update readme and docs

Author: refraction-ray

README.md

@@ -6,13 +6,23 @@ TensorCircuit is built on top of modern machine learning frameworks, and has the
 
 ## Basic Usage
 
+Please begin with [Quick Start](/docs/source/quickstart.rst) and [Jupyter Tutorials](https://github.com/quclub/tensorcircuit-tutorials/tree/master/tutorials).
+
+For more information and introductions, please refer to helpful scripts [examples](/examples) and [documentations](/docs/source). API docstrings (incomplete for now) and test cases in [tests](/tests) are also informative.
+
+The following are some minimal demos.
+
+Circuit manipulation:
+
 ```python
 import tensorcircuit as tc
 c = tc.Circuit(2)
 c.H(0)
 c.CNOT(0,1)
+c.rx(1, theta=0.2)
 print(c.wavefunction())
 print(c.expectation((tc.gates.z(), [1])))
+print(c.perfect_sampling())
 ```
 
 Runtime behavior customization:
@@ -23,10 +33,9 @@ tc.set_dtype("complex128")
 tc.set_contractor("greedy")
 ```
 
-Auto differentiations with jit:
+Automatic differentiations with jit:
 
 ```python
-@tc.backend.jit
 def forward(theta):
     c = tc.Circuit(2)
     c.R(0, theta=theta, alpha=0.5, phi=0.8)
@@ -38,13 +47,11 @@ theta = tc.gates.num_to_tensor(1.0)
 print(g(theta))
 ```
 
-Please begin with [Quick Start](/docs/source/quickstart.rst) and [Jupyter Tutorials](https://github.com/quclub/tensorcircuit-tutorials/tree/master/tutorials).
-
-For more information and introductions, please refer to examples and docs/source in this repo. API docstrings (incomplete for now) and test cases in tests are also helpful and informative.
-
 ## Contributing
 
-### Guidelines
+For contribution guidelines and notes, see [CONTRIBUTING](/CONTRIBUTING.md).
+
+### Cautions
 
 Please open issues or PRs.
 
@@ -56,8 +63,6 @@ Keep the codebase private!
 
 For development workflow, we suggest to first configure a good conda environment. The versions of dependecy package may vary in terms of development requirements. The minimum requirement is the [TensorNetwork](https://github.com/google/TensorNetwork) package (pip install suggested).
 
-For git workflow of contribution, see [CONTRIBUTING](/CONTRIBUTING.md).
-
 ### Docs
 
 ```bash
@@ -97,10 +102,6 @@ For now, we introduce one for all checker for development:
 ./check_all.sh
 ```
 
-### CI
-
-We currently use GitHub Action for test CI, but it has limited quota for free private repo.
-
 ## Research projects and application codes
 
 ### DQAS

docs/source/advance.rst

@@ -31,6 +31,8 @@ The two-qubit gates applied on the circuit can be decomposed via SVD, which may
             split=split_conf
         )
 
+Note ``max_singular_values`` must be specified to make the whole procedure static and thus jittable.
+
 
 SavedModel
 -----------------

docs/source/quickstart.rst

@@ -169,11 +169,11 @@ The related API design in TensorCircuit closely follows the functional programmi
 
 **AD support:**
 
-gradients, vjps, jvps, natural gradients, Jacobians and Hessians
+Gradients, vjps, jvps, natural gradients, Jacobians and Hessians
 
 **JIT support:**
 
-parameterized quantum circuit can run in a blink. Always use jit if the circuit will get evaluations multiple times, it greatly boost the simulation efficiency with two or three order time reduction. But also be caution, you need to be an expert on jit, otherwise the jitted function may return unexpected results or recompiling on every hit (wasting lots of time).
+Parameterized quantum circuit can run in a blink. Always use jit if the circuit will get evaluations multiple times, it greatly boost the simulation efficiency with two or three order time reduction. But also be caution, you need to be an expert on jit, otherwise the jitted function may return unexpected results or recompiling on every hit (wasting lots of time).
 
 **VMAP support:**
 

requirements-docker.txt

@@ -5,7 +5,7 @@ tensorflow==2.7
 tensornetwork==0.4.6
 graphviz
 jax==0.2.27
-# jablib indepedent specify the version
+# jaxlib indepedent specify the version in Dockerfile
 torch
 torchvision
 networkx