docs/source/tutorials/imag_time_evo.ipynb

{
 "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": "<Figure size 640x480 with 1 Axes>",
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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": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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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": "<Figure size 640x480 with 1 Axes>",
      "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": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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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()"
   ]
  }
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