 0.011444091796875 seconds\n", + "\n", + "Accuracy:(sigmoid as kernel) 0.695\n", + "time: 0.010396003723144531 seconds\n", + "\n", + "Accuracy:(qml as kernel) 0.66\n", + "time: 6.472219228744507 seconds\n" + ] + } + ], + "source": [ + "methods = [\"linear\", \"poly\", \"rbf\", \"sigmoid\"]\n", + "\n", + "for method in methods:\n", + " print()\n", + " t = time()\n", + "\n", + " k = standard_kernel(data_x=x_train, data_y=y_train, method=method)\n", + " y_pred = k.predict(x_test)\n", + " print(\"Accuracy:(%s as kernel)\" % method, metrics.accuracy_score(y_test, y_pred))\n", + "\n", + " print(\"time:\", time() - t, \"seconds\")\n", + "\n", + "print()\n", + "t = time()\n", + "\n", + "k = quantum_kernel(quantumTran=func_qt, data_x=x_train, data_y=y_train)\n", + "y_pred = k.predict(x_test)\n", + "print(\"Accuracy:(qml as kernel)\", metrics.accuracy_score(y_test, y_pred))\n", + "\n", + "print(\"time:\", time() - t, \"seconds\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## `SKLearn`的局限性\n", + "\n", + "因为`SKLearn`的局限性，`SKLearn`的`SVC`并不完全兼容量子机器学习（QML）。\n", + "\n", + "这是因为QML输出的为复数（布洛赫球上的坐标），而`SKLearn`只接受浮点数。这导致QML输出的结果必须在使用SVC之前转换为浮点数，从而可能导致精度损失。\n", + "\n", + "## 结论\n", + "\n", + "由于`SKLearn`的局限性，量子SVC在准确性和速度上都不如传统SVC。但是，如果这种局限性被消除，量子SVC可能会在准确性上都优于传统SVC。" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "tc2", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.11" + }, + "orig_nbformat": 4 + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/docs/source/tutorials/tfim_vqe_diffreph_cn.ipynb b/docs/source/tutorials/tfim_vqe_diffreph_cn.ipynb index eca8c1ad..14a5cbea 100644 --- a/docs/source/tutorials/tfim_vqe_diffreph_cn.ipynb +++ b/docs/source/tutorials/tfim_vqe_diffreph_cn.ipynb @@ -420,7 +420,9 @@ "\n", "Jx = np.array([1.0 for _ in range(n - 1)]) # xx 相互作用的强度 (OBC)\n", "Bz = np.array([1.0 for _ in range(n)]) # 横向场强\n", - "hamiltonian_mpo = tn.matrixproductstates.mpo.FiniteTFI(Jx, Bz, dtype=dtype) # 矩阵乘积算子\n", + "hamiltonian_mpo = tn.matrixproductstates.mpo.FiniteTFI(\n", + " Jx, Bz, dtype=dtype\n", + ") # 矩阵乘积算子\n", "hamiltonian_mpo = quoperator_mpo(hamiltonian_mpo) # 从 mpo 生成 QuOperator" ] }, diff --git a/examples/analog_evolution_interface.py b/examples/analog_evolution_interface.py new file mode 100644 index 00000000..9cc00a9b --- /dev/null +++ b/examples/analog_evolution_interface.py @@ -0,0 +1,40 @@ +""" +jax backend is required, experimental built-in interface for parameterized hamiltonian evolution +""" + +import optax +import tensorcircuit as tc +from tensorcircuit.experimental import evol_global, evol_local + +K = tc.set_backend("jax") + + +def h_fun(t, b): + return b * tc.gates.x().tensor + + +hy = tc.quantum.PauliStringSum2COO([[2, 0]]) + + +def h_fun2(t, b): + return b[2] * K.cos(b[0] * t + b[1]) * hy + + +@K.jit +@K.value_and_grad +def hybrid_evol(params): + c = tc.Circuit(2) + c.x([0, 1]) + c = evol_local(c, [1], h_fun, 1.0, params[0]) + c.cx(1, 0) + c.h(0) + c = evol_global(c, h_fun2, 1.0, params[1:]) + return K.real(c.expectation_ps(z=[0, 1])) + + +opt = K.optimizer(optax.adam(0.1)) +b = K.implicit_randn([4]) +for _ in range(50): + v, gs = hybrid_evol(b) + b = opt.update(gs, b) + print(v, b) diff --git a/examples/analog_evolution_jax.py b/examples/analog_evolution_jax.py new file mode 100644 index 00000000..f5e92ca0 --- /dev/null +++ b/examples/analog_evolution_jax.py @@ -0,0 +1,42 @@ +""" +Parameterized Hamiltonian (Pulse control/Analog simulation) with AD/JIT support using jax ode solver +""" + +import optax +from jax.experimental.ode import odeint +import tensorcircuit as tc + +K = tc.set_backend("jax") +tc.set_dtype("complex128") + +hx = tc.quantum.PauliStringSum2COO([[1]]) +hz = tc.quantum.PauliStringSum2COO([[3]]) + + +# psi = -i H psi +# we want to optimize the final z expectation over parameters params +# a single qubit example below + + +def final_z(b): + def f(y, t, b): + h = b[3] * K.sin(b[0] * t + b[1]) * hx + K.cos(b[2]) * hz + return -1.0j * K.sparse_dense_matmul(h, y) + + y0 = tc.array_to_tensor([1, 0]) + y0 = K.reshape(y0, [-1, 1]) + t = tc.array_to_tensor([0.0, 10.0], dtype=tc.rdtypestr) + yf = odeint(f, y0, t, b) + c = tc.Circuit(1, inputs=K.reshape(yf[-1], [-1])) + return K.real(c.expectation_ps(z=[0])) + + +vgf = K.jit(K.value_and_grad(final_z)) + + +opt = K.optimizer(optax.adam(0.1)) +b = K.implicit_randn([4]) +for _ in range(50): + v, gs = vgf(b) + b = opt.update(gs, b) + print(v, b) diff --git a/examples/analog_evolution_mint.py b/examples/analog_evolution_mint.py new file mode 100644 index 00000000..0af4fc04 --- /dev/null +++ b/examples/analog_evolution_mint.py @@ -0,0 +1,36 @@ +""" +jax backend analog evolution targeting at minimizing evolution time +""" + +import optax +import tensorcircuit as tc +from tensorcircuit.experimental import evol_global + +K = tc.set_backend("jax") + +hx = tc.quantum.PauliStringSum2COO([[1]]) + + +def h_fun(t, b): + return K.sin(b) * hx + + +def fast_evol(t, b): + lbd = 0.08 + c = tc.Circuit(1) + c = evol_global(c, h_fun, t, b) + loss = K.real(c.expectation_ps(z=[0])) + return loss + lbd * t**2, loss + # l2 regularization to minimize t while target z=-1 + + +vgf = K.jit(K.value_and_grad(fast_evol, argnums=(0, 1), has_aux=True)) + +opt = K.optimizer(optax.adam(0.05)) +b, t = tc.array_to_tensor(0.5, 1.0, dtype=tc.rdtypestr) + +for i in range(500): + (v, loss), gs = vgf(b, t) + b, t = opt.update(gs, (b, t)) + if i % 20 == 0: + print(v, loss, b, t) diff --git a/examples/cotengra_setting_bench.py b/examples/cotengra_setting_bench.py new file mode 100644 index 00000000..d1b3f1b7 --- /dev/null +++ b/examples/cotengra_setting_bench.py @@ -0,0 +1,162 @@ +""" +Optimization for performance comparison with different cotengra settings. +""" + +import itertools +import sys +import warnings + +import cotengra as ctg +import networkx as nx +import numpy as np + +sys.path.insert(0, "../") +import tensorcircuit as tc + +try: + import kahypar +except ImportError: + print("kahypar not installed, please install it to run this script.") + exit() + + +# suppress the warning from cotengra +warnings.filterwarnings( + "ignore", + message="The inputs or output of this tree are not ordered." + "Costs will be accurate but actually contracting requires " + "ordered indices corresponding to array axes.", +) + +K = tc.set_backend("jax") + + +def generate_circuit(param, g, n, nlayers): + # construct the circuit ansatz + c = tc.Circuit(n) + for i in range(n): + c.H(i) + for j in range(nlayers): + c = tc.templates.blocks.QAOA_block(c, g, param[j, 0], param[j, 1]) + return c + + +def trigger_cotengra_optimization(n, nlayers, graph): + + # define the loss function + def loss_f(params, n, nlayers): + + c = generate_circuit(params, graph, n, nlayers) + + loss = c.expectation_ps(z=[0, 1, 2], reuse=False) + + return K.real(loss) + + params = K.implicit_randn(shape=[nlayers, 2]) + + # run only once to trigger the compilation + K.jit( + loss_f, + static_argnums=(1, 2), + )(params, n, nlayers) + + +# define the benchmark parameters +n = 12 +nlayers = 12 + +# define the cotengra optimizer parameters +graph_args = { + "1D lattice": nx.convert_node_labels_to_integers( + nx.grid_graph((n, 1)) + ), # 1D lattice + "2D lattice": nx.convert_node_labels_to_integers( + nx.grid_graph((n // 5, n // (n // 5))) + ), # 2D lattice + "all-to-all connected": nx.convert_node_labels_to_integers( + nx.complete_graph(n) + ), # all-to-all connected +} + +methods_args = [ # https://cotengra.readthedocs.io/en/latest/advanced.html#drivers + "greedy", + "kahypar", + # "labels", + # "spinglass", # requires igraph + # "labelprop", # requires igraph + # "betweenness", # requires igraph + # "walktrap", # requires igraph + # "quickbb", # requires https://github.com/dechterlab/quickbb + # "flowcutter", # requires https://github.com/kit-algo/flow-cutter-pace17 +] + +optlib_args = [ # https://cotengra.readthedocs.io/en/latest/advanced.html#optimization-library + "optuna", # pip install optuna + # "random", # default when no library is installed + # "baytune", # pip install baytune + # "nevergrad", # pip install nevergrad + # "chocolate", # pip install git+https://github.com/AIworx-Labs/chocolate@master + # "skopt", # pip install scikit-optimize +] + +post_processing_args = [ # https://cotengra.readthedocs.io/en/latest/advanced.html#slicing-and-subtree-reconfiguration + (None, None), + # ("slicing_opts", {"target_size": 2**28}), + # ("slicing_reconf_opts", {"target_size": 2**28}), + ("reconf_opts", {}), + ("simulated_annealing_opts", {}), +] + +minimize_args = [ # https://cotengra.readthedocs.io/en/main/advanced.html#objective + # "flops", # minimize the total number of scalar operations + # "size", # minimize the size of the largest intermediate tensor + # "write", # minimize the sum of sizes of all intermediate tensors + "combo", # minimize the sum of FLOPS + α * WRITE where α is 64 +] + + +def get_optimizer(method, optlib, post_processing, minimize): + if post_processing[0] is None: + return ctg.HyperOptimizer( + methods=method, + optlib=optlib, + minimize=minimize, + parallel=True, + max_time=60, + max_repeats=128, + progbar=True, + ) + else: + return ctg.HyperOptimizer( + methods=method, + optlib=optlib, + minimize=minimize, + parallel=True, + max_time=60, + max_repeats=128, + progbar=True, + **{post_processing[0]: post_processing[1]}, + ) + + +if __name__ == "__main__": + for graph, method, optlib, post_processing, minimize in itertools.product( + graph_args.keys(), + methods_args, + optlib_args, + post_processing_args, + minimize_args, + ): + print( + f"graph: {graph}, method: {method}, optlib: {optlib}, " + f"post_processing: {post_processing}, minimize: {minimize}" + ) + tc.set_contractor( + "custom", + optimizer=get_optimizer(method, optlib, post_processing, minimize), + contraction_info=True, + preprocessing=True, + debug_level=2, # no computation + ) + trigger_cotengra_optimization(n, nlayers, graph_args[graph]) + print("-------------------------") diff --git a/examples/hamiltonian_building.py b/examples/hamiltonian_building.py index e00c6a7e..80385265 100644 --- a/examples/hamiltonian_building.py +++ b/examples/hamiltonian_building.py @@ -3,36 +3,101 @@ """ import time + +import jax import numpy as np import quimb +import scipy +import tensorflow as tf + import tensorcircuit as tc +tc.set_dtype("complex128") nwires = 20 -# tc outperforms quimb in large nwires +print("--------------------") -# 1. tc approach for TFIM +# 1.1 tc approach for TFIM (numpy backend) + +tc.set_backend("numpy") +print("hamiltonian building with tc (numpy backend)") +print("numpy version: ", np.__version__) +print("scipy version: ", scipy.__version__) g = tc.templates.graphs.Line1D(nwires, pbc=False) -time0 = time.time() -h1 = tc.quantum.heisenberg_hamiltonian( +time0 = time.perf_counter() +h11 = tc.quantum.heisenberg_hamiltonian( g, hzz=1, hxx=0, hyy=0, hz=0, hx=-1, hy=0, sparse=True, numpy=True ) -time1 = time.time() +time1 = time.perf_counter() + +print("tc (numpy) time: ", time1 - time0) +print("--------------------") + +# 1.2 tc approach for TFIM (jax backend) + +tc.set_backend("jax") +print("hamiltonian building with tc (jax backend)") +print("jax version: ", jax.__version__) + +g = tc.templates.graphs.Line1D(nwires, pbc=False) +time0 = time.perf_counter() +h12 = tc.quantum.heisenberg_hamiltonian( + g, hzz=1, hxx=0, hyy=0, hz=0, hx=-1, hy=0, sparse=True +) +time1 = time.perf_counter() + +print("tc (jax) time: ", time1 - time0) + +time0 = time.perf_counter() +h12 = tc.quantum.heisenberg_hamiltonian( + g, hzz=1, hxx=0, hyy=0, hz=0, hx=-1, hy=0, sparse=True +) +time1 = time.perf_counter() + +print("tc (jax) time (after jit): ", time1 - time0) +print("--------------------") + +# 1.3 tc approach for TFIM (tensorflow backend) + +tc.set_backend("tensorflow") +print("hamiltonian building with tc (tensorflow backend)") +print("tensorflow version: ", tf.__version__) + +g = tc.templates.graphs.Line1D(nwires, pbc=False) +time0 = time.perf_counter() +h13 = tc.quantum.heisenberg_hamiltonian( + g, hzz=1, hxx=0, hyy=0, hz=0, hx=-1, hy=0, sparse=True +) +time1 = time.perf_counter() + +print("tc (tensorflow) time: ", time1 - time0) + +time0 = time.perf_counter() +h13 = tc.quantum.heisenberg_hamiltonian( + g, hzz=1, hxx=0, hyy=0, hz=0, hx=-1, hy=0, sparse=True +) +time1 = time.perf_counter() + +print("tc (tensorflow) time (after jit): ", time1 - time0) + +print("--------------------") -print("tc time: ", time1 - time0) # 2. quimb approach for TFIM -builder = quimb.tensor.tensor_gen.SpinHam() +print("hamiltonian building with quimb") +print("quimb version: ", quimb.__version__) + +builder = quimb.tensor.SpinHam1D() # spin operator instead of Pauli matrix builder += 4, "Z", "Z" builder += -2, "X" -time0 = time.time() +time0 = time.perf_counter() h2 = builder.build_sparse(nwires) h2 = h2.tocoo() -time1 = time.time() +time1 = time.perf_counter() print("quimb time: ", time1 - time0) @@ -43,4 +108,25 @@ def assert_equal(h1, h2): np.testing.assert_allclose(h1.data, h2.data, atol=1e-5) -assert_equal(h1, h2) +# numpy +assert_equal(h11, h2) + +# jax +scipy_coo = scipy.sparse.coo_matrix( + ( + h12.data, + (h12.indices[:, 0], h12.indices[:, 1]), + ), + shape=h12.shape, +) +assert_equal(scipy_coo, h2) + +# tensorflow +scipy_coo = scipy.sparse.coo_matrix( + ( + h13.values, + (h13.indices[:, 0], h13.indices[:, 1]), + ), + shape=h13.shape, +) +assert_equal(scipy_coo, h2) diff --git a/examples/keras3_tc_integration.py b/examples/keras3_tc_integration.py new file mode 100644 index 00000000..ba45363c --- /dev/null +++ b/examples/keras3_tc_integration.py @@ -0,0 +1,95 @@ +""" +keras3 is excellent to use together with tc, we will have unique features including: +1. turn OO paradigm to functional paradigm, i.e. reuse keras layer function in functional programming +2. batch on neural network weights +""" + +import os + +os.environ["KERAS_BACKEND"] = "jax" +import keras_core as keras +import numpy as np +import optax +import tensorcircuit as tc + +K = tc.set_backend("jax") + +batch = 8 +n = 6 +layer = keras.layers.Dense(1, activation="sigmoid") +layer.build([batch, n]) + +data_x = np.random.choice([0, 1], size=batch * n).reshape([batch, n]) +# data_y = np.sum(data_x, axis=-1) % 2 +data_y = data_x[:, 0] +data_y = data_y.reshape([batch, 1]) +data_x = data_x.astype(np.float32) +data_y = data_y.astype(np.float32) + + +print("data", data_x, data_y) + + +def loss(xs, ys, params, weights): + c = tc.Circuit(n) + c.rx(range(n), theta=xs) + c.cx(range(n - 1), range(1, n)) + c.rz(range(n), theta=params) + outputs = K.stack([K.real(c.expectation_ps(z=[i])) for i in range(n)]) + ypred, _ = layer.stateless_call(weights, [], outputs) + return keras.losses.binary_crossentropy(ypred, ys), ypred + + +# common data batch practice +vgf = K.jit( + K.vectorized_value_and_grad( + loss, argnums=(2, 3), vectorized_argnums=(0, 1), has_aux=True + ) +) + +params = K.implicit_randn(shape=[n]) +w = K.implicit_randn(shape=[n, 1]) +b = K.implicit_randn(shape=[1]) +opt = K.optimizer(optax.adam(1e-2)) +# seems that currently keras3'optimizer doesn't support nested list of variables + +for i in range(100): + (v, yp), gs = vgf(data_x, data_y, params, [w, b]) + params, [w, b] = opt.update(gs, (params, [w, b])) + if i % 10 == 0: + print(K.mean(v)) + +m = keras.metrics.BinaryAccuracy() +m.update_state(data_y, yp[:, None]) +print("acc", m.result()) + + +# data batch with batched and quantum neural weights + +vgf2 = K.jit( + K.vmap( + K.vectorized_value_and_grad( + loss, argnums=(2, 3), vectorized_argnums=(0, 1), has_aux=True + ), + vectorized_argnums=(2, 3), + ) +) + +wbatch = 4 +params = K.implicit_randn(shape=[wbatch, n]) +w = K.implicit_randn(shape=[wbatch, n, 1]) +b = K.implicit_randn(shape=[wbatch, 1]) +opt = K.optimizer(optax.adam(1e-2)) +# seems that currently keras3'optimizer doesn't support nested list of variables + +for i in range(100): + (v, yp), gs = vgf2(data_x, data_y, params, [w, b]) + params, [w, b] = opt.update(gs, (params, [w, b])) + if i % 10 == 0: + print(K.mean(v, axis=-1)) + +for i in range(wbatch): + m = keras.metrics.BinaryAccuracy() + m.update_state(data_y, yp[0, :, None]) + print("acc", m.result()) + m.reset_state() diff --git a/examples/matprod_vmap.py b/examples/matprod_vmap.py new file mode 100644 index 00000000..bbf8f137 --- /dev/null +++ b/examples/matprod_vmap.py @@ -0,0 +1,42 @@ +""" +matrix product: a new twist +rewrite matrix product in a vmap style +""" + +from functools import partial + +import numpy as np +import tensorcircuit as tc + +for bk in ["jax", "tensorflow"]: + with tc.runtime_backend(bk) as K: + print("~~~~~~~~~~~~~~~~~~~~~") + print(f"using {K.name} backend") + + @partial(K.jit, jit_compile=True) + def mul(a, b): + return a @ b + + def ij(i, j): + """ + Inner product + """ + return K.tensordot(i, j, 1) + + vij = K.vmap(ij, vectorized_argnums=1) + vvij = K.vmap(vij, vectorized_argnums=0) + + @partial(K.jit, jit_compile=True) + def mul2(a, b): + b = K.transpose(b) + return vvij(a, b) + + for shape in [(256, 4096), (4096, 256), (2048, 2048)]: + print(shape) + a = K.implicit_randn(shape) + b = K.implicit_randn([shape[1], shape[0]]) + print("plain matprod") + r1, _, _ = tc.utils.benchmark(mul, a, b, tries=10) + print("vmap matprod") + r2, _, _ = tc.utils.benchmark(mul2, a, b, tries=10) + np.testing.assert_allclose(r1, r2, atol=1e-5) diff --git a/examples/mipt_pideal.py b/examples/mipt_pideal.py new file mode 100644 index 00000000..c419446b --- /dev/null +++ b/examples/mipt_pideal.py @@ -0,0 +1,112 @@ +""" +demo example of mipt in tc style, with ideal p for each history trajectory +p is also jittable now, change parameter p doesn't trigger recompiling +""" + +from functools import partial +import time +import numpy as np +from scipy import stats +import tensorcircuit as tc + +K = tc.set_backend("jax") +tc.set_dtype("complex128") +# tf backend is slow (at least on cpu) +tc.set_contractor("cotengra-16-64") + + +def delete2(pick, plist): + # pick = 0, 1 : return plist[pick]/(plist[0]+plist[1]) + # pick = 2: return 1 + indicator = (K.sign(1.5 - pick) + 1) / 2 # 0,1 : 1, 2: 0 + p = 0 + p += 1 - indicator + p += indicator / (plist[0] + plist[1]) * (plist[0] * (1 - pick) + plist[1] * pick) + return p + + +@partial(K.jit, static_argnums=(2, 3)) +def circuit_output(random_matrix, status, n, d, p): + """ + mipt circuit + + :param random_matrix: a float or complex tensor containing 4*4 random haar matrix wth size [d*n, 4, 4] + :type random_matrix: _type_ + :param status: a int tensor with element in 0 or 1 or 2 (no meausrement) with size d*n + :type status: _type_ + :param n: number of qubits + :type n: _type_ + :param d: number of depth + :type d: _type_ + :param p: measurement ratio + :type p: float + :return: output state + """ + random_matrix = K.reshape(random_matrix, [d, n, 4, 4]) + status = K.reshape(status, [d, n]) + inputs = None + bs_history = [] + prob_history = [] + for j in range(d): + if inputs is None: + c = tc.Circuit(n) + else: + c = tc.Circuit(n, inputs=inputs) + for i in range(0, n, 2): + c.unitary(i, (i + 1) % n, unitary=random_matrix[j, i]) + for i in range(1, n, 2): + c.unitary(i, (i + 1) % n, unitary=random_matrix[j, i]) + inputs = c.state() + c = tc.Circuit(n, inputs=inputs) + for i in range(n): + pick, plist = c.general_kraus( + [ + K.sqrt(p) * K.convert_to_tensor(np.array([[1.0, 0], [0, 0]])), + K.sqrt(p) * K.convert_to_tensor(np.array([[0, 0], [0, 1.0]])), + K.sqrt(1 - p) * K.eye(2), + ], + i, + status=status[j, i], + with_prob=True, + ) + bs_history.append(pick) + prob_history.append(delete2(pick, plist)) + inputs = c.state() + c = tc.Circuit(n, inputs=inputs) + inputs = c.state() + inputs /= K.norm(inputs) + bs_history = K.stack(bs_history) + prob_history = K.stack(prob_history) + return inputs, bs_history, prob_history, K.sum(K.log(prob_history + 1e-11)) + + +@partial(K.jit, static_argnums=(2, 3)) +def cals(random_matrix, status, n, d, p): + state, bs_history, prob_history, prob = circuit_output( + random_matrix, status, n, d, p + ) + rho = tc.quantum.reduced_density_matrix(state, cut=[i for i in range(n // 2)]) + return ( + tc.quantum.entropy(rho), + tc.quantum.renyi_entropy(rho, k=2), + bs_history, + prob_history, + prob, + ) + + +if __name__ == "__main__": + n = 12 + d = 12 + st = np.random.uniform(size=[d * n]) + ## assume all X gate instead + rm = [stats.unitary_group.rvs(4) for _ in range(d * n)] + rm = [r / np.linalg.det(r) for r in rm] + rm = np.stack(rm) + time0 = time.time() + print(cals(rm, st, n, d, 0.6)) + time1 = time.time() + st = np.random.uniform(size=[d * n]) + print(cals(rm, st, n, d, 0.1)) + time2 = time.time() + print(f"compiling time {time1-time0}, running time {time2-time1}") diff --git a/examples/rem_super_large_scale.py b/examples/rem_super_large_scale.py new file mode 100644 index 00000000..a10e7290 --- /dev/null +++ b/examples/rem_super_large_scale.py @@ -0,0 +1,54 @@ +""" +Demonstrate the failure of rem when qubit number is much larger than 1/p +""" + +from functools import partial +import numpy as np +import tensorcircuit as tc + + +def simulate_engine(p, ans): + fans = "" + for a in ans: + if p > np.random.uniform(): + if a == "0": + fans += "1" + else: + fans += "0" + else: + fans += a + return fans + + +def run(cs, shots, p=0.1): + # we assume only all 0 and all 1 results for simplicity + rds = [] + for c in cs: + if len(c.to_qir()) < 2: + ans = "0" * c._nqubits + else: + ans = "1" * c._nqubits + rd = {} + for _ in range(shots): + r = simulate_engine(p, ans) + rd[r] = rd.get(r, 0) + 1 + rds.append(rd) + return rds + + +if __name__ == "__main__": + for p in [0.1, 0.05, 0.02]: + print(p) + n = int(3 / p) + c = tc.Circuit(n) + c.x(range(n)) + runp = partial(run, p=p) + r = runp([c], 8192)[0] + mit = tc.results.rem.ReadoutMit(runp) + mit.cals_from_system(n) + for i in range(n): + print(i, "\n", mit.single_qubit_cals[i]) + rs = [] + for i in range(n): + rs.append([i, np.abs(mit.expectation(r, list(range(i))))]) + print(rs[i]) diff --git a/examples/shvqe.py b/examples/shvqe.py new file mode 100644 index 00000000..4083fa6d --- /dev/null +++ b/examples/shvqe.py @@ -0,0 +1,246 @@ +""" +Schrodinger-Heisenberg quantum variational eigensolver (SHVQE) with DQAS-style optimization. + +DQAS part is modified from: examples/clifford_optimization.py +""" + +import sys + +sys.path.insert(0, "../") + +import numpy as np +import tensorflow as tf + +import tensorcircuit as tc +from tensorcircuit.applications.vqes import construct_matrix_v3 + +ctype, rtype = tc.set_dtype("complex64") +K = tc.set_backend("tensorflow") + +n = 10 # the number of qubits (must be even for consistency later) +ncz = 2 # number of cz layers in Schrodinger circuit +nlayersq = ncz + 1 # Schrodinger parameter layers + +# training setup +epochs = 1000 +batch = 1000 + +# Hamiltonian +h6h = np.load("./h6_hamiltonian.npy") # reported in 0.99 A +hamiltonian = construct_matrix_v3(h6h.tolist()) + + +def hybrid_ansatz(structure, paramq, preprocess="direct", train=True): + """_summary_ + + Parameters + ---------- + structure : K.Tensor, (n//2, 2) + parameters to decide graph structure of Clifford circuits + paramq : K.Tensor, (nlayersq, n, 3) + parameters in quantum variational circuits, the last layer for Heisenberg circuits + preprocess : str, optional + preprocess, by default "direct" + + Returns + ------- + K.Tensor, [1,] + loss value + """ + c = tc.Circuit(n) + if preprocess == "softmax": + structure = K.softmax(structure, axis=-1) + elif preprocess == "most": + structure = K.onehot(K.argmax(structure, axis=-1), num=2) + elif preprocess == "direct": + pass + + structure = K.cast(structure, ctype) + structure = tf.reshape(structure, shape=[n // 2, 2]) + + # quantum variational in Schrodinger part, first consider a ring topol + for j in range(nlayersq): + if j != 0 and j != nlayersq - 1: + for i in range(j % 2, n, 2): + c.cz(i, (i + 1) % n) + for i in range(n): + c.rx(i, theta=paramq[j, i, 0]) + c.ry(i, theta=paramq[j, i, 1]) + c.rz(i, theta=paramq[j, i, 2]) + + # Clifford part, which is actually virtual + if train: + for j in range(0, n // 2 - 1): + dis = j + 1 + for i in range(0, n): + c.unitary( + i, + (i + dis) % n, + unitary=structure[j, 0] * tc.gates.ii().tensor + + structure[j, 1] * tc.gates.cz().tensor, + ) + + for i in range(0, n // 2): + c.unitary( + i, + i + n // 2, + unitary=structure[n // 2 - 1, 0] * tc.gates.ii().tensor + + structure[n // 2 - 1, 1] * tc.gates.cz().tensor, + ) + else: # if not for training, we just put nontrivial gates + for j in range(0, n // 2 - 1): + dis = j + 1 + for i in range(0, n): + if structure[j, 1] == 1: + c.cz(i, (i + dis) % n) + + for i in range(0, n // 2): + if structure[j, 1] == 1: + c.cz(i, i + n // 2) + + return c + + +def hybrid_vqe(structure, paramq, preprocess="direct"): + """_summary_ + + Parameters + ---------- + structure : K.Tensor, (n//2, 2) + parameters to decide graph structure of Clifford circuits + paramq : K.Tensor, (nlayersq, n, 3) + parameters in quantum variational circuits, the last layer for Heisenberg circuits + preprocess : str, optional + preprocess, by default "direct" + + Returns + ------- + K.Tensor, [1,] + loss value + """ + c = hybrid_ansatz(structure, paramq, preprocess) + return tc.templates.measurements.operator_expectation(c, hamiltonian) + + +def sampling_from_structure(structures, batch=1): + ch = structures.shape[-1] + prob = K.softmax(K.real(structures), axis=-1) + prob = K.reshape(prob, [-1, ch]) + p = prob.shape[0] + r = np.stack( + np.array( + [np.random.choice(ch, p=K.numpy(prob[i]), size=[batch]) for i in range(p)] + ) + ) + return r.transpose() + + +@K.jit +def best_from_structure(structures): + return K.argmax(structures, axis=-1) + + +def nmf_gradient(structures, oh): + """compute the Monte Carlo gradient with respect of naive mean-field probabilistic model + + Parameters + ---------- + structures : K.Tensor, (n//2, ch) + structure parameter for single- or two-qubit gates + oh : K.Tensor, (n//2, ch), onehot + a given structure sampled via strcuture parameters (in main function) + + Returns + ------- + K.Tensor, (n//2 * 2, ch) == (n, ch) + MC gradients + """ + choice = K.argmax(oh, axis=-1) + prob = K.softmax(K.real(structures), axis=-1) + indices = K.transpose( + K.stack([K.cast(tf.range(structures.shape[0]), "int64"), choice]) + ) + prob = tf.gather_nd(prob, indices) + prob = K.reshape(prob, [-1, 1]) + prob = K.tile(prob, [1, structures.shape[-1]]) + + return K.real( + tf.tensor_scatter_nd_add( + tf.cast(-prob, dtype=ctype), + indices, + tf.ones([structures.shape[0]], dtype=ctype), + ) + ) # in oh : 1-p, not in oh : -p + + +# vmap for a batch of structures +nmf_gradient_vmap = K.jit(K.vmap(nmf_gradient, vectorized_argnums=1)) + +# vvag for a batch of structures +vvag_hybrid = K.jit( + K.vectorized_value_and_grad(hybrid_vqe, vectorized_argnums=(0,), argnums=(1,)), + static_argnums=(2,), +) + + +def train_hybrid( + stddev=0.05, lr=None, epochs=2000, debug_step=50, batch=256, verbose=False +): + # params = K.implicit_randn([n//2, 2], stddev=stddev) + params = K.ones([n // 2, 2], dtype=float) + paramq = K.implicit_randn([nlayersq, n, 3], stddev=stddev) * 2 * np.pi + if lr is None: + lr = tf.keras.optimizers.schedules.ExponentialDecay(0.6, 100, 0.8) + structure_opt = K.optimizer(tf.keras.optimizers.Adam(lr)) + + avcost = 0 + avcost2 = 0 + loss_history = [] + for epoch in range(epochs): # iteration to update strcuture param + # random sample some structures + batched_stucture = K.onehot( + sampling_from_structure(params, batch=batch), + num=params.shape[-1], + ) + vs, gq = vvag_hybrid(batched_stucture, paramq, "direct") + loss_history.append(np.min(vs)) + gq = gq[0] + avcost = K.mean(vs) # average cost of the batch + gs = nmf_gradient_vmap(params, batched_stucture) # \nabla lnp + gs = K.mean(K.reshape(vs - avcost2, [-1, 1, 1]) * gs, axis=0) + # avcost2 is averaged cost in the last epoch + avcost2 = avcost + + [params, paramq] = structure_opt.update([gs, gq], [params, paramq]) + if epoch % debug_step == 0 or epoch == epochs - 1: + print("----------epoch %s-----------" % epoch) + print( + "batched average loss: ", + np.mean(vs), + "minimum candidate loss: ", + np.min(vs), + ) + + # max over choices, min over layers and qubits + minp = tf.math.reduce_min( + tf.math.reduce_max(tf.math.softmax(params), axis=-1) + ) + if minp > 0.5: + print("probability converged") + + if verbose: + print("strcuture parameter: \n", params.numpy()) + + cand_preset = best_from_structure(params) + print(cand_preset) + print("current recommendation loss: ", hybrid_vqe(params, paramq, "most")) + + loss_history = np.array(loss_history) + return hybrid_vqe(params, paramq, "most"), params, paramq, loss_history + + +print("Train hybrid.") +ee, params, paramq, loss_history = train_hybrid( + epochs=epochs, batch=batch, verbose=True +) +print("Energy:", ee) diff --git a/examples/stabilizer_simulation.py b/examples/stabilizer_simulation.py new file mode 100644 index 00000000..699983bf --- /dev/null +++ b/examples/stabilizer_simulation.py @@ -0,0 +1,151 @@ +import numpy as np +import stim + +import tensorcircuit as tc + +np.random.seed(0) + +tc.set_dtype("complex128") + +clifford_one_qubit_gates = ["H", "X", "Y", "Z", "S"] +clifford_two_qubit_gates = ["CNOT"] +clifford_gates = clifford_one_qubit_gates + clifford_two_qubit_gates + + +def genpair(num_qubits, count): + choice = list(range(num_qubits)) + for _ in range(count): + np.random.shuffle(choice) + x, y = choice[:2] + yield (x, y) + + +def random_clifford_circuit_with_mid_measurement(num_qubits, depth): + c = tc.Circuit(num_qubits) + operation_list = [] + for _ in range(depth): + for j, k in genpair(num_qubits, 2): + c.cnot(j, k) + operation_list.append(("CNOT", (j, k))) + for j in range(num_qubits): + gate_name = np.random.choice(clifford_one_qubit_gates) + getattr(c, gate_name)(j) + operation_list.append((gate_name, (j,))) + if np.random.uniform() < 0.2: + measured_qubit = np.random.randint(0, num_qubits - 1) + sample, p = c.measure_reference(measured_qubit, with_prob=True) + # Check if there is a non-zero probability to measure "0" for post-selection + if (sample == "0" and not np.isclose(p, 0.0)) or ( + sample == "1" and not np.isclose(p, 1.0) + ): + c.mid_measurement(measured_qubit, keep=0) + operation_list.append(("M", (measured_qubit,))) + return c, operation_list + + +def convert_operation_list_to_stim_circuit(operation_list): + stim_circuit = stim.Circuit() + for instruction in operation_list: + gate_name = instruction[0] + qubits = instruction[1] + stim_circuit.append(gate_name, qubits) + return stim_circuit + + +# ref: https://quantumcomputing.stackexchange.com/questions/16718/measuring-entanglement-entropy-using-a-stabilizer-circuit-simulator +def get_binary_matrix(z_stabilizers): + N = len(z_stabilizers) + binary_matrix = np.zeros((N, 2 * N)) + for row_idx, row in enumerate(z_stabilizers): + for col_idx, col in enumerate(row): + if col == 3: # Pauli Z + binary_matrix[row_idx, N + col_idx] = 1 + if col == 2: # Pauli Y + binary_matrix[row_idx, N + col_idx] = 1 + binary_matrix[row_idx, col_idx] = 1 + if col == 1: # Pauli X + binary_matrix[row_idx, col_idx] = 1 + return binary_matrix + + +def get_cut_binary_matrix(binary_matrix, cut): + N = len(binary_matrix) + new_indices = [i for i in range(N) if i in set(cut)] + [ + i + N for i in range(N) if i in set(cut) + ] + return binary_matrix[:, new_indices] + + +# ref: https://gist.github.com/StuartGordonReid/eb59113cb29e529b8105?permalink_comment_id=3268301#gistcomment-3268301 +def gf2_rank(matrix): + n = len(matrix[0]) + rank = 0 + for col in range(n): + j = 0 + rows = [] + while j < len(matrix): + if matrix[j][col] == 1: + rows += [j] + j += 1 + if len(rows) >= 1: + for c in range(1, len(rows)): + for k in range(n): + matrix[rows[c]][k] = (matrix[rows[c]][k] + matrix[rows[0]][k]) % 2 + matrix.pop(rows[0]) + rank += 1 + for row in matrix: + if sum(row) > 0: + rank += 1 + return rank + + +# ref: https://quantumcomputing.stackexchange.com/questions/27795/exact-probabilities-of-outcomes-for-clifford-circuits-with-mid-circuit-measureme +def simulate_stim_circuit_with_mid_measurement(stim_circuit): + simulator = stim.TableauSimulator() + + for instruction in stim_circuit.flattened(): + if instruction.name == "M": + for t in instruction.targets_copy(): + expectaction_value = simulator.peek_z(t.value) # 1, 0, -1 + # there is a non-zero probability to measure "0" if expectaction_value is not -1 + if expectaction_value != -1: + simulator.postselect_z(t.value, desired_value=0) + else: + simulator.do(instruction) + + return simulator.current_inverse_tableau() ** -1 + + +if __name__ == "__main__": + # Number of qubits + num_qubits = 12 + # Depth of the circuit + depth = 24 + # index list that is traced out to calculate the entanglement entropy + cut = [i for i in range(num_qubits // 3)] + + tc_circuit, op_list = random_clifford_circuit_with_mid_measurement( + num_qubits, depth + ) + print(tc_circuit.draw(output="text")) + + stim_circuit = convert_operation_list_to_stim_circuit(op_list) + + # Entanglement entropy calculation using stabilizer formalism + stabilizer_tableau = simulate_stim_circuit_with_mid_measurement(stim_circuit) + zs = [stabilizer_tableau.z_output(k) for k in range(len(stabilizer_tableau))] + binary_matrix = get_binary_matrix(zs) + cur_matrix = get_cut_binary_matrix(binary_matrix, cut) + stim_entropy = (gf2_rank(cur_matrix.tolist()) - len(cut)) * np.log(2) + print("Stim Entanglement Entropy:", stim_entropy) + + # Entanglement entropy calculation using TensorCircuit + state_vector = tc_circuit.wavefunction() + assert np.linalg.norm(state_vector) > 0 + # Normalize the state vector because mid-measurement operation is not unitary + state_vector /= np.linalg.norm(state_vector) + tc_entropy = tc.quantum.entanglement_entropy(state_vector, cut) + print("TensorCircuit Entanglement Entropy:", tc_entropy) + + # Check if the entanglement entropies are close + np.testing.assert_allclose(stim_entropy, tc_entropy, atol=1e-8) diff --git a/examples/variational_dynamics.py b/examples/variational_dynamics.py index a6e8fc88..39015fbd 100644 --- a/examples/variational_dynamics.py +++ b/examples/variational_dynamics.py @@ -46,6 +46,8 @@ def lhs_matrix(theta, psi0): vij = tc.backend.vmap(ij, vectorized_argnums=0) vvij = tc.backend.vmap(vij, vectorized_argnums=1) jacobian = ppsioverptheta(theta, psi0=psi0) + # fim = tc.backend.adjoint(jacobian)@jacobian is also ok + # speed comparison? jacobian = tc.backend.transpose(jacobian) fim = vvij(jacobian, jacobian) fim = tc.backend.real(fim) @@ -62,12 +64,16 @@ def energy(theta, psi0): wl = tc.backend.reshape(wl, [1, -1]) wr = tc.backend.reshape(wr, [-1, 1]) e = wl @ h @ wr + # use sparse matrix if required return tc.backend.real(e)[0, 0] eg = tc.backend.grad(energy, argnums=0) rhs = eg(theta, psi0) rhs = tc.backend.imag(rhs) return rhs + # for ITE, imag is replace with real + # a simpler way to get rhs in ITE case is to directly evaluate + # 0.5*\nabla @tc.backend.jit diff --git a/examples/vqe_noisyopt.py b/examples/vqe_noisyopt.py new file mode 100644 index 00000000..8bd18948 --- /dev/null +++ b/examples/vqe_noisyopt.py @@ -0,0 +1,222 @@ +""" +VQE with finite measurement shot noise +""" + +from functools import partial +import numpy as np +import optax +from noisyopt import minimizeCompass, minimizeSPSA +from tabulate import tabulate # pip install tabulate +import tensorcircuit as tc +from tensorcircuit import experimental as E + +seed = 42 +np.random.seed(seed) + +K = tc.set_backend("jax") +# note this script only supports jax backend + +n = 6 +nlayers = 4 + +# initial value of the parameters +initial_value = np.random.uniform(size=[n * nlayers * 2]) + +result = { + "Algorithm / Optimization": ["Without Shot Noise", "With Shot Noise"], + "SPSA (Gradient Free)": [], + "Compass Search (Gradient Free)": [], + "Adam (Gradient based)": [], +} + +# We use OBC 1D TFIM Hamiltonian in this script + +ps = [] +for i in range(n): + l = [0 for _ in range(n)] + l[i] = 1 + ps.append(l) + # X_i +for i in range(n - 1): + l = [0 for _ in range(n)] + l[i] = 3 + l[i + 1] = 3 + ps.append(l) + # Z_i Z_i+1 +w = [-1.0 for _ in range(n)] + [1.0 for _ in range(n - 1)] + + +def generate_circuit(param): + # construct the circuit ansatz + c = tc.Circuit(n) + for i in range(n): + c.H(i) + for j in range(nlayers): + for i in range(n - 1): + c.rzz(i, i + 1, theta=param[i, j, 0]) + for i in range(n): + c.rx(i, theta=param[i, j, 1]) + return c + + +def ps2xyz(psi): + # ps2xyz([1, 2, 2, 0]) = {"x": [0], "y": [1, 2], "z": []} + xyz = {"x": [], "y": [], "z": []} + for i, j in enumerate(psi): + if j == 1: + xyz["x"].append(i) + if j == 2: + xyz["y"].append(i) + if j == 3: + xyz["z"].append(i) + return xyz + + +@partial(K.jit, static_argnums=(2)) +def exp_val(param, key, shots=1024): + # expectation with shot noise + # ps, w: H = \sum_i w_i ps_i + # describing the system Hamiltonian as a weighted sum of Pauli string + c = generate_circuit(param) + if isinstance(shots, int): + shots = [shots for _ in range(len(ps))] + loss = 0 + for psi, wi, shot in zip(ps, w, shots): + key, subkey = K.random_split(key) + xyz = ps2xyz(psi) + loss += wi * c.sample_expectation_ps(**xyz, shots=shot, random_generator=subkey) + return K.real(loss) + + +@K.jit +def exp_val_analytical(param): + param = param.reshape(n, nlayers, 2) + c = generate_circuit(param) + loss = 0 + for psi, wi in zip(ps, w): + xyz = ps2xyz(psi) + loss += wi * c.expectation_ps(**xyz) + return K.real(loss) + + +# 0. Exact result + +hm = tc.quantum.PauliStringSum2COO(ps, w, numpy=True) +hm = K.to_dense(hm) +e, v = np.linalg.eigh(hm) +exact_gs_energy = e[0] +print("==================================================================") +print("Exact ground state energy: ", exact_gs_energy) +print("==================================================================") + +# 1.1 VQE with numerically exact expectation: gradient free + +print(">>> VQE without shot noise") + + +r = minimizeSPSA( + func=exp_val_analytical, + x0=initial_value, + niter=6000, + paired=False, +) + +print(r) +print(">> SPSA converged as:", exp_val_analytical(r.x)) +result["SPSA (Gradient Free)"].append(exp_val_analytical(r.x)) + +r = minimizeCompass( + func=exp_val_analytical, + x0=initial_value, + deltatol=0.1, + feps=1e-3, + paired=False, +) + +print(r) +print(">> Compass converged as:", exp_val_analytical(r.x)) +result["Compass Search (Gradient Free)"].append(exp_val_analytical(r.x)) + +# 1.2 VQE with numerically exact expectation: gradient based + +exponential_decay_scheduler = optax.exponential_decay( + init_value=1e-2, transition_steps=500, decay_rate=0.9 +) +opt = K.optimizer(optax.adam(exponential_decay_scheduler)) +param = initial_value.reshape((n, nlayers, 2)) # zeros stall the gradient +exp_val_grad_analytical = K.jit(K.value_and_grad(exp_val_analytical)) +for i in range(1000): + e, g = exp_val_grad_analytical(param) + param = opt.update(g, param) + if i % 100 == 99: + print(f"Expectation value at iteration {i}: {e}") + +print(">> Adam converged as:", exp_val_grad_analytical(param)[0]) +result["Adam (Gradient based)"].append(exp_val_grad_analytical(param)[0]) + +# 2.1 VQE with finite shot noise: gradient free + +print("==================================================================") +print(">>> VQE with shot noise") + + +rkey = K.get_random_state(seed) + + +def exp_val_wrapper(param): + param = param.reshape(n, nlayers, 2) + global rkey + rkey, skey = K.random_split(rkey) + # maintain stateless randomness in scipy optimize interface + return exp_val(param, skey, shots=1024) + + +r = minimizeSPSA( + func=exp_val_wrapper, + x0=initial_value, + niter=6000, + paired=False, +) +print(r) +print(">> SPSA converged as:", exp_val_wrapper(r["x"])) +result["SPSA (Gradient Free)"].append(exp_val_wrapper(r["x"])) + +r = minimizeCompass( + func=exp_val_wrapper, + x0=initial_value, + deltatol=0.1, + feps=1e-2, + paired=False, +) + +print(r) +print(">> Compass converged as:", exp_val_wrapper(r["x"])) +result["Compass Search (Gradient Free)"].append(exp_val_wrapper(r["x"])) + + +# 2.2 VQE with finite shot noise: gradient based + +exponential_decay_scheduler = optax.exponential_decay( + init_value=1e-2, transition_steps=500, decay_rate=0.9 +) +opt = K.optimizer(optax.adam(exponential_decay_scheduler)) +param = initial_value.reshape((n, nlayers, 2)) # zeros stall the gradient +exp_grad = E.parameter_shift_grad_v2(exp_val, argnums=0, random_argnums=1) +rkey = K.get_random_state(seed) + +for i in range(1000): + rkey, skey = K.random_split(rkey) + g = exp_grad(param, skey) + param = opt.update(g, param) + if i % 100 == 99: + rkey, skey = K.random_split(rkey) + print(f"Expectation value at iteration {i}: {exp_val(param, skey)}") + +# the real energy position after optimization +print(">> Adam converged as:", exp_val_analytical(param)) +result["Adam (Gradient based)"].append(exp_val_analytical(param)) + +print("==================================================================") +print(">>> Benchmark") +print(">> Exact ground state energy: ", exact_gs_energy) +print(tabulate(result, headers="keys", tablefmt="github")) diff --git a/examples/vqe_parallel_pmap.py b/examples/vqe_parallel_pmap.py new file mode 100644 index 00000000..54ea6922 --- /dev/null +++ b/examples/vqe_parallel_pmap.py @@ -0,0 +1,68 @@ +""" +jax pmap paradigm for vqe on multiple gpus +""" + +import os + +os.environ["XLA_FLAGS"] = "--xla_force_host_platform_device_count=8" +from functools import partial +import jax +import optax +import tensorcircuit as tc + +K = tc.set_backend("jax") +tc.set_contractor("cotengra") + + +def vqef(param, measure, n, nlayers): + c = tc.Circuit(n) + c.h(range(n)) + for i in range(nlayers): + c.rzz(range(n - 1), range(1, n), theta=param[i, 0]) + c.rx(range(n), theta=param[i, 1]) + return K.real( + tc.templates.measurements.parameterized_measurements(c, measure, onehot=True) + ) + + +def get_tfim_ps(n): + tfim_ps = [] + for i in range(n): + tfim_ps.append(tc.quantum.xyz2ps({"x": [i]}, n=n)) + for i in range(n): + tfim_ps.append(tc.quantum.xyz2ps({"z": [i, (i + 1) % n]}, n=n)) + return K.convert_to_tensor(tfim_ps) + + +vqg_vgf = jax.vmap(K.value_and_grad(vqef), in_axes=(None, 0, None, None)) + + +@partial( + jax.pmap, + axis_name="pmap", + in_axes=(0, 0, None, None), + static_broadcasted_argnums=(2, 3), +) +def update(param, measure, n, nlayers): + # Compute the gradients on the given minibatch (individually on each device). + loss, grads = vqg_vgf(param, measure, n, nlayers) + grads = K.sum(grads, axis=0) + grads = jax.lax.psum(grads, axis_name="pmap") + loss = K.sum(loss, axis=0) + loss = jax.lax.psum(loss, axis_name="pmap") + param = opt.update(grads, param) + return param, loss + + +if __name__ == "__main__": + n = 8 + nlayers = 4 + ndevices = 8 + m = get_tfim_ps(n) + m = K.reshape(m, [ndevices, m.shape[0] // ndevices] + list(m.shape[1:])) + param = K.stateful_randn(jax.random.PRNGKey(43), shape=[nlayers, 2, n], stddev=0.1) + param = K.stack([param] * ndevices) + opt = K.optimizer(optax.adam(1e-2)) + for _ in range(100): + param, loss = update(param, m, n, nlayers) + print(loss[0]) diff --git a/requirements/requirements-dev.txt b/requirements/requirements-dev.txt index f4d974b8..e6b3e293 100644 --- a/requirements/requirements-dev.txt +++ b/requirements/requirements-dev.txt @@ -1,14 +1,14 @@ -mypy==1.2.0 +mypy==1.5.1 pytest==6.2.4 pytest-cov pytest-benchmark pytest-xdist -black==23.3.0 +black[jupyter] sphinx>=4.0 pytest-lazy-fixture -pylint==2.11.1 -numpy==1.21.5 +pylint==2.17.5 furo sphinx-copybutton nbsphinx -myst-parser \ No newline at end of file +myst-parser +sphinx-design \ No newline at end of file diff --git a/requirements/requirements-docker-v2.txt b/requirements/requirements-docker-v2.txt new file mode 100644 index 00000000..5a99a02d --- /dev/null +++ b/requirements/requirements-docker-v2.txt @@ -0,0 +1,47 @@ +torch>2.0 # 2.0.1 +jax[cuda11_pip]==0.4.7 +tensorflow==2.11 +# tf 2.12 can make torch 2 hangs with runtime error +# check with hybrid_gpu_pipeline.py example +cupy-cuda11x==12.0.0 +tensornetwork==0.4.6 +graphviz +numpy==1.23.5 +scipy==1.10.1 +sympy==1.12 +cirq==1.1.0 +qiskit +matplotlib +jupyter +cotengra +networkx +optax==0.1.5 +kahypar +optuna +baytune +nevergrad +scikit-learn==1.2.2 +scikit-optimize +openfermion +quimb +openfermionpyscf +pennylane==0.30.0 +mthree==1.1.0 +mitiq==0.26.0 +# below is for development +mypy==1.3.0 +pytest +pytest-cov +pytest-benchmark +pytest-xdist +pytest-lazy-fixture +black==23.3.0 +sphinx>=4.0 +sphinx-intl +sphinx-copybutton +nbsphinx +furo +myst-parser +pylint +sphinx-design +# made in 202306 diff --git a/requirements/requirements-extra.txt b/requirements/requirements-extra.txt index 09cacbba..63e1f992 100644 --- a/requirements/requirements-extra.txt +++ b/requirements/requirements-extra.txt @@ -1,6 +1,10 @@ # extra dependencies for ci -qiskit +qiskit<1.0 +qiskit-aer<1.0 qiskit-nature -torch -jupyter +mitiq +cirq +torch==2.2.2 +# jupyter mthree==1.1.0 +openfermion diff --git a/requirements/requirements-rtd.txt b/requirements/requirements-rtd.txt index 4c2d71c9..8e93c419 100644 --- a/requirements/requirements-rtd.txt +++ b/requirements/requirements-rtd.txt @@ -14,4 +14,5 @@ furo==2022.4.7 sphinx-copybutton nbsphinx myst-parser -urllib3==1.26.15 \ No newline at end of file +urllib3==1.26.15 +sphinx-design \ No newline at end of file diff --git a/requirements/requirements.txt b/requirements/requirements.txt index 69ddfea0..97de418f 100644 --- a/requirements/requirements.txt +++ b/requirements/requirements.txt @@ -1,8 +1,7 @@ numpy scipy -cirq==0.13.1 -tensorflow==2.7 -tensornetwork +tensorflow<2.16 # tf 2.16 with integration of keras 3 seems a disaster... +tensornetwork-ng graphviz jax jaxlib diff --git a/setup.py b/setup.py index 6495eed6..8e176a49 100644 --- a/setup.py +++ b/setup.py @@ -11,19 +11,19 @@ version=__version__, author=__author__, author_email="shixinzhang@tencent.com", - description="Quantum circuits on top of tensor network", + description="High performance unified quantum computing framework for the NISQ era", long_description=long_description, long_description_content_type="text/markdown", url="https://github.com/tencent-quantum-lab/tensorcircuit", packages=setuptools.find_packages(), include_package_data=True, - install_requires=["numpy", "scipy", "tensornetwork", "networkx"], + install_requires=["numpy", "scipy", "tensornetwork-ng", "networkx"], extras_require={ - "tensorflow": ["tensorflow"], + "tensorflow": ["tensorflow<2.16"], "jax": ["jax", "jaxlib"], "torch": ["torch"], - "qiskit": ["qiskit"], - "cloud": ["qiskit", "mthree"], + "qiskit": ["qiskit<1.0"], + "cloud": ["qiskit<1.0", "mthree"], }, classifiers=[ "Programming Language :: Python :: 3", diff --git a/tensorcircuit/__init__.py b/tensorcircuit/__init__.py index 558439de..fb1c2e40 100644 --- a/tensorcircuit/__init__.py +++ b/tensorcircuit/__init__.py @@ -1,4 +1,4 @@ -__version__ = "0.9.1" +__version__ = "0.12.0" __author__ = "TensorCircuit Authors" __creator__ = "refraction-ray" @@ -40,6 +40,8 @@ from .quantum import QuOperator, QuVector, QuAdjointVector, QuScalar from . import compiler from . import cloud +from . import fgs +from .fgs import FGSSimulator try: from . import keras @@ -53,5 +55,16 @@ except ModuleNotFoundError: pass # in case torch is not installed +try: + import qiskit + + qiskit.QuantumCircuit.cnot = qiskit.QuantumCircuit.cx + qiskit.QuantumCircuit.toffoli = qiskit.QuantumCircuit.ccx + qiskit.QuantumCircuit.fredkin = qiskit.QuantumCircuit.cswap + + # amazing qiskit 1.0 nonsense... +except ModuleNotFoundError: + pass + # just for fun from .asciiart import set_ascii diff --git a/tensorcircuit/about.py b/tensorcircuit/about.py index 40f77c8f..d071c1dd 100644 --- a/tensorcircuit/about.py +++ b/tensorcircuit/about.py @@ -39,9 +39,12 @@ def about() -> None: print(f"TensorNetwork is not installed") try: - import cotengra as _ + import cotengra - print(f"Cotengra: installed") + try: + print(f"Cotengra version: {cotengra.__version__}") + except AttributeError: + print(f"Cotengra: installed") except ModuleNotFoundError: print(f"Cotengra is not installed") @@ -107,6 +110,10 @@ def about() -> None: except ModuleNotFoundError: print(f"Cirq is not installed") + from tensorcircuit import __version__ + + print(f"TensorCircuit version {__version__}") + if __name__ == "__main__": about() diff --git a/tensorcircuit/abstractcircuit.py b/tensorcircuit/abstractcircuit.py index b98c892f..2334aa39 100644 --- a/tensorcircuit/abstractcircuit.py +++ b/tensorcircuit/abstractcircuit.py @@ -1,22 +1,24 @@ """ Methods for abstract circuits independent of nodes, edges and contractions """ + # pylint: disable=invalid-name -from typing import Any, Callable, Dict, List, Optional, Sequence, Union, Tuple +import json +import logging from copy import deepcopy from functools import reduce from operator import add -import json -import logging +from typing import Any, Callable, Dict, List, Optional, Sequence, Tuple, Union import numpy as np import tensornetwork as tn from . import gates from .cons import backend, dtypestr -from .vis import qir2tex from .quantum import QuOperator +from .utils import is_sequence +from .vis import qir2tex logger = logging.getLogger(__name__) @@ -128,7 +130,25 @@ def apply(self: "AbstractCircuit", *index: int, **vars: Any) -> None: ir_dict=gate_dict, ) - return apply + def apply_list(self: "AbstractCircuit", *index: int, **vars: Any) -> None: + if isinstance(index[0], int): + apply(self, *index, **vars) + elif is_sequence(index[0]) or isinstance(index[0], range): + for i, ind in enumerate(zip(*index)): + nvars = {} + for k, v in vars.items(): + try: + nvars[k] = v[i] + except Exception: # pylint: disable=W0703 + # (TypeError, IndexError) is not enough, + # tensorflow.python.framework.errors_impl.InvalidArgumentError + # not ideally captured here + nvars[k] = v + apply(self, *ind, **nvars) + else: + raise ValueError("Illegal index specification") + + return apply_list @staticmethod def apply_general_gate_delayed( @@ -167,7 +187,16 @@ def apply( ir_dict=gate_dict, ) - return apply + def apply_list(self: "AbstractCircuit", *index: int, **kws: Any) -> None: + if isinstance(index[0], int): + apply(self, *index, **kws) + elif is_sequence(index[0]) or isinstance(index[0], range): + for ind in zip(*index): + apply(self, *ind, **kws) + else: + raise ValueError("Illegal index specification") + + return apply_list @classmethod def _meta_apply(cls) -> None: @@ -406,13 +435,58 @@ def inverse( c = type(self)(**circuit_params) for d in reversed(self._qir): if "parameters" not in d: - self.apply_general_gate_delayed( - d["gatef"].adjoint(), d["name"], mpo=d["mpo"] - )(c, *d["index"], split=d["split"]) + if d["gatef"].n in self.sgates and d["gatef"].n not in [ + "wroot", + "sd", + "td", + ]: + self.apply_general_gate_delayed( + d["gatef"], d["name"], mpo=d["mpo"] + )(c, *d["index"], split=d["split"]) + elif d["gatef"].n in ["sd", "td"]: + self.apply_general_gate_delayed( + getattr(gates, d["gatef"].n[:-1]), d["name"], mpo=d["mpo"] + )(c, *d["index"], split=d["split"]) + else: + self.apply_general_gate_delayed( + d["gatef"].adjoint(), d["name"], mpo=d["mpo"] + )(c, *d["index"], split=d["split"]) else: - self.apply_general_variable_gate_delayed( - d["gatef"].adjoint(), d["name"], mpo=d["mpo"] - )(c, *d["index"], **d["parameters"], split=d["split"]) + if d["gatef"].n in ["r", "cr"]: + params = {k: v for k, v in d["parameters"].items()} + if "theta" in params: + params["theta"] = -params.get("theta", 0.0) + self.apply_general_variable_gate_delayed( + d["gatef"], d["name"], mpo=d["mpo"] + )(c, *d["index"], **params, split=d["split"]) + elif d["gatef"].n in ["u", "cu"]: + params = {k: v for k, v in d["parameters"].items()} + # deepcopy fail with tf+jit + params["lbd"] = -d["parameters"].get("phi", 0) + np.pi + params["phi"] = -d["parameters"].get("lbd", 0) + np.pi + self.apply_general_variable_gate_delayed( + d["gatef"], d["name"], mpo=d["mpo"] + )(c, *d["index"], **params, split=d["split"]) + elif d["gatef"].n in self.vgates and d["gatef"].n not in [ + "any", + "exp", + "exp1", + ]: + params = {k: v for k, v in d["parameters"].items()} + df = 0.0 + if d["gatef"].n == "iswap": + df = 1.0 + params["theta"] = -params.get("theta", df) + self.apply_general_variable_gate_delayed( + d["gatef"], d["name"], mpo=d["mpo"] + )(c, *d["index"], **params, split=d["split"]) + + # TODO(@refraction-ray): multi control gate? + + else: + self.apply_general_variable_gate_delayed( + d["gatef"].adjoint(), d["name"], mpo=d["mpo"] + )(c, *d["index"], **d["parameters"], split=d["split"]) return c @@ -602,39 +676,41 @@ def gate_summary(self) -> Dict[str, int]: summary[d["name"]] = summary.get(d["name"], 0) + 1 return summary - def measure_instruction(self, index: int) -> None: + def measure_instruction(self, *index: int) -> None: """ add a measurement instruction flag, no effect on numerical simulation - :param index: the corresponding qubit + :param index: the corresponding qubits :type index: int """ l = len(self._qir) - d = { - "index": [index], - "name": "measure", - "gatef": "measure", - "instruction": True, - "pos": l, - } - self._extra_qir.append(d) + for ind in index: + d = { + "index": [ind], + "name": "measure", + "gatef": "measure", + "instruction": True, + "pos": l, + } + self._extra_qir.append(d) - def reset_instruction(self, index: int) -> None: + def reset_instruction(self, *index: int) -> None: """ add a reset instruction flag, no effect on numerical simulation - :param index: the corresponding qubit + :param index: the corresponding qubits :type index: int """ l = len(self._qir) - d = { - "index": [index], - "name": "reset", - "gatef": "reset", - "instruction": True, - "pos": l, - } - self._extra_qir.append(d) + for ind in index: + d = { + "index": [ind], + "name": "reset", + "gatef": "reset", + "instruction": True, + "pos": l, + } + self._extra_qir.append(d) def barrier_instruction(self, *index: List[int]) -> None: """ @@ -680,7 +756,7 @@ def to_qiskit( :type enable_inputs: bool, defaults to False :return: A qiskit object of this circuit. """ - from .translation import qir2qiskit, perm_matrix + from .translation import perm_matrix, qir2qiskit qir = self.to_qir() if enable_instruction: @@ -752,6 +828,7 @@ def draw(self, **kws: Any) -> Any: Visualise the circuit. This method recevies the keywords as same as qiskit.circuit.QuantumCircuit.draw. More details can be found here: https://qiskit.org/documentation/stubs/qiskit.circuit.QuantumCircuit.draw.html. + Interesting kws options include: ``idle_wires``(bool) :Example: >>> c = tc.Circuit(3) @@ -810,7 +887,7 @@ def from_qiskit( n = qc.num_qubits return qiskit2tc( # type: ignore - qc.data, + qc, n, inputs, circuit_constructor=cls, @@ -1096,6 +1173,11 @@ def append( self.__dict__.update(newc.__dict__) return self + def copy(self) -> "AbstractCircuit": + qir = self.to_qir() + c = type(self).from_qir(qir, self.circuit_param) + return c + def expectation( self, *ops: Tuple[tn.Node, List[int]], @@ -1112,6 +1194,7 @@ def expectation_ps( x: Optional[Sequence[int]] = None, y: Optional[Sequence[int]] = None, z: Optional[Sequence[int]] = None, + ps: Optional[Sequence[int]] = None, reuse: bool = True, noise_conf: Optional[Any] = None, nmc: int = 1000, @@ -1150,6 +1233,10 @@ def expectation_ps( :type y: Optional[Sequence[int]], optional :param z: sites to apply Z gate, defaults to None :type z: Optional[Sequence[int]], optional + :param ps: or one can apply a ps structures instead of ``x``, ``y``, ``z``, + e.g. [0, 1, 3, 0, 2, 2] for X_1Z_2Y_4Y_5 + defaults to None, ``ps`` can overwrite ``x``, ``y`` and ``z`` + :type ps: Optional[Sequence[int]], optional :param reuse: whether to cache and reuse the wavefunction, defaults to True :type reuse: bool, optional :param noise_conf: Noise Configuration, defaults to None @@ -1163,6 +1250,14 @@ def expectation_ps( :rtype: Tensor """ obs = [] + if ps is not None: + from .quantum import ps2xyz + + d = ps2xyz(ps) # type: ignore + x = d.get("x", None) + y = d.get("y", None) + z = d.get("z", None) + if x is not None: for i in x: obs.append([gates.x(), [i]]) # type: ignore diff --git a/tensorcircuit/applications/README.md b/tensorcircuit/applications/README.md index c63ef6cf..202e06cf 100644 --- a/tensorcircuit/applications/README.md +++ b/tensorcircuit/applications/README.md @@ -1,3 +1,6 @@ +Code implementation in this submodule `applications` are not very well maintained and extensively tested. There are indeed many interesting pieces, but try on your own risk. + + ## Differentiable Quantum Architecture Search In `applications`, framework and relevant applications of DQAS are implemented, mainly in `vags.py` and `dqas.py`. diff --git a/tensorcircuit/applications/__init__.py b/tensorcircuit/applications/__init__.py index 99d7c732..70d128b0 100644 --- a/tensorcircuit/applications/__init__.py +++ b/tensorcircuit/applications/__init__.py @@ -1,5 +1,5 @@ """ The application codebase is related to research and previous version of tensorcircuit, the code inside is subject to change, be caution to use. -Most of the useful code is refactored and copied to other parts of tensorcircuit. +Most of the useful code is and will be refactored and copied to other parts of tensorcircuit. """ diff --git a/tensorcircuit/applications/ai/__init__.py b/tensorcircuit/applications/ai/__init__.py new file mode 100644 index 00000000..e69de29b diff --git a/tensorcircuit/templates/ensemble.py b/tensorcircuit/applications/ai/ensemble.py similarity index 93% rename from tensorcircuit/templates/ensemble.py rename to tensorcircuit/applications/ai/ensemble.py index f8b97aee..a9d6b0d7 100644 --- a/tensorcircuit/templates/ensemble.py +++ b/tensorcircuit/applications/ai/ensemble.py @@ -4,24 +4,22 @@ from typing import Any, List, Optional import tensorflow as tf -import keras import numpy as np NDArray = Any kwargus = Any +model_type = Any class bagging: # A.K.A. voting def __init__(self) -> None: - self.models: List[keras.engine.functional.Functional] = [] + self.models: List[model_type] = [] self.model_trained: List[bool] = [] self.count = 0 self.need_confidence = True # Help in reducing numbers of get_confidence runs self.permit_train = False - def append( - self, model: keras.engine.functional.Functional, model_trained: bool - ) -> None: + def append(self, model: model_type, model_trained: bool) -> None: """ Add model to the voting method """ @@ -55,9 +53,13 @@ def train(self, **kwargs: kwargus) -> None: def compile(self, **kwargs: kwargus) -> None: self.permit_train = True + for i in range(self.count): if not self.model_trained[i]: - self.models[i].compile(**kwargs) + dict_kwargs = kwargs.copy() + # TODO(@refraction-ray): still not compatible with new optimizer + # https://github.com/tensorflow/tensorflow/issues/58973 + self.models[i].compile(**dict_kwargs) def __get_confidence(self, model_index: int, input: NDArray) -> NDArray: """ diff --git a/tensorcircuit/applications/dqas.py b/tensorcircuit/applications/dqas.py index d139fe01..161a2c73 100644 --- a/tensorcircuit/applications/dqas.py +++ b/tensorcircuit/applications/dqas.py @@ -1,6 +1,7 @@ """ Modules for DQAS framework """ + # possibly deprecated, multiprocessing is not the recommended way to do DQAS task now, using vmap! import sys @@ -486,9 +487,9 @@ def qaoa_simple_train( if "prob_model_func" in kws: pmf = kws["prob_model_func"] del kws["prob_model_func"] - kws[ - "prob_model" - ] = pmf() # in case keras model cannot pickled for multiprocessing map + kws["prob_model"] = ( + pmf() + ) # in case keras model cannot pickled for multiprocessing map if isinstance(graph, list): def graph_generator() -> Iterator[Graph]: diff --git a/tensorcircuit/applications/finance/__init__.py b/tensorcircuit/applications/finance/__init__.py new file mode 100644 index 00000000..e69de29b diff --git a/tensorcircuit/applications/finance/portfolio.py b/tensorcircuit/applications/finance/portfolio.py new file mode 100644 index 00000000..a9097241 --- /dev/null +++ b/tensorcircuit/applications/finance/portfolio.py @@ -0,0 +1,89 @@ +""" +Supplementary functions for portfolio optimization +""" + +from typing import Any + +import numpy as np + +Array = Any +Tensor = Any + + +def QUBO_from_portfolio(cov: Array, mean: Array, q: float, B: int, t: float) -> Tensor: + """ + convert portfolio parameters to a Q matrix + :param cov: n-by-n covariance numpy array + :param mean: numpy array of means + :param q: the risk preference of investor + :param B: budget + :param t: penalty factor + :return Q: n-by-n symmetric Q matrix + """ + n = cov.shape[0] + R = np.diag(mean) + S = np.ones((n, n)) - 2 * B * np.diag(np.ones(n)) + + Q = q * cov - R + t * S + return Q + + +class StockData: + """ + A class for converting real-world stock data to an annualized covariance matrix and annualized return. + + Attributes: + - data: A list of continuous stock data in the same time span. + - n_stocks: The number of stocks in the data. + - n_days: The number of trading days in the data. + + Methods: + - __init__(self, data): Initializes the StockData object. + - get_return(self, decimals=5): Calculates the annualized return. + - get_covariance(self, decimals=5): Calculates the annualized covariance matrix. + """ + + def __init__(self, data: Tensor): + """ + Initializes the StockData object. + + :param data: A list of continuous stock data in the same time span. + """ + self.data = data + self.n_stocks = len(data) + + # Check the number of days + n_days = [len(i) for i in data] + if max(n_days) != (sum(n_days) / len(n_days)): + raise Exception("Timespan of stocks should be the same") + self.n_days = len(data[1]) + + # Calculate the daily percentage price change + self.daily_change = [ + np.diff(data[i][:]) / data[i][:-1] for i in range(self.n_stocks) + ] + + def get_return(self, decimals: int = 5) -> Any: + """ + Calculates the annualized return (mu). + + :param decimals: Number of decimal places to round the result to (default: 5). + :return: The annualized return as an array rounded to the specified number of decimals. + """ + change = [[j + 1 for j in i] for i in self.daily_change] + ret = np.prod(change, axis=1) ** (252 / self.n_days) + return ret.round(decimals) + + def get_covariance(self, decimals: int = 5) -> Tensor: + """ + Calculates the annualized covariance matrix (sigma). + + :param decimals: Number of decimal places to round the result to (default: 5). + :return: The annualized covariance matrix rounded to the specified number of decimals. + """ + mean = np.mean(self.daily_change, axis=1) + relative_change = [ + [j - mean[i] for j in self.daily_change[i]] for i in range(6) + ] + cov = 252 / self.n_days * np.dot(relative_change, np.transpose(relative_change)) + return cov.round(decimals) diff --git a/tensorcircuit/applications/layers.py b/tensorcircuit/applications/layers.py index 18f53db6..64eef546 100644 --- a/tensorcircuit/applications/layers.py +++ b/tensorcircuit/applications/layers.py @@ -1,6 +1,7 @@ """ Module for functions adding layers of circuits """ + import itertools import logging import sys diff --git a/tensorcircuit/applications/optimization.py b/tensorcircuit/applications/optimization.py new file mode 100644 index 00000000..28c5c81a --- /dev/null +++ b/tensorcircuit/applications/optimization.py @@ -0,0 +1,364 @@ +""" +modules for QUBO problems in QAOA +""" + +from typing import List, Callable, Any, Optional, Tuple +from functools import partial + +import tensorflow as tf +import scipy.optimize as optimize + +from ..cons import backend +from ..quantum import measurement_results +from ..interfaces import scipy_interface +from ..templates.ansatz import QAOA_ansatz_for_Ising +from ..templates.conversions import QUBO_to_Ising + +Circuit = Any +Tensor = Any +Array = Any + + +def Ising_loss(c: Circuit, pauli_terms: Tensor, weights: List[float]) -> Any: + """ + computes the loss function for the Ising model based on a given quantum circuit, + a list of Pauli terms, and corresponding weights. + The offset is ignored. + + :param c: A quantum circuit object generating the state. + :param pauli_terms: A list of Pauli terms, where each term is represented as a list of 0/1 series. + :param weights: A list of weights corresponding to each Pauli term. + :return loss: A real number representing the computed loss value. + """ + loss = 0.0 + for k in range(len(pauli_terms)): + term = pauli_terms[k] + index_of_ones = [] + + for l in range(len(term)): + if term[l] == 1: + index_of_ones.append(l) + + # Compute expectation value based on the number of qubits involved in the Pauli term + if len(index_of_ones) == 1: + delta_loss = weights[k] * c.expectation_ps(z=[index_of_ones[0]]) + # Compute expectation value for a single-qubit Pauli term + else: + delta_loss = weights[k] * c.expectation_ps( + z=[index_of_ones[0], index_of_ones[1]] + ) + # Compute expectation value for a two-qubit Pauli term + + loss += delta_loss + + return backend.real(loss) + + +def QAOA_loss( + nlayers: int, + pauli_terms: Tensor, + weights: List[float], + params: List[float], + full_coupling: bool = False, + mixer: str = "X", +) -> Any: + """ + computes the loss function for the Quantum Approximate Optimization Algorithm (QAOA) applied to the Ising model. + + :param nlayers: The number of layers in the QAOA ansatz. + :param pauli_terms: A list of Pauli terms, where each term is represented as a list of 0/1 series. + :param weights: A list of weights corresponding to each Pauli term. + :param params: A list of parameter values used in the QAOA ansatz. + :param full_coupling (optional): A flag indicating whether to use all-to-all coupling in mixers. Default is False. + :paran mixer (optional): The mixer operator to use. Default is "X". The other options are "XY" and "ZZ". + :return: The computed loss value. + """ + c = QAOA_ansatz_for_Ising( + params, nlayers, pauli_terms, weights, mixer=mixer, full_coupling=full_coupling + ) + # Obtain the quantum circuit using QAOA_from_Ising function + + return Ising_loss(c, pauli_terms, weights) + # Compute the Ising loss using Ising_loss function on the obtained circuit + + +def QUBO_QAOA( + Q: Tensor, + nlayers: int, + iterations: int, + vvag: bool = False, + ncircuits: int = 10, + init_params: Optional[List[float]] = None, + mixer: str = "X", + learning_rate: float = 1e-2, + callback: Optional[Optional[Callable[[List[float], float], None]]] = None, + full_coupling: bool = False, +) -> Array: + """ + Performs the QAOA on a given QUBO problem. + Adam optimizer from TensorFlow is used. + + :param Q: The n-by-n square and symmetric Q-matrix representing the QUBO problem. + :param nlayers: The number of layers (depth) in the QAOA ansatz. + :param iterations: The number of iterations to run the optimization. + :param vvag (optional): A flag indicating whether to use vectorized variational adjoint gradient. Default is False. + :param ncircuits (optional): The number of circuits when using vectorized variational adjoint gradient. + Default is 10. + :param init_params (optional): The initial parameters for the ansatz circuit. + Default is None, which initializes the parameters randomly. + :paran mixer (optional): The mixer operator to use. Default is "X". The other options are "XY" and "ZZ". + :param learning_rate (optional): The learning rate for the Adam optimizer. Default is 1e-2. + :param callback (optional): A callback function that is executed during each iteration. Default is None. + :param full_coupling (optional): A flag indicating whether to use all-to-all coupling in mixers. Default is False. + :return params: The optimized parameters for the ansatz circuit. + """ + + pauli_terms, weights, _ = QUBO_to_Ising(Q) + + loss_val_grad = backend.value_and_grad( + partial( + QAOA_loss, + nlayers, + pauli_terms, + weights, + mixer=mixer, + full_coupling=full_coupling, + ) + ) + loss_val_grad = backend.jit(loss_val_grad, static_argnums=(1, 2)) + # Define the loss and gradients function using value_and_grad, which calculates both the loss value and gradients. + + if init_params is None: + params = backend.implicit_randn(shape=[2 * nlayers], stddev=0.5) + if vvag is True: + loss_val_grad = backend.vvag(loss_val_grad, argnums=0, vectorized_argnums=0) + params = backend.implicit_randn(shape=[ncircuits, 2 * nlayers], stddev=0.1) + # If init_params is not provided, initialize the parameters randomly. + # If vvag flag is set to True, use vectorized variational adjoint gradient (vvag) with multiple circuits. + else: + params = init_params + # If init_params is provided, use the provided parameters. + # Initialize the parameters for the ansatz circuit. + + # This can improve the performance by pre-compiling the loss and gradients function. + + opt = backend.optimizer(tf.keras.optimizers.Adam(learning_rate)) + # Define the optimizer (Adam optimizer) with the specified learning rate. + + for _ in range(iterations): + loss, grads = loss_val_grad(params) + # Calculate the loss and gradients using the loss_val_grad_jit function. + + params = opt.update(grads, params) + # Update the parameters using the optimizer and gradients. + + if callback is not None: + callback(loss, params) + # Execute the callback function with the current loss and parameters. + + return params + # Return the optimized parameters for the ansatz circuit. + + +def cvar_value(r: List[float], p: List[float], percent: float) -> Any: + """ + Compute the Conditional Value at Risk (CVaR) based on the measurement results. + + :param r: The observed outcomes after measurements. + :param p: Probabilities associated with each observed outcome. + :param percent: The cut-off percentage for CVaR computation. + :return: The calculated CVaR value. + """ + sorted_indices = tf.argsort(r) + p_sorted = tf.cast(tf.gather(p, sorted_indices), dtype=tf.float32) + r_sorted = tf.cast(tf.gather(r, sorted_indices), dtype=tf.float32) + + # Calculate the cumulative sum of sorted probabilities. + cumsum_p = tf.math.cumsum(p_sorted) + + # Create a tensor that evaluates to 1 if the condition is met, otherwise 0. + mask = tf.cast(tf.math.less(cumsum_p, percent), dtype=tf.float32) + + # Use mask to filter and sum the required elements for CVaR. + cvar_numerator = tf.reduce_sum(mask * p_sorted * r_sorted) + + # Compute the last remaining portion that exceeds the cut-off percentage. + last_portion_index = tf.math.argmax(tf.math.greater_equal(cumsum_p, percent)) + last_portion = (percent - cumsum_p[last_portion_index - 1]) * r_sorted[ + last_portion_index + ] + + # Calculate the final CVaR. + cvar_result = (cvar_numerator + last_portion) / percent + + return cvar_result + + +def cvar_from_circuit(circuit: Circuit, nsamples: int, Q: Tensor, alpha: float) -> Any: + """ + Directly calculate the Conditional Value at Risk (CVaR) from a circuit. + The CVaR depends on a bunch of measurements. + + :param circuit: The quantum circuit used to prepare the state. + :param nsamples: The number of samples to take for measurements. + :param Q: The Q-matrix representing the Quadratic Unconstrained Binary Optimization (QUBO) problem. + :param alpha: The cut-off percentage for CVaR. + :return: The calculated CVaR value. + """ + # Obtain and normalize measurement results + measurement_data = circuit.state() + results = measurement_results( + measurement_data, counts=nsamples, format="sample_int", jittable=True + ) + n_counts = tf.shape(results)[0] + + # Determine the number of qubits in the circuit and generate all possible states + n_qubits = len(Q) + all_states = tf.constant([format(i, f"0{n_qubits}b") for i in range(2**n_qubits)]) + all_binary = tf.reshape( + tf.strings.to_number(tf.strings.bytes_split(all_states), tf.float32), + (2**n_qubits, n_qubits), + ) + all_decimal = tf.range(2**n_qubits, dtype=tf.int32) + + # Convert the Q matrix to a TensorFlow tensor + Q_tensor = tf.convert_to_tensor(Q, dtype=tf.float32) + + # calculate cost values + values = tf.reduce_sum(all_binary * tf.matmul(all_binary, Q_tensor), axis=1) + + # Count the occurrences of each state and calculate probabilities + state_counts = tf.reduce_sum( + tf.cast(tf.equal(tf.reshape(results, [-1, 1]), all_decimal), tf.int32), axis=0 + ) + probabilities = tf.cast(state_counts, dtype=tf.float32) / tf.cast( + n_counts, dtype=tf.float32 + ) + + # Calculate CVaR + cvar_result = cvar_value(values, probabilities, alpha) + + return cvar_result + + +def cvar_from_expectation(circuit: Circuit, Q: Tensor, alpha: float) -> Any: + """ + Calculate the Conditional Value at Risk (CVaR) from the expectation values of a quantum circuit. + + :param circuit: The quantum circuit. + :param Q: The Q-matrix representing the Quadratic Unconstrained Binary Optimization (QUBO) problem. + :param alpha: The cut-off percentage for CVaR. + :return: The calculated CVaR value. + """ + + # Calculate the probability amplitudes for quantum circuit outcomes. + prob = tf.convert_to_tensor(circuit.probability(), dtype=tf.float32) + + # Generate all possible binary states for the given Q-matrix. + n_qubits = len(Q) + all_states = tf.constant( + [format(i, "0" + str(n_qubits) + "b") for i in range(2 ** len(Q))] + ) + all_binary = tf.reshape( + tf.strings.to_number(tf.strings.bytes_split(all_states), tf.float32), + (2**n_qubits, n_qubits), + ) + + # Convert the Q-matrix to a TensorFlow tensor. + Q_tensor = tf.convert_to_tensor(Q, dtype=tf.float32) + + # calculate cost values + elementwise_product = tf.multiply(all_binary, tf.matmul(all_binary, Q_tensor)) + values = tf.reduce_sum(elementwise_product, axis=1) + + # Calculate the CVaR value using the computed values and the probability distribution. + cvar_result = cvar_value(values, prob, alpha) + + return cvar_result + + +def cvar_loss( + nlayers: int, + Q: Tensor, + nsamples: int, + alpha: float, + expectation_based: bool, + params: List[float], +) -> Any: + """ + Calculate the CVaR loss for a given QUBO problem using the QAOA ansatz. + + :param nlayers: The number of layers (depth) in the QAOA ansatz. + :param Q: The Q-matrix representing the Quadratic Unconstrained Binary Optimization (QUBO) problem. + :param nsamples: The number of samples to take for measurements in the CVaR calculation. + :param alpha: The cut-off percentage for CVaR. + :param expectation_based: A flag indicating the type of CVaR ansatz (measurement-based or expectation-based). + :param params: The parameters for the QAOA ansatz circuit. + :return: The calculated CVaR loss. + """ + + pauli_terms, weights, _ = QUBO_to_Ising(Q) + + c = QAOA_ansatz_for_Ising(params, nlayers, pauli_terms, weights) + # Generate the QAOA ansatz circuit for the given parameters. + + if expectation_based is False: + return cvar_from_circuit(c, nsamples, Q, alpha) + # Calculate CVaR using circuit-based measurement results. + elif expectation_based is True: + return cvar_from_expectation(c, Q, alpha) + # Calculate CVaR using expectation values of the circuit. + else: + raise ValueError("Invalid CVaR ansatz type.") + # Raise an error if an invalid CVaR ansatz type is provided. + + +def QUBO_QAOA_cvar( + Q: Tensor, + nlayers: int, + alpha: float, + nsamples: int = 1000, + callback: Optional[Callable[[List[float], float], None]] = None, + expectation_based: bool = False, + maxiter: int = 1000, + init_params: Optional[Tuple[float,]] = None, +) -> Array: + """ + Perform the QUBO QAOA optimization with CVaR as the loss function. + + :param Q: The n-by-n square and symmetric Q-matrix representing the QUBO problem. + :param ansatz: The ansatz function to be used for QAOA. + :param nlayers: The number of layers (depth) in the QAOA ansatz. + :param alpha: The cut-off percentage for CVaR. + :param nsamples: The number of samples for measurements in the CVaR calculation. Default is 1000. + :param callback: A callback function to be called after each iteration. Default is None. + :param expectation_based: A flag indicating the type of CVaR ansatz (measurement-based or expectation-based). + Default is False. + :param maxiter: The maximum number of iterations for the optimization. Default is 1000. + :return: The optimized parameters for the ansatz circuit. + """ + loss = partial(cvar_loss, nlayers, Q, nsamples, alpha, expectation_based) + + f_scipy = scipy_interface(loss, shape=(2 * nlayers,), jit=True, gradient=False) + + if init_params is None: + params = backend.implicit_randn(shape=[2 * nlayers], stddev=0.5) + # If init_params is not provided, initialize the parameters randomly. + else: + params = init_params + # If init_params is provided, use the provided parameters. + + # Initialize the parameters for the ansatz circuit. + params = backend.implicit_randn(shape=[2 * nlayers], stddev=0.5) + + r = optimize.minimize( + f_scipy, + params, + method="COBYLA", + callback=callback, + options={"maxiter": maxiter}, + ) + # Perform the optimization using the COBYLA method from scipy.optimize. + + return r.x + # Return the optimized parameters for the ansatz circuit. diff --git a/tensorcircuit/applications/physics/__init__.py b/tensorcircuit/applications/physics/__init__.py new file mode 100644 index 00000000..e69de29b diff --git a/tensorcircuit/applications/physics/baseline.py b/tensorcircuit/applications/physics/baseline.py new file mode 100644 index 00000000..9105abaf --- /dev/null +++ b/tensorcircuit/applications/physics/baseline.py @@ -0,0 +1,57 @@ +""" +baseline calculators for physical systems +""" + +import numpy as np + + +def TFIM1Denergy( + L: int, Jzz: float = 1.0, Jx: float = 1.0, Pauli: bool = True +) -> float: + # PBC + # nice tutorial: https://arxiv.org/pdf/2009.09208.pdf + # further investigation on 1 TFIM solution structure is required + # will fail on AFM phase Jzz>Jx and Jzz>0 and odd sites (frustration in boundary) + e = 0 + if Pauli: + Jx *= 2 + Jzz *= 4 + for i in range(L): + q = np.pi * (2 * i - (1 + (-1) ** L) / 2) / L + e -= np.abs(Jx) / 2 * np.sqrt(1 + Jzz**2 / 4 / Jx**2 - Jzz / Jx * np.cos(q)) + return e + + +def Heisenberg1Denergy(L: int, Pauli: bool = True, maxiters: int = 1000) -> float: + # PBC + error = 1e-15 + eps = 1e-20 # avoid zero division + phi = np.zeros([L // 2, L // 2]) + phi2 = np.zeros([L // 2, L // 2]) + lamb = np.array([2 * i + 1 for i in range(L // 2)]) + for _ in range(maxiters): + k = 1 / L * (2 * np.pi * lamb + np.sum(phi, axis=-1) - np.diag(phi)) + for i in range(L // 2): + for j in range(L // 2): + phi2[i, j] = ( + np.arctan( + 2 + / ( + 1 / (np.tan(k[i] / 2) + eps) + - 1 / (np.tan(k[j] / 2) + eps) + + eps + ) + ) + * 2 + ) + if np.allclose(phi, phi2, rtol=error): # converged + break + phi = phi2.copy() + else: + raise ValueError( + "the maxiters %s is too small for bethe ansatz to converge" % maxiters + ) + e = -np.sum(1 - np.cos(k)) + L / 4 + if Pauli is True: + e *= 4 + return e # type: ignore diff --git a/tensorcircuit/applications/physics/fss.py b/tensorcircuit/applications/physics/fss.py new file mode 100644 index 00000000..f0490509 --- /dev/null +++ b/tensorcircuit/applications/physics/fss.py @@ -0,0 +1,110 @@ +""" +finite size scaling tools +""" + +from typing import List, Tuple, Optional + +import numpy as np + + +def data_collapse( + n: List[int], + p: List[float], + obs: List[List[float]], + pc: float, + nu: float, + beta: float = 0, + obs_type: int = 1, + fit_type: int = 0, + dobs: Optional[List[List[float]]] = None, +) -> Tuple[List[float], List[List[float]], List[List[float]], float]: + xL: List[List[float]] = [] # x=(p-pc)L^(1/\nv) + yL: List[List[float]] = [] # y=S(p,L)-S(pc,L) or S(p,L) + pc_list = [] + if not isinstance(p[0], list): + p = [p for _ in n] # type: ignore + for n0 in range(len(n)): + xL.append([]) + yL.append([]) + for p0 in range(len(p[n0])): # type: ignore + xL[n0].append((p[n0][p0] - pc) * (n[n0] ** (1 / nu))) # type: ignore + pc_L = pc_linear_interpolation(p[n0], obs[n0], pc) # type: ignore + if obs_type == 0: + yL[n0].append((obs[n0][p0] - pc_L) * n[n0] ** beta) + # entanglement with only collapse and no crossing + else: + yL[n0].append(obs[n0][p0] * n[n0] ** beta) + # tripartite mutual information + pc_list.append(pc_L) + if fit_type == 0: + xL_all = [] + for i in range(len(xL)): + xL_all.extend(xL[i]) + yL_ave = [] + loss = [] + for x0 in range(len(xL_all)): + ybar_list = [] + for n0 in range(len(n)): + if xL_all[x0] >= xL[n0][0] and xL_all[x0] <= xL[n0][-1]: + yinsert = pc_linear_interpolation(xL[n0], yL[n0], xL_all[x0]) + ybar_list.append(yinsert) + + ybar = np.mean(ybar_list) + mean_squared = [(ybar_list[i] - ybar) ** 2 for i in range(len(ybar_list))] + loss.append(np.sum(mean_squared)) + yL_ave.append(ybar) + loss = np.sum(loss) + + return pc_list, xL, yL, loss # type: ignore + + # fit_type == 1 + if dobs is None: + raise ValueError("uncertainty of each y has to be specified in `dobs`") + + datas = [] + for n0 in range(len(n)): + for i in range(len(xL[n0])): + datas.append([xL[n0][i], yL[n0][i], dobs[n0][i]]) + datas = sorted(datas, key=lambda x: x[0]) + loss = _quality_objective_v2(datas) # type: ignore + return pc_list, xL, yL, loss # type: ignore + + +def _quality_objective_v2(datas: List[List[float]]) -> float: + # https://journals.aps.org/prb/supplemental/10.1103/PhysRevB.101.060301/Supplement.pdf + loss = [] + for i in range(len(datas) - 2): + # i, i+1, i+2 + x, y, d = datas[i + 1] + x1, y1, d1 = datas[i] + x2, y2, d2 = datas[i + 2] + if np.abs(x - x1) < 1e-4 or np.abs(x - x2) < 1e-4: + continue + ybar = ((x2 - x) * y1 - (x1 - x) * y2) / (x2 - x1) + delta = ( + d**2 + + d1**2 * (x2 - x) ** 2 / (x2 - x1) ** 2 + + d2**2 * (x1 - x) ** 2 / (x2 - x1) ** 2 + ) + w = (y - ybar) ** 2 / delta + loss.append(w) + return np.mean(loss) # type: ignore + + +def pc_linear_interpolation(p: List[float], SA: List[float], pc_input: float) -> float: + if pc_input in p: + pc_index = p.index(pc_input) + pc = SA[pc_index] + else: + pr_index = 0 + for p0 in range(len(p)): + if p[p0] > pc_input: + pr_index = p0 + break + + x = [p[pr_index - 1], p[pr_index]] + y = [SA[pr_index - 1], SA[pr_index]] + linear_model = np.polyfit(x, y, 1) + linear_model_fn = np.poly1d(linear_model) + pc = linear_model_fn(pc_input) + return pc diff --git a/tensorcircuit/applications/utils.py b/tensorcircuit/applications/utils.py index a2db4fee..3ca54ff2 100644 --- a/tensorcircuit/applications/utils.py +++ b/tensorcircuit/applications/utils.py @@ -2,6 +2,7 @@ A collection of useful function snippets that irrelevant with the main modules or await for further refactor """ + import logging from typing import Any, Callable, Iterator, Optional, Sequence, Tuple @@ -388,6 +389,8 @@ def repr2array(inputs: str) -> Array: return np.array(outputs) +# duplicated, will remove later +# use the version in applications.physics.baseline.py def TFIM1Denergy( L: int, Jzz: float = 1.0, Jx: float = 1.0, Pauli: bool = True ) -> float: diff --git a/tensorcircuit/applications/vags.py b/tensorcircuit/applications/vags.py index 80e5b74a..b2b5a612 100644 --- a/tensorcircuit/applications/vags.py +++ b/tensorcircuit/applications/vags.py @@ -1,6 +1,7 @@ """ DQAS application kernels as vag functions """ + from functools import lru_cache, partial, reduce import logging import operator diff --git a/tensorcircuit/applications/vqes.py b/tensorcircuit/applications/vqes.py index ba279365..a542268b 100644 --- a/tensorcircuit/applications/vqes.py +++ b/tensorcircuit/applications/vqes.py @@ -1,6 +1,7 @@ """ VQNHE application """ + from functools import lru_cache from itertools import product import time diff --git a/tensorcircuit/asciiart.py b/tensorcircuit/asciiart.py index b63b317e..b5c9e3b4 100644 --- a/tensorcircuit/asciiart.py +++ b/tensorcircuit/asciiart.py @@ -1,6 +1,7 @@ """ Some ascii art from https://www.asciiart.eu/, have fun! """ + # pylint: disable=invalid-name import hashlib diff --git a/tensorcircuit/backends/abstract_backend.py b/tensorcircuit/backends/abstract_backend.py index e6f69f97..4a7ccecd 100644 --- a/tensorcircuit/backends/abstract_backend.py +++ b/tensorcircuit/backends/abstract_backend.py @@ -1,6 +1,7 @@ """ Backend magic inherited from tensornetwork: abstract backend """ + # pylint: disable=invalid-name # pylint: disable=unused-variable @@ -25,7 +26,7 @@ def copy(self: Any, a: Tensor) -> Tensor: :param a: tensor in matrix form :type a: Tensor - :return: matrix exponential of matrix ``a`` + :return: the copy tensor of ``a`` :rtype: Tensor """ raise NotImplementedError( @@ -345,6 +346,34 @@ def adjoint(self: Any, a: Tensor) -> Tensor: """ return self.conj(self.transpose(a)) + def det(self: Any, a: Tensor) -> Tensor: + """ + Return the determinant scalar of a tensor ``a`` + + :param a: Input tensor + :type a: Tensor + :return: determinant of ``a`` + :rtype: Tensor + """ + raise NotImplementedError( + "Backend '{}' has not implemented `det`.".format(self.name) + ) + + def schur(self: Any, a: Tensor, output: str = "real") -> Tuple[Tensor, Tensor]: + """ + Compute Schur decomposition of a matrix. + + :param a: _description_ + :type a: Tensor + :param output: _description_, defaults to "real" + :type output: str, optional + :return: T, Z so that ZTZ^H = a + :rtype: Tuple[Tensor, Tensor] + """ + raise NotImplementedError( + "Backend '{}' has not implemented `schur`.".format(self.name) + ) + def i(self: Any, dtype: str) -> Tensor: """ Return 1.j in as a tensor compatible with the backend. @@ -1511,16 +1540,19 @@ def wrapper(*args: Any, **kws: Any) -> Any: args, tuple( [ - self.reshape( - self.eye(self.sizen(arg), dtype=arg.dtype), - [-1] + list(self.shape_tuple(arg)), - ) - if i == argnum - else self.reshape( - self.zeros( - [self.sizen(arg), self.sizen(arg)], dtype=arg.dtype - ), - [-1] + list(self.shape_tuple(arg)), + ( + self.reshape( + self.eye(self.sizen(arg), dtype=arg.dtype), + [-1] + list(self.shape_tuple(arg)), + ) + if i == argnum + else self.reshape( + self.zeros( + [self.sizen(arg), self.sizen(arg)], + dtype=arg.dtype, + ), + [-1] + list(self.shape_tuple(arg)), + ) ) for i, arg in enumerate(args) ] @@ -1579,16 +1611,18 @@ def _first(x: Sequence[Any]) -> Any: args, collect( [ - self.reshape( - self.eye(self.sizen(v), dtype=v.dtype), - [-1] + list(self.shape_tuple(v)), - ) - if i == k - else self.reshape( - self.zeros( - [self.sizen(v), self.sizen(v)], dtype=v.dtype - ), - [-1] + list(self.shape_tuple(v)), + ( + self.reshape( + self.eye(self.sizen(v), dtype=v.dtype), + [-1] + list(self.shape_tuple(v)), + ) + if i == k + else self.reshape( + self.zeros( + [self.sizen(v), self.sizen(v)], dtype=v.dtype + ), + [-1] + list(self.shape_tuple(v)), + ) ) for i, v in enumerate(values) ] diff --git a/tensorcircuit/backends/cupy_backend.py b/tensorcircuit/backends/cupy_backend.py index 4aa58d06..11260d19 100644 --- a/tensorcircuit/backends/cupy_backend.py +++ b/tensorcircuit/backends/cupy_backend.py @@ -1,6 +1,7 @@ """ CuPy backend. Not in the tensornetwork package and highly experimental. """ + # pylint: disable=invalid-name import logging diff --git a/tensorcircuit/backends/jax_backend.py b/tensorcircuit/backends/jax_backend.py index 472066ea..33be28fd 100644 --- a/tensorcircuit/backends/jax_backend.py +++ b/tensorcircuit/backends/jax_backend.py @@ -1,17 +1,19 @@ """ Backend magic inherited from tensornetwork: jax backend """ + # pylint: disable=invalid-name -from functools import partial import logging import warnings +from functools import partial from typing import Any, Callable, Optional, Sequence, Tuple, Union import numpy as np -from scipy.sparse import coo_matrix import tensornetwork +from scipy.sparse import coo_matrix from tensornetwork.backends.jax import jax_backend + from .abstract_backend import ExtendedBackend logger = logging.getLogger(__name__) @@ -156,12 +158,19 @@ def _rq_jax( return r, q +def _eigh_jax(self: Any, tensor: Tensor) -> Tensor: + from .jax_ops import adaware_eigh_jit as adaware_eigh + + return adaware_eigh(tensor) + + tensornetwork.backends.jax.jax_backend.JaxBackend.convert_to_tensor = ( _convert_to_tensor_jax ) tensornetwork.backends.jax.jax_backend.JaxBackend.svd = _svd_jax tensornetwork.backends.jax.jax_backend.JaxBackend.qr = _qr_jax tensornetwork.backends.jax.jax_backend.JaxBackend.rq = _rq_jax +tensornetwork.backends.jax.jax_backend.JaxBackend.eigh = _eigh_jax class JaxBackend(jax_backend.JaxBackend, ExtendedBackend): # type: ignore @@ -188,8 +197,8 @@ def __init__(self) -> None: "Jax not installed, please switch to a different " "backend or install Jax." ) - from jax.experimental import sparse import jax.scipy + from jax.experimental import sparse try: import optax @@ -295,7 +304,13 @@ def i(self, dtype: Any = None) -> Tensor: dtype = npdtype # type: ignore if isinstance(dtype, str): dtype = getattr(jnp, dtype) - return np.array(1j, dtype=dtype) + return jnp.array(1j, dtype=dtype) + + def det(self, a: Tensor) -> Tensor: + return jnp.linalg.det(a) + + def schur(self, a: Tensor, output: str = "real") -> Tuple[Tensor, Tensor]: + return jsp.linalg.schur(a, output=output) # type: ignore def real(self, a: Tensor) -> Tensor: return jnp.real(a) @@ -405,7 +420,7 @@ def searchsorted(self, a: Tensor, v: Tensor, side: str = "left") -> Tensor: return jnp.searchsorted(a, v, side) def tree_map(self, f: Callable[..., Any], *pytrees: Any) -> Any: - return libjax.tree_map(f, *pytrees) + return libjax.tree_util.tree_map(f, *pytrees) def tree_flatten(self, pytree: Any) -> Tuple[Any, Any]: return libjax.tree_util.tree_flatten(pytree) # type: ignore @@ -616,7 +631,7 @@ def is_sparse(self, a: Tensor) -> bool: return isinstance(a, sparse.BCOO) # type: ignore def device(self, a: Tensor) -> str: - dev = a.device() + (dev,) = a.devices() return self._dev2str(dev) def device_move(self, a: Tensor, dev: Any) -> Tensor: @@ -743,7 +758,7 @@ def wrapper( gs = list(gs) for i, (j, g) in enumerate(zip(argnums_list, gs)): if j not in vectorized_argnums: # type: ignore - gs[i] = libjax.tree_map(partial(jnp.sum, axis=0), g) + gs[i] = libjax.tree_util.tree_map(partial(jnp.sum, axis=0), g) if isinstance(argnums, int): gs = gs[0] else: diff --git a/tensorcircuit/backends/jax_ops.py b/tensorcircuit/backends/jax_ops.py index 63cd2e33..2eaf2f1b 100644 --- a/tensorcircuit/backends/jax_ops.py +++ b/tensorcircuit/backends/jax_ops.py @@ -1,6 +1,7 @@ """ Customized ops for ML framework """ + # pylint: disable=invalid-name from typing import Any, Tuple, Sequence @@ -13,7 +14,8 @@ @jax.custom_vjp def adaware_svd(A: Array) -> Any: - return jnp.linalg.svd(A, full_matrices=False) + u, s, v = jnp.linalg.svd(A, full_matrices=False) + return (u, s, v) def _safe_reciprocal(x: Array, epsilon: float = 1e-15) -> Array: @@ -66,7 +68,7 @@ def jaxsvd_bwd(r: Sequence[Array], tangents: Sequence[Array]) -> Tuple[Array]: return (grad_a,) -adaware_svd.defvjp(jaxsvd_fwd, jaxsvd_bwd) +adaware_svd.defvjp(jaxsvd_fwd, jaxsvd_bwd) # type: ignore adaware_svd_jit = jax.jit(adaware_svd) @@ -76,8 +78,8 @@ def jaxsvd_bwd(r: Sequence[Array], tangents: Sequence[Array]) -> Tuple[Array]: @jax.custom_vjp def adaware_qr(A: Array) -> Any: - # q, r = jnp.linalg.qr(A) - return jnp.linalg.qr(A) + q, r = jnp.linalg.qr(A) + return (q, r) def jaxqr_fwd(A: Array) -> Any: @@ -142,6 +144,32 @@ def _QrGradSquareAndDeepMatrices(q: Array, r: Array, dq: Array, dr: Array) -> Ar return (result,) -adaware_qr.defvjp(jaxqr_fwd, jaxqr_bwd) +adaware_qr.defvjp(jaxqr_fwd, jaxqr_bwd) # type: ignore adaware_qr_jit = jax.jit(adaware_qr) + + +@jax.custom_vjp +def adaware_eigh(A: Array) -> Array: + return jnp.linalg.eigh(A) + + +def jaxeigh_fwd(A: Array) -> Array: + e, v = jnp.linalg.eigh(A) + return (e, v), (A, e, v) + + +def jaxeigh_bwd(r: Array, tangents: Array) -> Array: + a, e, v = r + de, dv = tangents + eye_n = jnp.eye(a.shape[-1], dtype=a.dtype) + f = _safe_reciprocal(e[..., jnp.newaxis, :] - e[..., jnp.newaxis] + eye_n) - eye_n + middle = jnp.diag(de) + jnp.multiply(f, (v.T @ dv)) + grad_a = jnp.conj(v) @ middle @ v.T + return (grad_a,) + + +# denegerate eigev values lead nan in eigh gradients, while tf has fixed that long ago + +adaware_eigh.defvjp(jaxeigh_fwd, jaxeigh_bwd) +adaware_eigh_jit = jax.jit(adaware_eigh) diff --git a/tensorcircuit/backends/numpy_backend.py b/tensorcircuit/backends/numpy_backend.py index 2d22b94d..df3dc043 100644 --- a/tensorcircuit/backends/numpy_backend.py +++ b/tensorcircuit/backends/numpy_backend.py @@ -1,6 +1,7 @@ """ Backend magic inherited from tensornetwork: numpy backend """ + # pylint: disable=invalid-name import logging @@ -9,7 +10,7 @@ import numpy as np import tensornetwork -from scipy.linalg import expm, solve +from scipy.linalg import expm, solve, schur from scipy.special import softmax, expit from scipy.sparse import coo_matrix, issparse from tensornetwork.backends.numpy import numpy_backend @@ -131,6 +132,12 @@ def dtype(self, a: Tensor) -> str: def numpy(self, a: Tensor) -> Tensor: return a + def det(self, a: Tensor) -> Tensor: + return np.linalg.det(a) + + def schur(self, a: Tensor, output: str = "real") -> Tuple[Tensor, Tensor]: + return schur(a, output=output) # type: ignore + def i(self, dtype: Any = None) -> Tensor: if not dtype: dtype = npdtype # type: ignore diff --git a/tensorcircuit/backends/pytorch_backend.py b/tensorcircuit/backends/pytorch_backend.py index 7362cc47..3214c72c 100644 --- a/tensorcircuit/backends/pytorch_backend.py +++ b/tensorcircuit/backends/pytorch_backend.py @@ -1,6 +1,7 @@ """ Backend magic inherited from tensornetwork: pytorch backend """ + # pylint: disable=invalid-name import logging @@ -306,6 +307,9 @@ def i(self, dtype: Any = None) -> Tensor: dtype = getattr(torchlib, dtype) return torchlib.tensor(1j, dtype=dtype) + def det(self, a: Tensor) -> Tensor: + return torchlib.linalg.det(a) + def real(self, a: Tensor) -> Tensor: try: a = torchlib.real(a) diff --git a/tensorcircuit/backends/pytorch_ops.py b/tensorcircuit/backends/pytorch_ops.py index 182101fd..e801a4ca 100644 --- a/tensorcircuit/backends/pytorch_ops.py +++ b/tensorcircuit/backends/pytorch_ops.py @@ -1,6 +1,7 @@ """ Customized ops for ML framework """ + # pylint: disable=invalid-name from typing import Any diff --git a/tensorcircuit/backends/tensorflow_backend.py b/tensorcircuit/backends/tensorflow_backend.py index a77ea1d7..365bd521 100644 --- a/tensorcircuit/backends/tensorflow_backend.py +++ b/tensorcircuit/backends/tensorflow_backend.py @@ -1,8 +1,11 @@ """ Backend magic inherited from tensornetwork: tensorflow backend """ + # pylint: disable=invalid-name +import os +import re from functools import reduce, partial from operator import mul from typing import Any, Callable, Optional, Sequence, Tuple, Union @@ -225,6 +228,120 @@ def _rq_tf( return r, q +def _svd_tf( + self: Any, + tensor: Tensor, + pivot_axis: int = -1, + max_singular_values: Optional[int] = None, + max_truncation_error: Optional[float] = None, + relative: Optional[bool] = False, +) -> Tuple[Tensor, Tensor, Tensor, Tensor]: + """Computes the singular value decomposition (SVD) of a tensor. + + The SVD is performed by treating the tensor as a matrix, with an effective + left (row) index resulting from combining the axes `tensor.shape[:pivot_axis]` + and an effective right (column) index resulting from combining the axes + `tensor.shape[pivot_axis:]`. + + For example, if `tensor` had a shape (2, 3, 4, 5) and `pivot_axis` was 2, then + `u` would have shape (2, 3, 6), `s` would have shape (6), and `vh` would + have shape (6, 4, 5). + + If `max_singular_values` is set to an integer, the SVD is truncated to keep + at most this many singular values. + + If `max_truncation_error > 0`, as many singular values will be truncated as + possible, so that the truncation error (the norm of discarded singular + values) is at most `max_truncation_error`. + If `relative` is set `True` then `max_truncation_err` is understood + relative to the largest singular value. + + If both `max_singular_values` snd `max_truncation_error` are specified, the + number of retained singular values will be + `min(max_singular_values, nsv_auto_trunc)`, where `nsv_auto_trunc` is the + number of singular values that must be kept to maintain a truncation error + smaller than `max_truncation_error`. + + The output consists of three tensors `u, s, vh` such that: + ```python + u[i1,...,iN, j] * s[j] * vh[j, k1,...,kM] == tensor[i1,...,iN, k1,...,kM] + ``` + Note that the output ordering matches numpy.linalg.svd rather than tf.svd. + + Args: + tf: The tensorflow module. + tensor: A tensor to be decomposed. + pivot_axis: Where to split the tensor's axes before flattening into a + matrix. + max_singular_values: The number of singular values to keep, or `None` to + keep them all. + max_truncation_error: The maximum allowed truncation error or `None` to not + do any truncation. + relative: Multiply `max_truncation_err` with the largest singular value. + + Returns: + u: Left tensor factor. + s: Vector of ordered singular values from largest to smallest. + vh: Right tensor factor. + s_rest: Vector of discarded singular values (length zero if no + truncation). + """ + left_dims = tf.shape(tensor)[:pivot_axis] + right_dims = tf.shape(tensor)[pivot_axis:] + + tensor = tf.reshape(tensor, [tf.reduce_prod(left_dims), tf.reduce_prod(right_dims)]) + + eps = os.environ.get("TC_BACKENDS_TENSORFLOW_BACKEND__SVD_TF_EPS") + if eps is not None: + eps = 10 ** (-int(eps)) + tensor += eps * tf.ones(tensor.shape, dtype=tensor.dtype) + # for numerical stability at least in tf+cpu + s, u, v = tf.linalg.svd(tensor) + + if max_singular_values is None: + max_singular_values = tf.size(s, out_type=tf.int64) + else: + max_singular_values = tf.constant(max_singular_values, dtype=tf.int64) + + if max_truncation_error is not None: + # Cumulative norms of singular values in ascending order. + trunc_errs = tf.sqrt(tf.cumsum(tf.square(s), reverse=True)) + # If relative is true, rescale max_truncation error with the largest + # singular value to yield the absolute maximal truncation error. + if relative: + abs_max_truncation_error = max_truncation_error * s[0] + else: + abs_max_truncation_error = max_truncation_error + # We must keep at least this many singular values to ensure the + # truncation error is <= abs_max_truncation_error. + num_sing_vals_err = tf.math.count_nonzero( + tf.cast(trunc_errs > abs_max_truncation_error, dtype=tf.int32) + ) + else: + num_sing_vals_err = max_singular_values + + num_sing_vals_keep = tf.minimum(max_singular_values, num_sing_vals_err) + + # tf.svd() always returns the singular values as a vector of float{32,64}. + # since tf.math_ops.real is automatically applied to s. This causes + # s to possibly not be the same dtype as the original tensor, which can cause + # issues for later contractions. To fix it, we recast to the original dtype. + s = tf.cast(s, tensor.dtype) + + s_rest = s[num_sing_vals_keep:] + s = s[:num_sing_vals_keep] + u = u[:, :num_sing_vals_keep] + v = v[:, :num_sing_vals_keep] + + vh = tf.linalg.adjoint(v) + + dim_s = tf.shape(s)[0] # must use tf.shape (not s.shape) to compile + u = tf.reshape(u, tf.concat([left_dims, [dim_s]], axis=-1)) + vh = tf.reshape(vh, tf.concat([[dim_s], right_dims], axis=-1)) + + return u, s, vh, s_rest + + # temporary hot replace until new version of tensorflow is released, # see issue: https://github.com/google/TensorNetwork/issues/940 # avoid buggy tensordot2 in tensornetwork @@ -240,6 +357,7 @@ def _rq_tf( ) tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.qr = _qr_tf tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.rq = _rq_tf +tensornetwork.backends.tensorflow.tensorflow_backend.TensorFlowBackend.svd = _svd_tf class TensorFlowBackend(tensorflow_backend.TensorFlowBackend, ExtendedBackend): # type: ignore @@ -262,6 +380,9 @@ def __init__(self) -> None: tf.sparse.SparseTensor.__add__ = tf.sparse.add self.minor = int(tf.__version__.split(".")[1]) self.name = "tensorflow" + logger = tf.get_logger() # .setLevel('ERROR') + logger.addFilter(lambda s: not re.match(".*You are casting.*", s.getMessage())) + # ignore casting warning by logger def eye( self, N: int, dtype: Optional[str] = None, M: Optional[int] = None @@ -360,6 +481,9 @@ def i(self, dtype: Any = None) -> Tensor: dtype = getattr(tf, dtype) return tf.constant(1j, dtype=dtype) + def det(self, a: Tensor) -> Tensor: + return tf.linalg.det(a) + def min(self, a: Tensor, axis: Optional[int] = None) -> Tensor: return tf.reduce_min(a, axis=axis) diff --git a/tensorcircuit/backends/tf_ops.py b/tensorcircuit/backends/tf_ops.py index 27327722..d7b6d380 100644 --- a/tensorcircuit/backends/tf_ops.py +++ b/tensorcircuit/backends/tf_ops.py @@ -1,6 +1,7 @@ """ Customized ops for ML framework """ + # pylint: disable=invalid-name from typing import Any diff --git a/tensorcircuit/basecircuit.py b/tensorcircuit/basecircuit.py index bad32b0f..468c6a1b 100644 --- a/tensorcircuit/basecircuit.py +++ b/tensorcircuit/basecircuit.py @@ -1,6 +1,7 @@ """ Quantum circuit: common methods for all circuit classes as MixIn """ + # pylint: disable=invalid-name from typing import Any, Dict, List, Optional, Sequence, Tuple, Union @@ -81,7 +82,7 @@ def coloring_copied_nodes( node.id = getattr(n0, "id", id(n0)) @staticmethod - def copy( + def copy_nodes( nodes: Sequence[tn.Node], dangling: Optional[Sequence[tn.Edge]] = None, conj: Optional[bool] = False, @@ -111,7 +112,7 @@ def copy( def _copy( self, conj: Optional[bool] = False ) -> Tuple[List[tn.Node], List[tn.Edge]]: - return self.copy(self._nodes, self._front, conj) + return self.copy_nodes(self._nodes, self._front, conj) def apply_general_gate( self, @@ -171,7 +172,7 @@ def apply_general_gate( self._front[index[0]] = n1[0] self._front[index[1]] = n2[1] if self.is_dm: - [n1l, n2l], _ = self.copy([n1, n2], conj=True) + [n1l, n2l], _ = self.copy_nodes([n1, n2], conj=True) n1l[1] ^ self._front[index[0] + nq] n2l[2] ^ self._front[index[1] + nq] self._nodes.append(n1l) @@ -186,7 +187,7 @@ def apply_general_gate( self._front[index[0]] = n1[0] self._front[index[1]] = n2[1] if self.is_dm: - [n1l, n2l], _ = self.copy([n1, n2], conj=True) + [n1l, n2l], _ = self.copy_nodes([n1, n2], conj=True) n2l[1] ^ self._front[index[0] + nq] n1l[2] ^ self._front[index[1] + nq] self._nodes.append(n1l) @@ -203,7 +204,7 @@ def apply_general_gate( # gate.id = id(gate) self._nodes.append(gate) if self.is_dm: - lgates, _ = self.copy([gate], conj=True) + lgates, _ = self.copy_nodes([gate], conj=True) lgate = lgates[0] self._nodes.append(lgate) for i, ind in enumerate(index): diff --git a/tensorcircuit/circuit.py b/tensorcircuit/circuit.py index ade0cafa..a293e3df 100644 --- a/tensorcircuit/circuit.py +++ b/tensorcircuit/circuit.py @@ -1,6 +1,7 @@ """ Quantum circuit: the state simulator """ + # pylint: disable=invalid-name from typing import Any, Callable, Dict, List, Optional, Sequence, Tuple @@ -507,6 +508,7 @@ def _general_kraus_2( kraus: Sequence[Gate], *index: int, status: Optional[float] = None, + with_prob: bool = False, name: Optional[str] = None, ) -> Tensor: # the graph building time is frustratingly slow, several minutes @@ -554,16 +556,20 @@ def calculate_kraus_p(i: int) -> Tensor: k / backend.cast(backend.sqrt(w) + eps, dtypestr) for w, k in zip(prob, kraus_tensor) ] - - return self.unitary_kraus( + pick = self.unitary_kraus( new_kraus, *index, prob=prob, status=status, name=name ) + if with_prob is False: + return pick + else: + return pick, prob def general_kraus( self, kraus: Sequence[Gate], *index: int, status: Optional[float] = None, + with_prob: bool = False, name: Optional[str] = None, ) -> Tensor: """ @@ -583,7 +589,9 @@ def general_kraus( when the random number will be generated automatically :type status: Optional[float], optional """ - return self._general_kraus_2(kraus, *index, status=status, name=name) + return self._general_kraus_2( + kraus, *index, status=status, with_prob=with_prob, name=name + ) apply_general_kraus = general_kraus diff --git a/tensorcircuit/cloud/__init__.py b/tensorcircuit/cloud/__init__.py index acd5bb51..56d5a724 100644 --- a/tensorcircuit/cloud/__init__.py +++ b/tensorcircuit/cloud/__init__.py @@ -1,3 +1,5 @@ from . import apis from . import abstraction from . import wrapper +from .wrapper import batch_expectation_ps +from .apis import submit_task diff --git a/tensorcircuit/cloud/apis.py b/tensorcircuit/cloud/apis.py index 8449ec74..0e4f6eb6 100644 --- a/tensorcircuit/cloud/apis.py +++ b/tensorcircuit/cloud/apis.py @@ -212,6 +212,7 @@ def set_token( # file_token = backend.tree_map(b64decode_s, file_token) except json.JSONDecodeError: logger.warning("token file loading failure, set empty token instead") + # TODO(@refraction-ray): better conflict solve with multiprocessing file_token = {} else: file_token = {} @@ -236,9 +237,9 @@ def set_token( if cached: # file_token = backend.tree_map(b64encode_s, saved_token) file_token = {k: b64encode_s(v) for k, v in saved_token.items()} - - with open(authpath, "w") as f: - json.dump(file_token, f) + if file_token: + with open(authpath, "w") as f: + json.dump(file_token, f) return saved_token diff --git a/tensorcircuit/cloud/local.py b/tensorcircuit/cloud/local.py index aa11681a..6d48f8e6 100644 --- a/tensorcircuit/cloud/local.py +++ b/tensorcircuit/cloud/local.py @@ -39,7 +39,7 @@ def submit_task( **kws: Any ) -> List[Task]: def _circuit2result(c: AbstractCircuit) -> Dict[str, Any]: - if device.name == "testing": + if device.name in ["testing", "default"]: count = c.sample(batch=shots, allow_state=True, format="count_dict_bin") # type: ignore else: raise ValueError("Unsupported device from local provider: %s" % device.name) diff --git a/tensorcircuit/cloud/quafu_provider.py b/tensorcircuit/cloud/quafu_provider.py index a852b905..f1d1f9bf 100644 --- a/tensorcircuit/cloud/quafu_provider.py +++ b/tensorcircuit/cloud/quafu_provider.py @@ -10,6 +10,7 @@ from .abstraction import Device, sep, Task from ..abstractcircuit import AbstractCircuit +from ..utils import is_sequence logger = logging.getLogger(__name__) @@ -43,18 +44,28 @@ def c2qasm(c: Any) -> str: s = c.to_openqasm() return s # type: ignore - source = c2qasm(circuit) + if not is_sequence(circuit): + source = c2qasm(circuit) + else: + source = [c2qasm(c) for c in circuit] # type: ignore user = User() user.save_apitoken(token) - nq = int(source.split("\n")[2].split("[")[1].split("]")[0]) # type: ignore - qc = QuantumCircuit(nq) - qc.from_openqasm(source) - task = Task_() - device_name = device.name.split(sep)[-1] - task.config(backend=device_name, shots=shots, compile=compile) - res = task.send(qc, wait=False) - wrapper = Task(res.taskid, device=device) - return wrapper + + def c2task(source: str) -> Task: + nq = int(source.split("\n")[2].split("[")[1].split("]")[0]) # type: ignore + qc = QuantumCircuit(nq) + qc.from_openqasm(source) + task = Task_() + device_name = device.name.split(sep)[-1] + task.config(backend=device_name, shots=shots, compile=compile) + res = task.send(qc, wait=False) + wrapper = Task(res.taskid, device=device) + return wrapper + + if not is_sequence(source): + return c2task(source) # type: ignore + else: + return [c2task(s) for s in source] # type: ignore def resubmit_task(task: Task, token: str) -> Task: diff --git a/tensorcircuit/cloud/tencent.py b/tensorcircuit/cloud/tencent.py index dc99ed80..fc37460a 100644 --- a/tensorcircuit/cloud/tencent.py +++ b/tensorcircuit/cloud/tencent.py @@ -65,7 +65,7 @@ def list_properties(device: Device, token: Optional[str] = None) -> Dict[str, An for bit in r["bits"]: bits_dict[bit["Qubit"]] = bit r["bits"] = bits_dict - r["native_gates"] = ["h", "rz", "x", "y", "z", "cz"] # handcoded + r["native_gates"] = ["h", "rz", "x", "y", "z", "cz", "cx"] # handcoded return r # type: ignore else: raise ValueError("No device with the name: %s" % device) @@ -124,6 +124,7 @@ def submit_task( circuit: Optional[Union[AbstractCircuit, Sequence[AbstractCircuit]]] = None, source: Optional[Union[str, Sequence[str]]] = None, remarks: Optional[str] = None, + group: Optional[str] = None, compiling: bool = False, compiled_options: Optional[Dict[str, Any]] = None, enable_qiskit_initial_mapping: bool = False, @@ -261,6 +262,7 @@ def c2qasm(c: Any, compiling: bool) -> str: "lang": lang, "prior": prior, "remarks": remarks, + "group": group, } ) @@ -273,6 +275,7 @@ def c2qasm(c: Any, compiling: bool) -> str: "lang": lang, "prior": prior, "remarks": remarks, + "group": group, } r = rpost_json( tencent_base_url + "task/submit", json=json, headers=tencent_headers(token) diff --git a/tensorcircuit/cloud/utils.py b/tensorcircuit/cloud/utils.py index 296e66df..fe15a56f 100644 --- a/tensorcircuit/cloud/utils.py +++ b/tensorcircuit/cloud/utils.py @@ -1,6 +1,7 @@ """ utility functions for cloud connection """ + from typing import Any, Callable, Optional from functools import wraps import inspect diff --git a/tensorcircuit/cloud/wrapper.py b/tensorcircuit/cloud/wrapper.py index 85d35e9a..f43f9ea9 100644 --- a/tensorcircuit/cloud/wrapper.py +++ b/tensorcircuit/cloud/wrapper.py @@ -1,7 +1,8 @@ """ higher level wrapper shortcut for submit_task """ -from typing import Any, Callable, Dict, List, Optional, Sequence, Union + +from typing import Any, Callable, Dict, List, Optional, Sequence, Tuple, Union import logging import time @@ -14,6 +15,7 @@ from ..cons import backend from ..quantum import ps2xyz from ..compiler import DefaultCompiler +from ..compiler.simple_compiler import simple_compile from .apis import submit_task, get_device from .abstraction import Device @@ -25,7 +27,6 @@ def batch_submit_template( device: str, batch_limit: int = 64, **kws: Any ) -> Callable[..., List[counts.ct]]: - # TODO(@refraction-ray): adpative batch def run( cs: Union[Circuit, Sequence[Circuit]], shots: int = 8192, **nkws: Any ) -> List[counts.ct]: @@ -150,6 +151,7 @@ def batch_expectation_ps( ws: Optional[List[float]] = None, shots: int = 8192, with_rem: bool = True, + compile_func: Optional[Callable[[Circuit], Tuple[Circuit, Dict[str, Any]]]] = None, batch_limit: int = 64, batch_submit_func: Optional[Callable[..., List[counts.ct]]] = None, ) -> Union[Any, List[Any]]: @@ -196,38 +198,50 @@ def batch_expectation_ps( if ws is None: return backend.real(backend.stack(results)) else: - return backend.real(backend.sum([w * r for w, r in zip(ws, results)])) + sumr = sum([w * r for w, r in zip(ws, results)]) + return backend.convert_to_tensor(sumr) cs = [] infos = [] exps = [] if isinstance(device, str): device = get_device(device) - dc = DefaultCompiler( - { - "coupling_map": device.topology(), - } - ) + if compile_func is None: + try: + coupling_map = device.topology() + compile_func = DefaultCompiler( + { + "coupling_map": coupling_map, + } + ) + except (AttributeError, ValueError): + compile_func = DefaultCompiler() + c1, info = compile_func(c) # type: ignore + if not info.get("logical_physical_mapping", None): + info["logical_physical_mapping"] = {i: i for i in range(c._nqubits)} for ps in pss: # TODO(@refraction-ray): Pauli string grouping # https://docs.pennylane.ai/en/stable/_modules/pennylane/pauli/grouping/group_observables.html - c1 = Circuit.from_qir(c.to_qir()) + c2 = Circuit.from_qir(c1.to_qir()) exp = [] for j, i in enumerate(ps): if i == 1: - c1.H(j) # type: ignore + c2.H(info["logical_physical_mapping"][j]) # type: ignore + c2, _ = simple_compile(c2) exp.append(j) + elif i == 2: - c1.rx(j, theta=np.pi / 2) # type: ignore + c2.rx(info["logical_physical_mapping"][j], theta=np.pi / 2) # type: ignore + c2, _ = simple_compile(c2) exp.append(j) elif i == 3: exp.append(j) - for i in range(c1._nqubits): - c1.measure_instruction(i) - c1, info = dc(c1) - # bug for measure instruction! - # TODO(@refraction-ray): two steps compiling with pre compilation - cs.append(c1) + for i in range(c._nqubits): + c2.measure_instruction(info["logical_physical_mapping"][i]) + # c1, info = compile_func(c1) # type: ignore + # TODO(@refraction-ray): two steps compiling with pre compilation: + # basically done, require some fine tuning for performance + cs.append(c2) infos.append(info) exps.append(exp) @@ -302,6 +316,6 @@ def batch_expectation_ps( counts.expectation(raw_counts[i], exps[i]) for i in range(len(raw_counts)) ] if ws is not None: - sumr = backend.sum([w * r for w, r in zip(ws, results)]) - return sumr + sumr = sum([w * r for w, r in zip(ws, results)]) + return backend.convert_to_tensor(sumr) return backend.stack(results) diff --git a/tensorcircuit/compiler/__init__.py b/tensorcircuit/compiler/__init__.py index 43f92b99..d5f812fe 100644 --- a/tensorcircuit/compiler/__init__.py +++ b/tensorcircuit/compiler/__init__.py @@ -2,6 +2,7 @@ Experimental module, no software agnostic unified interface for now, only reserve for internal use """ + from .composed_compiler import Compiler, DefaultCompiler, default_compile from . import simple_compiler from . import qiskit_compiler diff --git a/tensorcircuit/compiler/qiskit_compiler.py b/tensorcircuit/compiler/qiskit_compiler.py index e54dd1a4..1f946359 100644 --- a/tensorcircuit/compiler/qiskit_compiler.py +++ b/tensorcircuit/compiler/qiskit_compiler.py @@ -2,8 +2,8 @@ compiler interface via qiskit """ -from typing import Any, Dict, Optional import re +from typing import Any, Dict, Optional from ..abstractcircuit import AbstractCircuit from ..circuit import Circuit @@ -71,7 +71,7 @@ def _get_positional_logical_mapping_from_qiskit(qc: Any) -> Dict[int, int]: positional_logical_mapping = {} for inst in qc.data: if inst[0].name == "measure": - positional_logical_mapping[i] = inst[1][0].index + positional_logical_mapping[i] = qc.find_bit(inst[1][0]).index i += 1 return positional_logical_mapping @@ -95,16 +95,17 @@ def _get_logical_physical_mapping_from_qiskit( for inst in qc_after.data: if inst[0].name == "measure": if qc_before is None: - logical_q = inst[2][0].index + logical_q = qc_after.find_bit(inst[2][0]).index else: for instb in qc_before.data: if ( instb[0].name == "measure" - and instb[2][0].index == inst[2][0].index + and qc_before.find_bit(instb[2][0]).index + == qc_after.find_bit(inst[2][0]).index ): - logical_q = instb[1][0].index + logical_q = qc_before.find_bit(instb[1][0]).index break - logical_physical_mapping[logical_q] = inst[1][0].index + logical_physical_mapping[logical_q] = qc_after.find_bit(inst[1][0]).index return logical_physical_mapping diff --git a/tensorcircuit/compiler/simple_compiler.py b/tensorcircuit/compiler/simple_compiler.py index f1641594..868a678e 100644 --- a/tensorcircuit/compiler/simple_compiler.py +++ b/tensorcircuit/compiler/simple_compiler.py @@ -289,7 +289,7 @@ def simple_compile( ) c = replace_r(circuit, **compiled_options) - c = replace_u(circuit, **compiled_options) + c = replace_u(c, **compiled_options) qir = c.to_qir() len0 = len(qir) qir = merge(qir, **compiled_options) diff --git a/tensorcircuit/cons.py b/tensorcircuit/cons.py index 5c3fb78d..c2ffa8f8 100644 --- a/tensorcircuit/cons.py +++ b/tensorcircuit/cons.py @@ -1,6 +1,7 @@ """ Constants and setups """ + # pylint: disable=invalid-name import logging @@ -152,7 +153,7 @@ def set_dtype(dtype: Optional[str] = None, set_global: bool = True) -> Tuple[str raise ValueError(f"Unsupported data type: {dtype}") try: - from jax.config import config + from jax import config except ImportError: config = None # type: ignore diff --git a/tensorcircuit/densitymatrix.py b/tensorcircuit/densitymatrix.py index ec0277a6..dc52fe4a 100644 --- a/tensorcircuit/densitymatrix.py +++ b/tensorcircuit/densitymatrix.py @@ -1,6 +1,7 @@ """ Quantum circuit class but with density matrix simulator """ + # pylint: disable=invalid-name from functools import reduce @@ -86,7 +87,7 @@ def __init__( for i, n in enumerate(mps_nodes): mps_nodes[i].tensor = backend.cast(n.tensor, dtypestr) # type: ignore mps_edges = mps_inputs.out_edges + mps_inputs.in_edges - self._nodes, self._front = self.copy(mps_nodes, mps_edges) + self._nodes, self._front = self.copy_nodes(mps_nodes, mps_edges) self.coloring_nodes(self._nodes) self._double_nodes_front() @@ -131,7 +132,7 @@ def __init__( self._extra_qir: List[Dict[str, Any]] = [] def _double_nodes_front(self) -> None: - lnodes, lfront = self.copy(self._nodes, self._front, conj=True) + lnodes, lfront = self.copy_nodes(self._nodes, self._front, conj=True) self._front.extend(lfront) self._nodes.extend(lnodes) @@ -333,9 +334,11 @@ def apply_general_kraus( ) -> None: # incompatible API for now kraus = [ - k - if isinstance(k, tn.Node) - else Gate(backend.cast(backend.convert_to_tensor(k), dtypestr)) + ( + k + if isinstance(k, tn.Node) + else Gate(backend.cast(backend.convert_to_tensor(k), dtypestr)) + ) for k in kraus ] self.check_kraus(kraus) diff --git a/tensorcircuit/experimental.py b/tensorcircuit/experimental.py index b2de6451..8eba9a43 100644 --- a/tensorcircuit/experimental.py +++ b/tensorcircuit/experimental.py @@ -7,14 +7,17 @@ import numpy as np -from .cons import backend, dtypestr +from .cons import backend, dtypestr, contractor, rdtypestr +from .gates import Gate Tensor = Any +Circuit = Any def adaptive_vmap( f: Callable[..., Any], vectorized_argnums: Union[int, Sequence[int]] = 0, + static_argnums: Optional[Union[int, Sequence[int]]] = None, chunk_size: Optional[int] = None, ) -> Callable[..., Any]: if chunk_size is None: @@ -44,7 +47,10 @@ def wrapper(*args: Any, **kws: Any) -> Tensor: reshape_args.append(arg) if s2 != 0: rest_args.append(arg_rest) - _vmap = backend.vmap(f, vectorized_argnums) + _vmap = backend.jit( + backend.vmap(f, vectorized_argnums=vectorized_argnums), + static_argnums=static_argnums, + ) r = [] for i in range(s1): # currently using naive python loop for simplicity @@ -53,16 +59,16 @@ def wrapper(*args: Any, **kws: Any) -> Tensor: for j, a in enumerate(reshape_args) ] r.append(_vmap(*nreshape_args, **kws)) - r = backend.stack(r) - rshape = list(backend.shape_tuple(r)) - if len(rshape) == 2: - nshape = [rshape[0] * rshape[1]] - else: - nshape = [rshape[0] * rshape[1], -1] - r = backend.reshape(r, nshape) + r = backend.tree_map(lambda *x: backend.concat(x), *r) + # rshape = list(backend.shape_tuple(r)) + # if len(rshape) == 2: + # nshape = [rshape[0] * rshape[1]] + # else: + # nshape = [rshape[0] * rshape[1], -1] + # r = backend.reshape(r, nshape) if s2 != 0: rest_r = _vmap(*rest_args, **kws) - return backend.concat([r, rest_r]) + return backend.tree_map(lambda *x: backend.concat(x), r, rest_r) return r return wrapper @@ -345,6 +351,7 @@ def grad_f(*args: Any, **kws: Any) -> Any: # TODO(@refraction-ray): add SPSA gradient wrapper similar to parameter shift +# -- using noisyopt package instead def finite_difference_differentiator( @@ -433,3 +440,88 @@ def _evol(t: Tensor) -> Tensor: return callback(psi_exact) return backend.stack([_evol(t) for t in tlist]) + + +def evol_local( + c: Circuit, + index: Sequence[int], + h_fun: Callable[..., Tensor], + t: float, + *args: Any, + **solver_kws: Any +) -> Circuit: + """ + ode evolution of time dependent Hamiltonian on circuit of given indices + [only jax backend support for now] + + :param c: _description_ + :type c: Circuit + :param index: _description_ + :type index: Sequence[int] + :param h_fun: h_fun should return a dense Hamiltonian matrix + with input arguments time and *args + :type h_fun: Callable[..., Tensor] + :param t: evolution time + :type t: float + :return: _description_ + :rtype: Circuit + """ + from jax.experimental.ode import odeint + + s = c.state() + n = c._nqubits + l = len(index) + + def f(y: Tensor, t: Tensor, *args: Any) -> Tensor: + y = backend.reshape2(y) + y = Gate(y) + h = -1.0j * h_fun(t, *args) + h = backend.reshape2(h) + h = Gate(h) + edges = [] + for i in range(n): + if i not in index: + edges.append(y[i]) + else: + j = index.index(i) + edges.append(h[j]) + h[j + l] ^ y[i] + y = contractor([y, h], output_edge_order=edges) + return backend.reshape(y.tensor, [-1]) + + ts = backend.stack([0.0, t]) + ts = backend.cast(ts, dtype=rdtypestr) + s1 = odeint(f, s, ts, *args, **solver_kws) + return type(c)(n, inputs=s1[-1]) + + +def evol_global( + c: Circuit, h_fun: Callable[..., Tensor], t: float, *args: Any, **solver_kws: Any +) -> Circuit: + """ + ode evolution of time dependent Hamiltonian on circuit of all qubits + [only jax backend support for now] + + :param c: _description_ + :type c: Circuit + :param h_fun: h_fun should return a **SPARSE** Hamiltonian matrix + with input arguments time and *args + :type h_fun: Callable[..., Tensor] + :param t: _description_ + :type t: float + :return: _description_ + :rtype: Circuit + """ + from jax.experimental.ode import odeint + + s = c.state() + n = c._nqubits + + def f(y: Tensor, t: Tensor, *args: Any) -> Tensor: + h = -1.0j * h_fun(t, *args) + return backend.sparse_dense_matmul(h, y) + + ts = backend.stack([0.0, t]) + ts = backend.cast(ts, dtype=rdtypestr) + s1 = odeint(f, s, ts, *args, **solver_kws) + return type(c)(n, inputs=s1[-1]) diff --git a/tensorcircuit/fgs.py b/tensorcircuit/fgs.py new file mode 100644 index 00000000..a7012701 --- /dev/null +++ b/tensorcircuit/fgs.py @@ -0,0 +1,931 @@ +""" +Fermion Gaussian state simulator +""" + +from typing import Any, Dict, List, Optional, Tuple + +import numpy as np + +try: + import openfermion +except ModuleNotFoundError: + pass + +from .cons import backend, dtypestr, rdtypestr, get_backend +from .circuit import Circuit +from . import quantum + +Tensor = Any + + +def onehot_matrix(i: int, j: int, N: int) -> Tensor: + m = np.zeros([N, N]) + m[i, j] = 1 + m = backend.convert_to_tensor(m) + m = backend.cast(m, dtypestr) + return m + + +# TODO(@refraction-ray): efficiency benchmark with jit +# TODO(@refraction-ray): FGS mixed state support? +# TODO(@refraction-ray): overlap? + + +class FGSSimulator: + r""" + main refs: https://arxiv.org/pdf/2306.16595.pdf, + https://arxiv.org/abs/2209.06945, + https://scipost.org/SciPostPhysLectNotes.54/pdf + + convention: + for Hamiltonian (c^dagger, c)H(c, c^\dagger) + for correlation <(c, c^\dagger)(c^\dagger, c)> + c' = \alpha^\dagger (c, c^\dagger) + """ + + def __init__( + self, + L: int, + filled: Optional[List[int]] = None, + alpha: Optional[Tensor] = None, + hc: Optional[Tensor] = None, + cmatrix: Optional[Tensor] = None, + ): + """ + _summary_ + + :param L: system size + :type L: int + :param filled: the fermion site that is fully occupied, defaults to None + :type filled: Optional[List[int]], optional + :param alpha: directly specify the alpha tensor as the input + :type alpha: Optional[Tensor], optional + :param hc: the input is given as the ground state of quadratic Hamiltonian ``hc`` + :type hc: Optional[Tensor], optional + :param cmatrix: only used for debug, defaults to None + :type cmatrix: Optional[Tensor], optional + """ + if filled is None: + filled = [] + self.L = L + if alpha is None: + if hc is None: + self.alpha = self.init_alpha(filled, L) + else: + _, _, self.alpha = self.fermion_diagonalization(hc, L) + else: + self.alpha = alpha + self.alpha0 = self.alpha + self.wtransform = self.wmatrix(L) + self.cmatrix = cmatrix + self.otcmatrix: Dict[Tuple[int, int], Tensor] = {} + + @classmethod + def fermion_diagonalization( + cls, hc: Tensor, L: int + ) -> Tuple[Tensor, Tensor, Tensor]: + es, u = backend.eigh(hc) + es = es[::-1] + u = u[:, ::-1] + alpha = u[:, :L] + return es, u, alpha + + @classmethod + def fermion_diagonalization_2( + cls, hc: Tensor, L: int + ) -> Tuple[Tensor, Tensor, Tensor]: + w = cls.wmatrix(L) + hm = 0.25 * w @ hc @ backend.adjoint(w) + hm = backend.real((-1.0j) * hm) + hd, om = backend.schur(hm, output="real") + # order not kept + # eps = 1e-10 + # idm = backend.convert_to_tensor(np.array([[1.0, 0], [0, 1.0]])) + # idm = backend.cast(idm, dtypestr) + # xm = backend.convert_to_tensor(np.array([[0, 1.0], [1.0, 0]])) + # xm = backend.cast(xm, dtypestr) + # for i in range(0, 2 * L, 2): + # (backend.sign(hd[i, i + 1] + eps) + 1) / 2 * idm - ( + # backend.sign(hd[i, i + 1] + eps) - 1 + # ) / 2 * xm + # print(hd) + + es = backend.adjoint(w) @ (1.0j * hd) @ w + u = 0.5 * backend.adjoint(w) @ backend.transpose(om) @ w + alpha = backend.adjoint(u)[:, :L] + # c' = u@c + # e_k (c^\dagger_k c_k - c_k c^\dagger_k) + return es, u, alpha + + @staticmethod + def wmatrix(L: int) -> Tensor: + w = np.zeros([2 * L, 2 * L], dtype=complex) + for i in range(2 * L): + if i % 2 == 1: + w[i, (i - 1) // 2] = 1.0j + w[i, (i - 1) // 2 + L] = -1.0j + else: + w[i, i // 2] = 1 + w[i, i // 2 + L] = 1 + return backend.convert_to_tensor(w) + + @staticmethod + def init_alpha(filled: List[int], L: int) -> Tensor: + alpha = np.zeros([2 * L, L]) + for i in range(L): + if i not in filled: + alpha[i, i] = 1 + else: + alpha[i + L, i] = 1 + alpha = backend.convert_to_tensor(alpha) + alpha = backend.cast(alpha, dtypestr) + return alpha + + def get_alpha(self) -> Tensor: + return self.alpha + + def get_cmatrix(self, now_i: bool = True, now_j: bool = True) -> Tensor: + # otoc in FGS language, see: https://arxiv.org/pdf/1908.03292.pdf + # https://journals.aps.org/prb/pdf/10.1103/PhysRevB.99.054205 + # otoc for non=hermitian system is more subtle due to the undefined normalization + # of operator and not considered here, see: https://arxiv.org/pdf/2305.12054.pdf + if self.cmatrix is not None and now_i is True and now_j is True: + return self.cmatrix + elif now_i is True and now_j is True: + cmatrix = self.alpha @ backend.adjoint(self.alpha) + self.cmatrix = cmatrix + return cmatrix + elif now_i is True: # new i old j + if (1, 0) in self.otcmatrix: + return self.otcmatrix[(1, 0)] + cmatrix = self.alpha @ backend.adjoint(self.alpha0) + self.otcmatrix[(1, 0)] = cmatrix + return cmatrix + elif now_j is True: # old i new j + if (0, 1) in self.otcmatrix: + return self.otcmatrix[(0, 1)] + cmatrix = self.alpha0 @ backend.adjoint(self.alpha) + self.otcmatrix[(0, 1)] = cmatrix + return cmatrix + else: # initial cmatrix + if (0, 0) in self.otcmatrix: + return self.otcmatrix[(0, 0)] + cmatrix = self.alpha0 @ backend.adjoint(self.alpha0) + self.otcmatrix[(0, 0)] = cmatrix + return cmatrix + + def get_reduced_cmatrix(self, subsystems_to_trace_out: List[int]) -> Tensor: + m = self.get_cmatrix() + if subsystems_to_trace_out is None: + subsystems_to_trace_out = [] + keep = [i for i in range(self.L) if i not in subsystems_to_trace_out] + keep += [i + self.L for i in range(self.L) if i not in subsystems_to_trace_out] + keep = backend.convert_to_tensor(keep) + + def slice_(a: Tensor) -> Tensor: + return backend.gather1d(a, keep) + + slice_ = backend.vmap(slice_) + m = backend.gather1d(slice_(m), keep) + return m + + def renyi_entropy(self, n: int, subsystems_to_trace_out: List[int]) -> Tensor: + """ + compute renyi_entropy of order ``n`` for the fermion state + + :param n: _description_ + :type n: int + :param subsystems_to_trace_out: system sites to be traced out + :type subsystems_to_trace_out: List[int] + :return: _description_ + :rtype: Tensor + """ + m = self.get_reduced_cmatrix(subsystems_to_trace_out) + lbd, _ = backend.eigh(m) + lbd = backend.real(lbd) + lbd = backend.relu(lbd) + eps = 1e-6 + + entropy = backend.sum(backend.log(lbd**n + (1 - lbd) ** n + eps)) + s = 1 / (2 * (1 - n)) * entropy + return s + + def entropy(self, subsystems_to_trace_out: Optional[List[int]] = None) -> Tensor: + """ + compute von Neumann entropy for the fermion state + + :param subsystems_to_trace_out: _description_, defaults to None + :type subsystems_to_trace_out: Optional[List[int]], optional + :return: _description_ + :rtype: Tensor + """ + m = self.get_reduced_cmatrix(subsystems_to_trace_out) # type: ignore + lbd, _ = backend.eigh(m) + lbd = backend.real(lbd) + lbd = backend.relu(lbd) + # lbd /= backend.sum(lbd) + eps = 1e-6 + entropy = -backend.sum( + lbd * backend.log(lbd + eps) + (1 - lbd) * backend.log(1 - lbd + eps) + ) + return entropy / 2 + + def evol_hamiltonian(self, h: Tensor) -> None: + r""" + Evolve as :math:`e^{-i/2 \hat{h}}` + + :param h: _description_ + :type h: Tensor + """ + # e^{-i/2 H} + h = backend.cast(h, dtype=dtypestr) + self.alpha = backend.expm(-1.0j * h) @ self.alpha + self.cmatrix = None + self.otcmatrix = {} + + def evol_ihamiltonian(self, h: Tensor) -> None: + r""" + Evolve as :math:`e^{-1/2 \hat{h}}` + + :param h: _description_ + :type h: Tensor + """ + # e^{-1/2 H} + h = backend.cast(h, dtype=dtypestr) + self.alpha = backend.expm(h) @ self.alpha + self.orthogonal() + self.cmatrix = None + self.otcmatrix = {} + + def evol_ghamiltonian(self, h: Tensor) -> None: + r""" + Evolve as :math:`e^{-1/2 i \hat{h}}` with h generally non-Hermitian + + :param h: _description_ + :type h: Tensor + """ + # e^{-1/2 H} + h = backend.cast(h, dtype=dtypestr) + self.alpha = backend.expm(-1.0j * backend.adjoint(h)) @ self.alpha + self.orthogonal() + self.cmatrix = None + self.otcmatrix = {} + + def orthogonal(self) -> None: + q, _ = backend.qr(self.alpha) + self.alpha = q + + @staticmethod + def hopping(chi: Tensor, i: int, j: int, L: int) -> Tensor: + # chi * ci dagger cj + hc. + chi = backend.convert_to_tensor(chi) + chi = backend.cast(chi, dtypestr) + m = chi / 2 * onehot_matrix(i, j, 2 * L) + m += -chi / 2 * onehot_matrix(j + L, i + L, 2 * L) + m += backend.adjoint(m) + return m + + def evol_hp(self, i: int, j: int, chi: Tensor = 0) -> None: + r""" + The evolve Hamiltonian is :math:`\chi c_i^\dagger c_j +h.c.` + + :param i: _description_ + :type i: int + :param j: _description_ + :type j: int + :param chi: _description_, defaults to 0 + :type chi: Tensor, optional + """ + self.evol_hamiltonian(self.hopping(chi, i, j, self.L)) + + @staticmethod + def chemical_potential(chi: Tensor, i: int, L: int) -> Tensor: + chi = backend.convert_to_tensor(chi) + chi = backend.cast(chi, dtypestr) + m = chi / 2 * onehot_matrix(i, i, 2 * L) + m += -chi / 2 * onehot_matrix(i + L, i + L, 2 * L) + return m + + @staticmethod + def sc_pairing(chi: Tensor, i: int, j: int, L: int) -> Tensor: + chi = backend.convert_to_tensor(chi) + chi = backend.cast(chi, dtypestr) + m = chi / 2 * onehot_matrix(i, j + L, 2 * L) + m += -chi / 2 * onehot_matrix(j, i + L, 2 * L) + m += backend.adjoint(m) + return m + + def evol_sp(self, i: int, j: int, chi: Tensor = 0) -> None: + r""" + The evolve Hamiltonian is :math:`chi c_i^\dagger c_j^\dagger +h.c.` + + + :param i: _description_ + :type i: int + :param j: _description_ + :type j: int + :param chi: _description_, defaults to 0 + :type chi: Tensor, optional + """ + self.evol_hamiltonian(self.sc_pairing(chi, i, j, self.L)) + + def evol_cp(self, i: int, chi: Tensor = 0) -> None: + r""" + The evolve Hamiltonian is :math:`chi c_i^\dagger c_i` + + :param i: _description_ + :type i: int + :param chi: _description_, defaults to 0 + :type chi: Tensor, optional + """ + self.evol_hamiltonian(self.chemical_potential(chi, i, self.L)) + + def evol_icp(self, i: int, chi: Tensor = 0) -> None: + r""" + The evolve Hamiltonian is :math:`chi c_i^\dagger c_i` with :math:`\exp^{-H/2}` + + :param i: _description_ + :type i: int + :param chi: _description_, defaults to 0 + :type chi: Tensor, optional + """ + self.evol_ihamiltonian(self.chemical_potential(chi, i, self.L)) + + def get_bogoliubov_uv(self) -> Tuple[Tensor, Tensor]: + return ( + backend.gather1d( + self.alpha, backend.convert_to_tensor([i for i in range(self.L)]) + ), + backend.gather1d( + self.alpha, + backend.convert_to_tensor([i + self.L for i in range(self.L)]), + ), + ) + + def get_cmatrix_majorana(self) -> Tensor: + r""" + correlation matrix defined in majorana basis + convention: :math:`gamma_0 = c_0 + c_0^\dagger` + :math:`gamma_1 = i(c_0 - c_0^\dagger)` + + :return: _description_ + :rtype: Tensor + """ + c = self.get_cmatrix() + return self.wtransform @ c @ backend.adjoint(self.wtransform) + + def get_covariance_matrix(self) -> Tensor: + m = self.get_cmatrix_majorana() + return -1.0j * (2 * m - backend.eye(self.L * 2)) + + def expectation_2body( + self, i: int, j: int, now_i: bool = True, now_j: bool = True + ) -> Tensor: + """ + expectation of two fermion terms + convention: (c, c^\dagger) + for i>L, c_{i-L}^\dagger is assumed + + :param i: _description_ + :type i: int + :param j: _description_ + :type j: int + :return: _description_ + :rtype: Tensor + """ + return self.get_cmatrix(now_i, now_j)[i][(j + self.L) % (2 * self.L)] + + def expectation_4body(self, i: int, j: int, k: int, l: int) -> Tensor: + """ + expectation of four fermion terms using Wick Thm + convention: (c, c^\dagger) + for i>L, c_{i-L}^\dagger is assumed + + :param i: _description_ + :type i: int + :param j: _description_ + :type j: int + :param k: _description_ + :type k: int + :param l: _description_ + :type l: int + :return: _description_ + :rtype: Tensor + """ + e = ( + self.expectation_2body(i, j) * self.expectation_2body(k, l) + - self.expectation_2body(i, k) * self.expectation_2body(j, l) + + self.expectation_2body(i, l) * self.expectation_2body(j, k) + ) + return e + + def post_select(self, i: int, keep: int = 1) -> None: + """ + post select (project) the fermion state to occupation eigenstate + = ``keep`` + + :param i: _description_ + :type i: int + :param keep: _description_, defaults to 1 + :type keep: int, optional + """ + # i is not jittable, keep is jittable + L = backend.convert_to_tensor(self.L) + i = backend.convert_to_tensor(i) + L = backend.cast(L, "int32") + i = backend.cast(i, "int32") + keep = backend.convert_to_tensor(keep) + keep = backend.cast(keep, "int32") + alpha = self.alpha + # if keep == 0: + i = i + L * (1 - keep) + i0 = backend.argmax(backend.abs(alpha[(i + L) % (2 * L), :])) + i0 = backend.cast(i0, "int32") + alpha1 = alpha - backend.reshape(alpha[:, i0], [-1, 1]) @ backend.reshape( + alpha[(i + L) % (2 * L), :] / alpha[(i + L) % (2 * L), i0], [1, -1] + ) + mask1 = backend.onehot(i0, alpha.shape[1]) + mask1 = backend.cast(mask1, dtypestr) + mask0 = backend.ones(alpha.shape[1]) - mask1 + mask12d = backend.tile(mask1[None, :], [alpha.shape[0], 1]) + mask02d = backend.tile(mask0[None, :], [alpha.shape[0], 1]) + alpha1 = mask02d * alpha1 + mask12d * alpha + r = [] + for j in range(2 * self.L): + indicator = ( + backend.sign(backend.cast((i - j), rdtypestr) ** 2 - 0.5) + 1 + ) / 2 + # i=j indicator = 0, i!=j indicator = 1 + indicator = backend.cast(indicator, dtypestr) + r.append( + backend.ones([self.L]) * indicator + + backend.ones([self.L]) * mask1 * (1 - indicator) + ) + # if j != i: + # r.append(backend.ones([L])) + # else: + # r.append(backend.ones([L]) * mask1) + mask2 = backend.stack(r) + alpha1 = alpha1 * mask2 + r = [] + for j in range(2 * self.L): + indicator = ( + backend.sign( + (backend.cast((i + L) % (2 * L) - j, rdtypestr)) ** 2 - 0.5 + ) + + 1 + ) / 2 + r.append(1 - indicator) + newcol = backend.stack(r) + # newcol = np.zeros([2 * self.L]) + # newcol[(i + L) % (2 * L)] = 1 + # newcol = backend.convert_to_tensor(newcol) + newcol = backend.cast(newcol, dtypestr) + alpha1 = alpha1 * mask02d + backend.tile(newcol[:, None], [1, self.L]) * mask12d + q, _ = backend.qr(alpha1) + self.alpha = q + + def cond_measure(self, ind: int, status: float, with_prob: bool = False) -> Tensor: + p0 = backend.real(self.get_cmatrix()[ind, ind]) + prob = backend.convert_to_tensor([p0, 1 - p0]) + status = backend.convert_to_tensor(status) + status = backend.cast(status, rdtypestr) + eps = 1e-12 + keep = (backend.sign(status - p0 + eps) + 1) / 2 + self.post_select(ind, keep) + if with_prob is False: + return keep + else: + return keep, prob + + # def product(self, other): + # # self@other + # gamma1 = self.get_covariance_matrix() + # gamma2 = other.get_covariance_matrix() + # den = backend.inv(1 + gamma1 @ gamma2) + # idm = backend.eye(2 * self.L) + # covm = idm - (idm - gamma2) @ den @ (idm - gamma1) + # cm = (1.0j * covm + idm) / 2 + # cmatrix = backend.adjoint(self.wtransform) @ cm @ self.wtransform * 0.25 + # return type(self)(self.L, cmatrix=cmatrix) + + def overlap(self, other: "FGSSimulator") -> Tensor: + """ + overlap upto a U(1) phase + + :param other: _description_ + :type other: FGSSimulator + :return: _description_ + :rtype: _type_ + """ + u, v = self.get_bogoliubov_uv() + u1, v1 = other.get_bogoliubov_uv() + return backend.sqrt( + backend.abs(backend.det(backend.adjoint(u1) @ u + backend.adjoint(v1) @ v)) + ) + + +npb = get_backend("numpy") + + +class FGSTestSimulator: + """ + Never use, only for correctness testing + stick to numpy backend and no jit/ad/vmap is available + """ + + def __init__( + self, + L: int, + filled: Optional[List[int]] = None, + state: Optional[Tensor] = None, + hc: Optional[Tensor] = None, + ): + if filled is None: + filled = [] + self.L = L + if state is not None: + self.state = state + elif hc is not None: + self.state = self.fermion_diagonalization(hc, L) + else: + self.state = self.init_state(filled, L) + self.state0 = self.state + + @staticmethod + def init_state(filled: List[int], L: int) -> Tensor: + c = Circuit(L) + for i in filled: + c.x(i) # type: ignore + return c.state() + + @classmethod + def fermion_diagonalization(cls, hc: Tensor, L: int) -> Tensor: + h = cls.get_hmatrix(hc, L) + _, u = np.linalg.eigh(h) + return u[:, 0] + + @staticmethod + def get_hmatrix(hc: Tensor, L: int) -> Tensor: + hm = np.zeros([2**L, 2**L], dtype=complex) + for i in range(L): + for j in range(L): + op = openfermion.FermionOperator(f"{str(i)}^ {str(j)}") + hm += ( + hc[i, j] * openfermion.get_sparse_operator(op, n_qubits=L).todense() + ) + + for i in range(L, 2 * L): + for j in range(L): + op = openfermion.FermionOperator(f"{str(i-L)} {str(j)}") + hm += ( + hc[i, j] * openfermion.get_sparse_operator(op, n_qubits=L).todense() + ) + + for i in range(L): + for j in range(L, 2 * L): + op = openfermion.FermionOperator(f"{str(i)}^ {str(j-L)}^") + hm += ( + hc[i, j] * openfermion.get_sparse_operator(op, n_qubits=L).todense() + ) + + for i in range(L, 2 * L): + for j in range(L, 2 * L): + op = openfermion.FermionOperator(f"{str(i-L)} {str(j-L)}^") + hm += ( + hc[i, j] * openfermion.get_sparse_operator(op, n_qubits=L).todense() + ) + + return hm + + @staticmethod + def hopping_jw(chi: Tensor, i: int, j: int, L: int) -> Tensor: + op = chi * openfermion.FermionOperator(f"{str(i)}^ {str(j)}") + np.conj( + chi + ) * openfermion.FermionOperator(f"{str(j)}^ {str(i)}") + sop = openfermion.transforms.jordan_wigner(op) + m = openfermion.get_sparse_operator(sop, n_qubits=L).todense() + return m + + @staticmethod + def chemical_potential_jw(chi: Tensor, i: int, L: int) -> Tensor: + op = chi * openfermion.FermionOperator(f"{str(i)}^ {str(i)}") + sop = openfermion.transforms.jordan_wigner(op) + m = openfermion.get_sparse_operator(sop, n_qubits=L).todense() + return m + + def evol_hamiltonian(self, h: Tensor) -> None: + self.state = npb.expm(-1 / 2 * 1.0j * h) @ npb.reshape(self.state, [-1, 1]) + self.state = npb.reshape(self.state, [-1]) + + def evol_ihamiltonian(self, h: Tensor) -> None: + self.state = npb.expm(-1 / 2 * h) @ npb.reshape(self.state, [-1, 1]) + self.state = npb.reshape(self.state, [-1]) + self.orthogonal() + + def evol_ghamiltonian(self, h: Tensor) -> None: + self.state = npb.expm(-1 / 2 * 1.0j * h) @ npb.reshape(self.state, [-1, 1]) + self.state = npb.reshape(self.state, [-1]) + self.orthogonal() + + def evol_hp(self, i: int, j: int, chi: Tensor = 0) -> None: + self.evol_hamiltonian(self.hopping_jw(chi, i, j, self.L)) + + def evol_cp(self, i: int, chi: Tensor = 0) -> None: + self.evol_hamiltonian(self.chemical_potential_jw(chi, i, self.L)) + + def evol_icp(self, i: int, chi: Tensor = 0) -> None: + self.evol_ihamiltonian(self.chemical_potential_jw(chi, i, self.L)) + + @staticmethod + def sc_pairing_jw(chi: Tensor, i: int, j: int, L: int) -> Tensor: + op = chi * openfermion.FermionOperator(f"{str(i)}^ {str(j)}^") + np.conj( + chi + ) * openfermion.FermionOperator(f"{str(j)} {str(i)}") + sop = openfermion.transforms.jordan_wigner(op) + m = openfermion.get_sparse_operator(sop, n_qubits=L).todense() + return m + + def evol_sp(self, i: int, j: int, chi: Tensor = 0) -> None: + self.evol_hamiltonian(self.sc_pairing_jw(chi, i, j, self.L)) + + def orthogonal(self) -> None: + self.state /= backend.norm(self.state) + + def get_ot_cmatrix(self, h: Tensor, now_i: bool = True) -> Tensor: + alpha1_jw = self.state + cmatrix = np.zeros([2 * self.L, 2 * self.L], dtype=complex) + for i in range(self.L): + for j in range(self.L): + op1 = openfermion.FermionOperator(f"{str(i)}") + op2 = openfermion.FermionOperator(f"{str(j)}^") + + m1 = openfermion.get_sparse_operator(op1, n_qubits=self.L).todense() + m2 = openfermion.get_sparse_operator(op2, n_qubits=self.L).todense() + eh = npb.expm(-1 / 2 * 1.0j * h) + eh1 = npb.expm(1 / 2 * 1.0j * h) + if now_i is True: + cmatrix[i, j] = backend.item( + ( + backend.reshape(backend.adjoint(alpha1_jw), [1, -1]) + @ eh1 + @ m1 + @ eh + @ m2 + @ backend.reshape(alpha1_jw, [-1, 1]) + )[0, 0] + ) + else: + cmatrix[i, j] = backend.item( + ( + backend.reshape(backend.adjoint(alpha1_jw), [1, -1]) + @ m1 + @ eh1 + @ m2 + @ eh + @ backend.reshape(alpha1_jw, [-1, 1]) + )[0, 0] + ) + for i in range(self.L, 2 * self.L): + for j in range(self.L): + op1 = openfermion.FermionOperator(f"{str(i-self.L)}^") + op2 = openfermion.FermionOperator(f"{str(j)}^") + + m1 = openfermion.get_sparse_operator(op1, n_qubits=self.L).todense() + m2 = openfermion.get_sparse_operator(op2, n_qubits=self.L).todense() + eh = npb.expm(-1 / 2 * 1.0j * h) + eh1 = npb.expm(1 / 2 * 1.0j * h) + + if now_i is True: + cmatrix[i, j] = backend.item( + ( + backend.reshape(backend.adjoint(alpha1_jw), [1, -1]) + @ eh1 + @ m1 + @ eh + @ m2 + @ backend.reshape(alpha1_jw, [-1, 1]) + )[0, 0] + ) + else: + cmatrix[i, j] = backend.item( + ( + backend.reshape(backend.adjoint(alpha1_jw), [1, -1]) + @ m1 + @ eh1 + @ m2 + @ eh + @ backend.reshape(alpha1_jw, [-1, 1]) + )[0, 0] + ) + + for i in range(self.L): + for j in range(self.L, 2 * self.L): + op1 = openfermion.FermionOperator(f"{str(i)}") + op2 = openfermion.FermionOperator(f"{str(j-self.L)}") + + m1 = openfermion.get_sparse_operator(op1, n_qubits=self.L).todense() + m2 = openfermion.get_sparse_operator(op2, n_qubits=self.L).todense() + eh = npb.expm(-1 / 2 * 1.0j * h) + eh1 = npb.expm(1 / 2 * 1.0j * h) + + if now_i is True: + cmatrix[i, j] = backend.item( + ( + backend.reshape(backend.adjoint(alpha1_jw), [1, -1]) + @ eh1 + @ m1 + @ eh + @ m2 + @ backend.reshape(alpha1_jw, [-1, 1]) + )[0, 0] + ) + else: + cmatrix[i, j] = backend.item( + ( + backend.reshape(backend.adjoint(alpha1_jw), [1, -1]) + @ m1 + @ eh1 + @ m2 + @ eh + @ backend.reshape(alpha1_jw, [-1, 1]) + )[0, 0] + ) + for i in range(self.L, 2 * self.L): + for j in range(self.L, 2 * self.L): + op1 = openfermion.FermionOperator(f"{str(i-self.L)}^ ") + op2 = openfermion.FermionOperator(f"{str(j-self.L)}") + + m1 = openfermion.get_sparse_operator(op1, n_qubits=self.L).todense() + m2 = openfermion.get_sparse_operator(op2, n_qubits=self.L).todense() + eh = npb.expm(-1 / 2 * 1.0j * h) + eh1 = npb.expm(1 / 2 * 1.0j * h) + + if now_i is True: + cmatrix[i, j] = backend.item( + ( + backend.reshape(backend.adjoint(alpha1_jw), [1, -1]) + @ eh1 + @ m1 + @ eh + @ m2 + @ backend.reshape(alpha1_jw, [-1, 1]) + )[0, 0] + ) + else: + cmatrix[i, j] = backend.item( + ( + backend.reshape(backend.adjoint(alpha1_jw), [1, -1]) + @ m1 + @ eh1 + @ m2 + @ eh + @ backend.reshape(alpha1_jw, [-1, 1]) + )[0, 0] + ) + + return cmatrix + + def get_cmatrix(self) -> Tensor: + alpha1_jw = self.state + cmatrix = np.zeros([2 * self.L, 2 * self.L], dtype=complex) + for i in range(self.L): + for j in range(self.L): + op = openfermion.FermionOperator(f"{str(i)} {str(j)}^") + m = openfermion.get_sparse_operator(op, n_qubits=self.L).todense() + cmatrix[i, j] = backend.item( + ( + backend.reshape(backend.adjoint(alpha1_jw), [1, -1]) + @ m + @ backend.reshape(alpha1_jw, [-1, 1]) + )[0, 0] + ) + for i in range(self.L, 2 * self.L): + for j in range(self.L): + op = openfermion.FermionOperator(f"{str(i-self.L)}^ {str(j)}^") + m = openfermion.get_sparse_operator(op, n_qubits=self.L).todense() + cmatrix[i, j] = backend.item( + ( + backend.reshape(backend.adjoint(alpha1_jw), [1, -1]) + @ m + @ backend.reshape(alpha1_jw, [-1, 1]) + )[0, 0] + ) + for i in range(self.L): + for j in range(self.L, 2 * self.L): + op = openfermion.FermionOperator(f"{str(i)} {str(j-self.L)}") + m = openfermion.get_sparse_operator(op, n_qubits=self.L).todense() + cmatrix[i, j] = backend.item( + ( + backend.reshape(backend.adjoint(alpha1_jw), [1, -1]) + @ m + @ backend.reshape(alpha1_jw, [-1, 1]) + )[0, 0] + ) + for i in range(self.L, 2 * self.L): + for j in range(self.L, 2 * self.L): + op = openfermion.FermionOperator(f"{str(i-self.L)}^ {str(j-self.L)}") + m = openfermion.get_sparse_operator(op, n_qubits=self.L).todense() + cmatrix[i, j] = backend.item( + ( + backend.reshape(backend.adjoint(alpha1_jw), [1, -1]) + @ m + @ backend.reshape(alpha1_jw, [-1, 1]) + )[0, 0] + ) + return cmatrix + + def get_cmatrix_majorana(self) -> Tensor: + alpha1_jw = self.state + cmatrix = np.zeros([2 * self.L, 2 * self.L], dtype=complex) + for i in range(2 * self.L): + for j in range(2 * self.L): + op = openfermion.MajoranaOperator((i,)) * openfermion.MajoranaOperator( + (j,) + ) + if j % 2 + i % 2 == 1: + op *= -1 + # convention diff in jordan wigner + # c\dagger = X\pm iY + + op = openfermion.jordan_wigner(op) + m = openfermion.get_sparse_operator(op, n_qubits=self.L).todense() + cmatrix[i, j] = backend.item( + ( + backend.reshape(backend.adjoint(alpha1_jw), [1, -1]) + @ m + @ backend.reshape(alpha1_jw, [-1, 1]) + )[0, 0] + ) + + return cmatrix + + def expectation_4body(self, i: int, j: int, k: int, l: int) -> Tensor: + s = "" + if i < self.L: + s += str(i) + "" + else: + s += str(i - self.L) + "^ " + if j < self.L: + s += str(j) + "" + else: + s += str(j - self.L) + "^ " + if k < self.L: + s += str(k) + "" + else: + s += str(k - self.L) + "^ " + if l < self.L: + s += str(l) + "" + else: + s += str(l - self.L) + "^ " + op = openfermion.FermionOperator(s) + m = openfermion.get_sparse_operator(op, n_qubits=self.L).todense() + return ( + npb.reshape(npb.adjoint(self.state), [1, -1]) + @ m + @ npb.reshape(self.state, [-1, 1]) + )[0, 0] + + def entropy(self, subsystems_to_trace_out: Optional[List[int]] = None) -> Tensor: + rm = quantum.reduced_density_matrix(self.state, subsystems_to_trace_out) # type: ignore + return quantum.entropy(rm) + + def renyi_entropy(self, n: int, subsystems_to_trace_out: List[int]) -> Tensor: + rm = quantum.reduced_density_matrix(self.state, subsystems_to_trace_out) + return quantum.renyi_entropy(rm, n) + + def overlap(self, other: "FGSTestSimulator") -> Tensor: + return backend.tensordot(backend.conj(self.state), other.state, 1) + + def get_dm(self) -> Tensor: + s = backend.reshape(self.state, [-1, 1]) + return s @ backend.adjoint(s) + + def product(self, other: "FGSTestSimulator") -> Tensor: + rho1 = self.get_dm() + rho2 = other.get_dm() + rho = rho1 @ rho2 + rho /= backend.trace(rho) + return rho + + def post_select(self, i: int, keep: int = 1) -> None: + c = Circuit(self.L, inputs=self.state) + c.post_select(i, keep) + s = c.state() + s /= backend.norm(s) + self.state = s + + def cond_measure(self, ind: int, status: float, with_prob: bool = False) -> Tensor: + p0 = self.get_cmatrix()[ind, ind] + prob = [p0, 1 - p0] + if status < p0: + self.post_select(ind, 0) + keep = 0 + else: + self.post_select(ind, 1) + keep = 1 + + if with_prob is False: + return keep + else: + return keep, prob diff --git a/tensorcircuit/gates.py b/tensorcircuit/gates.py index 40fa9b26..412230e2 100644 --- a/tensorcircuit/gates.py +++ b/tensorcircuit/gates.py @@ -13,7 +13,7 @@ import tensornetwork as tn from scipy.stats import unitary_group -from .cons import backend, dtypestr, npdtype +from .cons import backend, dtypestr, npdtype, runtime_backend from .utils import arg_alias thismodule = sys.modules[__name__] @@ -389,6 +389,9 @@ def meta_gate() -> None: setattr(thismodule, n + "_gate", temp) setattr(thismodule, n, temp) + with runtime_backend("numpy"): # backward compatibility + setattr(thismodule, "pauli_gates", [i(), x(), y(), z()]) # type: ignore + meta_gate() @@ -544,7 +547,7 @@ def r_gate(theta: float = 0, alpha: float = 0, phi: float = 0) -> Gate: General single qubit rotation gate .. math:: - R(\theta, \alpha, \phi) = j \cos(\theta) I + R(\theta, \alpha, \phi) = \cos(\theta) I - j \cos(\phi) \sin(\alpha) \sin(\theta) X - j \sin(\phi) \sin(\alpha) \sin(\theta) Y - j \sin(\theta) \cos(\alpha) Z diff --git a/tensorcircuit/interfaces/__init__.py b/tensorcircuit/interfaces/__init__.py index f257d387..1f8cc608 100644 --- a/tensorcircuit/interfaces/__init__.py +++ b/tensorcircuit/interfaces/__init__.py @@ -14,3 +14,6 @@ from .scipy import scipy_interface, scipy_optimize_interface from .torch import torch_interface, pytorch_interface, torch_interface_kws from .tensorflow import tensorflow_interface, tf_interface + + +# TODO(@refraction-ray): jax interface using puer_callback and custom_vjp diff --git a/tensorcircuit/interfaces/torch.py b/tensorcircuit/interfaces/torch.py index e346b757..8fcdb2e2 100644 --- a/tensorcircuit/interfaces/torch.py +++ b/tensorcircuit/interfaces/torch.py @@ -12,6 +12,8 @@ Tensor = Any +# TODO(@refraction-ray): new paradigm compatible with torch functional trasnformation + def torch_interface( fun: Callable[..., Any], jit: bool = False, enable_dlpack: bool = False diff --git a/tensorcircuit/mps_base.py b/tensorcircuit/mps_base.py index 1b09b5a8..d8234c2b 100644 --- a/tensorcircuit/mps_base.py +++ b/tensorcircuit/mps_base.py @@ -1,12 +1,21 @@ """ FiniteMPS from tensornetwork with bug fixed """ + # pylint: disable=invalid-name from typing import Any, Optional, List, Sequence import numpy as np -from tensornetwork.linalg.node_linalg import conj + +try: + from tensornetwork.linalg.node_linalg import conj + + # google tn +except ModuleNotFoundError: + # tc tn + from tensornetwork.matrixproductstates.utils import conj + import tensornetwork as tn import tensornetwork.ncon_interface as ncon from tensornetwork.network_components import Node @@ -127,7 +136,6 @@ def set_center_position(site: int) -> None: if center_position is None: center_position = site1 - if use_svd: U, S, V, tw = self.backend.svd( tensor, @@ -136,6 +144,7 @@ def set_center_position(site: int) -> None: max_truncation_error=max_truncation_err, relative=relative, ) + # Note: fix the center position bug here if center_position == site2: left_tensor = U diff --git a/tensorcircuit/mpscircuit.py b/tensorcircuit/mpscircuit.py index 8a37b3ed..7fc4052e 100644 --- a/tensorcircuit/mpscircuit.py +++ b/tensorcircuit/mpscircuit.py @@ -1,6 +1,7 @@ """ Quantum circuit: MPS state simulator """ + # pylint: disable=invalid-name from functools import reduce @@ -52,6 +53,11 @@ def split_tensor( return backend.qr(tensor) # type: ignore +# AD + MPS can lead to numerical stability issue +# E ./tensorflow/core/kernels/linalg/svd_op_impl.h:110] Eigen::BDCSVD failed with error code 3 +# this is now solved by setting os.environ["TC_BACKENDS_TENSORFLOW_BACKEND__SVD_TF_EPS"]="10" + + class MPSCircuit(AbstractCircuit): """ ``MPSCircuit`` class. diff --git a/tensorcircuit/noisemodel.py b/tensorcircuit/noisemodel.py index 0b03d966..9a1d85ac 100644 --- a/tensorcircuit/noisemodel.py +++ b/tensorcircuit/noisemodel.py @@ -1,6 +1,7 @@ """ General Noise Model Construction. """ + import logging from functools import partial from typing import Any, Sequence, Optional, List, Dict, Tuple, Callable, Union diff --git a/tensorcircuit/quantum.py b/tensorcircuit/quantum.py index ab837c7f..23bb926c 100644 --- a/tensorcircuit/quantum.py +++ b/tensorcircuit/quantum.py @@ -7,11 +7,13 @@ import tensorcircuit.quantum as qu """ + # pylint: disable=invalid-name -from functools import reduce, partial import logging -from operator import or_, mul, matmul +import os +from functools import partial, reduce +from operator import matmul, mul, or_ from typing import ( Any, Callable, @@ -26,19 +28,18 @@ ) import numpy as np -from tensornetwork.network_components import AbstractNode, Node, Edge, connect -from tensornetwork.network_components import CopyNode -from tensornetwork.network_operations import get_all_nodes, copy, reachable -from tensornetwork.network_operations import get_subgraph_dangling, remove_node - -try: - import tensorflow as tf -except ImportError: - pass +from tensornetwork.network_components import AbstractNode, CopyNode, Edge, Node, connect +from tensornetwork.network_operations import ( + copy, + get_all_nodes, + get_subgraph_dangling, + reachable, + remove_node, +) from .cons import backend, contractor, dtypestr, npdtype, rdtypestr -from .backends import get_backend -from .utils import is_m1mac, arg_alias +from .gates import Gate, num_to_tensor +from .utils import arg_alias Tensor = Any Graph = Any @@ -1159,318 +1160,327 @@ def quimb2qop(qb_mpo: Any) -> QuOperator: return qop -try: +def heisenberg_hamiltonian( + g: Graph, + hzz: float = 1.0, + hxx: float = 1.0, + hyy: float = 1.0, + hz: float = 0.0, + hx: float = 0.0, + hy: float = 0.0, + sparse: bool = True, + numpy: bool = False, +) -> Tensor: + """ + Generate Heisenberg Hamiltonian with possible external fields. + Currently requires tensorflow installed + + :Example: - def _id(x: Any) -> Any: - return x + >>> g = tc.templates.graphs.Line1D(6) + >>> h = qu.heisenberg_hamiltonian(g, sparse=False) + >>> tc.backend.eigh(h)[0][:10] + array([-11.2111025, -8.4721365, -8.472136 , -8.472136 , -6. , + -5.123106 , -5.123106 , -5.1231055, -5.1231055, -5.1231055], + dtype=float32) + + :param g: input circuit graph + :type g: Graph + :param hzz: zz coupling, default is 1.0 + :type hzz: float + :param hxx: xx coupling, default is 1.0 + :type hxx: float + :param hyy: yy coupling, default is 1.0 + :type hyy: float + :param hz: External field on z direction, default is 0.0 + :type hz: float + :param hx: External field on y direction, default is 0.0 + :type hx: float + :param hy: External field on x direction, default is 0.0 + :type hy: float + :param sparse: Whether to return sparse Hamiltonian operator, default is True. + :type sparse: bool, defalts True + :param numpy: whether return the matrix in numpy or tensorflow form + :type numpy: bool, defaults False, + + :return: Hamiltonian measurements + :rtype: Tensor + """ + n = len(g.nodes) + ls = [] + weight = [] + for e in g.edges: + if hzz != 0: + r = [0 for _ in range(n)] + r[e[0]] = 3 + r[e[1]] = 3 + ls.append(r) + weight.append(hzz) + if hxx != 0: + r = [0 for _ in range(n)] + r[e[0]] = 1 + r[e[1]] = 1 + ls.append(r) + weight.append(hxx) + if hyy != 0: + r = [0 for _ in range(n)] + r[e[0]] = 2 + r[e[1]] = 2 + ls.append(r) + weight.append(hyy) + for node in g.nodes: + if hz != 0: + r = [0 for _ in range(n)] + r[node] = 3 + ls.append(r) + weight.append(hz) + if hx != 0: + r = [0 for _ in range(n)] + r[node] = 1 + ls.append(r) + weight.append(hx) + if hy != 0: + r = [0 for _ in range(n)] + r[node] = 2 + ls.append(r) + weight.append(hy) + ls = num_to_tensor(ls) + weight = num_to_tensor(weight) + if sparse: + r = PauliStringSum2COO_numpy(ls, weight) + if numpy: + return r + return backend.coo_sparse_matrix_from_numpy(r) + return PauliStringSum2Dense(ls, weight, numpy=numpy) + + +def PauliStringSum2Dense( + ls: Sequence[Sequence[int]], + weight: Optional[Sequence[float]] = None, + numpy: bool = False, +) -> Tensor: + """ + Generate dense matrix from Pauli string sum. + Currently requires tensorflow installed. - if is_m1mac(): - compiled_jit = _id + + :param ls: 2D Tensor, each row is for a Pauli string, + e.g. [1, 0, 0, 3, 2] is for :math:`X_0Z_3Y_4` + :type ls: Sequence[Sequence[int]] + :param weight: 1D Tensor, each element corresponds the weight for each Pauli string + defaults to None (all Pauli strings weight 1.0) + :type weight: Optional[Sequence[float]], optional + :param numpy: default False. If True, return numpy coo + else return backend compatible sparse tensor + :type numpy: bool + :return: the tensorflow dense matrix + :rtype: Tensor + """ + sparsem = PauliStringSum2COO_numpy(ls, weight) + if numpy: + return sparsem.todense() + sparsem = backend.coo_sparse_matrix_from_numpy(sparsem) + densem = backend.to_dense(sparsem) + return densem + + +# already implemented as backend method +# +# def _tf2numpy_sparse(a: Tensor) -> Tensor: +# return get_backend("numpy").coo_sparse_matrix( +# indices=a.indices, +# values=a.values, +# shape=a.get_shape(), +# ) + +# def _numpy2tf_sparse(a: Tensor) -> Tensor: +# return get_backend("tensorflow").coo_sparse_matrix( +# indices=np.array([a.row, a.col]).T, +# values=a.data, +# shape=a.shape, +# ) + + +def PauliStringSum2COO( + ls: Sequence[Sequence[int]], + weight: Optional[Sequence[float]] = None, + numpy: bool = False, +) -> Tensor: + """ + Generate sparse tensor from Pauli string sum. + Currently requires tensorflow installed + + :param ls: 2D Tensor, each row is for a Pauli string, + e.g. [1, 0, 0, 3, 2] is for :math:`X_0Z_3Y_4` + :type ls: Sequence[Sequence[int]] + :param weight: 1D Tensor, each element corresponds the weight for each Pauli string + defaults to None (all Pauli strings weight 1.0) + :type weight: Optional[Sequence[float]], optional + :param numpy: default False. If True, return numpy coo + else return backend compatible sparse tensor + :type numpy: bool + :return: the scipy coo sparse matrix + :rtype: Tensor + """ + # numpy version is 3* faster! + + nterms = len(ls) + # n = len(ls[0]) + # s = 0b1 << n + if weight is None: + weight = [1.0 for _ in range(nterms)] + weight = num_to_tensor(weight) + ls = num_to_tensor(ls) + # rsparse = get_backend("numpy").coo_sparse_matrix( + # indices=np.array([[0, 0]], dtype=np.int64), + # values=np.array([0.0], dtype=getattr(np, dtypestr)), + # shape=(s, s), + # ) + global PauliString2COO_jit + if backend.name not in PauliString2COO_jit: + PauliString2COO_jit[backend.name] = backend.jit( + PauliString2COO, jit_compile=True + ) + rsparses = [ + backend.numpy(PauliString2COO_jit[backend.name](ls[i], weight[i])) # type: ignore + for i in range(nterms) + ] + rsparse = _dc_sum(rsparses) + # auto transformed into csr format!! + + # for i in range(nterms): + # rsparse += get_backend("tensorflow").numpy(PauliString2COO(ls[i], weight[i])) + rsparse = rsparse.tocoo() + if numpy: + return rsparse + return backend.coo_sparse_matrix_from_numpy(rsparse) + + +def _dc_sum(l: List[Any]) -> Any: + """ + For the sparse sum, the speed is determined by the non zero terms, + so the DC way to do the sum can indeed bring some speed advantage (several times) + + :param l: _description_ + :type l: List[Any] + :return: _description_ + :rtype: Any + """ + n = len(l) + if n > 2: + return _dc_sum(l[: n // 2]) + _dc_sum(l[n // 2 :]) else: - compiled_jit = partial(get_backend("tensorflow").jit, jit_compile=True) - - def heisenberg_hamiltonian( - g: Graph, - hzz: float = 1.0, - hxx: float = 1.0, - hyy: float = 1.0, - hz: float = 0.0, - hx: float = 0.0, - hy: float = 0.0, - sparse: bool = True, - numpy: bool = False, - ) -> Tensor: - """ - Generate Heisenberg Hamiltonian with possible external fields. - Currently requires tensorflow installed + return sum(l) - :Example: - >>> g = tc.templates.graphs.Line1D(6) - >>> h = qu.heisenberg_hamiltonian(g, sparse=False) - >>> tc.backend.eigh(h)[0][:10] - array([-11.2111025, -8.4721365, -8.472136 , -8.472136 , -6. , - -5.123106 , -5.123106 , -5.1231055, -5.1231055, -5.1231055], - dtype=float32) - - :param g: input circuit graph - :type g: Graph - :param hzz: zz coupling, default is 1.0 - :type hzz: float - :param hxx: xx coupling, default is 1.0 - :type hxx: float - :param hyy: yy coupling, default is 1.0 - :type hyy: float - :param hz: External field on z direction, default is 0.0 - :type hz: float - :param hx: External field on y direction, default is 0.0 - :type hx: float - :param hy: External field on x direction, default is 0.0 - :type hy: float - :param sparse: Whether to return sparse Hamiltonian operator, default is True. - :type sparse: bool, defalts True - :param numpy: whether return the matrix in numpy or tensorflow form - :type numpy: bool, defaults False, - - :return: Hamiltonian measurements - :rtype: Tensor - """ - n = len(g.nodes) - ls = [] - weight = [] - for e in g.edges: - if hzz != 0: - r = [0 for _ in range(n)] - r[e[0]] = 3 - r[e[1]] = 3 - ls.append(r) - weight.append(hzz) - if hxx != 0: - r = [0 for _ in range(n)] - r[e[0]] = 1 - r[e[1]] = 1 - ls.append(r) - weight.append(hxx) - if hyy != 0: - r = [0 for _ in range(n)] - r[e[0]] = 2 - r[e[1]] = 2 - ls.append(r) - weight.append(hyy) - for node in g.nodes: - if hz != 0: - r = [0 for _ in range(n)] - r[node] = 3 - ls.append(r) - weight.append(hz) - if hx != 0: - r = [0 for _ in range(n)] - r[node] = 1 - ls.append(r) - weight.append(hx) - if hy != 0: - r = [0 for _ in range(n)] - r[node] = 2 - ls.append(r) - weight.append(hy) - ls = tf.constant(ls) - weight = tf.constant(weight) - ls = get_backend("tensorflow").cast(ls, dtypestr) - weight = get_backend("tensorflow").cast(weight, dtypestr) - if sparse: - r = PauliStringSum2COO_numpy(ls, weight) - if numpy: - return r - return backend.coo_sparse_matrix_from_numpy(r) - return PauliStringSum2Dense(ls, weight, numpy=numpy) - - def PauliStringSum2Dense( - ls: Sequence[Sequence[int]], - weight: Optional[Sequence[float]] = None, - numpy: bool = False, - ) -> Tensor: - """ - Generate dense matrix from Pauli string sum. - Currently requires tensorflow installed. - - - :param ls: 2D Tensor, each row is for a Pauli string, - e.g. [1, 0, 0, 3, 2] is for :math:`X_0Z_3Y_4` - :type ls: Sequence[Sequence[int]] - :param weight: 1D Tensor, each element corresponds the weight for each Pauli string - defaults to None (all Pauli strings weight 1.0) - :type weight: Optional[Sequence[float]], optional - :param numpy: default False. If True, return numpy coo - else return backend compatible sparse tensor - :type numpy: bool - :return: the tensorflow dense matrix - :rtype: Tensor - """ - sparsem = PauliStringSum2COO_numpy(ls, weight) - if numpy: - return sparsem.todense() - sparsem = backend.coo_sparse_matrix_from_numpy(sparsem) - densem = backend.to_dense(sparsem) - return densem - - # already implemented as backend method - # - # def _tf2numpy_sparse(a: Tensor) -> Tensor: - # return get_backend("numpy").coo_sparse_matrix( - # indices=a.indices, - # values=a.values, - # shape=a.get_shape(), - # ) - - # def _numpy2tf_sparse(a: Tensor) -> Tensor: - # return get_backend("tensorflow").coo_sparse_matrix( - # indices=np.array([a.row, a.col]).T, - # values=a.data, - # shape=a.shape, - # ) - - def PauliStringSum2COO( - ls: Sequence[Sequence[int]], - weight: Optional[Sequence[float]] = None, - numpy: bool = False, - ) -> Tensor: - """ - Generate sparse tensor from Pauli string sum. - Currently requires tensorflow installed - - :param ls: 2D Tensor, each row is for a Pauli string, - e.g. [1, 0, 0, 3, 2] is for :math:`X_0Z_3Y_4` - :type ls: Sequence[Sequence[int]] - :param weight: 1D Tensor, each element corresponds the weight for each Pauli string - defaults to None (all Pauli strings weight 1.0) - :type weight: Optional[Sequence[float]], optional - :param numpy: default False. If True, return numpy coo - else return backend compatible sparse tensor - :type numpy: bool - :return: the scipy coo sparse matrix - :rtype: Tensor - """ - # numpy version is 3* faster! - - nterms = len(ls) - # n = len(ls[0]) - # s = 0b1 << n - if weight is None: - weight = [1.0 for _ in range(nterms)] - if not (isinstance(weight, tf.Tensor) or isinstance(weight, tf.Variable)): - weight = tf.constant(weight, dtype=getattr(tf, dtypestr)) - # rsparse = get_backend("numpy").coo_sparse_matrix( - # indices=np.array([[0, 0]], dtype=np.int64), - # values=np.array([0.0], dtype=getattr(np, dtypestr)), - # shape=(s, s), - # ) - rsparses = [ - get_backend("tensorflow").numpy(PauliString2COO(ls[i], weight[i])) # type: ignore - for i in range(nterms) - ] - rsparse = _dc_sum(rsparses) - # auto transformed into csr format!! +PauliStringSum2COO_numpy = partial(PauliStringSum2COO, numpy=True) - # for i in range(nterms): - # rsparse += get_backend("tensorflow").numpy(PauliString2COO(ls[i], weight[i])) # type: ignore - rsparse = rsparse.tocoo() - if numpy: - return rsparse - return backend.coo_sparse_matrix_from_numpy(rsparse) - def _dc_sum(l: List[Any]) -> Any: - """ - For the sparse sum, the speed is determined by the non zero terms, - so the DC way to do the sum can indeed bring some speed advantage (several times) +def PauliStringSum2COO_tf( + ls: Sequence[Sequence[int]], weight: Optional[Sequence[float]] = None +) -> Tensor: + """ + Generate tensorflow sparse matrix from Pauli string sum + [deprecated] - :param l: _description_ - :type l: List[Any] - :return: _description_ - :rtype: Any - """ - n = len(l) - if n > 2: - return _dc_sum(l[: n // 2]) + _dc_sum(l[n // 2 :]) - else: - return sum(l) + :param ls: 2D Tensor, each row is for a Pauli string, + e.g. [1, 0, 0, 3, 2] is for :math:`X_0Z_3Y_4` + :type ls: Sequence[Sequence[int]] + :param weight: 1D Tensor, each element corresponds the weight for each Pauli string + defaults to None (all Pauli strings weight 1.0) + :type weight: Optional[Sequence[float]], optional + :return: the tensorflow coo sparse matrix + :rtype: Tensor + """ + import tensorflow as tf - PauliStringSum2COO_numpy = partial(PauliStringSum2COO, numpy=True) + nterms = len(ls) + n = len(ls[0]) + s = 0b1 << n + if weight is None: + weight = [1.0 for _ in range(nterms)] + if not (isinstance(weight, tf.Tensor) or isinstance(weight, tf.Variable)): + weight = tf.constant(weight, dtype=getattr(tf, dtypestr)) + rsparse = tf.SparseTensor( + indices=tf.constant([[0, 0]], dtype=tf.int64), + values=tf.constant([0.0], dtype=weight.dtype), # type: ignore + dense_shape=(s, s), + ) + for i in range(nterms): + rsparse = tf.sparse.add(rsparse, PauliString2COO(ls[i], weight[i])) # type: ignore + # very slow sparse.add? + return rsparse - def PauliStringSum2COO_tf( - ls: Sequence[Sequence[int]], weight: Optional[Sequence[float]] = None - ) -> Tensor: - """ - Generate tensorflow sparse matrix from Pauli string sum - - :param ls: 2D Tensor, each row is for a Pauli string, - e.g. [1, 0, 0, 3, 2] is for :math:`X_0Z_3Y_4` - :type ls: Sequence[Sequence[int]] - :param weight: 1D Tensor, each element corresponds the weight for each Pauli string - defaults to None (all Pauli strings weight 1.0) - :type weight: Optional[Sequence[float]], optional - :return: the tensorflow coo sparse matrix - :rtype: Tensor - """ - nterms = len(ls) - n = len(ls[0]) - s = 0b1 << n - if weight is None: - weight = [1.0 for _ in range(nterms)] - if not (isinstance(weight, tf.Tensor) or isinstance(weight, tf.Variable)): - weight = tf.constant(weight, dtype=getattr(tf, dtypestr)) - rsparse = tf.SparseTensor( - indices=tf.constant([[0, 0]], dtype=tf.int64), - values=tf.constant([0.0], dtype=weight.dtype), # type: ignore - dense_shape=(s, s), - ) - for i in range(nterms): - rsparse = tf.sparse.add(rsparse, PauliString2COO(ls[i], weight[i])) # type: ignore - # very slow sparse.add? - return rsparse - @compiled_jit - def PauliString2COO(l: Sequence[int], weight: Optional[float] = None) -> Tensor: - """ - Generate tensorflow sparse matrix from Pauli string sum - - :param l: 1D Tensor representing for a Pauli string, - e.g. [1, 0, 0, 3, 2] is for :math:`X_0Z_3Y_4` - :type l: Sequence[int] - :param weight: the weight for the Pauli string - defaults to None (all Pauli strings weight 1.0) - :type weight: Optional[float], optional - :return: the tensorflow sparse matrix - :rtype: Tensor - """ - n = len(l) - one = tf.constant(0b1, dtype=tf.int64) - idx_x = tf.constant(0b0, dtype=tf.int64) - idx_y = tf.constant(0b0, dtype=tf.int64) - idx_z = tf.constant(0b0, dtype=tf.int64) - i = tf.constant(0, dtype=tf.int64) - for j in l: - # i, j from enumerate is python, non jittable when cond using tensor - if j == 1: # xi - idx_x += tf.bitwise.left_shift(one, n - i - 1) - elif j == 2: # yi - idx_y += tf.bitwise.left_shift(one, n - i - 1) - elif j == 3: # zi - idx_z += tf.bitwise.left_shift(one, n - i - 1) - i += 1 - - if weight is None: - weight = tf.constant(1.0, dtype=tf.complex64) - return ps2coo_core(idx_x, idx_y, idx_z, weight, n) - - @compiled_jit - def ps2coo_core( - idx_x: Tensor, idx_y: Tensor, idx_z: Tensor, weight: Tensor, nqubits: int - ) -> Tuple[Tensor, Tensor]: - dtype = weight.dtype - s = 0b1 << nqubits - idx1 = tf.cast(tf.range(s), dtype=tf.int64) - idx2 = (idx1 ^ idx_x) ^ (idx_y) - indices = tf.transpose(tf.stack([idx1, idx2])) - tmp = idx1 & (idx_y | idx_z) - e = idx1 * 0 - ny = 0 - for i in range(nqubits): - # if tmp[i] is power of 2 (non zero), then e[i] = 1 - e ^= tf.bitwise.right_shift(tmp, i) & 0b1 - # how many 1 contained in idx_y - ny += tf.bitwise.right_shift(idx_y, i) & 0b1 - ny = tf.math.mod(ny, 4) - values = ( - tf.cast((1 - 2 * e), dtype) - * tf.math.pow(tf.constant(-1.0j, dtype=dtype), tf.cast(ny, dtype)) - * weight - ) - return tf.SparseTensor(indices=indices, values=values, dense_shape=(s, s)) # type: ignore +def PauliString2COO(l: Sequence[int], weight: Optional[float] = None) -> Tensor: + """ + Generate sparse matrix from Pauli string sum -except (NameError, ImportError): - logger.info( - "tensorflow is not installed, and sparse Hamiltonian generation utilities are disabled" + :param l: 1D Tensor representing for a Pauli string, + e.g. [1, 0, 0, 3, 2] is for :math:`X_0Z_3Y_4` + :type l: Sequence[int] + :param weight: the weight for the Pauli string + defaults to None (all Pauli strings weight 1.0) + :type weight: Optional[float], optional + :return: the tensorflow sparse matrix + :rtype: Tensor + """ + n = len(l) + l = num_to_tensor(l, dtype="int64") + # l = backend.cast(l, dtype="int64") + one = num_to_tensor(0b1, dtype="int64") + idx_x = num_to_tensor(0b0, dtype="int64") + idx_y = num_to_tensor(0b0, dtype="int64") + idx_z = num_to_tensor(0b0, dtype="int64") + i = num_to_tensor(0, dtype="int64") + # for j in l: + for j in range(n): + oh = backend.onehot(l[j], 4) + s = backend.left_shift(one, n - i - 1) + oh = backend.cast(oh, dtype="int64") + idx_x += oh[1] * s + idx_y += oh[2] * s + idx_z += oh[3] * s + + # if j == 1: # xi + # idx_x += backend.left_shift(one, n - i - 1) + # elif j == 2: # yi + # idx_y += backend.left_shift(one, n - i - 1) + # elif j == 3: # zi + # idx_z += backend.left_shift(one, n - i - 1) + i += 1 + + if weight is None: + weight = num_to_tensor(1.0, dtype="complex64") + return ps2coo_core(idx_x, idx_y, idx_z, weight, n) + + +PauliString2COO_jit = {"numpy": PauliString2COO} + + +def ps2coo_core( + idx_x: Tensor, idx_y: Tensor, idx_z: Tensor, weight: Tensor, nqubits: int +) -> Tuple[Tensor, Tensor]: + s = 0b1 << nqubits + idx1 = num_to_tensor(backend.arange(s), dtype="int64") + idx2 = (idx1 ^ idx_x) ^ (idx_y) + indices = backend.transpose(backend.stack([idx1, idx2])) + tmp = idx1 & (idx_y | idx_z) + e = idx1 * 0 + ny = 0 + for i in range(nqubits): + # if tmp[i] is power of 2 (non zero), then e[i] = 1 + e ^= backend.right_shift(tmp, i) & 0b1 + # how many 1 contained in idx_y + ny += backend.right_shift(idx_y, i) & 0b1 + ny = backend.mod(ny, 4) + values = ( + num_to_tensor(1 - 2 * e) + * ((num_to_tensor(-1.0j) ** num_to_tensor(ny))) + * weight ) + return backend.coo_sparse_matrix(indices=indices, values=values, shape=(s, s)) # type: ignore + # some quantum quatities below @@ -1502,7 +1512,7 @@ def op2tensor( @op2tensor -def entropy(rho: Union[Tensor, QuOperator], eps: float = 1e-12) -> Tensor: +def entropy(rho: Union[Tensor, QuOperator], eps: Optional[float] = None) -> Tensor: """ Compute the entropy from the given density matrix ``rho``. @@ -1540,9 +1550,15 @@ def entanglement2(param, n, nlayers): :return: Entropy on the given density matrix. :rtype: Tensor """ + eps_env = os.environ.get("TC_QUANTUM_ENTROPY_EPS") + if eps is None and eps_env is None: + eps = 1e-12 + elif eps is None and eps_env is not None: + eps = 10 ** (-int(eps_env)) rho += eps * backend.cast(backend.eye(rho.shape[-1]), rho.dtype) # type: ignore lbd = backend.real(backend.eigh(rho)[0]) lbd = backend.relu(lbd) + lbd /= backend.sum(lbd) # we need the matrix anyway for AD. entropy = -backend.sum(lbd * backend.log(lbd + eps)) return backend.real(entropy) @@ -1580,6 +1596,51 @@ def trace_product(*o: Union[Tensor, QuOperator]) -> Tensor: return backend.trace(prod) +@op2tensor +def entanglement_entropy(state: Tensor, cut: Union[int, List[int]]) -> Tensor: + rho = reduced_density_matrix(state, cut) + return entropy(rho) + + +def reduced_wavefunction( + state: Tensor, cut: List[int], measure: Optional[List[int]] = None +) -> Tensor: + """ + Compute the reduced wavefunction from the quantum state ``state``. + The fixed measure result is guaranteed by users, + otherwise final normalization may required in the return + + :param state: _description_ + :type state: Tensor + :param cut: the list of position for qubit to be reduced + :type cut: List[int] + :param measure: the fixed results of given qubits in the same shape list as ``cut`` + :type measure: List[int] + :return: _description_ + :rtype: Tensor + """ + if measure is None: + measure = [0 for _ in cut] + s = backend.reshape2(state) + n = len(backend.shape_tuple(s)) + s_node = Gate(s) + end_nodes = [] + for c, m in zip(cut, measure): + rt = backend.cast(backend.convert_to_tensor(1 - m), dtypestr) * backend.cast( + backend.convert_to_tensor(np.array([1.0, 0.0])), dtypestr + ) + backend.cast(backend.convert_to_tensor(m), dtypestr) * backend.cast( + backend.convert_to_tensor(np.array([0.0, 1.0])), dtypestr + ) + end_node = Gate(rt) + end_nodes.append(end_node) + s_node[c] ^ end_node[0] + new_node = contractor( + [s_node] + end_nodes, + output_edge_order=[s_node[i] for i in range(n) if i not in cut], + ) + return backend.reshape(new_node.tensor, [-1]) + + def reduced_density_matrix( state: Union[Tensor, QuOperator], cut: Union[int, List[int]], @@ -1789,6 +1850,76 @@ def truncated_free_energy( return energy - renyi / beta +@op2tensor +def partial_transpose(rho: Tensor, transposed_sites: List[int]) -> Tensor: + """ + _summary_ + + :param rho: density matrix + :type rho: Tensor + :param transposed_sites: sites int list to be transposed + :type transposed_sites: List[int] + :return: _description_ + :rtype: Tensor + """ + rho = backend.reshape2(rho) + rho_node = Gate(rho) + n = len(rho.shape) // 2 + left_edges = [] + right_edges = [] + for i in range(n): + if i not in transposed_sites: + left_edges.append(rho_node[i]) + right_edges.append(rho_node[i + n]) + else: + left_edges.append(rho_node[i + n]) + right_edges.append(rho_node[i]) + rhot_op = QuOperator(out_edges=left_edges, in_edges=right_edges) + rhot = rhot_op.eval_matrix() + return rhot + + +@op2tensor +def entanglement_negativity(rho: Tensor, transposed_sites: List[int]) -> Tensor: + """ + _summary_ + + :param rho: _description_ + :type rho: Tensor + :param transposed_sites: _description_ + :type transposed_sites: List[int] + :return: _description_ + :rtype: Tensor + """ + rhot = partial_transpose(rho, transposed_sites) + es = backend.eigvalsh(rhot) + rhot_m = backend.sum(backend.abs(es)) + return (backend.log(rhot_m) - 1.0) / 2.0 + + +@op2tensor +def log_negativity(rho: Tensor, transposed_sites: List[int], base: str = "e") -> Tensor: + """ + _summary_ + + :param rho: _description_ + :type rho: Tensor + :param transposed_sites: _description_ + :type transposed_sites: List[int] + :param base: whether use 2 based log or e based log, defaults to "e" + :type base: str, optional + :return: _description_ + :rtype: Tensor + """ + rhot = partial_transpose(rho, transposed_sites) + es = backend.eigvalsh(rhot) + rhot_m = backend.sum(backend.abs(es)) + een = backend.log(rhot_m) + if base in ["2", 2]: + return een / backend.cast(backend.log(2.0), rdtypestr) + return een + + @partial(op2tensor, op_argnums=(0, 1)) def trace_distance(rho: Tensor, rho0: Tensor, eps: float = 1e-12) -> Tensor: """ @@ -2033,7 +2164,10 @@ def count_vector2dict(count: Tensor, n: int, key: str = "bin") -> Dict[Any, int] :return: _description_ :rtype: _type_ """ - d = {i: backend.numpy(count[i]).item() for i in range(2**n)} + from .interfaces import which_backend + + b = which_backend(count) + d = {i: b.numpy(count[i]).item() for i in range(2**n)} if key == "int": return d else: diff --git a/tensorcircuit/results/counts.py b/tensorcircuit/results/counts.py index 78695734..a4800cc4 100644 --- a/tensorcircuit/results/counts.py +++ b/tensorcircuit/results/counts.py @@ -1,6 +1,7 @@ """ dict related functionalities """ + from typing import Any, Dict, Optional, Sequence import numpy as np @@ -9,6 +10,8 @@ Tensor = Any ct = Dict[str, int] +# TODO(@refraction-ray): merge_count + def reverse_count(count: ct) -> ct: ncount = {} @@ -109,6 +112,8 @@ def plot_histogram(data: Any, **kws: Any) -> Any: See ``qiskit.visualization.plot_histogram``: https://qiskit.org/documentation/stubs/qiskit.visualization.plot_histogram.html + interesting kw options include: ``number_to_keep`` (int) + :param data: _description_ :type data: Any :return: _description_ @@ -116,4 +121,4 @@ def plot_histogram(data: Any, **kws: Any) -> Any: """ from qiskit.visualization import plot_histogram - return plot_histogram(data) + return plot_histogram(data, **kws) diff --git a/tensorcircuit/results/qem/__init__.py b/tensorcircuit/results/qem/__init__.py new file mode 100644 index 00000000..c895d370 --- /dev/null +++ b/tensorcircuit/results/qem/__init__.py @@ -0,0 +1,14 @@ +from . import qem_methods + +apply_zne = qem_methods.apply_zne +zne_option = qem_methods.zne_option # type: ignore + +apply_dd = qem_methods.apply_dd +dd_option = qem_methods.dd_option # type: ignore +used_qubits = qem_methods.used_qubits +prune_ddcircuit = qem_methods.prune_ddcircuit +add_dd = qem_methods.add_dd + +apply_rc = qem_methods.apply_rc +rc_circuit = qem_methods.rc_circuit +rc_candidates = qem_methods.rc_candidates diff --git a/tensorcircuit/results/qem/benchmark_circuits.py b/tensorcircuit/results/qem/benchmark_circuits.py new file mode 100644 index 00000000..368cc828 --- /dev/null +++ b/tensorcircuit/results/qem/benchmark_circuits.py @@ -0,0 +1,107 @@ +""" +circuits for quantum chip benchmark +""" + +from typing import Any, List, Dict, Tuple +import logging + +logger = logging.getLogger(__name__) + +import networkx as nx + +try: + from mitiq.benchmarks import ( + generate_ghz_circuit, + generate_mirror_circuit, + generate_rb_circuits, + generate_w_circuit, + ) + from mitiq.interface import convert_from_mitiq +except ModuleNotFoundError: + logger.warning("mitiq is not installed, please ``pip install mitiq`` first") + + +from ... import Circuit + + +def ghz_circuit(num_qubits: int) -> Tuple[Any, Dict[str, float]]: + cirq = generate_ghz_circuit(num_qubits) + ideal = {"0" * num_qubits: 0.5, "1" * num_qubits: 0.5} + qisc = convert_from_mitiq(cirq, "qiskit") + circuit = Circuit.from_qiskit(qisc, qisc.num_qubits) + return circuit, ideal + + +def w_circuit(num_qubits: int) -> Tuple[Any, Dict[str, float]]: + # Efficient quantum algorithms for GHZ and W states https://arxiv.org/abs/1807.05572 + # Werner-state with linear complexity {'1000': 0.25, '0100': 0.25, '0010': 0.25, '0001': 0.25} + cirq = generate_w_circuit(num_qubits) + + ideal = {} + for i in range(num_qubits): + bitstring = "0" * i + "1" + "0" * (num_qubits - i - 1) + ideal[bitstring] = 1 / num_qubits + + qisc = convert_from_mitiq(cirq, "qiskit") + circuit = Circuit.from_qiskit(qisc, qisc.num_qubits) + return circuit, ideal + + +def rb_circuit(num_qubits: int, depth: int) -> Tuple[Any, Dict[str, float]]: + # num_qubits limited to 1 or 2 + cirq = generate_rb_circuits(num_qubits, depth)[0] + ideal = {"0" * num_qubits: 1.0} + qisc = convert_from_mitiq(cirq, "qiskit") + circuit = Circuit.from_qiskit(qisc, qisc.num_qubits) + return circuit, ideal + + +def mirror_circuit( + depth: int, + two_qubit_gate_prob: float, + connectivity_graph: nx.Graph, + seed: int, + two_qubit_gate_name: str = "CNOT", +) -> Tuple[Any, Dict[str, float]]: + # Measuring the Capabilities of Quantum Computers https://arxiv.org/pdf/2008.11294.pdf + cirq, bitstring_list = generate_mirror_circuit( + nlayers=depth, + two_qubit_gate_prob=two_qubit_gate_prob, + connectivity_graph=connectivity_graph, + two_qubit_gate_name=two_qubit_gate_name, + seed=seed, + ) + ideal_bitstring = "".join(map(str, bitstring_list)) + ideal = {ideal_bitstring: 1.0} + qisc = convert_from_mitiq(cirq, "qiskit") + circuit = Circuit.from_qiskit(qisc, qisc.num_qubits) + return circuit, ideal + + +def QAOA_circuit( + graph: List[Tuple[int]], weight: List[float], params: List[float] +) -> Any: # internal API don't use + nlayers = len(params) + + qlist = [] + for i in range(len(graph)): + for j in range(2): + qlist.append(graph[i][j]) + qlist = list(set(qlist)) + + nqubit = max(qlist) + 1 + + c = Circuit(nqubit) + for i in qlist: + c.h(i) # type: ignore + + for i in range(nlayers): + for e in range(len(graph)): + c.cnot(graph[e][0], graph[e][1]) # type: ignore + c.rz(graph[e][1], theta=params[i, 0] * weight[e]) # type: ignore + c.cnot(graph[e][0], graph[e][1]) # type: ignore + + for k in qlist: + c.rx(k, theta=params[i, 1] * 2) # type: ignore + + return c diff --git a/tensorcircuit/results/qem/qem_methods.py b/tensorcircuit/results/qem/qem_methods.py new file mode 100644 index 00000000..68199e49 --- /dev/null +++ b/tensorcircuit/results/qem/qem_methods.py @@ -0,0 +1,383 @@ +""" +quantum error mitigation functionalities +""" + +from typing import Any, List, Union, Optional, Dict, Tuple, Callable, Sequence +from itertools import product +import functools +from functools import partial +import collections +import operator +from random import choice +import logging + +logger = logging.getLogger(__name__) + +import numpy as np + +try: + from mitiq import zne, ddd + from mitiq.zne.scaling import fold_gates_at_random + + zne_option = zne + dd_option = ddd +except ModuleNotFoundError: + logger.warning("mitiq is not installed, please ``pip install mitiq`` first") + zne_option = None + dd_option = None + +from ... import Circuit +from ... import backend, gates +from ...compiler import simple_compiler + +Gate = gates.Gate + + +def apply_zne( + circuit: Any, + executor: Callable[[Union[Any, Sequence[Any]]], Any], + factory: Optional[Any], + scale_noise: Optional[Callable[[Any, float], Any]] = None, + num_to_average: int = 1, + **kws: Any, +) -> Any: + """ + Apply zero-noise extrapolation (ZNE) and return the mitigated results. + + :param circuit: The aim circuit. + :type circuit: Any + :param executor: A executor that executes a single circuit or a batch of circuits and return results. + :type executor: Callable[[Union[Any, Sequence[Any]]], Any] + :param factory: Determines the extropolation method. + :type factory: Optional[Factory] + :param scale_noise: The scaling function for the aim circuit, defaults to fold_gates_at_random + :type scale_noise: Callable[[Any, float], Any], optional + :param num_to_average: Number of times expectation values are computed by + the executor, average each point, defaults to 1. + :type num_to_average: int, optional + :return: Mitigated average value by ZNE. + :rtype: float + """ + if scale_noise is None: + scale_noise = fold_gates_at_random + + def executortc(c): # type: ignore + c = Circuit.from_qiskit(c, c.num_qubits) + return executor(c) + + circuit = circuit.to_qiskit(enable_instruction=True) + result = zne.execute_with_zne( + circuit=circuit, + executor=executortc, + factory=factory, + scale_noise=scale_noise, + num_to_average=num_to_average, + **kws, + ) + return result + + +def prune_ddcircuit(c: Any, qlist: List[int]) -> Any: + """ + Discard DD sequence on idle qubits and Discard identity gate + (no identity/idle gate on device now) filled in DD sequence. + + :param c: circuit + :type c: Any + :param qlist: qubit list to apply DD sequence + :type qlist: list + :return: new circuit + :rtype: Any + """ + qir = c.to_qir() + cnew = Circuit(c.circuit_param["nqubits"]) + for d in qir: + if d["index"][0] in qlist: + if_iden = np.sum(abs(np.array([[1, 0], [0, 1]]) - d["gate"].get_tensor())) + if if_iden > 1e-4: + if "parameters" not in d: + cnew.apply_general_gate_delayed(d["gatef"], d["name"])( + cnew, *d["index"] + ) + else: + cnew.apply_general_variable_gate_delayed(d["gatef"], d["name"])( + cnew, *d["index"], **d["parameters"] + ) + return cnew + + +def used_qubits(c: Any) -> List[int]: + """ + Create a qubit list that includes all qubits having gate manipulation. + + :param c: a circuit + :type c: Any + :return: qubit list + :rtype: List + """ + qir = c.to_qir() + qlist = [] + for d in qir: + for i in range(len(d["index"])): + if d["index"][i] not in qlist: + qlist.append(d["index"][i]) + return qlist + + +def add_dd(c: Any, rule: Callable[[int], Any]) -> Any: + """ + Add DD sequence to A circuit + + :param c: circuit + :type c: Any + :param rule: The rule to conduct the DD sequence + :type rule: Callable[[int], Any] + :return: new circuit + :rtype: Any + """ + nqubit = c.circuit_param["nqubits"] + input_circuit = c.to_qiskit() + circuit_dd = dd_option.insert_ddd_sequences(input_circuit, rule=rule) + circuit_dd = Circuit.from_qiskit(circuit_dd, nqubit) + return circuit_dd + + +def apply_dd( + circuit: Any, + executor: Callable[[Any], Any], + rule: Union[Callable[[int], Any], List[str]], + rule_args: Optional[Dict[str, Any]] = None, + num_trials: int = 1, + full_output: bool = False, + ignore_idle_qubit: bool = True, + fulldd: bool = False, + iscount: bool = False, +) -> Union[ + float, Tuple[float, List[Any]], Dict[str, float], Tuple[Dict[str, float], List[Any]] +]: + """ + Apply dynamic decoupling (DD) and return the mitigated results. + + + :param circuit: The aim circuit. + :type circuit: Any + :param executor: A executor that executes a circuit and return results. + :type executor: Callable[[Any], Any] + :param rule: The rule to construct DD sequence, can use default rule "dd_option.rules.xx" + or custom rule "['X','X']" + :type rule: Union[Callable[[int], Any], List[str]] + :param rule_args:An optional dictionary of keyword arguments for ``rule``, defaults to {}. + :type rule_args: Dict[str, Any], optional + :param num_trials: The number of independent experiments to average over, defaults to 1 + :type num_trials: int, optional + :param full_output: If ``False`` only the mitigated expectation value is + returned. If ``True`` a dictionary containing all DD data is + returned too, defaults to False + :type full_output: bool, optional + :param ig_idle_qubit: ignore the DD sequences that added to unused qubits, defaults to True + :type ig_idle_qubit: bool, optional + :param fulldd: dd sequence full fill the idle circuits, defaults to False + :type fulldd: bool, optional + :param iscount: whether the output is bit string, defaults to False + :type iscount: bool, optional + :return: mitigated expectation value or mitigated expectation value and DD circuit information + :rtype: Union[float, Tuple[float, Dict[str, Any]]] + """ + if rule_args is None: + rule_args = {} + + def dd_rule(slack_length: int, spacing: int = -1) -> Any: + """ + Set DD rule. + + :param slack_length: Length of idle window to fill. Automatically calculated for a circuit. + :type slack_length: int + :param spacing: How many identity spacing gates to apply between dynamical + decoupling gates, defaults to -1 + :type spacing: int, optional + """ + dd_sequence = dd_option.rules.general_rule( + slack_length=slack_length, + spacing=spacing, + gates=gates, + ) + return dd_sequence + + if isinstance(rule, list): + import cirq + + gates = [] + for i in rule: + gates.append(getattr(cirq, i)) + rule = dd_rule + + if ignore_idle_qubit is True: + qlist = used_qubits(circuit) + else: + qlist = list(range(circuit.circuit_param["nqubits"])) + + rule_partial = partial( + rule, **rule_args + ) # rule_args influence the finall DD sequence + c2 = circuit + c3 = add_dd(c2, rule_partial) + c3 = prune_ddcircuit(c3, qlist) + if fulldd is True: + while c2.to_openqasm() != c3.to_openqasm(): + c2 = c3 + c3 = add_dd(c2, rule_partial) + c3 = prune_ddcircuit(c3, qlist) + + exp = [] + for i in range(num_trials): # type: ignore + exp.append(executor(c3)) + + if iscount is True: + sumcount = dict( + functools.reduce(operator.add, map(collections.Counter, exp)) # type:ignore + ) # type:ignore + result = {k: sumcount[k] / num_trials for k in sumcount.keys()} + else: + result = np.mean(exp) # type:ignore + + if full_output is True: + result = [result, c3] # type:ignore + + # def executortc(c): + # c = Circuit.from_qiskit(c, c.num_qubits) + # c = prune_ddcircuit(c,qlist) + # return executor(c) + # circuit = circuit.to_qiskit() + # result = ddd.execute_with_ddd( + # circuit=circuit, + # executor=executortc, + # rule=rule, + # rule_args=rule_args, + # num_trials=num_trials, + # full_output=full_output, + # ) + + return result # type:ignore + + +def rc_candidates(gate: Gate) -> List[Any]: + pauli = [m.tensor for m in gates.pauli_gates] + if isinstance(gate, gates.Gate): + gate = gate.tensor + gatem = backend.reshapem(gate) + r = [] + for combo in product(*[range(4) for _ in range(4)]): + i = ( + np.kron(pauli[combo[0]], pauli[combo[1]]) + @ gatem + @ np.kron(pauli[combo[2]], pauli[combo[3]]) + ) + if np.allclose(i, gatem, atol=1e-4): + r.append(combo) + elif np.allclose(i, -gatem, atol=1e-4): + r.append(combo) + return r + + +def _apply_gate(c: Any, i: int, j: int) -> Any: + if i == 0: + c.i(j) + elif i == 1: + c.x(j) + elif i == 2: + c.y(j) + elif i == 3: + c.z(j) + return c + + +candidate_dict = {} # type: ignore + + +def rc_circuit(c: Any) -> Any: + qir = c.to_qir() + cnew = Circuit(c.circuit_param["nqubits"]) + for d in qir: + if len(d["index"]) == 2: + if d["gate"].name in candidate_dict: + rc_cand = candidate_dict[d["gate"].name] + rc_list = choice(rc_cand) + else: + rc_cand = rc_candidates(d["gate"]) + rc_list = choice(rc_cand) + candidate_dict[d["gate"].name] = rc_cand + + cnew = _apply_gate(cnew, rc_list[0], d["index"][0]) + cnew = _apply_gate(cnew, rc_list[1], d["index"][1]) + if "parameters" not in d: + cnew.apply_general_gate_delayed(d["gatef"], d["name"])( + cnew, *d["index"] + ) + else: + cnew.apply_general_variable_gate_delayed(d["gatef"], d["name"])( + cnew, *d["index"], **d["parameters"] + ) + cnew = _apply_gate(cnew, rc_list[2], d["index"][0]) + cnew = _apply_gate(cnew, rc_list[3], d["index"][1]) + else: + if "parameters" not in d: + cnew.apply_general_gate_delayed(d["gatef"], d["name"])( + cnew, *d["index"] + ) + else: + cnew.apply_general_variable_gate_delayed(d["gatef"], d["name"])( + cnew, *d["index"], **d["parameters"] + ) + return cnew + + +def apply_rc( + circuit: Any, + executor: Callable[[Any], Any], + num_to_average: int = 1, + simplify: bool = True, + iscount: bool = False, + **kws: Any, +) -> Tuple[float, List[Any]]: + """ + Apply Randomized Compiling or Pauli twirling on two-qubit gates. + + :param circuit: Input circuit + :type circuit: Any + :param executor: A executor that executes a circuit and return results. + :type executor: Callable[[Any], Any] + :param num_to_average: Number of circuits for RC, defaults to 1 + :type num_to_average: int, optional + :param simplify: Whether simplify the circuits by merging single qubit gates, defaults to True + :type simplify: bool, optional + :param iscount: whether the output is bit string, defaults to False + :type iscount: bool, optional + :return: Mitigated results by RC + :rtype: float + """ + exp = [] + circuit_list = [] + for _ in range(num_to_average): + circuit1 = rc_circuit(circuit) + + if simplify is True: + circuit1 = prune_ddcircuit( + circuit1, qlist=list(range(circuit1.circuit_param["nqubits"])) + ) + circuit1 = simple_compiler.merge(circuit1) + + exp.append(executor(circuit1)) + circuit_list.append(circuit1) + + if iscount is True: + sumcount = dict( + functools.reduce(operator.add, map(collections.Counter, exp)) # type:ignore + ) # type:ignore + result = {k: sumcount[k] / num_to_average for k in sumcount.keys()} + else: + result = np.mean(exp) # type:ignore + + return result, circuit_list # type:ignore + + +# TODO(yuqinchen) add executor with batch ability diff --git a/tensorcircuit/results/readout_mitigation.py b/tensorcircuit/results/readout_mitigation.py index ef205800..d701dcc1 100644 --- a/tensorcircuit/results/readout_mitigation.py +++ b/tensorcircuit/results/readout_mitigation.py @@ -1,6 +1,7 @@ """ readout error mitigation functionalities """ + # Part of the code in this file is from mthree: https://github.com/Qiskit-Partners/mthree (Apache2) # https://journals.aps.org/prxquantum/pdf/10.1103/PRXQuantum.2.040326 @@ -811,9 +812,11 @@ def expectation( ] else: diagonal_op = [ - [1, -1] @ inv_single_qubit_cals[i] - if i in z1 - else [1, 1] @ inv_single_qubit_cals[i] + ( + [1, -1] @ inv_single_qubit_cals[i] + if i in z1 + else [1, 1] @ inv_single_qubit_cals[i] + ) for i in range(n) ] diff --git a/tensorcircuit/shadows.py b/tensorcircuit/shadows.py new file mode 100644 index 00000000..63cad7f6 --- /dev/null +++ b/tensorcircuit/shadows.py @@ -0,0 +1,485 @@ +""" +Classical shadows functions +""" + +from typing import Any, Union, Optional, Sequence, Tuple, List +from string import ascii_letters as ABC + +import numpy as np + +from .cons import backend, dtypestr, rdtypestr +from .circuit import Circuit + +Tensor = Any + + +def shadow_bound( + observables: Union[Tensor, Sequence[int]], epsilon: float, delta: float = 0.01 +) -> Tuple[int, int]: + r"""Calculate the shadow bound of the Pauli observables, please refer to the Theorem S1 and Lemma S3 in + Huang, H.-Y., R. Kueng, and J. Preskill, 2020, Nat. Phys. 16, 1050. + + :param observables: shape = (nq,) or (M, nq), where nq is the number of qubits, M is the number of observables + :type: Union[Tensor, Sequence[int]] + :param epsilon: error on the estimator + :type: float + :param delta: rate of failure for the bound to hold + :type: float + + :return Nk: number of snapshots + :rtype: int + :return k: number of equal parts to split the shadow snapshot states to compute the median of means. + k=1 (default) corresponds to simply taking the mean over all shadow snapshot states. + :rtype: int + """ + count = np.sign(np.asarray(observables)) + if len(count.shape) == 1: + count = count[None, :] + M = count.shape[0] + k = np.ceil(2 * np.log(2 * M / delta)) + max_length = np.max(np.sum(count, axis=1)) + N = np.ceil((34 / epsilon**2) * 3**max_length) + return int(N * k), int(k) + + +def shadow_snapshots( + psi: Tensor, + pauli_strings: Tensor, + status: Optional[Tensor] = None, + sub: Optional[Sequence[int]] = None, + measurement_only: bool = False, +) -> Tensor: + r"""To generate the shadow snapshots from given pauli string observables on psi + + :param psi: shape = (2 ** nq,), where nq is the number of qubits + :type: Tensor + :param pauli_strings: shape = (ns, nq), where ns is the number of pauli strings + :type: Tensor + :param status: shape = None or (ns, repeat), where repeat is the times to measure on one pauli string + :type: Optional[Tensor] + :param sub: qubit indices of subsystem + :type: Optional[Sequence[int]] + :param measurement_only: return snapshots (True) or snapshot states (False), default=False + :type: bool + + :return snapshots: shape = (ns, repeat, nq) if measurement_only=True otherwise (ns, repeat, nq, 2, 2) + :rtype: Tensor + """ + pauli_strings = backend.cast(pauli_strings, dtype="int32") - 1 + ns, nq = pauli_strings.shape + if 2**nq != len(psi): + raise ValueError( + f"The number of qubits of psi and pauli_strings should be the same, " + f"but got {nq} and {int(np.log2(len(psi)))}." + ) + if status is None: + status = backend.convert_to_tensor(np.random.rand(ns, 1)) + elif status.shape[0] != ns: + raise ValueError(f"status.shape[0] should be {ns}, but got {status.shape[0]}.") + status = backend.cast(status, dtype=rdtypestr) + repeat = status.shape[1] + + angles = backend.cast( + backend.convert_to_tensor( + [ + [-np.pi / 2, np.pi / 4, 0], + [np.pi / 4, np.pi / 2, 0], + [0, 0, 0], + ] + ), + dtype=rdtypestr, + ) # (3, 3) + + def proj_measure(pauli_string: Tensor, st: Tensor) -> Tensor: + c_ = Circuit(nq, inputs=psi) + for i in range(nq): + c_.r( # type: ignore + i, + theta=backend.gather1d( + backend.gather1d(angles, backend.gather1d(pauli_string, i)), 0 + ), + alpha=backend.gather1d( + backend.gather1d(angles, backend.gather1d(pauli_string, i)), 1 + ), + phi=backend.gather1d( + backend.gather1d(angles, backend.gather1d(pauli_string, i)), 2 + ), + ) + return c_.sample(batch=repeat, format="sample_bin", allow_state=True, status=st) + + vpm = backend.vmap(proj_measure, vectorized_argnums=(0, 1)) + snapshots = vpm(pauli_strings, status) # (ns, repeat, nq) + if measurement_only: + return snapshots if sub is None else slice_sub(snapshots, sub) + else: + return local_snapshot_states(snapshots, pauli_strings + 1, sub) + + +def local_snapshot_states( + snapshots: Tensor, pauli_strings: Tensor, sub: Optional[Sequence[int]] = None +) -> Tensor: + r"""To generate the local snapshots states from snapshots and pauli strings + + :param snapshots: shape = (ns, repeat, nq) + :type: Tensor + :param pauli_strings: shape = (ns, nq) or (ns, repeat, nq) + :type: Tensor + :param sub: qubit indices of subsystem + :type: Optional[Sequence[int]] + + :return lss_states: shape = (ns, repeat, nq, 2, 2) + :rtype: Tensor + """ + pauli_strings = backend.cast(pauli_strings, dtype="int32") - 1 + if len(pauli_strings.shape) < len(snapshots.shape): + pauli_strings = backend.tile( + pauli_strings[:, None, :], (1, snapshots.shape[1], 1) + ) # (ns, repeat, nq) + + X_dm = backend.cast( + backend.convert_to_tensor([[[1, 1], [1, 1]], [[1, -1], [-1, 1]]]) / 2, + dtype=dtypestr, + ) + Y_dm = backend.cast( + backend.convert_to_tensor( + np.array([[[1, -1j], [1j, 1]], [[1, 1j], [-1j, 1]]]) / 2 + ), + dtype=dtypestr, + ) + Z_dm = backend.cast( + backend.convert_to_tensor([[[1, 0], [0, 0]], [[0, 0], [0, 1]]]), dtype=dtypestr + ) + pauli_dm = backend.stack((X_dm, Y_dm, Z_dm), axis=0) # (3, 2, 2, 2) + + def dm(p: Tensor, s: Tensor) -> Tensor: + return backend.gather1d(backend.gather1d(pauli_dm, p), s) + + v = backend.vmap(dm, vectorized_argnums=(0, 1)) + vv = backend.vmap(v, vectorized_argnums=(0, 1)) + vvv = backend.vmap(vv, vectorized_argnums=(0, 1)) + + lss_states = vvv(pauli_strings, snapshots) + if sub is not None: + lss_states = slice_sub(lss_states, sub) + return 3 * lss_states - backend.eye(2)[None, None, None, :, :] + + +def global_shadow_state( + snapshots: Tensor, + pauli_strings: Optional[Tensor] = None, + sub: Optional[Sequence[int]] = None, +) -> Tensor: + r"""To generate the global shadow state from local snapshot states or snapshots and pauli strings + + :param snapshots: shape = (ns, repeat, nq, 2, 2) or (ns, repeat, nq) + :type: Tensor + :param pauli_strings: shape = None or (ns, nq) or (ns, repeat, nq) + :type: Optional[Tensor] + :param sub: qubit indices of subsystem + :type: Optional[Sequence[int]] + + :return gsdw_state: shape = (2 ** nq, 2 ** nq) + :rtype: Tensor + """ + if pauli_strings is not None: + if len(snapshots.shape) != 3: + raise ValueError( + f"snapshots should be 3-d if pauli_strings is not None, got {len(snapshots.shape)}-d instead." + ) + lss_states = local_snapshot_states( + snapshots, pauli_strings, sub + ) # (ns, repeat, nq_sub, 2, 2) + else: + if sub is not None: + lss_states = slice_sub(snapshots, sub) + else: + lss_states = snapshots # (ns, repeat, nq, 2, 2) + + nq = lss_states.shape[2] + + def tensor_prod(dms: Tensor) -> Tensor: + res = backend.gather1d(dms, 0) + for i in range(1, nq): + res = backend.kron(res, backend.gather1d(dms, i)) + return res + + v = backend.vmap(tensor_prod, vectorized_argnums=0) + vv = backend.vmap(v, vectorized_argnums=0) + gss_states = vv(lss_states) + return backend.mean(gss_states, axis=(0, 1)) + + +def expectation_ps_shadow( + snapshots: Tensor, + pauli_strings: Optional[Tensor] = None, + x: Optional[Sequence[int]] = None, + y: Optional[Sequence[int]] = None, + z: Optional[Sequence[int]] = None, + ps: Optional[Sequence[int]] = None, + k: int = 1, +) -> List[Tensor]: + r"""To calculate the expectation value of an observable on shadow snapshot states + + :param snapshots: shape = (ns, repeat, nq, 2, 2) or (ns, repeat, nq) + :type: Tensor + :param pauli_strings: shape = None or (ns, nq) or (ns, repeat, nq) + :type: Optional[Tensor] + :param x: sites to apply X gate, defaults to None + :type: Optional[Sequence[int]] + :param y: sites to apply Y gate, defaults to None + :type: Optional[Sequence[int]] + :param z: sites to apply Z gate, defaults to None + :type: Optional[Sequence[int]] + :param ps: or one can apply a ps structures instead of x, y, z, e.g. [1, 1, 0, 2, 3, 0] for X_0X_1Y_3Z_4 + defaults to None, ps can overwrite x, y and z + :type: Optional[Sequence[int]] + :param k: Number of equal parts to split the shadow snapshot states to compute the median of means. + k=1 (default) corresponds to simply taking the mean over all shadow snapshot states. + :type: int + + :return expectation values: shape = (k,) + :rtype: List[Tensor] + """ + if pauli_strings is not None: + if len(snapshots.shape) != 3: + raise ValueError( + f"snapshots should be 3-d if pauli_strings is not None, got {len(snapshots.shape)}-d instead." + ) + lss_states = local_snapshot_states( + snapshots, pauli_strings + ) # (ns, repeat, nq, 2, 2) + else: + lss_states = snapshots # (ns, repeat, nq, 2, 2) + ns, repeat, nq, _, _ = lss_states.shape + ns *= repeat + ss_states = backend.reshape(lss_states, (ns, nq, 2, 2)) + + if ps is None: + ps = [0] * nq + if x is not None: + for i in x: + ps[i] = 1 + if y is not None: + for i in y: + ps[i] = 2 + if z is not None: + for i in z: + ps[i] = 3 + elif len(ps) != nq: + raise ValueError( + f"The number of qubits of the shadow state is {nq}, but got a {len(ps)}-qubit pauli string observable." + ) + ps = backend.cast(backend.convert_to_tensor(ps), dtype="int32") # (nq,) + + paulis = backend.convert_to_tensor( + backend.cast( + np.array( + [ + [[1, 0], [0, 1]], + [[0, 1], [1, 0]], + [[0, -1j], [1j, 0]], + [[1, 0], [0, -1]], + ] + ), + dtype=dtypestr, + ) + ) # (4, 2, 2) + + def trace_paulis_prod(dm: Tensor, idx: Tensor) -> Tensor: + return backend.real(backend.trace(backend.gather1d(paulis, idx) @ dm)) + + v = backend.vmap(trace_paulis_prod, vectorized_argnums=(0, 1)) # (nq,) + + def prod(dm: Tensor) -> Tensor: + return backend.shape_prod(v(dm, ps)) + + vv = backend.vmap(prod, vectorized_argnums=0) # (ns,) + + batch = int(np.ceil(ns / k)) + return [backend.mean(vv(ss_states[i : i + batch])) for i in range(0, ns, batch)] + + +def entropy_shadow( + snapshots: Tensor, + pauli_strings: Optional[Tensor] = None, + sub: Optional[Sequence[int]] = None, + alpha: int = 2, +) -> Tensor: + r"""To calculate the Renyi entropy of a subsystem from shadow state or shadow snapshot states + + :param snapshots: shape = (ns, repeat, nq, 2, 2) or (ns, repeat, nq) + :type: Tensor + :param pauli_strings: shape = None or (ns, nq) or (ns, repeat, nq) + :type: Optional[Tensor] + :param sub: qubit indices of subsystem + :type: Optional[Sequence[int]] + :param alpha: order of the Renyi entropy, alpha=1 corresponds to the von Neumann entropy + :type: int + + :return Renyi entropy: shape = () + :rtype: Tensor + """ + if alpha <= 0: + raise ValueError("Alpha should not be less than 1!") + + sdw_rdm = global_shadow_state(snapshots, pauli_strings, sub) # (2 ** nq, 2 ** nq) + + evs = backend.relu(backend.real(backend.eigvalsh(sdw_rdm))) + evs /= backend.sum(evs) + if alpha == 1: + return -backend.sum(evs * backend.log(evs + 1e-12)) + else: + return backend.log(backend.sum(backend.power(evs, alpha))) / (1 - alpha) + + +def renyi_entropy_2(snapshots: Tensor, sub: Optional[Sequence[int]] = None) -> Tensor: + r"""To calculate the second order Renyi entropy of a subsystem from snapshot, please refer to + Brydges, T. et al. Science 364, 260–263 (2019). This function is not jitable. + + :param snapshots: shape = (ns, repeat, nq) + :type: Tensor + :param sub: qubit indices of subsystem + :type: Optional[Sequence[int]] + + :return second order Renyi entropy: shape = () + :rtype: Tensor + """ + if sub is not None: + snapshots = slice_sub(snapshots, sub) + snapshots = backend.cast(snapshots, dtype="int32") + ns, repeat, nq = snapshots.shape + + count = {} + for i, ss in enumerate(snapshots): + for s in ss: + s = tuple(backend.numpy(s)) + if s not in count: + count[s] = np.zeros(ns) + count[s][i] += 1 + + tr = 0.0 + for x in count: + for y in count: + h = np.sum((np.asarray(x) + np.asarray(y)) % 2) + pp_mean = np.mean(count[x] * count[y]) / repeat / repeat + tr += pp_mean * (-2.0) ** (-h) + return -np.log(tr * 2**nq) + + +def global_shadow_state1( + snapshots: Tensor, + pauli_strings: Optional[Tensor] = None, + sub: Optional[Sequence[int]] = None, +) -> Tensor: + r"""To generate the global snapshots states from local snapshot states or snapshots and pauli strings + + :param snapshots: shape = (ns, repeat, nq, 2, 2) or (ns, repeat, nq) + :type: Tensor + :param pauli_strings: shape = None or (ns, nq) or (ns, repeat, nq) + :type: Optional[Tensor] + :param sub: qubit indices of subsystem + :type: Optional[Sequence[int]] + + :return gsdw_state: shape = (2 ** nq, 2 ** nq) + :rtype: Tensor + """ + if pauli_strings is not None: + if len(snapshots.shape) != 3: + raise ValueError( + f"snapshots should be 3-d if pauli_strings is not None, got {len(snapshots.shape)}-d instead." + ) + lss_states = local_snapshot_states( + snapshots, pauli_strings, sub + ) # (ns, repeat, nq_sub, 2, 2) + else: + if sub is not None: + lss_states = slice_sub(snapshots, sub) + else: + lss_states = snapshots # (ns, repeat, nq, 2, 2) + lss_states = backend.transpose( + lss_states, (2, 0, 1, 3, 4) + ) # (nq, ns, repeat, 2, 2) + nq, ns, repeat, _, _ = lss_states.shape + + old_indices = [f"ab{ABC[2 + 2 * i: 4 + 2 * i]}" for i in range(nq)] + new_indices = f"ab{ABC[2:2 * nq + 2:2]}{ABC[3:2 * nq + 2:2]}" + + gss_states = backend.reshape( + backend.einsum( + f'{",".join(old_indices)}->{new_indices}', *lss_states, optimize=True + ), + (ns, repeat, 2**nq, 2**nq), + ) + return backend.mean(gss_states, axis=(0, 1)) + + +def global_shadow_state2( + snapshots: Tensor, + pauli_strings: Optional[Tensor] = None, + sub: Optional[Sequence[int]] = None, +) -> Tensor: + r"""To generate the global snapshots states from local snapshot states or snapshots and pauli strings + + :param snapshots: shape = (ns, repeat, nq, 2, 2) or (ns, repeat, nq) + :type: Tensor + :param pauli_strings: shape = None or (ns, nq) or (ns, repeat, nq) + :type: Optional[Tensor] + :param sub: qubit indices of subsystem + :type: Optional[Sequence[int]] + + :return gsdw_state: shape = (2 ** nq, 2 ** nq) + :rtype: Tensor + """ + if pauli_strings is not None: + if len(snapshots.shape) != 3: + raise ValueError( + f"snapshots should be 3-d if pauli_strings is not None, got {len(snapshots.shape)}-d instead." + ) + lss_states = local_snapshot_states( + snapshots, pauli_strings, sub + ) # (ns, repeat, nq_sub, 2, 2) + else: + if sub is not None: + lss_states = slice_sub(snapshots, sub) + else: + lss_states = snapshots # (ns, repeat, nq, 2, 2) + nq = lss_states.shape[2] + + old_indices = [f"{ABC[2 * i: 2 + 2 * i]}" for i in range(nq)] + new_indices = f"{ABC[0:2 * nq:2]}{ABC[1:2 * nq:2]}" + + def tensor_prod(dms: Tensor) -> Tensor: + return backend.reshape( + backend.einsum( + f'{",".join(old_indices)}->{new_indices}', *dms, optimize=True + ), + (2**nq, 2**nq), + ) + + v = backend.vmap(tensor_prod, vectorized_argnums=0) + vv = backend.vmap(v, vectorized_argnums=0) + gss_states = vv(lss_states) + return backend.mean(gss_states, axis=(0, 1)) + + +def slice_sub(entirety: Tensor, sub: Sequence[int]) -> Tensor: + r"""To slice off the subsystem + + :param entirety: shape = (ns, repeat, nq, 2, 2) or (ns, repeat, nq) + :type: Tensor + :param sub: qubit indices of subsystem + :type: Sequence[int] + + :return subsystem: shape = (ns, repeat, nq_sub, 2, 2) + :rtype: Tensor + """ + if len(entirety.shape) < 3: + entirety = entirety[:, None, :] + + def slc(x: Tensor, idx: Tensor) -> Tensor: + return backend.gather1d(x, idx) + + v = backend.vmap(slc, vectorized_argnums=(1,)) + vv = backend.vmap(v, vectorized_argnums=(0,)) + vvv = backend.vmap(vv, vectorized_argnums=(0,)) + return vvv(entirety, backend.convert_to_tensor(sub)) diff --git a/tensorcircuit/simplify.py b/tensorcircuit/simplify.py index 6123c8dd..1cbcfc6a 100644 --- a/tensorcircuit/simplify.py +++ b/tensorcircuit/simplify.py @@ -1,6 +1,7 @@ """ Tensornetwork Simplification """ + # part of the implementations and ideas are inspired from # https://github.com/jcmgray/quimb/blob/a2968050eba5a8a04ced4bdaa5e43c4fb89edc33/quimb/tensor/tensor_core.py#L7309-L8293 # (Apache 2.0) diff --git a/tensorcircuit/templates/__init__.py b/tensorcircuit/templates/__init__.py index e40637e3..be2236ab 100644 --- a/tensorcircuit/templates/__init__.py +++ b/tensorcircuit/templates/__init__.py @@ -1,5 +1,9 @@ +from . import ansatz from . import blocks from . import chems from . import dataset from . import graphs from . import measurements +from . import conversions + +costfunctions = measurements diff --git a/tensorcircuit/templates/ansatz.py b/tensorcircuit/templates/ansatz.py new file mode 100644 index 00000000..0bb96258 --- /dev/null +++ b/tensorcircuit/templates/ansatz.py @@ -0,0 +1,93 @@ +""" +Shortcuts for reusable circuit ansatz +""" + +from typing import Any, List + +from ..circuit import Circuit as Circ + +Tensor = Any +Circuit = Any + + +def QAOA_ansatz_for_Ising( + params: List[float], + nlayers: int, + pauli_terms: Tensor, + weights: List[float], + full_coupling: bool = False, + mixer: str = "X", +) -> Circuit: + """ + Construct the QAOA ansatz for the Ising Model. + The number of qubits is determined by `pauli_terms`. + + :param params: A list of parameter values used in the QAOA ansatz. + :param nlayers: The number of layers in the QAOA ansatz. + :pauli_terms: A list of Pauli terms, where each term is represented as a list of 0/1 series. + :param weights: A list of weights corresponding to each Pauli term. + :param full_coupling (optional): A flag indicating whether to use all-to-all coupling in mixers. Default is False. + :paran mixer (optional): The mixer operator to use. Default is "X". The other options are "XY" and "ZZ". + :return: QAOA ansatz for Ising model. + """ + nqubits = len(pauli_terms[0]) + c: Any = Circ(nqubits) + for i in range(nqubits): + c.h(i) # Apply Hadamard gate to each qubit + + for j in range(nlayers): + # cost terms + for k, term in enumerate(pauli_terms): + index_of_ones = [] + for l in range(len(term)): + if term[l] == 1: + index_of_ones.append(l) + if len(index_of_ones) == 1: + c.rz(index_of_ones[0], theta=2 * weights[k] * params[2 * j]) + # Apply Rz gate with angle determined by weight and current parameter value + elif len(index_of_ones) == 2: + c.rzz( + index_of_ones[0], + index_of_ones[1], + theta=weights[k] * params[2 * j], + ) + # Apply exp1 gate with a custom unitary (zz_matrix) + # and angle determined by weight and current parameter value + else: + raise ValueError("Invalid number of Z terms") + + # prepare the coupling map for mixer terms + pairs = [] + if full_coupling is False: + for q0 in list(range(0, nqubits - 1, 2)) + list(range(1, nqubits - 1, 2)): + pairs.append([q0, q0 + 1]) + pairs.append([nqubits - 1, 0]) + elif full_coupling is True: + for q0 in range(nqubits - 1): + for q1 in range(q0 + 1, nqubits): + pairs.append([q0, q1]) + else: + raise ValueError("Invalid input.") + + # standard mixer + if mixer == "X": + for i in range(nqubits): + c.rx( + i, theta=params[2 * j + 1] + ) # Apply Rx gate with angle determined by current parameter value + + # XY mixer + elif mixer == "XY": + for [q0, q1] in pairs: + c.rxx(q0, q1, theta=params[2 * j + 1]) + c.ryy(q0, q1, theta=params[2 * j + 1]) + + # ZZ mixer + elif mixer == "ZZ": + for [q0, q1] in pairs: + c.rzz(q0, q1, theta=params[2 * j + 1]) + + else: + raise ValueError("Invalid mixer type.") + + return c diff --git a/tensorcircuit/templates/blocks.py b/tensorcircuit/templates/blocks.py index eacc2b42..1e376903 100644 --- a/tensorcircuit/templates/blocks.py +++ b/tensorcircuit/templates/blocks.py @@ -1,6 +1,7 @@ """ Shortcuts for measurement patterns on circuit """ + # circuit in, circuit out # pylint: disable=invalid-name diff --git a/tensorcircuit/templates/chems.py b/tensorcircuit/templates/chems.py index 0ac3a0da..bc0a2184 100644 --- a/tensorcircuit/templates/chems.py +++ b/tensorcircuit/templates/chems.py @@ -2,37 +2,6 @@ Useful utilities for quantum chemistry related task """ -from typing import Any, Tuple +from .conversions import get_ps # pylint:disable=unused-import -import numpy as np - -Tensor = Any - - -def get_ps(qo: Any, n: int) -> Tuple[Tensor, Tensor]: - """ - Get Pauli string array and weights array for a qubit Hamiltonian - as a sum of Pauli strings defined in openfermion ``QubitOperator``. - - :param qo: ``openfermion.ops.operators.qubit_operator.QubitOperator`` - :type qo: ``openfermion.ops.operators.qubit_operator.QubitOperator`` - :param n: The number of qubits - :type n: int - :return: Pauli String array and weights array - :rtype: Tuple[Tensor, Tensor] - """ - value = {"X": 1, "Y": 2, "Z": 3} - terms = qo.terms - res = [] - wts = [] - for key in terms: - bit = np.zeros(n, dtype=int) - for i in range(len(key)): - bit[key[i][0]] = value[key[i][1]] - w = terms[key] - res_t = tuple() # type: ignore - for i in range(n): - res_t = res_t + (bit[i],) - res.append(res_t) - wts.append(w) - return np.array(res), np.array(wts) +# backward compatibility for the entry point diff --git a/tensorcircuit/templates/conversions.py b/tensorcircuit/templates/conversions.py new file mode 100644 index 00000000..d848e405 --- /dev/null +++ b/tensorcircuit/templates/conversions.py @@ -0,0 +1,94 @@ +""" +helper functions for conversions +""" + +from typing import Any, Tuple, List + +import numpy as np + +Tensor = Any +Array = Any + + +def get_ps(qo: Any, n: int) -> Tuple[Tensor, Tensor]: + """ + Get Pauli string array and weights array for a qubit Hamiltonian + as a sum of Pauli strings defined in openfermion ``QubitOperator``. + + :param qo: ``openfermion.ops.operators.qubit_operator.QubitOperator`` + :type qo: ``openfermion.ops.operators.qubit_operator.QubitOperator`` + :param n: The number of qubits + :type n: int + :return: Pauli String array and weights array + :rtype: Tuple[Tensor, Tensor] + """ + value = {"X": 1, "Y": 2, "Z": 3} + terms = qo.terms + res = [] + wts = [] + for key in terms: + bit = np.zeros(n, dtype=int) + for i in range(len(key)): + bit[key[i][0]] = value[key[i][1]] + w = terms[key] + res_t = tuple() # type: ignore + for i in range(n): + res_t = res_t + (bit[i],) + res.append(res_t) + wts.append(w) + return np.array(res), np.array(wts) + + +def QUBO_to_Ising(Q: Tensor) -> Tuple[Tensor, List[float], float]: + """ + Cnvert the Q matrix into a the indication of pauli terms, the corresponding weights, and the offset. + The outputs are used to construct an Ising Hamiltonian for QAOA. + + :param Q: The n-by-n square and symmetric Q-matrix. + :return pauli_terms: A list of 0/1 series, where each element represents a Pauli term. + A value of 1 indicates the presence of a Pauli-Z operator, while a value of 0 indicates its absence. + :return weights: A list of weights corresponding to each Pauli term. + :return offset: A float representing the offset term of the Ising Hamiltonian. + """ + + # input is n-by-n symmetric numpy array corresponding to Q-matrix + # output is the components of Ising Hamiltonian + + n = Q.shape[0] + + # square matrix check + if Q[0].shape[0] != n: + raise ValueError("Matrix is not a square matrix.") + + offset = ( + np.triu(Q, 0).sum() / 2 + ) # Calculate the offset term of the Ising Hamiltonian + pauli_terms = [] # List to store the Pauli terms + weights = ( + -np.sum(Q, axis=1) / 2 + ) # Calculate the weights corresponding to each Pauli term + + for i in range(n): + term = np.zeros(n) + term[i] = 1 + pauli_terms.append( + term.tolist() + ) # Add a Pauli term corresponding to a single qubit + + for i in range(n - 1): + for j in range(i + 1, n): + term = np.zeros(n) + term[i] = 1 + term[j] = 1 + pauli_terms.append( + term.tolist() + ) # Add a Pauli term corresponding to a two-qubit interaction + + weight = ( + Q[i][j] / 2 + ) # Calculate the weight for the two-qubit interaction term + weights = np.concatenate( + (weights, weight), axis=None + ) # Add the weight to the weights list + + return pauli_terms, weights, offset diff --git a/tensorcircuit/templates/graphs.py b/tensorcircuit/templates/graphs.py index 4b2e1c9c..e382085c 100644 --- a/tensorcircuit/templates/graphs.py +++ b/tensorcircuit/templates/graphs.py @@ -1,6 +1,7 @@ """ Some common graphs and lattices """ + # pylint: disable=invalid-name from functools import partial diff --git a/tensorcircuit/templates/measurements.py b/tensorcircuit/templates/measurements.py index aca804d9..63f5c5b7 100644 --- a/tensorcircuit/templates/measurements.py +++ b/tensorcircuit/templates/measurements.py @@ -1,6 +1,7 @@ """ Shortcuts for measurement patterns on circuit """ + # circuit in, scalar out from typing import Any diff --git a/tensorcircuit/translation.py b/tensorcircuit/translation.py index 6e867fd5..73b973b6 100644 --- a/tensorcircuit/translation.py +++ b/tensorcircuit/translation.py @@ -2,43 +2,45 @@ Circuit object translation in different packages """ -from typing import Any, Dict, List, Optional, Tuple, Union, Sequence -from copy import deepcopy import logging +from copy import deepcopy +from typing import Any, Dict, List, Optional, Sequence, Tuple, Union + import numpy as np logger = logging.getLogger(__name__) try: - from qiskit import QuantumCircuit - from qiskit.circuit.library import XXPlusYYGate - from qiskit.extensions import UnitaryGate import qiskit.quantum_info as qi - from qiskit.extensions.exceptions import ExtensionError - from qiskit.circuit.quantumcircuitdata import CircuitInstruction - from qiskit.circuit.parametervector import ParameterVectorElement + import symengine + import sympy + from qiskit import QuantumCircuit from qiskit.circuit import Parameter, ParameterExpression + from qiskit.circuit.exceptions import CircuitError + from qiskit.circuit.library import HamiltonianGate, UnitaryGate, XXPlusYYGate + from qiskit.circuit.parametervector import ParameterVectorElement + from qiskit.circuit.quantumcircuitdata import CircuitInstruction except ImportError: logger.warning( "Please first ``pip install -U qiskit`` to enable related functionality in translation module" ) CircuitInstruction = Any + QuantumCircuit = Any try: import cirq except ImportError: - logger.warning( + logger.info( "Please first ``pip install -U cirq`` to enable related functionality in translation module" ) from . import gates from .circuit import Circuit -from .densitymatrix import DMCircuit2 from .cons import backend +from .densitymatrix import DMCircuit2 from .interfaces.tensortrans import tensor_to_numpy - Tensor = Any @@ -125,7 +127,7 @@ def qir2cirq( support more element in qir, e.g. barrier, measure... """ - class CustomizedCirqGate(cirq.Gate): + class CustomizedCirqGate(cirq.Gate): # type: ignore def __init__(self, uMatrix: Any, name: str, nqubit: int): super(CustomizedCirqGate, self) self.uMatrix = uMatrix @@ -138,7 +140,9 @@ def _num_qubits_(self) -> int: def _unitary_(self) -> Any: return self.uMatrix - def _circuit_diagram_info_(self) -> List[str]: + def _circuit_diagram_info_( + self, *args: Optional[cirq.CircuitDiagramInfoArgs] + ) -> List[str]: return [self.name] * self.nqubit if extra_qir is not None and len(extra_qir) > 0: @@ -235,6 +239,7 @@ def qir2qiskit( qiskit_circ = QuantumCircuit(n) if initialization is not None: qiskit_circ.initialize(initialization) + measure_cbit = 0 for gate_info in qir: index = gate_info["index"] gate_name = str(gate_info["gatef"]) @@ -306,9 +311,8 @@ def qir2qiskit( # Error can be presented if theta is actually complex in this procedure. exp_op = qi.Operator(unitary) index_reversed = [x for x in index[::-1]] - qiskit_circ.hamiltonian( - exp_op, time=theta, qubits=index_reversed, label=qis_name - ) + gate = HamiltonianGate(data=exp_op, time=theta, label=qis_name) + qiskit_circ.append(gate, index_reversed) elif gate_name == "multicontrol": unitary = backend.numpy(backend.convert_to_tensor(parameters["unitary"])) ctrl_str = "".join(map(str, parameters["ctrl"]))[::-1] @@ -325,7 +329,8 @@ def qir2qiskit( ) qiskit_circ.unitary(qop, index[::-1], label=qis_name) elif gate_name == "measure": - qiskit_circ.measure(index[0], index[0]) + qiskit_circ.measure(index[0], measure_cbit) + measure_cbit += 1 elif gate_name == "reset": qiskit_circ.reset(index[0]) elif gate_name == "barrier": @@ -338,7 +343,7 @@ def qir2qiskit( qop = qi.Operator(gatem) try: qiskit_circ.unitary(qop, index[::-1], label=qis_name) - except ExtensionError: + except (CircuitError, ValueError) as _: logger.warning( "omit non unitary gate in tensorcircuit when transforming to qiskit: %s" % gate_name @@ -354,7 +359,7 @@ def _translate_qiskit_params( gate_info: CircuitInstruction, binding_params: Any ) -> List[float]: parameters = [] - for p in gate_info[0].params: + for p in gate_info.operation.params: if isinstance(p, ParameterVectorElement): parameters.append(binding_params[p.index]) elif isinstance(p, Parameter): @@ -363,30 +368,37 @@ def _translate_qiskit_params( if len(p.parameters) == 0: parameters.append(float(p)) continue - if len(p.parameters) != 1: - raise ValueError( - f"Can't translate parameter expression with more than 1 parameters: {p}" - ) - p_real = list(p.parameters)[0] - if not isinstance(p_real, ParameterVectorElement): - raise TypeError( - "Parameters in parameter expression should be ParameterVectorElement" - ) + # note "sym" != "sim" expr = p.sympify().simplify() - # only allow simple expressions like 1.0 * theta - if not expr.is_Mul: - raise ValueError(f"Unsupported parameter expression: {p}") - arg1, arg2 = expr.args - if arg1.is_number and arg2.is_symbol: - coeff = arg1 - elif arg1.is_symbol and arg2.is_number: - coeff = arg2 + if isinstance(expr, symengine.Expr): # qiskit uses symengine if available + expr = expr._sympy_() # sympy.Expr + + if expr.is_algebraic_expr(): # numpy ufuncs are not used + lambdify_module_name = "numpy" else: - raise ValueError(f"Unsupported parameter expression: {p}") - # taking real part here because using complex type will result in a type error - # for tf backend when the binding parameter is real - parameters.append(float(coeff) * binding_params[p_real.index]) + if backend.name == "pytorch": + lambdify_module_name = "math" + else: + lambdify_module_name = backend.name + + for free_symbol in expr.free_symbols: + # replace names: theta[0] -> theta_0 + # ParameterVector creates symbols with brackets like theta[0] + # but sympy.lambdify does not allow brackets in symbol names + free_symbol.name = free_symbol.name.replace("[", "_").replace("]", "") + + parameter_list = list(p.parameters) + sympy_symbols = [param._symbol_expr for param in parameter_list] + # replace names again: theta[0] -> theta_0 + sympy_symbols = [ + sympy.Symbol(str(symbol).replace("[", "_").replace("]", "")) + for symbol in sympy_symbols + ] + lam_f = sympy.lambdify(sympy_symbols, expr, modules=lambdify_module_name) + parameters.append( + lam_f(*[binding_params[param.index] for param in parameter_list]) + ) else: # numbers, arrays, etc. parameters.append(p) @@ -399,7 +411,7 @@ def ctrl_str2ctrl_state(ctrl_str: str, nctrl: int) -> List[int]: def qiskit2tc( - qcdata: List[CircuitInstruction], + qc: QuantumCircuit, n: int, inputs: Optional[List[float]] = None, is_dm: bool = False, @@ -408,19 +420,18 @@ def qiskit2tc( binding_params: Optional[Union[Sequence[float], Dict[Any, float]]] = None, ) -> Any: r""" - Generate a tensorcircuit circuit using the quantum circuit data in qiskit. + Generate a tensorcircuit circuit from the qiskit circuit. :Example: >>> qisc = QuantumCircuit(2) >>> qisc.h(0) >>> qisc.x(1) - >>> qc = tc.translation.qiskit2tc(qisc.data, 2) + >>> qc = tc.translation.qiskit2tc(qisc, 2) >>> qc.to_qir()[0]['gatef'] - h - :param qcdata: Quantum circuit data from qiskit. - :type qcdata: List[CircuitInstruction] + :param qc: A quantum circuit in qiskit. + :type qc: QuantumCircuit :param n: # of qubits :type n: int :param inputs: Input state of the circuit. Default is None. @@ -431,7 +442,7 @@ def qiskit2tc( :type circuit_params: Optional[Dict[str, Any]] :param binding_params: (variational) parameters for the circuit. Could be either a sequence or dictionary depending on the type of parameters in the Qiskit circuit. - For ``ParameterVectorElement`` use sequence. For ``Parameter`` use dictionary + For ``ParameterVectorElement`` use sequence. For ``Parameter`` use dictionary. :type binding_params: Optional[Union[Sequence[float], Dict[Any, float]]] :return: A quantum circuit in tensorcircuit :rtype: Any @@ -447,17 +458,17 @@ def qiskit2tc( if "nqubits" not in circuit_params: circuit_params["nqubits"] = n if ( - len(qcdata) > 0 - and qcdata[0][0].name == "initialize" + len(qc.data) > 0 + and qc.data[0][0].name == "initialize" and "inputs" not in circuit_params ): - circuit_params["inputs"] = perm_matrix(n) @ np.array(qcdata[0][0].params) + circuit_params["inputs"] = perm_matrix(n) @ np.array(qc.data[0][0].params) if inputs is not None: circuit_params["inputs"] = inputs tc_circuit: Any = Circ(**circuit_params) - for gate_info in qcdata: - idx = [qb.index for qb in gate_info[1]] + for gate_info in qc.data: + idx = [qc.find_bit(qb).index for qb in gate_info.qubits] gate_name = gate_info[0].name parameters = _translate_qiskit_params(gate_info, binding_params) if gate_name in [ @@ -486,6 +497,13 @@ def qiskit2tc( getattr(tc_circuit, gate_name)(*idx, theta=parameters) elif gate_name in ["crx_o0", "cry_o0", "crz_o0"]: getattr(tc_circuit, "o" + gate_name[1:-3])(*idx, theta=parameters) + elif gate_name in ["r"]: + getattr(tc_circuit, "u")( + *idx, + theta=parameters[0], + phi=parameters[1] - np.pi / 2, + lbd=-parameters[1] + np.pi / 2, + ) elif gate_name in ["u3", "u"]: getattr(tc_circuit, "u")( *idx, theta=parameters[0], phi=parameters[1], lbd=parameters[2] @@ -512,7 +530,8 @@ def qiskit2tc( tc_circuit.multicontrol( *idx, ctrl=ctrl_state, unitary=gates._x_matrix, name="x" ) - elif gate_name[0] == "c" and gate_name[:7] != "circuit": + elif gate_name[0] == "c" and gate_name[:7] != "circuit" and gate_name != "cu": + # qiskit cu bug, see https://github.com/tencent-quantum-lab/tensorcircuit/issues/199 for i in range(1, len(gate_name)): if (gate_name[-i] == "o") & (gate_name[-i - 1] == "_"): break diff --git a/tensorcircuit/vis.py b/tensorcircuit/vis.py index 092216b8..19834d95 100644 --- a/tensorcircuit/vis.py +++ b/tensorcircuit/vis.py @@ -1,6 +1,7 @@ """ Visualization on circuits """ + import os import subprocess from uuid import uuid4 diff --git a/tests/test_backends.py b/tests/test_backends.py index f63de48d..3c73c1ab 100644 --- a/tests/test_backends.py +++ b/tests/test_backends.py @@ -300,6 +300,17 @@ def test_backend_methods_2(backend): np.maximum(arr, 0), atol=1e-4, ) + np.testing.assert_allclose( + tc.backend.det(tc.backend.convert_to_tensor(np.eye(3) * 2)), 8, atol=1e-5 + ) + + +# @pytest.mark.parametrize("backend", [lf("npb"), lf("tfb"), lf("jaxb"), lf("torchb")]) +# def test_backend_array(backend): +# a = tc.backend.array([[0, 1], [1, 0]]) +# assert tc.interfaces.which_backend(a).name == tc.backend.name +# a = tc.backend.array([[0, 1], [1, 0]], dtype=tc.rdtypestr) +# assert tc.dtype(a) == "float32" @pytest.mark.parametrize("backend", [lf("npb"), lf("tfb"), lf("jaxb"), lf("torchb")]) diff --git a/tests/test_circuit.py b/tests/test_circuit.py index 14c7784f..81f20762 100644 --- a/tests/test_circuit.py +++ b/tests/test_circuit.py @@ -1,8 +1,9 @@ # pylint: disable=invalid-name -import sys import os +import sys from functools import partial + import numpy as np import opt_einsum as oem import pytest @@ -422,6 +423,10 @@ def test_expectation_ps(backend): c.H(0) r = c.expectation_ps(z=[1], x=[0]) np.testing.assert_allclose(tc.backend.numpy(r), 1, atol=1e-5) + r1 = c.expectation_ps(ps=[1, 3]) + np.testing.assert_allclose(tc.backend.numpy(r1), 1, atol=1e-5) + r1 = c.expectation_ps(z=[1, 2], ps=[1, 3]) + np.testing.assert_allclose(tc.backend.numpy(r1), 1, atol=1e-5) def test_probability(): @@ -971,6 +976,7 @@ def test_qir2cirq(backend): def test_qir2qiskit(backend): try: import qiskit.quantum_info as qi + from tensorcircuit.translation import perm_matrix except ImportError: pytest.skip("qiskit is not installed") @@ -1070,9 +1076,11 @@ def test_qir2qiskit(backend): def test_qiskit2tc(): try: - from qiskit import QuantumCircuit import qiskit.quantum_info as qi + from qiskit import QuantumCircuit + from qiskit.circuit.library import HamiltonianGate from qiskit.circuit.library.standard_gates import MCXGate, SwapGate + from tensorcircuit.translation import perm_matrix except ImportError: pytest.skip("qiskit is not installed") @@ -1083,7 +1091,8 @@ def test_qiskit2tc(): zz = np.array([[1, 0, 0, 0], [0, -1, 0, 0], [0, 0, -1, 0], [0, 0, 0, 1]]) exp_op = qi.Operator(zz) for i in range(n): - qisc.hamiltonian(exp_op, time=np.random.uniform(), qubits=[i, (i + 1) % n]) + gate = HamiltonianGate(exp_op, time=np.random.uniform()) + qisc.append(gate, [i, (i + 1) % n]) qisc.fredkin(1, 2, 3) qisc.cswap(1, 2, 3) qisc.swap(0, 1) @@ -1101,6 +1110,9 @@ def test_qiskit2tc(): qisc.x(3) qisc.y(3) qisc.z(3) + qisc.cu( + 5.868768495722669, 2.24809352294186, 3.59102783505607, 2.0223650288392, 1, 3 + ) qisc.cnot(0, 1) qisc.cy(0, 1) qisc.cz(0, 1, ctrl_state=0) @@ -1118,6 +1130,7 @@ def test_qiskit2tc(): qisc.crz(np.random.uniform(), 2, 3, ctrl_state=0) qisc.crz(np.random.uniform(), 2, 3, ctrl_state=0) qisc.crz(np.random.uniform(), 2, 3, ctrl_state=0) + qisc.r(np.random.uniform(), np.random.uniform(), 1) qisc.unitary(exp_op, [1, 3]) mcx_g = MCXGate(3, ctrl_state="010") qisc.append(mcx_g, [0, 1, 2, 3]) @@ -1138,29 +1151,37 @@ def test_qiskit2tc(): np.testing.assert_allclose(qis_unitary2, qis_unitary, atol=1e-5) -@pytest.mark.parametrize("backend", [lf("tfb"), lf("jaxb")]) +@pytest.mark.parametrize("backend", [lf("tfb"), lf("jaxb"), lf("torchb")]) def test_qiskit2tc_parameterized(backend): try: - from qiskit.circuit import QuantumCircuit, Parameter - from qiskit.quantum_info import Operator + from qiskit.circuit import Parameter, ParameterVector, QuantumCircuit from qiskit.circuit.library import TwoLocal + from qiskit.quantum_info import Operator from qiskit_nature.second_q.circuit.library import UCCSD - from qiskit_nature.second_q.mappers import ParityMapper, QubitConverter + from qiskit_nature.second_q.mappers import ParityMapper except ImportError: pytest.skip("qiskit or qiskit-nature is not installed") from tensorcircuit.translation import perm_matrix mapper = ParityMapper() - converter = QubitConverter(mapper=mapper, two_qubit_reduction=True) - ansatz1 = UCCSD(2, [1, 1], converter) + ansatz1 = UCCSD(2, [1, 1], mapper) ansatz2 = TwoLocal(2, rotation_blocks="ry", entanglement_blocks="cz") ansatz3 = QuantumCircuit(1) ansatz3_param = Parameter("θ") ansatz3.rx(ansatz3_param, 0) - ansatz_list = [ansatz1, ansatz2, ansatz3] + ansatz4 = QuantumCircuit(1) + ansatz4_param = ParameterVector("φ", 3) + ansatz4.rx(2.0 * ansatz4_param[0] + 5.0, 0) + ansatz4.ry(ansatz4_param[0] * ansatz4_param[1] + ansatz4_param[2], 0) + ansatz4.rz( + np.exp(np.sin(ansatz4_param[0])) + + np.abs(ansatz4_param[1]) / np.arctan(ansatz4_param[2]), + 0, + ) + ansatz_list = [ansatz1, ansatz2, ansatz3, ansatz4] for ansatz in ansatz_list: n = ansatz.num_qubits - if ansatz in [ansatz1, ansatz2]: + if ansatz in [ansatz1, ansatz2, ansatz4]: params = np.random.rand(ansatz.num_parameters) else: params = {ansatz3_param: 0.618} @@ -1170,25 +1191,25 @@ def test_qiskit2tc_parameterized(backend): # test jit @tc.backend.jit - def get_unitary(_params): + def get_unitary(params): return tc.Circuit.from_qiskit( - ansatz, inputs=np.eye(2**n), binding_params=_params + ansatz, inputs=np.eye(2**n), binding_params=params ).state() tc_unitary = get_unitary(params) tc_unitary = np.reshape(tc_unitary, [2**n, 2**n]) - p_mat = perm_matrix(n) + p_mat = tc.array_to_tensor(perm_matrix(n)) np.testing.assert_allclose( p_mat @ tc_unitary @ p_mat, qiskit_unitary, atol=1e-5 ) # test grad - def cost_fn(_params): - return tc.backend.real(tc.backend.sum(get_unitary(_params))) + def cost_fn(params): + return tc.backend.real(tc.backend.sum(get_unitary(params))) - if ansatz in [ansatz1, ansatz2]: + if ansatz in [ansatz1, ansatz2, ansatz4]: grad = tc.backend.grad(cost_fn)(tc.backend.convert_to_tensor(params)) - assert np.sum(np.isnan(grad)) == 0 + assert tc.backend.sum(tc.num_to_tensor(np.isnan(grad))) == 0 else: # tf only supports tf tensor as input grad = tc.backend.grad(cost_fn)( @@ -1200,8 +1221,8 @@ def cost_fn(_params): @pytest.mark.parametrize("backend", [lf("npb"), lf("tfb"), lf("jaxb")]) def test_qiskit_vs_tc_intialization(backend): try: - from qiskit import QuantumCircuit import qiskit.quantum_info as qi + from qiskit import QuantumCircuit except ImportError: pytest.skip("qiskit is not installed") @@ -1303,6 +1324,25 @@ def test_circuit_inverse(backend): np.testing.assert_allclose(c.state(), inputs, atol=1e-5) +@pytest.mark.parametrize("backend", [lf("npb"), lf("tfb"), lf("jaxb")]) +def test_circuit_inverse_2(backend): + inputs = np.random.uniform(size=[8]) + inputs /= np.linalg.norm(inputs) + c = tc.Circuit(3, inputs=inputs) + c.iswap(0, 1) + c.iswap(1, 0, theta=0.6) + c.rxx(1, 2, theta=-0.2) + c.cu(0, 1, lbd=2.0, theta=-0.7) + c.r(2, alpha=0.3) + c.sd(2) + c.cx(1, 2) + c.unitary(0, unitary=tc.gates._x_matrix) + c1 = c.inverse() + c.append(c1) + print(c.draw()) + np.testing.assert_allclose(c.state(), inputs, atol=1e-5) + + @pytest.mark.parametrize("backend", [lf("tfb"), lf("jaxb")]) def test_jittable_amplitude(backend): # @tc.backend.jit @@ -1536,3 +1576,80 @@ def simple_ansatz(param): vs, gs = v_ansatz(K.ones([2, 3], dtype="float32")) assert K.shape_tuple(gs) == (2, 3) np.testing.assert_allclose(K.numpy(vs), -1.0 * K.ones([2]), atol=1e-5) + + +@pytest.mark.parametrize("backend", [lf("tfb"), lf("jaxb"), lf("npb")]) +def test_fancy_circuit_indexing(backend): + c = tc.Circuit(4) + c.cx([0, 1], [-1, -2]) + c.h(range(c._nqubits)) + c.rz([0], theta=0.2) + c.rx([1, 2], theta=[0.3, 0.5]) + c.rzz([2, 3], [0, 1], theta=tc.backend.ones([2])) + c.rxx([2, 0, 1], [0, 1, 2], theta=tc.backend.ones([1])) + assert c.gate_count("h") == 4 + assert c.gate_count("rzz") == 2 + assert c.gate_count("rxx") == 3 + + +@pytest.mark.parametrize("backend", [lf("tfb"), lf("jaxb"), lf("npb")]) +def test_general_kraus(backend): + c = tc.Circuit(2) + c.h([0, 1]) + p = 0.5 + status = [0.3, 0.8] + rs = [] + for i in range(2): + rs.append( + c.general_kraus( + [ + np.sqrt(p) * np.array([[1.0, 0], [0, 0]]), + np.sqrt(p) * np.array([[0, 0], [0, 1.0]]), + np.sqrt(1 - p) * np.eye(2), + ], + i, + status=status[i], + ) + ) + np.testing.assert_allclose(rs[0], 1) + np.testing.assert_allclose(rs[1], 2) + np.testing.assert_allclose(c.expectation_ps(z=[0]), -1, atol=1e-5) + np.testing.assert_allclose(c.expectation_ps(z=[1]), 0, atol=1e-5) + + +@pytest.mark.parametrize("backend", [lf("tfb"), lf("jaxb"), lf("npb")]) +def test_general_kraus_with_prob(backend): + c = tc.Circuit(2) + c.h([0, 1]) + p = 0.5 + status = [0.3, 0.8] + rs = [] + for i in range(2): + rs.append( + c.general_kraus( + [ + np.sqrt(p) * np.array([[1.0, 0], [0, 0]]), + np.sqrt(p) * np.array([[0, 0], [0, 1.0]]), + np.sqrt(1 - p) * np.eye(2), + ], + i, + status=status[i], + with_prob=True, + ) + ) + np.testing.assert_allclose(rs[0][0], 1) + np.testing.assert_allclose(rs[1][0], 2) + np.testing.assert_allclose(c.expectation_ps(z=[0]), -1, atol=1e-5) + np.testing.assert_allclose(c.expectation_ps(z=[1]), 0, atol=1e-5) + np.testing.assert_allclose(rs[0][1], [0.25, 0.25, 0.5], atol=1e-5) + np.testing.assert_allclose(rs[1][1], [0.25, 0.25, 0.5], atol=1e-5) + np.testing.assert_allclose(tc.backend.norm(c.state()), 1, atol=1e-5) + + +@pytest.mark.parametrize("backend", [lf("tfb"), lf("jaxb"), lf("npb")]) +def test_circuit_copy(backend): + c = tc.Circuit(2) + c.h(0) + c1 = c.copy() + c.rz(0, theta=0.1) + assert c1.gate_count() == 1 diff --git a/tests/test_cloud.py b/tests/test_cloud.py index f71e8e4d..fb24d318 100644 --- a/tests/test_cloud.py +++ b/tests/test_cloud.py @@ -161,6 +161,11 @@ def test_batch_exp_ps(): [1, -1], atol=1e-1, ) + np.testing.assert_allclose( + wrapper.batch_expectation_ps(c, pss, device="local::default", with_rem=False), + [1, -1], + atol=1e-1, + ) def test_batch_submit_template(): diff --git a/tests/test_ensemble.py b/tests/test_ensemble.py index 5aec52cc..92869fd8 100644 --- a/tests/test_ensemble.py +++ b/tests/test_ensemble.py @@ -2,15 +2,19 @@ import sys import tensorflow as tf import numpy as np +import pytest thisfile = os.path.abspath(__file__) modulepath = os.path.dirname(os.path.dirname(thisfile)) sys.path.insert(0, modulepath) -from tensorcircuit.templates.ensemble import bagging +from tensorcircuit.applications.ai.ensemble import bagging +@pytest.mark.xfail( + int(tf.__version__.split(".")[1]) >= 16, reason="legacy optimizer fails tf>=2.16" +) def test_ensemble_bagging(): data_amount = 100 # Amount of data to be used linear_dimension = 4 # linear demension of the data @@ -52,7 +56,7 @@ def model(): obj_bagging.append(model(), False) obj_bagging.compile( loss=tf.keras.losses.BinaryCrossentropy(), - optimizer=tf.keras.optimizers.Adam(lr), + optimizer=tf.keras.optimizers.legacy.Adam(lr), metrics=[tf.keras.metrics.AUC(), "acc"], ) obj_bagging.train( diff --git a/tests/test_fgs.py b/tests/test_fgs.py new file mode 100644 index 00000000..dd307b3c --- /dev/null +++ b/tests/test_fgs.py @@ -0,0 +1,267 @@ +import numpy as np +import pytest +from pytest_lazyfixture import lazy_fixture as lf +import tensorflow as tf + +try: + import openfermion as _ +except ModuleNotFoundError: + pytestmark = pytest.mark.skip("skip fgs test due to missing openfermion module") + +import tensorcircuit as tc + +F = tc.fgs.FGSSimulator +FT = tc.fgs.FGSTestSimulator + + +@pytest.mark.parametrize("backend", [lf("npb"), lf("tfb"), lf("jaxb")]) +def test_cmatrix(backend, highp): + import openfermion + + def asymmetric_hopping(J, gamma, i, j, L): + m0 = tc.fgs.onehot_matrix(i, j, 2 * L) - tc.fgs.onehot_matrix( + j + L, i + L, 2 * L + ) + m = (J + gamma) * m0 + (J - gamma) * tc.backend.adjoint(m0) + return m / 2 + + def asymmetric_hopping_jw(J, gamma, i, j, L): + op = (J + gamma) * openfermion.FermionOperator(f"{str(i)}^ {str(j)}") + np.conj( + J - gamma + ) * openfermion.FermionOperator(f"{str(j)}^ {str(i)}") + sop = openfermion.transforms.jordan_wigner(op) + m = openfermion.get_sparse_operator(sop, n_qubits=L).todense() + return m + + c = tc.fgs.FGSSimulator(4, [0]) + c1 = tc.fgs.FGSTestSimulator(4, [0]) + c.evol_hp(0, 1, 1.2) + c1.evol_hp(0, 1, 1.2) + c.evol_icp(2, 0.5) + c1.evol_icp(2, 0.5) + c.evol_cp(0, -0.8) + c1.evol_cp(0, -0.8) + c.evol_sp(1, 0, 0.5) + c1.evol_sp(1, 0, 0.5) + c.evol_ghamiltonian(asymmetric_hopping(1, 0.5, 0, 2, 4)) + c1.evol_ghamiltonian(np.array(asymmetric_hopping_jw(1, 0.5, 0, 2, 4))) + c.evol_sp(1, 2, 1.5) + c1.evol_sp(1, 2, 1.5) + c.evol_ihamiltonian(c.chemical_potential(1.0, 1, 4)) + c1.evol_ihamiltonian(c1.chemical_potential_jw(1.0, 1, 4)) + np.testing.assert_allclose( + c1.get_cmatrix_majorana(), c.get_cmatrix_majorana(), atol=1e-5 + ) + np.testing.assert_allclose(c1.get_cmatrix(), c.get_cmatrix(), atol=1e-5) + np.testing.assert_allclose(c1.entropy([0, 2]), c.entropy([0, 2]), atol=1e-5) + np.testing.assert_allclose( + c1.renyi_entropy(2, [1]), c.renyi_entropy(2, [1]), atol=1e-5 + ) + + +@pytest.mark.parametrize("backend", [lf("npb"), lf("tfb"), lf("jaxb")]) +def test_otoc(backend, highp): + c = tc.FGSSimulator(4, [0, 1]) + c1 = tc.fgs.FGSTestSimulator(4, [0, 1]) + h = c.hopping(0.6, 1, 2, 4) + h += c.hopping(-0.8, 3, 2, 4) + h += c.chemical_potential(0.3, 2, 4) + h1 = c1.hopping_jw(0.6, 1, 2, 4) + h1 += c1.hopping_jw(-0.8, 3, 2, 4) + h1 += c1.chemical_potential_jw(0.3, 2, 4) + c.evol_hamiltonian(h) + m = c.get_cmatrix(now_i=True, now_j=False) + m0 = c1.get_ot_cmatrix(h1) + np.testing.assert_allclose(m, m0, atol=1e-5) + m = c.get_cmatrix(now_i=False, now_j=True) + m0 = c1.get_ot_cmatrix(h1, now_i=False) + np.testing.assert_allclose(m, m0, atol=1e-5) + + +@pytest.mark.parametrize("backend", [lf("tfb"), lf("jaxb")]) +def test_fgs_ad(backend, highp): + import optax + + N = 18 + + def f(chi): + c = tc.fgs.FGSSimulator(N, [0]) + for i in range(N - 1): + c.evol_hp(i, i + 1, chi[i]) + cm = c.get_cmatrix() + return -tc.backend.real(1 - cm[N, N]) + + chi_vg = tc.backend.jit(tc.backend.value_and_grad(f)) + + if tc.backend.name == "tensorflow": + opt = tc.backend.optimizer(tf.keras.optimizers.Adam(1e-2)) + else: + opt = tc.backend.optimizer(optax.adam(1e-2)) + + param = tc.backend.ones([N - 1], dtype="float64") + for _ in range(300): + vs, gs = chi_vg(param) + param = opt.update(gs, param) + + np.testing.assert_allclose(vs, -0.9986, atol=1e-2) + + +@pytest.mark.parametrize("backend", [lf("npb"), lf("tfb"), lf("jaxb")]) +def test_hamiltonian_generation(backend): + hc = F.chemical_potential(0.8, 0, 3) + h1 = FT.get_hmatrix(hc, 3) + 0.4 * tc.backend.eye(2**3) + # constant shift + h2 = FT.chemical_potential_jw(0.8, 0, 3) + np.testing.assert_allclose(h1, h2, atol=1e-5) + + hc = F.hopping(0.8j, 0, 1, 3) + h1 = FT.get_hmatrix(hc, 3) + h2 = FT.hopping_jw(0.8j, 0, 1, 3) + np.testing.assert_allclose(h1, h2, atol=1e-5) + + hc = F.sc_pairing(0.8, 1, 0, 3) + h1 = FT.get_hmatrix(hc, 3) + h2 = FT.sc_pairing_jw(0.8, 1, 0, 3) + np.testing.assert_allclose(h1, h2, atol=1e-5) + + +@pytest.mark.parametrize("backend", [lf("npb"), lf("tfb"), lf("jaxb")]) +def test_ground_state(backend, highp): + N = 3 + hc = ( + F.hopping(1.0, 0, 1, N) + + F.hopping(1.0, 1, 2, N) + + F.chemical_potential(0.4, 0, N) + - F.chemical_potential(0.4, 1, N) + + F.sc_pairing(0.8, 0, 1, N) + ) + + c = F(N, hc=hc) + c1 = FT(N, hc=hc) + + np.testing.assert_allclose(c.get_cmatrix(), c1.get_cmatrix(), atol=1e-6) + np.testing.assert_allclose(c1.entropy([0]), c.entropy([0]), atol=1e-5) + + +@pytest.mark.parametrize("backend", [lf("npb"), lf("tfb"), lf("jaxb")]) +def test_post_select(backend, highp): + for ind in [0, 1, 2]: + for keep in [0, 1]: + c = F(3, filled=[0, 2]) + c.evol_hp(0, 1, 0.2) + c.evol_cp(0, 0.5) + c.evol_hp(1, 2, 0.3j) + c.evol_cp(1, -0.8) + c.evol_sp(0, 2, 0.3) + c.post_select(ind, keep) + c1 = FT(3, filled=[0, 2]) + c1.evol_hp(0, 1, 0.2) + c1.evol_cp(0, 0.5) + c1.evol_hp(1, 2, 0.3j) + c1.evol_cp(1, -0.8) + c1.evol_sp(0, 2, 0.3) + c1.post_select(ind, keep) + np.testing.assert_allclose(c.get_cmatrix(), c1.get_cmatrix(), atol=1e-5) + + +@pytest.mark.parametrize("backend", [lf("tfb"), lf("jaxb")]) +def test_jittable_measure(backend): + @tc.backend.jit + def get_cmatrix(status): + r = [] + c = F(3, filled=[0]) + c.evol_hp(0, 1, 0.2) + c.evol_cp(0, 0.5) + c.evol_hp(1, 2, 0.3j) + r.append(c.cond_measure(1, status[0])) + c.evol_cp(1, -0.8) + r.append(c.cond_measure(2, status[1])) + r.append(c.cond_measure(1, status[3])) + c.evol_sp(0, 2, 0.3) + c.evol_hp(2, 1, 0.2) + c.evol_hp(0, 1, 0.8) + return c.get_cmatrix(), tc.backend.stack(r) + + def get_cmatrix_baseline(status): + r = [] + c = FT(3, filled=[0]) + c.evol_hp(0, 1, 0.2) + c.evol_cp(0, 0.5) + c.evol_hp(1, 2, 0.3j) + r.append(c.cond_measure(1, status[0])) + c.evol_cp(1, -0.8) + r.append(c.cond_measure(2, status[1])) + r.append(c.cond_measure(1, status[3])) + c.evol_sp(0, 2, 0.3) + c.evol_hp(2, 1, 0.2) + c.evol_hp(0, 1, 0.8) + return c.get_cmatrix(), np.array(r) + + status = np.array([0.2, 0.83, 0.61, 0.07]) + m, his = get_cmatrix(tc.backend.convert_to_tensor(status)) + m1, his1 = get_cmatrix_baseline(status) + np.testing.assert_allclose(m, m1, atol=1e-5) + np.testing.assert_allclose(his, his1, atol=1e-5) + + +@pytest.mark.parametrize("backend", [lf("npb"), lf("tfb"), lf("jaxb")]) +def test_exp_2body(backend): + c = F(3, filled=[1]) + np.testing.assert_allclose(c.expectation_2body(4, 1), 1.0, atol=1e-5) + np.testing.assert_allclose(c.expectation_2body(5, 2), 0.0, atol=1e-5) + np.testing.assert_allclose(c.expectation_2body(1, 4), 0.0, atol=1e-5) + + +@pytest.mark.parametrize("backend", [lf("npb"), lf("tfb"), lf("jaxb")]) +def test_exp_4body(backend): + c = F(4, filled=[0, 2]) + c.evol_hp(0, 1, 0.3) + c.evol_hp(2, 3, 0.3) + c.evol_sp(0, 3, 0.5) + c.evol_sp(0, 2, 0.9) + c.evol_cp(0, -0.4) + + c1 = FT(4, filled=[0, 2]) + c1.evol_hp(0, 1, 0.3) + c1.evol_hp(2, 3, 0.3) + c1.evol_sp(0, 3, 0.5) + c1.evol_sp(0, 2, 0.9) + c1.evol_cp(0, -0.4) + + np.testing.assert_allclose( + c.expectation_4body(0, 4, 1, 5), c.expectation_4body(0, 4, 1, 5), atol=1e-5 + ) + np.testing.assert_allclose( + c.expectation_4body(0, 1, 4, 5), c.expectation_4body(0, 1, 4, 5), atol=1e-5 + ) + np.testing.assert_allclose( + c.expectation_4body(0, 4, 2, 6), c.expectation_4body(0, 4, 2, 6), atol=1e-5 + ) + np.testing.assert_allclose( + c.expectation_4body(0, 2, 3, 1), c.expectation_4body(0, 2, 3, 1), atol=1e-5 + ) + np.testing.assert_allclose( + c.expectation_4body(0, 1, 4, 6), c.expectation_4body(0, 1, 4, 6), atol=1e-5 + ) + np.testing.assert_allclose( + c.expectation_4body(1, 0, 6, 7), c.expectation_4body(1, 0, 6, 7), atol=1e-5 + ) + + +@pytest.mark.parametrize("backend", [lf("npb"), lf("tfb"), lf("jaxb")]) +def test_overlap(backend): + def compute_overlap(FGScls): + c = FGScls(3, filled=[0, 2]) + c.evol_hp(0, 1, 1.2) + c.evol_hp(1, 2, 0.3) + c.evol_cp(0, 0.5) + c.evol_sp(0, 2, 0.3) + c1 = FGScls(3, filled=[0, 2]) + c1.evol_hp(0, 1, 0.2) + c1.evol_hp(1, 2, 0.6) + c1.evol_sp(1, 0, -1.1) + return tc.backend.abs(c.overlap(c1)) + + np.testing.assert_allclose( + compute_overlap(tc.FGSSimulator), compute_overlap(tc.fgs.FGSTestSimulator), 1e-5 + ) diff --git a/tests/test_keras.py b/tests/test_keras.py index 187a316e..3564f828 100644 --- a/tests/test_keras.py +++ b/tests/test_keras.py @@ -129,6 +129,9 @@ def qf(inputs, param): def test_keras_layer_inputs_dict(tfb): + # https://github.com/tensorflow/tensorflow/issues/65306 + # keras3 for tf2.16+ fails to accept complex valued input for keras layers + # which is vital for quantum applications n = 3 p = 0.1 K = tc.backend diff --git a/tests/test_miscs.py b/tests/test_miscs.py index 5a40d94e..b7a201cb 100644 --- a/tests/test_miscs.py +++ b/tests/test_miscs.py @@ -16,6 +16,7 @@ from tensorcircuit import experimental from tensorcircuit.quantum import PauliString2COO, PauliStringSum2COO from tensorcircuit.applications.vqes import construct_matrix_v2 +from tensorcircuit.applications.physics.baseline import TFIM1Denergy, Heisenberg1Denergy i, x, y, z = [t.tensor for t in tc.gates.pauli_gates] @@ -218,3 +219,38 @@ def fsum1(param1, param2): np.testing.assert_allclose(g1, g3, atol=1e-5) np.testing.assert_allclose(g2, g4, atol=1e-5) + + +def test_evol(jaxb): + def h_square(t, b): + return (tc.backend.sign(t - 1.0) + 1) / 2 * b * tc.gates.x().tensor + + c = tc.Circuit(3) + c.x(0) + c.cx(0, 1) + c.h(2) + c = experimental.evol_local( + c, [1], h_square, 2.0, tc.backend.convert_to_tensor(0.2) + ) + c.rx(1, theta=np.pi - 0.4) + np.testing.assert_allclose(c.expectation_ps(z=[1]), 1.0, atol=1e-5) + + ixi = tc.quantum.PauliStringSum2COO([[0, 1, 0]]) + + def h_square_sparse(t, b): + return (tc.backend.sign(t - 1.0) + 1) / 2 * b * ixi + + c = tc.Circuit(3) + c.x(0) + c.cx(0, 1) + c.h(2) + c = experimental.evol_global( + c, h_square_sparse, 2.0, tc.backend.convert_to_tensor(0.2) + ) + c.rx(1, theta=np.pi - 0.4) + np.testing.assert_allclose(c.expectation_ps(z=[1]), 1.0, atol=1e-5) + + +def test_energy_baseline(): + print(TFIM1Denergy(10)) + print(Heisenberg1Denergy(10)) diff --git a/tests/test_qaoa.py b/tests/test_qaoa.py index fae3c69a..a1b762f9 100644 --- a/tests/test_qaoa.py +++ b/tests/test_qaoa.py @@ -7,11 +7,14 @@ sys.path.insert(0, modulepath) import numpy as np +import pytest from tensorcircuit.applications.dqas import set_op_pool from tensorcircuit.applications.graphdata import get_graph from tensorcircuit.applications.layers import Hlayer, rxlayer, zzlayer from tensorcircuit.applications.vags import evaluate_vag +from tensorcircuit.templates.ansatz import QAOA_ansatz_for_Ising +from tensorcircuit.circuit import Circuit def test_vag(tfb): @@ -25,3 +28,59 @@ def test_vag(tfb): ) print(expene, eneg, p) np.testing.assert_allclose(ene.numpy(), -7.01, rtol=1e-2) + + +cases = [ + ("X", True), + ("X", False), + ("XY", True), + ("XY", False), + ("ZZ", True), + ("ZZ", False), +] + + +@pytest.fixture +def example_inputs(): + params = [0.1, 0.2, 0.3, 0.4] + nlayers = 2 + pauli_terms = [[0, 1, 0], [1, 0, 1]] + weights = [0.5, -0.5] + return params, nlayers, pauli_terms, weights + + +@pytest.mark.parametrize("mixer, full_coupling", cases) +def test_QAOA_ansatz_for_Ising(example_inputs, full_coupling, mixer): + params, nlayers, pauli_terms, weights = example_inputs + circuit = QAOA_ansatz_for_Ising( + params, nlayers, pauli_terms, weights, full_coupling, mixer + ) + n = len(pauli_terms[0]) + assert isinstance(circuit, Circuit) + assert circuit._nqubits == n + + if mixer == "X": + assert circuit.gate_count() == n + nlayers * (len(pauli_terms) + n) + elif mixer == "XY": + if full_coupling is False: + assert circuit.gate_count() == n + nlayers * (len(pauli_terms) + 2 * n) + else: + assert circuit.gate_count() == n + nlayers * ( + len(pauli_terms) + sum(range(n + 1)) + ) + else: + if full_coupling is False: + assert circuit.gate_count() == n + nlayers * (len(pauli_terms) + n) + else: + assert circuit.gate_count() == n + nlayers * ( + len(pauli_terms) + sum(range(n + 1)) / 2 + ) + + +@pytest.mark.parametrize("mixer, full_coupling", [("AB", True), ("XY", 1), ("TC", 5)]) +def test_QAOA_ansatz_errors(example_inputs, full_coupling, mixer): + params, nlayers, pauli_terms, weights = example_inputs + with pytest.raises(ValueError): + QAOA_ansatz_for_Ising( + params, nlayers, pauli_terms, weights, full_coupling, mixer + ) diff --git a/tests/test_qem.py b/tests/test_qem.py new file mode 100644 index 00000000..6ef01cec --- /dev/null +++ b/tests/test_qem.py @@ -0,0 +1,152 @@ +from functools import partial +import pytest +from pytest_lazyfixture import lazy_fixture as lf +import numpy as np +import networkx as nx + +import tensorcircuit as tc +from tensorcircuit.noisemodel import NoiseConf +from tensorcircuit.results import qem +from tensorcircuit.results.qem import ( + zne_option, + apply_zne, + dd_option, + apply_dd, + apply_rc, +) +from tensorcircuit.results.qem import benchmark_circuits + + +@pytest.mark.parametrize("backend", [lf("tfb"), lf("jaxb")]) +def test_benchmark_circuits(backend): + # QAOA + graph = [(2, 0), (0, 3), (1, 2)] + weight = [1] * len(graph) + params = np.array([[1, 1]]) + + _ = benchmark_circuits.QAOA_circuit(graph, weight, params) + + # mirror circuit + # return circuit and ideal counts {"01000":1} + _, _ = benchmark_circuits.mirror_circuit( + depth=5, two_qubit_gate_prob=1, connectivity_graph=nx.complete_graph(3), seed=20 + ) + + # GHZ circuit + _ = benchmark_circuits.generate_ghz_circuit(10) + + # Werner-state with linear complexity + # {'1000': 0.25, '0100': 0.25, '0010': 0.25, '0001': 0.25} + _ = benchmark_circuits.generate_w_circuit(5) + + # RB cirucit + _ = benchmark_circuits.generate_rb_circuits(2, 7)[0] + + +@pytest.mark.parametrize("backend", [lf("tfb"), lf("jaxb")]) +def test_zne(backend): + c = tc.Circuit(2) + for _ in range(3): + c.rx(range(2), theta=0.4) + + error1 = tc.channels.generaldepolarizingchannel(0.01, 1) + noise_conf = NoiseConf() + noise_conf.add_noise("rx", error1) + + def execute(circuit): + value = circuit.expectation_ps(z=[0], noise_conf=noise_conf, nmc=10000) + return value + + random_state = np.random.RandomState(0) + noise_scaling_function = partial( + zne_option.scaling.fold_gates_at_random, + # fidelities = {"single": 1.0}, + random_state=random_state, + ) + factory = zne_option.inference.PolyFactory(scale_factors=[1, 3, 5], order=1) + # factory = zne_option.inference.ExpFactory(scale_factors=[1,1.5,2],asymptote=0.) + # factory = zne_option.inference.RichardsonFactory(scale_factors=[1,1.5,2]) + # factory = zne_option.inference.AdaExpFactory(steps=5, asymptote=0.) + + result = apply_zne( + circuit=c, + executor=execute, + factory=factory, + scale_noise=noise_scaling_function, + num_to_average=1, + ) + + ideal_value = c.expectation_ps(z=[0]) + mit_value = result + + np.testing.assert_allclose(ideal_value, mit_value, atol=4e-2) + + +@pytest.mark.parametrize("backend", [lf("tfb"), lf("jaxb")]) +def test_dd(backend): + c = tc.Circuit(2) + for _ in range(3): + c.rx(range(2), theta=0.4) + + def execute(circuit): + value = circuit.expectation_ps(z=[0]) + return value + + def execute2(circuit): + key = tc.backend.get_random_state(42) + count = circuit.sample( + batch=1000, allow_state=True, format_="count_dict_bin", random_generator=key + ) + return count + + _ = apply_dd( + circuit=c, + executor=execute, + rule=["X", "X"], + rule_args={"spacing": -1}, + full_output=True, + ignore_idle_qubit=True, + fulldd=False, + ) + + _ = apply_dd( + circuit=c, + executor=execute2, + rule=dd_option.rules.xyxy, + rule_args={"spacing": -1}, + full_output=True, + ignore_idle_qubit=True, + fulldd=True, + iscount=True, + ) + + # wash circuit based on use_qubits and washout iden gates + _ = qem.prune_ddcircuit(c, qlist=list(range(c.circuit_param["nqubits"]))) + + +@pytest.mark.parametrize("backend", [lf("tfb"), lf("jaxb")]) +def test_rc(backend): + c = tc.Circuit(2) + for _ in range(3): + c.rx(range(2), theta=0.4) + c.cnot(0, 1) + + def execute(circuit): + value = circuit.expectation_ps(z=[0]) + return value + + def execute2(circuit): + key = tc.backend.get_random_state(42) + count = circuit.sample( + batch=1000, allow_state=True, format_="count_dict_bin", random_generator=key + ) + return count + + _ = apply_rc(circuit=c, executor=execute, num_to_average=6, simplify=False) + + _ = apply_rc( + circuit=c, executor=execute2, num_to_average=6, simplify=True, iscount=True + ) + + # generate a circuit with rc + _ = qem.rc_circuit(c) diff --git a/tests/test_quantum.py b/tests/test_quantum.py index 609111ad..63ff755e 100644 --- a/tests/test_quantum.py +++ b/tests/test_quantum.py @@ -1,13 +1,13 @@ # pylint: disable=invalid-name -from functools import partial import os import sys +from functools import partial import numpy as np import pytest -from pytest_lazyfixture import lazy_fixture as lf import tensornetwork as tn +from pytest_lazyfixture import lazy_fixture as lf thisfile = os.path.abspath(__file__) modulepath = os.path.dirname(os.path.dirname(thisfile)) @@ -312,7 +312,8 @@ def test_extract_from_measure(backend): np.testing.assert_allclose(r, 1, atol=1e-5) -def test_heisenberg_ham(tfb): +@pytest.mark.parametrize("backend", [lf("npb"), lf("tfb"), lf("jaxb")]) +def test_heisenberg_ham(backend): g = tc.templates.graphs.Line1D(6) h = tc.quantum.heisenberg_hamiltonian(g, sparse=False) e, _ = tc.backend.eigh(h) @@ -364,6 +365,38 @@ def test_expectation_quantum(backend): np.testing.assert_allclose(exp1, exp2, atol=1e-5) +@pytest.mark.parametrize("backend", [lf("npb"), lf("tfb"), lf("jaxb")]) +def test_ee(backend): + c = tc.Circuit(3) + c.h(0) + c.cx(0, 1) + c.cx(1, 2) + s = c.state() + np.testing.assert_allclose( + tc.quantum.entanglement_entropy(s, [0, 1]), np.log(2.0), atol=1e-5 + ) + + +@pytest.mark.parametrize("backend", [lf("npb"), lf("tfb"), lf("jaxb")]) +def test_negativity(backend, highp): + c = tc.DMCircuit(2) + c.h(0) + c.cnot(0, 1) + c.depolarizing(0, px=0.1, py=0.1, pz=0.1) + dm = c.state() + np.testing.assert_allclose( + tc.quantum.log_negativity(dm, [0], base="2"), 0.485427, atol=1e-5 + ) + np.testing.assert_allclose( + tc.quantum.partial_transpose(tc.quantum.partial_transpose(dm, [0]), [0]), + dm, + atol=1e-6, + ) + np.testing.assert_allclose( + tc.quantum.entanglement_negativity(dm, [1]), -0.33176, atol=1e-5 + ) + + @pytest.mark.parametrize("backend", [lf("npb"), lf("tfb"), lf("jaxb")]) def test_tn2qop(backend): nwires = 6 @@ -466,3 +499,28 @@ def test_ps2xyz(): xyz.update({"y": []}) assert tc.quantum.ps2xyz([0, 1, 3]) == xyz assert tc.quantum.ps2xyz([0, 1, 3, 0]) == xyz + + +@pytest.mark.parametrize("backend", [lf("npb"), lf("tfb"), lf("jaxb")]) +def test_reduced_wavefunction(backend): + c = tc.Circuit(3) + c.h(0) + c.cnot(0, 1) + r = c.cond_measure(0) + s = c.state() + s1 = tc.quantum.reduced_wavefunction(s, [0, 2], [r, 0]) + if tc.backend.cast(r, tc.rdtypestr) < 0.5: + np.testing.assert_allclose(s1, np.array([1, 0]), atol=1e-5) + else: + np.testing.assert_allclose(s1, np.array([0, 1]), atol=1e-5) + + c = tc.Circuit(3) + c.h(0) + c.cnot(0, 1) + s = c.state() + s1 = tc.quantum.reduced_wavefunction(s, [2], [0]) + + c1 = tc.Circuit(2) + c1.h(0) + c1.cnot(0, 1) + np.testing.assert_allclose(s1, c1.state(), atol=1e-5) diff --git a/tests/test_shadows.py b/tests/test_shadows.py new file mode 100644 index 00000000..9d6406b6 --- /dev/null +++ b/tests/test_shadows.py @@ -0,0 +1,160 @@ +import pytest +from pytest_lazyfixture import lazy_fixture as lf +import numpy as np +import tensorcircuit as tc +from tensorcircuit.shadows import ( + shadow_bound, + shadow_snapshots, + global_shadow_state, + entropy_shadow, + renyi_entropy_2, + expectation_ps_shadow, + global_shadow_state1, +) + + +@pytest.mark.parametrize("backend", [lf("tfb"), lf("jaxb")]) +def test_jit(backend): + nq, repeat = 8, 5 + ps = [1, 0, 0, 0, 2, 0, 0, 0] + sub = (1, 3, 6, 7) + error = 0.1 + ns, k = shadow_bound(ps, error) + ns //= repeat + + thetas = 2 * np.random.rand(2, nq) - 1 + + c = tc.Circuit(nq) + for i in range(nq): + c.H(i) + for i in range(2): + for j in range(nq): + c.cnot(j, (j + 1) % nq) + for j in range(nq): + c.rz(j, theta=thetas[i, j] * np.pi) + + psi = c.state() + pauli_strings = tc.backend.convert_to_tensor(np.random.randint(1, 4, size=(ns, nq))) + status = tc.backend.convert_to_tensor(np.random.rand(ns, repeat)) + + def classical_shadow(psi, pauli_strings, status): + lss_states = shadow_snapshots(psi, pauli_strings, status) + expc = expectation_ps_shadow(lss_states, ps=ps, k=k) + ent = entropy_shadow(lss_states, sub=sub, alpha=2) + return expc, ent + + csjit = tc.backend.jit(classical_shadow) + + exact_expc = c.expectation_ps(ps=ps) + exact_rdm = tc.quantum.reduced_density_matrix(psi, cut=[0, 2, 4, 5]) + exact_ent = tc.quantum.renyi_entropy(exact_rdm, k=2) + expc, ent = csjit(psi, pauli_strings, status) + expc = np.median(expc) + + np.testing.assert_allclose(expc, exact_expc, atol=error) + np.testing.assert_allclose(ent, exact_ent, atol=5 * error) + + +@pytest.mark.parametrize("backend", [lf("tfb"), lf("jaxb")]) +def test_state(backend): + nq, ns = 2, 10000 + + c = tc.Circuit(nq) + c.H(0) + c.cnot(0, 1) + + psi = c.state() + bell_state = psi[:, None] @ psi[None, :] + + pauli_strings = tc.backend.convert_to_tensor(np.random.randint(1, 4, size=(ns, nq))) + status = tc.backend.convert_to_tensor(np.random.rand(ns, 5)) + lss_states = shadow_snapshots(c.state(), pauli_strings, status) + sdw_state = global_shadow_state(lss_states) + sdw_state1 = global_shadow_state1(lss_states) + + np.testing.assert_allclose(sdw_state, bell_state, atol=0.1) + np.testing.assert_allclose(sdw_state1, bell_state, atol=0.1) + + +@pytest.mark.parametrize("backend", [lf("tfb"), lf("jaxb")]) +def test_ent(backend): + nq, ns, repeat = 6, 1000, 500 + + thetas = 2 * np.random.rand(2, nq) - 1 + + c = tc.Circuit(nq) + for i in range(nq): + c.H(i) + for i in range(2): + for j in range(nq): + c.cnot(j, (j + 1) % nq) + for j in range(nq): + c.rz(j, theta=thetas[i, j] * np.pi) + + sub = [1, 4] + psi = c.state() + + pauli_strings = tc.backend.convert_to_tensor(np.random.randint(1, 4, size=(ns, nq))) + status = tc.backend.convert_to_tensor(np.random.rand(ns, repeat)) + snapshots = shadow_snapshots(psi, pauli_strings, status, measurement_only=True) + + exact_rdm = tc.quantum.reduced_density_matrix( + psi, cut=[i for i in range(nq) if i not in sub] + ) + exact_ent = tc.quantum.renyi_entropy(exact_rdm, k=2) + ent = entropy_shadow(snapshots, pauli_strings, sub, alpha=2) + ent2 = renyi_entropy_2(snapshots, sub) + + np.testing.assert_allclose(ent, exact_ent, atol=0.1) + np.testing.assert_allclose(ent2, exact_ent, atol=0.1) + + +# @pytest.mark.parametrize("backend", [lf("tfb"), lf("jaxb")]) +# def test_expc(backend): +# import pennylane as qml +# +# nq, ns, repeat = 6, 2000, 1000 +# +# thetas = 2 * np.random.rand(2, nq) - 1 +# +# c = tc.Circuit(nq) +# for i in range(nq): +# c.H(i) +# for i in range(2): +# for j in range(nq): +# c.cnot(j, (j + 1) % nq) +# for j in range(nq): +# c.rz(j, theta=thetas[i, j] * np.pi) +# +# ps = [1, 0, 0, 0, 0, 3] +# sub = [1, 4] +# psi = c.state() +# +# pauli_strings = tc.backend.convert_to_tensor(np.random.randint(1, 4, size=(ns, nq))) +# status = tc.backend.convert_to_tensor(np.random.rand(ns, repeat)) +# snapshots = shadow_snapshots(psi, pauli_strings, status, measurement_only=True) +# +# exact_expc = c.expectation_ps(ps=ps) +# exact_rdm = tc.quantum.reduced_density_matrix( +# psi, cut=[i for i in range(nq) if i not in sub] +# ) +# exact_ent = tc.quantum.renyi_entropy(exact_rdm, k=2) +# print(exact_expc, exact_ent) +# +# expc = np.median(expection_ps_shadow(snapshots, pauli_strings, ps=ps, k=9)) +# ent = entropy_shadow(snapshots, pauli_strings, sub, alpha=2) +# ent2 = renyi_entropy_2(snapshots, sub) +# print(expc, ent, ent2) +# +# pl_snapshots = np.asarray(snapshots).reshape(ns * repeat, nq) +# pl_ps = np.tile(np.asarray(pauli_strings - 1)[:, None, :], (1, repeat, 1)).reshape( +# ns * repeat, nq +# ) +# shadow = qml.ClassicalShadow(pl_snapshots, pl_ps) +# H = qml.PauliX(0) @ qml.PauliZ(5) +# pl_expc = shadow.expval(H, k=9) +# pl_ent = shadow.entropy(sub, alpha=2) +# print(pl_expc, pl_ent) +# +# assert np.isclose(expc, pl_expc) +# assert np.isclose(ent, pl_ent) diff --git a/tests/test_templates.py b/tests/test_templates.py index c22b6a73..79e2b176 100644 --- a/tests/test_templates.py +++ b/tests/test_templates.py @@ -1,7 +1,8 @@ # pylint: disable=invalid-name -import sys import os +import sys + import numpy as np import pytest from pytest_lazyfixture import lazy_fixture as lf @@ -25,7 +26,7 @@ def test_any_measurement(): np.testing.assert_allclose(r2, 0.0, atol=1e-5) -@pytest.mark.parametrize("backend", [lf("jaxb"), lf("tfb"), lf("jaxb")]) +@pytest.mark.parametrize("backend", [lf("jaxb"), lf("tfb")]) def test_parameterized_local_measurement(backend): c = tc.Circuit(3) c.X(0) @@ -160,10 +161,6 @@ def test_operator_measurement(backend): ) dense = tc.array_to_tensor(np.kron(tc.gates._x_matrix, np.eye(2))) sparse = tc.quantum.PauliString2COO([1, 0]) - if tc.backend.name == "jax": - sparse = tc.backend.coo_sparse_matrix( - sparse.indices, sparse.values, sparse.shape - ) for h in [dense, sparse, mpo]: @@ -178,3 +175,34 @@ def f(theta): np.testing.assert_allclose(v, 0.84147, atol=1e-4) np.testing.assert_allclose(g, 0.54032, atol=1e-4) + + +@pytest.fixture +def symmetric_matrix(): + matrix = np.array([[-5.0, -2.0], [-2.0, 6.0]]) + nsym_matrix = np.array( + [[1.0, 2.0, 3.0], [2.0, 4.0, 5.0], [3.0, 5.0, 6.0], [8.0, 7.0, 6.0]] + ) + return matrix, nsym_matrix + + +def test_QUBO_to_Ising(symmetric_matrix): + matrix1, matrix2 = symmetric_matrix + pauli_terms, weights, offset = tc.templates.conversions.QUBO_to_Ising(matrix1) + n = matrix1.shape[0] + expected_num_terms = n + n * (n - 1) // 2 + assert len(pauli_terms) == expected_num_terms + assert len(weights) == expected_num_terms + assert isinstance(pauli_terms, list) + assert isinstance(weights, np.ndarray) + assert isinstance(offset, float) + assert pauli_terms == [ + [1, 0], + [0, 1], + [1, 1], + ] + assert all(weights == np.array([3.5, -2.0, -1.0])) + assert offset == -0.5 + + with pytest.raises(ValueError): + tc.templates.conversions.QUBO_to_Ising(matrix2) diff --git a/tests/test_torchnn.py b/tests/test_torchnn.py index 6acb7b17..88549248 100644 --- a/tests/test_torchnn.py +++ b/tests/test_torchnn.py @@ -14,7 +14,7 @@ try: import torch except ImportError: - pytest.skip("torch is not installed") + pytest.skip("torch is not installed", allow_module_level=True) @pytest.mark.parametrize("backend", [lf("tfb"), lf("jaxb"), lf("torchb")])