VQE-H2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "a0b68733",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import pennylane as qml\n",
    "from pennylane import qchem\n",
    "\n",
    "import numpy as np\n",
    "import qiskit\n",
    "from qiskit import QuantumCircuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "669c0b79",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.quantum_info import Statevector\n",
    "\n",
    "def getStatevector(circuit):\n",
    "    \"\"\"\n",
    "        从qiskit的QuantumCircuit实例中获取最终的状态向量\n",
    "        \n",
    "    \"\"\"\n",
    "    return Statevector(circuit).data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "a5e8873c",
   "metadata": {},
   "outputs": [],
   "source": [
    "from functools import reduce\n",
    "\n",
    "# eg. Dag(|a>) = <a|\n",
    "Dag = lambda matrix: matrix.conj().T\n",
    "# eg. Kron(I, X, Y) = I ⊗ X ⊗ Y，计算张量用\n",
    "Kron = lambda *matrices: reduce(np.kron, matrices)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dfae8027",
   "metadata": {},
   "source": [
    "## 1. Building the electronic Hamiltonian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "6bc05907",
   "metadata": {},
   "outputs": [],
   "source": [
    "# https://pennylane.ai/qml/demos/tutorial_vqe.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e21a4ec3",
   "metadata": {},
   "outputs": [],
   "source": [
    "symbols = [\"H\", \"H\"]\n",
    "coordinates = np.array([0.0, 0.0, -0.6614, 0.0, 0.0, 0.6614])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "74bf6394",
   "metadata": {},
   "source": [
    "### 1.1 using qml"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "24c8690a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of qubits =  4\n",
      "The Hamiltonian is    (-0.24274501260941383) [Z2]\n",
      "+ (-0.24274501260941383) [Z3]\n",
      "+ (-0.042072551947440084) [I0]\n",
      "+ (0.1777135822909176) [Z0]\n",
      "+ (0.1777135822909176) [Z1]\n",
      "+ (0.12293330449299354) [Z0 Z2]\n",
      "+ (0.12293330449299354) [Z1 Z3]\n",
      "+ (0.1676833885560135) [Z0 Z3]\n",
      "+ (0.1676833885560135) [Z1 Z2]\n",
      "+ (0.17059759276836806) [Z0 Z1]\n",
      "+ (0.17627661394181787) [Z2 Z3]\n",
      "+ (-0.04475008406301996) [Y0 Y1 X2 X3]\n",
      "+ (-0.04475008406301996) [X0 X1 Y2 Y3]\n",
      "+ (0.04475008406301996) [Y0 X1 X2 Y3]\n",
      "+ (0.04475008406301996) [X0 Y1 Y2 X3]\n"
     ]
    }
   ],
   "source": [
    "# 基于JW变换构建的H2哈密顿量\n",
    "H, qubits = qml.qchem.molecular_hamiltonian(symbols, coordinates)\n",
    "print(\"Number of qubits = \", qubits)\n",
    "print(\"The Hamiltonian is \", H)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "3eb01b40",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([-0.04207255,  0.17771358,  0.17771358,  0.17059759,  0.04475008,\n",
       "         -0.04475008, -0.04475008,  0.04475008, -0.24274501,  0.1229333 ,\n",
       "         -0.24274501,  0.16768339,  0.16768339,  0.1229333 ,  0.17627661], requires_grad=False),\n",
       " [Identity(wires=[0]),\n",
       "  PauliZ(wires=[0]),\n",
       "  PauliZ(wires=[1]),\n",
       "  PauliZ(wires=[0]) @ PauliZ(wires=[1]),\n",
       "  PauliY(wires=[0]) @ PauliX(wires=[1]) @ PauliX(wires=[2]) @ PauliY(wires=[3]),\n",
       "  PauliY(wires=[0]) @ PauliY(wires=[1]) @ PauliX(wires=[2]) @ PauliX(wires=[3]),\n",
       "  PauliX(wires=[0]) @ PauliX(wires=[1]) @ PauliY(wires=[2]) @ PauliY(wires=[3]),\n",
       "  PauliX(wires=[0]) @ PauliY(wires=[1]) @ PauliY(wires=[2]) @ PauliX(wires=[3]),\n",
       "  PauliZ(wires=[2]),\n",
       "  PauliZ(wires=[0]) @ PauliZ(wires=[2]),\n",
       "  PauliZ(wires=[3]),\n",
       "  PauliZ(wires=[0]) @ PauliZ(wires=[3]),\n",
       "  PauliZ(wires=[1]) @ PauliZ(wires=[2]),\n",
       "  PauliZ(wires=[1]) @ PauliZ(wires=[3]),\n",
       "  PauliZ(wires=[2]) @ PauliZ(wires=[3])])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Hamiltonian.terms() 获取该哈密顿量中的每个组成成分\n",
    "# \n",
    "# 例如第5项：PauliY(wires=[0]) @ PauliX(wires=[1]) @ PauliX(wires=[2]) @ PauliY(wires=[3])\n",
    "# 对应系数是 0.04475008\n",
    "# 对应一个哈密顿量的分量（组成成分）为：0.04475008 * Y ⊗ X ⊗ X ⊗ Y，以此类推\n",
    "# \n",
    "H.terms()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b0eef3d",
   "metadata": {},
   "source": [
    "### 1.2 Manual build"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "92aa35d1",
   "metadata": {},
   "outputs": [],
   "source": [
    "I = np.eye(2)\n",
    "\n",
    "# pauli matrixes\n",
    "X = np.matrix([\n",
    "    [0, 1], [1, 0]\n",
    "])\n",
    "Y = np.matrix([\n",
    "    [0, -1j], [1j, 0]\n",
    "])\n",
    "Z = np.matrix([\n",
    "    [1, 0], [0, -1]\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "51e13085",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 基于上述分解结果，手动构建初始的Hamilton量\n",
    "# Kron(Y, X, X, Y) 即计算 Y ⊗ X ⊗ X ⊗ Y\n",
    "Hami = \\\n",
    "    -0.04207255 * Kron(I, I, I, I) +\\\n",
    "    0.17771358  * Kron(Z, I, I, I) +\\\n",
    "    0.17771358  * Kron(I, Z, I, I) +\\\n",
    "    0.17059759  * Kron(Z, Z, I, I) +\\\n",
    "    0.04475008  * Kron(Y, X, X, Y) +\\\n",
    "    -0.04475008 * Kron(Y, Y, X, X) +\\\n",
    "    -0.04475008 * Kron(X, X, Y, Y) +\\\n",
    "    0.04475008  * Kron(X, Y, Y, X) +\\\n",
    "    -0.24274501 * Kron(I, I, Z, I) +\\\n",
    "    0.1229333   * Kron(Z, I, Z, I) +\\\n",
    "    -0.24274501 * Kron(I, I, I, Z) +\\\n",
    "    0.16768339  * Kron(Z, I, I, Z) +\\\n",
    "    0.16768339  * Kron(I, Z, Z, I) +\\\n",
    "    0.1229333   * Kron(I, Z, I, Z) +\\\n",
    "    0.17627661  * Kron(I, I, Z, Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "93e33673",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(16, 16)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Hami.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a62097cb",
   "metadata": {},
   "source": [
    "## 2. Initial state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "c16a9102",
   "metadata": {},
   "outputs": [],
   "source": [
    "def reset_endianness_circuit(qubits):\n",
    "    \"\"\"\n",
    "        重置qiskit端序\n",
    "        \n",
    "        简单说因为pennylane得到的分解中例如 PauliZ(wires=[0]) @ PauliZ(wires=[1]\n",
    "        其中wires=[0]并不对应qiskit里的qubit[0]（而是qubit[3]，因为端序的问题）\n",
    "        所以用这个线路把qiskit的端序重置下\n",
    "        \n",
    "        eg.下图的resetCircuit线路，处理前，从下到上才对应wires=[0]，wires=[1]，...\n",
    "        用SWAP把比特交换下就变成正常的顺序（从上到下对应wires=[0]，wires=[1]，...）\n",
    "        \n",
    "    \"\"\"\n",
    "    circuit = QuantumCircuit(qubits)\n",
    "    for i in range(qubits // 2):\n",
    "        circuit.swap(i, qubits - i - 1)\n",
    "    circuit.barrier()\n",
    "    \n",
    "    return circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "f719bb36",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 371.107x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "resetCircuit = reset_endianness_circuit(4)\n",
    "resetCircuit.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "4a2d6b41",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_initial_circuit(electrons, qubits):\n",
    "    \"\"\"\n",
    "        对应 hf = qml.qchem.hf_state(electrons, qubits)\n",
    "        即获取初始的电子轨道占据情况（hf_state）\n",
    "        \n",
    "        eg. electrons=2(电子数)，qubtis=4(比特数，即总轨道数) => [1, 1, 0, 0]（两个电子占据低位轨道）\n",
    "    \"\"\"\n",
    "    circuit = QuantumCircuit(qubits)\n",
    "    [ circuit.x(i) for i in range(electrons) ]\n",
    "    circuit.barrier()\n",
    "    \n",
    "    return circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "40fb3be2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 287.496x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# test - get initial state circuit\n",
    "\n",
    "electrons = 2 # 电子数\n",
    "# qubits 计算方法：\n",
    "# \n",
    "# 1. H2 \n",
    "# H原子外层电子层数一层，最多可容纳2电子 => 可能的原子轨道数2\n",
    "# 故氢分子是 2*2=4\n",
    "#\n",
    "# 2. H2O\n",
    "# 类推，O原子外层电子数两层，最多可容纳10个电子（2,8） => 原子轨道总数10\n",
    "# H2O: 2 * 2 + 10 = 14 (qubit) \n",
    "qubits = 4\n",
    "\n",
    "initCircuit = get_initial_circuit(electrons, qubits)\n",
    "initCircuit.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "210838c7",
   "metadata": {},
   "source": [
    "## 3. Ansatz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "8c941ea5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 文章 https://arxiv.org/pdf/1812.09976.pdf 提到，VQE拟设大致有两种类型\n",
    "#  physically-motivated ansatze (PMA) 与 hardware heuristic ansatze (HHA), \n",
    "# \n",
    "# 1. PMA 类似于受分子物理理论的影响，设计的某种拟设，比如Givens Rotation，拟设有明确的物理意义：对应单激发或双激发，\n",
    "# 那么调参可能对应与调某种激发发生的概率\n",
    "\n",
    "# 2. HHA 则类似于搭建神经网络，就是借助计算力暴力求解，搭建的拟设没有具体的物理意义，就像神经网络一样，所以精度可能不如上面的PMA\n",
    "\n",
    "# 以下考虑了PMA和HHA的两种拟设构建方式，PMA基于Givens Rotation（理论上还有其他的方法，待研究），HHA用了自设的某个量子神经网络结构"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7aa694b3",
   "metadata": {},
   "source": [
    "### 3.1 Givens rotation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "b83d834a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 参考 https://pennylane.ai/qml/demos/tutorial_givens_rotations.html"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4150eac",
   "metadata": {},
   "source": [
    "<img src=\"images/givens.png\" width=800 align='left'>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "194cca7e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "single excitations:  [[0, 2], [1, 3]]\n",
      "----------\n",
      "double excitations:  [[0, 1, 2, 3]]\n"
     ]
    }
   ],
   "source": [
    "singles, doubles = qml.qchem.excitations(electrons, qubits)\n",
    "print('single excitations: ', singles) # 对应所有可能的单激发\n",
    "print('-' * 10)\n",
    "print('double excitations: ', doubles) # 对应所有可能的双激发\n",
    "\n",
    "# eg. H2分子，初始轨道占据情况(hf_state) 为[1, 1, 0, 0]\n",
    "# 存在单激发，[0, 2] 对应电子占据状态从 [1, 1, 0, 0] => [0， 1， 1， 0] 即位置0的电子跃迁到位置2\n",
    "# 存在双激发，[0, 1, 2, 3] 对应电子占据状态从 [1, 1, 0, 0] => [0， 0， 1， 1]，即位置0与1的电子一同跃迁至轨道2,3 \n",
    "\n",
    "# 吉文斯旋转（Givens Rotation）通过一组量子门来表示刻画所有可能的激发情况，从而构成拟设（此处细节有待研究）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "8d3dd1db",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "single excitations:  [[0, 2], [0, 4], [1, 3], [1, 5]]\n",
      "----------\n",
      "double excitations:  [[0, 1, 2, 3], [0, 1, 2, 5], [0, 1, 3, 4], [0, 1, 4, 5]]\n"
     ]
    }
   ],
   "source": [
    "# Test - excitations\n",
    "\n",
    "singles_test, doubles_test = qml.qchem.excitations(2, 6)\n",
    "# ↑: 0 2 4, ↓: 1, 3, 5\n",
    "# single: 0 -> 2, 0 -> 4, 1 -> 3, 1 -> 5\n",
    "# double: [0, 1] -> [2, 3], [0, 1] -> [2, 5], [0, 1] -> [4, 3], [0, 1] -> [4, 5]\n",
    "print('single excitations: ', singles_test) # 对应所有可能的单激发\n",
    "print('-' * 10)\n",
    "print('double excitations: ', doubles_test) # 对应所有可能的双激发"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eaa91fb6",
   "metadata": {},
   "source": [
    "<img src=\"images/double.png\" width=400 align='left' />"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3fbfa894",
   "metadata": {},
   "source": [
    "### - single excitation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "fb3fa296",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[CNOT(wires=[0, 2]), CRY(8, wires=[2, 0]), CNOT(wires=[0, 2])]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 使用PennyLane的静态函数获取Givens Rotation的具体门实现\n",
    "qml.SingleExcitation.compute_decomposition(8, wires=(0, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "0f054268",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_single_excitation_circuit(param, qubits):\n",
    "    \"\"\"\n",
    "        参考上述分解结果，构建通用的单激发Givens Rotation线路\n",
    "        \n",
    "        -> https://arxiv.org/pdf/2106.13839.pdf\n",
    "        \n",
    "    \"\"\"\n",
    "    circuit = QuantumCircuit(4)\n",
    "    \n",
    "    circuit.cx(*qubits)\n",
    "    circuit.cry(param, *list(reversed(qubits)))\n",
    "    circuit.cx(*qubits)\n",
    "    circuit.barrier()\n",
    "    \n",
    "    return circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "d6b7cb10",
   "metadata": {},
   "outputs": [],
   "source": [
    "def single_excitation(theta):\n",
    "    circuit = QuantumCircuit(2, name='single_excitation')\n",
    "    \n",
    "    circuit.cx(0, 1)\n",
    "    circuit.cry(theta, 1, 0)\n",
    "    circuit.cx(0, 1)\n",
    "    circuit.barrier()\n",
    "    \n",
    "    return circuit.to_instruction()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "f616e95e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 371.107x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# test - single excitation givens rotation\n",
    "\n",
    "singleExcitationCircuit = QuantumCircuit(4)\n",
    "singleExcitationCircuit.append(single_excitation(0.5), [0, 2])\n",
    "singleExcitationCircuit.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "cbb1c4f2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 454.719x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# test - single excitation givens rotation\n",
    "\n",
    "singleExcitationCircuit = get_single_excitation_circuit(1, [0, 2])\n",
    "singleExcitationCircuit.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "668b42d0",
   "metadata": {},
   "source": [
    "### - double excitation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "17ea6450",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[CNOT(wires=[2, 3]),\n",
       " CNOT(wires=[0, 2]),\n",
       " Hadamard(wires=[3]),\n",
       " Hadamard(wires=[0]),\n",
       " CNOT(wires=[2, 3]),\n",
       " CNOT(wires=[0, 1]),\n",
       " RY(1.0, wires=[1]),\n",
       " RY(-1.0, wires=[0]),\n",
       " CNOT(wires=[0, 3]),\n",
       " Hadamard(wires=[3]),\n",
       " CNOT(wires=[3, 1]),\n",
       " RY(1.0, wires=[1]),\n",
       " RY(-1.0, wires=[0]),\n",
       " CNOT(wires=[2, 1]),\n",
       " CNOT(wires=[2, 0]),\n",
       " RY(-1.0, wires=[1]),\n",
       " RY(1.0, wires=[0]),\n",
       " CNOT(wires=[3, 1]),\n",
       " Hadamard(wires=[3]),\n",
       " CNOT(wires=[0, 3]),\n",
       " RY(-1.0, wires=[1]),\n",
       " RY(1.0, wires=[0]),\n",
       " CNOT(wires=[0, 1]),\n",
       " CNOT(wires=[2, 0]),\n",
       " Hadamard(wires=[0]),\n",
       " Hadamard(wires=[3]),\n",
       " CNOT(wires=[0, 2]),\n",
       " CNOT(wires=[2, 3])]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 同样使用PennyLane的静态函数获取Givens Rotation的具体门实现\n",
    "qml.DoubleExcitation.compute_decomposition(8, wires=(0, 1, 2, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "88f75733",
   "metadata": {},
   "outputs": [],
   "source": [
    "def double_excitation(param):\n",
    "    circuit = QuantumCircuit(4, name='double_excitation')\n",
    "    \n",
    "    circuit.cx(2, 3)\n",
    "    circuit.cx(0, 2)\n",
    "    circuit.h(3)\n",
    "    circuit.h(0)\n",
    "    circuit.cx(2, 3)\n",
    "    circuit.cx(0, 1)\n",
    "    circuit.ry(param/8, 1)\n",
    "    circuit.ry(-param/8, 0)\n",
    "    circuit.cx(0, 3)\n",
    "    circuit.h(3)\n",
    "    circuit.cx(3, 1)\n",
    "    circuit.ry(param/8, 1)\n",
    "    circuit.ry(-param/8, 0)\n",
    "    circuit.cx(2, 1)\n",
    "    circuit.cx(2, 0)\n",
    "    circuit.ry(-param/8, 1)\n",
    "    circuit.ry(param/8, 0)\n",
    "    circuit.cx(3, 1)\n",
    "    circuit.h(3)\n",
    "    circuit.cx(0, 3)\n",
    "    circuit.ry(-param/8, 1)\n",
    "    circuit.ry(param/8, 0)\n",
    "    circuit.cx(0, 1)\n",
    "    circuit.cx(2, 0)\n",
    "    circuit.h(0)\n",
    "    circuit.h(3)\n",
    "    circuit.cx(0, 2)\n",
    "    circuit.cx(2, 3)\n",
    "    \n",
    "    return circuit.to_instruction()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "2f1c3b40",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_double_excitation_circuit(param, qubits):\n",
    "    \"\"\"\n",
    "        参考上述分解结果，构建通用的双激发Givens Rotation线路\n",
    "        \n",
    "        -> https://arxiv.org/pdf/2106.13839.pdf\n",
    "        \n",
    "    \"\"\"\n",
    "    circuit = QuantumCircuit(4)\n",
    "    \n",
    "    circuit.cx(qubits[2], qubits[3])\n",
    "    circuit.cx(qubits[0], qubits[2])\n",
    "    circuit.h(qubits[3])\n",
    "    circuit.h(qubits[0])\n",
    "    circuit.cx(qubits[2], qubits[3])\n",
    "    circuit.cx(qubits[0], qubits[1])\n",
    "    circuit.ry(param/8, qubits[1])\n",
    "    circuit.ry(-param/8, qubits[0])\n",
    "    circuit.cx(qubits[0], qubits[3])\n",
    "    circuit.h(qubits[3])\n",
    "    circuit.cx(qubits[3], qubits[1])\n",
    "    circuit.ry(param/8, qubits[1])\n",
    "    circuit.ry(-param/8, qubits[0])\n",
    "    circuit.cx(qubits[2], qubits[1])\n",
    "    circuit.cx(qubits[2], qubits[0])\n",
    "    circuit.ry(-param/8, qubits[1])\n",
    "    circuit.ry(param/8, qubits[0])\n",
    "    circuit.cx(qubits[3], qubits[1])\n",
    "    circuit.h(qubits[3])\n",
    "    circuit.cx(qubits[0], qubits[3])\n",
    "    circuit.ry(-param/8, qubits[1])\n",
    "    circuit.ry(param/8, qubits[0])\n",
    "    circuit.cx(qubits[0], qubits[1])\n",
    "    circuit.cx(qubits[2], qubits[0])\n",
    "    circuit.h(qubits[0])\n",
    "    circuit.h(qubits[3])\n",
    "    circuit.cx(qubits[0], qubits[2])\n",
    "    circuit.cx(qubits[2], qubits[3])\n",
    "    circuit.barrier()\n",
    "    \n",
    "    return circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ea0e532",
   "metadata": {},
   "source": [
    "<img src=\"images/G.png\" width=940 align='left'>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "139caa66",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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gu33r2ZWzsTJiv/TwkOd57fNJnCq28NDg5yq3t27eEYAN33/CoWM/0Dd2GC0CQjlVfJwVW99i6vzbmDTiXfp3GQHAiBv+hs1mZceBdCYOf7vyPNFhvar9OhwpPMijqT0oLj3J4F6PcHVgO7bvW8d7a6axM2cDMx9YXWX1NiNtNB7uDbij7xOUV5Tx8VfP88xbQ3kjZU+Vb1x1SRFzQWnrZmAuzGHCsNcZ2P3PAAzp9QgvL/orn3z1gt2xh47u5oP1M4kOu46ZD66pvOQZ1ON+7p8VxYufPEK39vtwd3Ov8TzNA0KZcs9HmEznVwm9O99GUmp35i15gmljv6j2dcdP5fPSonH0ix3O5JELKrcP6fUILy0az0df/g+D4x+mZdM2lz3Lf9+/j6Z+LZk9LgMfL7/K7V0ibmDq/NtYnfkuN3W/F4DH73iV7Oe38uyCEcx9bDuLNsxm+751/GXoi7Rtdf5DZmw2G7PS7qW84iyzH/2GNq1iKs95V/9JWK3Wame5rtNQPk5/nrLyEgZ0vbvK/hEDnmLMH6bZbRvaexwPP9+Fd1f9qzJiXSMTWZ35LjsOpDs8jyOvfz6ZE8XH+Nd9yyq/SQ3p9QjzlibzwfpZrNj6FoN6jLF7zVW+gfzzz0sqfx/jIhJISu3Bsk1zq8xZl3Rj3wVt/P5TAhq1ILHrPXbb70yYWPXYnYuw2WwM65did88m8KpW3NT9zxwpPMjevG9/0zzD+qVU/ocPEBnclWvaJZK5dxUlZ4uqfV36dx9SXnGWgT3GcLLYYvdPfMfBWG1WMrNXXfYcB/J3sD//OxK6jKD83Fm783UK742Xpy9b96yoPN7PJ4BJIxZQcCqfya8N4u1VU4mPGsLQ65Iqj9l3eBs5R3ZyU7c/2wXsAje3mv8Ru7DSAygtO8Op4uOcLT9DXNv+/Hg0i+LSUzU6r9Vq5etdi4m4ukuVVfbw/pNwM7mx4ftPqrzu1t7j7X4f24d0x7thI/Is2TWa4/eilZgLyi/YT/uQ7lVWT039W9LIu7HdNnPBAQDCWkRXOU/oT9vMBftpH1LzTz4P/enyyP7cUWzds4IjhQcJC6r63gA/Hs0CYOK8AdWeu/D0kcue48L55q+YwvwVUxyfr8j+fNFhvbgzYSILVv+bJn5BPDHsdbv9F/4AR1zd5bLnuFyFRUd584un2LhzESeKjlbZX1xyAl8v/1993pPFxyg5W1T5+/tz/j5NaOLfkvzj+6vsa9mk6orX36cpp84c/9Uz/J4UMblsP/8u/EvnrBW/+/td+BDjlOHzaerX0uExv+ZS8sL5bu8zge7tBzo8ppFPgN2vyyvK2LJ7OQCnzxRw9MSP+Ps2vez3rCmbzcaT827k0NEsbu09nsiQbvh4XYW7yZ3lW95gzbcLsNqqv1StDW7V3FJw9odNK2IuqGWTNuQdy+ac9Zzdauz4qXyKSk7YH/tTBHKO7KRVYFu7fT8e2QVA0E/fgf28mwDn/zD/kqPv3BccPJpFVGhP+21HduHm5n7RZ5euDmwHnL8Xc01k9auxy3XhfG5u7pd9vtc+n8Se3C2MvXkG76+bwb/fHc7Lf82svNS7OjASOH9ZWRPVfWPYn/8d+/O3c/eAvzP6Jvvnvz7/5tXLPo8jV/k2w6ehHweP7Kyy7/SZQgpO5dO2Q9xln8/ZdE/MBfWK/iOFRUdYuXW+3fa0tdOrHBsfNQSTycQH62dSca68cvvxU/ks3/IGLQJCKy+VfLz8aOIXxLa9a+y+++Yf38/GnZ9WO8/762bYHZ+dm8m32avoEnED3g0bVfu6vrHDaODRkPkrpnDWwU9Vi0tOUlZxttrX/1LE1V0IC+rE0k1zHEb33LkKTv0s0N/88Dkfpz9HYtfRDOuXzBPD3iD32B5mf/L/98TatoolrEU0X2S8To65ahQutUrx9mzE6ZLCKsddWPXYsN9+wPy9w/tVF76Opxx8g/klNzc3ekYNZm/et2T8YP+DlffW/gerzcp1nW6t5tX1j1ZiLmhYvxTWfLuA5z4cS3buVsJaRLN9/zp2Hfyaq3wD7Y4Nad6eO/om8/66GTz+ch/6xd3JmdLzj1iUnC3iybvetVvNDbkuiTe/eIrJrw6iV6ehHD91mGVfzyEsqBO7D2U4nOdo4UGe/N+biI8eQsGpfBZtnI1nA28euPnij0c0axzMuNte4bkP7mfMzI4MuGYUzQNCOVl8jAP5O9i481NefWLXZf9432QyMXH426TM7c8D/xPDwO73EdoimrPlZ8iz7GXD9x9z36Bp3NT9Xo6fymfme6O5OrAdj946G4CeUbdwa+/xfPLVC3RrfxMJccMxmUw8cecbpMy9gUdTe5x/xCKoE0UlJ/hu/3q6tx/I0N6PVjtTh9CebMpayoufJBEd1gs3N3fiIvrTunlHwlpE8/66GZwtO0NI8/bkHtvDsk1zCWvZmezcrXbn6di6J4s2zObFjx+hR8eb8XBvQIfW19KySbjD971v0LNk7lnJlLeGMiT+EVoFRrBj/5es255G5zZ9uLHr6Mv6mtYHipgL8vMJ4LlH0pmz5HFW/bQai2nTl1kPriVl3g1Vjh9783SuDoxg8caXefWzJ2ng7kmH1tcyacQCOre53u7Y4f0mcqbkJKsy32b7/nWEtoji8WGvkZ27tdqIPXv/F8xZ8jjzV0yhrLyEjq17MvaWmQ5/mvdLA7v/meDASD5cP4tlm+ZSVHoCf99AQpq1Z/RN/6SJX9Cv+tpEXB3HK499y8I10/h612KWbpqDd0M/ggLCuLHbvXRpdwNWq5XpC0dRfPYU08ausFstjr15BjsOfMnzHz1YGYn2Id2ZPS6Dd1f9k/Xb32fppjn4+wbSIaQH0WHXXXSeP13/GObj+0nf8SHLNs3BarNWPuz6rzHLmLv0CVZufYvSsmLCgjqRfOdb7M/fXiViCXF3sTfvW9Ztf48vv/sAq83KE8PeqDZiLQJCSR23mbeW/53Vme9QVHr+Ydfh/Scx8oanDPWEv8nm7LtyV6hzZbA21dlTiNSNhHHgXkt/60r3xETE0IyzZhSpRnHJSYc3/n/Ow8MTf58mdTSR1CVFTAzvpUXjWbn1rYseE9OmL/99eF3dDCR1ShETw7szIYUB11z87wz+8iFWcR2KmBheaIsoQltEOXsMcRLd2BcRQ1PERMTQFDERMTRFTEQMTRETEUNTxETE0BQxETE0RUxEDE0RExFDU8RExNAUMRExNEVMRAxNERMRQ7siImaxWEhJSSEiIgIvLy9CQkIYP348xcXFjBkzBpPJxOzZs509pp3cY3t4c/nfefTFntz+TDOGPOXHg/8Tx7ur/01JWbGzxxOpN1z+f8Wzbds2Bg0ahNlsxtfXl6ioKA4fPkxqair79u2joOD8R1zFxcU5d9Bf+CLjdRZvfIn4qCHc0GUk7u4N2L5vLW9+8RRfbn+f1Ec30bCBt7PHFHE6l46YxWJh8ODBmM1mJkyYwJQpU/Dz8wNgxowZTJw4EQ8PD0wmEzExl/7knbp0fefbuSthEr7eV1VuGxz/EFcHtmPB6n/z+TevMfS6pIucQeTK4NKXk+PGjSM3N5ekpCRmzZpVGTCAlJQUYmNjqaioICwsDH9/fydOWlX7kG52AbugX+ydAOSYv6/rkUTqJZeNWFZWFmlpaQQGBjJt2jSHx3Tt2hWA2NjYym0ffvghf/rTnwgNDcXHx4cOHTrwt7/9jaKiojqZ+1KOncwFIKBRCydPIlI/uGzEFi5ciNVqZeTIkTRq1MjhMd7e5+8p/Txis2bNwt3dnWeffZbPP/+chx9+mFdeeYWBAwditVrrZPbqnLOe491V/8TdzYP+XUY4dRaR+sJl74mtWbMGgISEhGqPyc09v6r5ecSWLFlCs2bNKn/dt29fmjVrxsiRI/nqq6/o06dPLU18aa8s/iu7Dn7NfYOeJaR5e6fNIVKfuGzEDh48CEBoaKjD/RUVFWzYsAGwj9jPA3ZBt27dAMjLy6vRLN26dcNsNttt8/TwZl5S9mWf480vnmbRhtncfO0D3NV/Uo3mEHGWdpHtKKuo/rNBg4KC2LJlS43O7bIRKy4+/yxVSYnjL1xaWhoWiwU/Pz/Cw8Mveq61a9cC0LFjxxrNYjabqwTQq4HPZb9+/opneHf1v7ip+58Z/6c5NZpBxJnyDx+mtPxMrZzbZSMWFBREYWEhmZmZxMfH2+3Lz88nOTkZgJiYGEwmU7XnycvL4+mnn2bgwIE1fpYsKCioyjZPj8t7xmv+imd4e+VUEruO5vHbX73orCL1VctWrS65Eqspl43YgAEDyMrKYvr06SQmJhIZGQlARkYGo0aNwmKxABd/yLWoqIg//vGPeHp68vrrr9d4FkfL5HNlsDb14q97e+U/eHvlVAZcM4onhr2Om5vL/hxGXFz2nmzcPWvn3C4bsZSUFBYsWMChQ4eIjo6mQ4cOlJaWsnfvXgYNGkRYWBjLly+3ux/2cyUlJQwePJgDBw6Qnp5Oy5Yt63T+RRteYv6KKTRv3Jpr2g1gzbcL7PYH+LWga2Rinc4kUh+5bMSCg4NJT08nOTmZ9evXk5OTQ1RUFHPnzmXs2LG0bdsWwGHEysvLuf3229myZQurV68mKqruP11696EMAI6e+JEZaaOr7I9p01cREwFMNpvN5uwh6lpRURH+/v6YTCZOnz6Nj8//32S3Wq0MHz6cxYsX89lnn9G/f/9ameFyLidFXEXCOHQ5+XvauXMnNpuNyMhIu4AB/OUvf+GDDz7gySefxMfHh02bNlXua9u2rcNHMETEea7IO8U7duwAHF9Kfv755wD85z//IT4+3u6fZcuW1emcInJpV+RK7GIRy8nJqeNpROS30EpMRAztilyJXfh7lSJifFfkSkxEXIciJiKGpoiJiKEpYiJiaIqYiBiaIiYihqaIiYihKWIiYmiKmIgYmiImIoamiImIoSliImJoipiIGJoiJiKGpoiJiKEpYiJiaIqYiBiaIiYihqaIiYihKWIiYmiKmIgYmiImIoamiImIoSliImJoipiIGJoiJiKGpoiJiKEpYiJiaIqYiBiaIiYihqaIiYihKWIiYmiKmIgYmiImIoamiImIoSliImJoipiIGJoiJiKGpoiJiKEpYiJiaIqYiBiaIiYihqaIiYihKWIiYmiKmIgY2hURMYvFQkpKChEREXh5eRESEsL48eMpLi5mzJgxmEwmZs+e7ewxRaQGPJw9QG3btm0bgwYNwmw24+vrS1RUFIcPHyY1NZV9+/ZRUFAAQFxcnHMH/YVDR3fzzqp/kJ2XyfFThzl3rpzmjVvTo8MfuKNfMk39Wzp7RJF6waUjZrFYGDx4MGazmQkTJjBlyhT8/PwAmDFjBhMnTsTDwwOTyURMTIyTp7V37GQuBafyua7TrTS7Khh3Nw8OmHewbPM81m5/jzmPbSOgUXNnjynidCabzWZz9hC1ZcSIESxcuJCkpCRefPHFKvvj4uLYvn074eHh7N+/v05nO1cGa1N//evWb/+Af70zjPv/MJ07E1J+/8FEakHCOHD3rJ1zu+w9saysLNLS0ggMDGTatGkOj+natSsAsbGxldvS09MZMGAALVu2pGHDhgQHB3PnnXeSlZVVJ3NfSouAUACKSgqdPIlI/eCyl5MLFy7EarUycuRIGjVq5PAYb29vwD5ihYWFdO7cmQcffJDmzZuTm5vLtGnTiI+P5/vvvyc4OLhO5r+grLyUkrIiyspLOXhkF69+NhGAHh3+UKdziNRXLhuxNWvWAJCQkFDtMbm5uYB9xIYMGcKQIUPsjuvevTvt27fno48+Yvz48bUwbfU+++ZVXvr00cpfBwWE8eRd79C5zfV1OodIfeWyETt48CAAoaGhDvdXVFSwYcMGwD5ijjRt2hQAD4+afbm6deuG2Wy22+bp4c28pOxLvva66KG0btaBkrIi9uZ9y9e7FnOy2FKjOUScpV1kO8oqSqrdHxQUxJYtW2p0bpeNWHFxMQAlJY6/cGlpaVgsFvz8/AgPD6+y/9y5c1itVg4ePMikSZMICgpi2LBhNZrFbDaTl5dnt82rgc9lvbZZ42CaNT5/CXtdp6Fc3/lPJKV252z5Ge7qP6lG84jUtfzDhyktP1Mr53bZiAUFBVFYWEhmZibx8fF2+/Lz80lOTgYgJiYGk8lU5fV9+/atXKlFRESwZs0amjVrVuNZfsnTw7tG52rTKoa2V3dhycaXFTExjJatWl1yJVZTLhuxAQMGkJWVxfTp00lMTCQyMhKAjIwMRo0ahcVy/pKsuodcX3vtNU6cOMGBAweYOXMmN954Ixs2bKB169a/ehZHy+SaPmIBUFZewukzBTV7sYgTZO/J1iMWv1ZKSgpNmzbl0KFDREdH07lzZ9q1a0ePHj1o06YN/fv3B6q/H9a+fXuuvfZahg8fzurVqzl9+jQzZsyos/kLTpkdbt+2dy055u/pENqzzmYRqc9cdiUWHBxMeno6ycnJrF+/npycHKKiopg7dy5jx46lbdu2wKVv6gM0btyYiIgI9u7dW9tjV0r9+GGOn84nLqI/LRqHUlZRSnbuVtZtfw/vhn48eMt/62wWkfrMZSMG0LFjR5YuXVple1FRETk5Obi5udGpU6dLnufo0aPs3r2ba6+9tjbGdCihy12s3Dqf1Vvf5kTxMUyYaBEQys09H2RY32SaB/z6y1oRV+TSEavOzp07sdlsREZG4uNj/1PCu+++m4iICOLi4mjcuDHZ2dk899xzeHh48Nhjj9XZjH1jh9E3tmY/DRW5klyREduxYwfg+FKyZ8+ezJ8/nxdeeIHS0lJCQkJISEhg8uTJ1T5zJiLOo4j9QlJSEklJSXU9kojUkMv+dPJiLhYxETGWK3IlduHvVYqI8V2RKzERcR2KmIgYmiImIoamiImIoSliImJoipiIGJoiJiKGpoiJiKEpYiJiaIqYiBiaIiYihmay2Ww2Zw9xJbLZwFru7ClE6oZbA3DweTy/C0VMRAxNl5MiYmiKmIgYmiImIoamiImIoSliImJoipiIGJoiJiKGpoiJiKEpYiJiaIqYiBiaIiYihqaIiYihKWIiYmiKmIgYmiImIoamiImIoSliImJoipiIGJoiJiKGpoiJiKEpYiJiaIqYiBiaIiYihqaIiYihKWIiYmj/B5i4y3GsRE+bAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 371.107x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# test - double excitation givens rotation\n",
    "\n",
    "doubleExcitationCircuit = QuantumCircuit(4)\n",
    "doubleExcitationCircuit.append(double_excitation(0.5), [0, 1, 2, 3])\n",
    "doubleExcitationCircuit.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "d695a17c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 956.385x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit_H2 = QuantumCircuit(4)\n",
    "circuit_H2.x(0)\n",
    "circuit_H2.x(1)\n",
    "\n",
    "circuit_H2.append(single_excitation(0.5), [0, 2])\n",
    "circuit_H2.append(single_excitation(0.5), [1, 3])\n",
    "circuit_H2.append(double_excitation(0.5), [0, 1, 2, 3])\n",
    "\n",
    "circuit_H2.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "fa87b030",
   "metadata": {},
   "outputs": [],
   "source": [
    "# |1100> -> |0011>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "3000363c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1959.72x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# test - double excitation givens rotation\n",
    "\n",
    "doubleExcitationCircuit = get_double_excitation_circuit(1, [0, 1, 2, 3])\n",
    "doubleExcitationCircuit.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd82dac1",
   "metadata": {},
   "source": [
    "### - full Givens rotation circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "6c7ad0c6",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_givens_circuit(params, detail=False):\n",
    "    \"\"\"\n",
    "        组装完整的基于Givens Rotation的拟设线路，包含所有的单激发与双激发\n",
    "        \n",
    "        注：https://pennylane.ai/qml/demos/tutorial_vqe.html 的例子求解H2分子时候，\n",
    "        基于某种化学假设，只考虑了双激发（不清楚具体理由），这边实现的是同时考虑所有单激发与双激发\n",
    "        结果也可以正常求得\n",
    "        \n",
    "        单激发与双激发的类型这里暂时写死，有待未来完善\n",
    "        \n",
    "    \"\"\"\n",
    "    # 1100 -> 0110 1001 0011\n",
    "    singles = [[0, 2], [1, 3]]\n",
    "    doubles = [[0, 1, 2, 3]]\n",
    "    \n",
    "    circuit = QuantumCircuit(4)\n",
    "    \n",
    "    idx = 0\n",
    "    \n",
    "    for single in singles:\n",
    "        if detail:\n",
    "            circuit = circuit.compose(get_single_excitation_circuit(params[idx], single))\n",
    "        else:\n",
    "            circuit.append(single_excitation(params[idx]), single)\n",
    "        idx += 1\n",
    "        \n",
    "    for double in doubles:\n",
    "        if detail:\n",
    "            circuit = circuit.compose(get_double_excitation_circuit(params[idx], double))\n",
    "        else:\n",
    "            circuit.append(double_excitation(params[idx]), double)\n",
    "        idx += 1\n",
    "        \n",
    "    return circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "1f7429c6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 872.774x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "givensCircuit = get_givens_circuit([0, 1, 2])\n",
    "givensCircuit.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "928feeae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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LkyTz588//rXHHnssn/vc53L++edn9OjRmTVrVv7gD/4g+/fvH5TcA6Gnp/f8ptM9hquc5LF/7h3H0Lft58XNvWN3cXP31d/+S3L46Onf/+0XkgOHz1yeoaKtrS0PP/xw2traio4CAAAAAFCxmi26vvWtb6Wnpyc33XRTxowZc9J7Ro0aleTEouuBBx7IsGHD8sd//Mf53ve+l9/+7d/ON7/5zSxatCg9VdIErX8j6eru25g93b3jGPp2FFh0/Xx/dZRBnV3Ja2/2bczRY8k/V9GKtf46duxY9u/fn2PHjr3/zQAAAAAAQ1zNntG1atWqJMlVV111ynva29uTnFh0fec738m55557/PNPfOITOffcc3PTTTflRz/6UT7+8Y+focQDp79/rP/n15NLpg5sFgbezr3Fzz/tA8VmeD/93WJxzevJVbMHNstQs3Hjxtxwww157LHHMmeOg8kAAAAAgOpWs0XXtm3bkiTnn3/+Sa8fPXo0q1evTnJi0fWLJde7PvKRjyRJOjr6f5DVjBkz0tg4OAvorl76ZCa2LujzuH/4pxfzf/zapwc+EAPqk7+1Ms0XXH7Sa7+7KBk36tRjx5X+9fWrn33ved4+mHzt6V/++hf+083Z+cozp5m2GAv/04M5b8Fn+jxu6xtdmTr1koEPdAYtWbKkT/d3dnYmSb773e/mhRdeOO1xjzzySJ/mAQAAAAA4XS0tLXn++ef7NbZmi64DBw4kSQ4ePHjS6ytWrMiuXbsyduzYXHDBBe/5rGee6f2j/uzZ/V/q8e4flwfDO++8079xhw9XVOYxOA4fPvXegeNGJRNGv/8zGhtP776TeeutN4f878nB7j7u3fk/9fT0DPn39m919/G9Hjp06PhrX8ZW2/cFAAAAAKgPNVt0tbS0ZM+ePVm7dm2uuOKKE651dnbmK1/5SpJk3rx5aWhoOOVzOjo68od/+IdZtGhRFixY0O88kydPHrQVXUe7d/Vv3MFdmTJlygCnYaANazj12Upvn7zXPW5cqbfk6ulJ3j703vee6llnj2vKsaH+e/JOV7+GHXp7Z9X9b2D06L41lqVS6fhrX8ZW2/cFAAAAAKgeLS0t/R7bUC6XywOYZci47bbb8o1vfCOtra35wQ9+kJkzZyZJ1qxZk5tvvjmvv/56jhw5kltvvTUPPvjgSZ+xf//+fPKTn8zOnTuzZs2aTJ48uU8ZDhw4kDFjxhx/VlNTU2Vv6jSta0/+6z/2fdwXP5nM8bfsIe/ba5NnNvRv7Fc/27uSq6s7+erf9u8Z/+cNSdPI/o0dLDv3Jvc92fdxn7k0+eSsgc9zJm3cuLFP969bt65fZ3TNmlVl3xgAAAAAoC4MzhKjAixbtiznnHNOduzYkTlz5mTu3LmZMWNGFi5cmAsvvDBXX311khPP5/pFBw8ezOLFi7Nly5Z8//vf73PJVaTZH0zO7mOnNrEpmV09b7GuTZ1Y3NznjBn6JVeStIxPZkzq25gRw5KF772LaU2YOXNmVq9efbz8BwAAAACoZjVbdE2dOjXPPvtsrrvuupRKpWzdujUTJ07MQw89lKeeeiqbNm1KcvKi68iRI7nhhhvy/PPP53vf+14uvvjiwY5fkcbG5PMLk8ZT78h44v0Nya8u7B3H0Hf+OcXNfV6Bc/fVZy9NRvZhc9bPXJqMroISr1IjRozIxIkTM2LEiKKjAAAAAABUrKarjdmzZ+fJJ5/Mvn37sm/fvvzkJz/Jb/7mb+bAgQPZunVrGhsbc8kll5wwpqenJzfddFN++MMf5tvf/nYWLlxYUPrKzP5g8p8/lgx/n5/w8Mbe+2Z/cHByUbnmsckF5xYz92VVtOLpg2cnX7oqGX3W+9/7Hz+cXDnjzGcaCrZv357f+Z3fyfbt24uOAgAAAABQsT6sd6gd69atS7lczsyZMzN69OgTrt166635m7/5m9x1110ZPXp0nnvuuePXpk2blnPPLahh6IcF5/Vu4fajV5I1W5LDR//12sjhvaXFxy7qvYfq8rEZyZa3BnfOc8Yks6qsEL3wA8my65IfbUqe25zsP3zi9Uvbkl+5KGlrLiReIfbt25dnnnkmt956a9FRAAAAAAAqVpdF18svv5zk5NsWfu9730uS3HfffbnvvvtOuPYXf/EXWbJkyRnPN5Baxic3LEw+/aGkfXdy+EgyckTvOU8lO5dVrfnnJd95MenqHrw5P37R6W+HOZRMGJ18ekGyaG6y/efJw/+YdL+TjC0lN19ZdDoAAAAAACqh6Po3tm7dOshpBkdpRDJ9UtEpGCjDh/Wew/Z//8PgzHfeOcnHZg7OXGfK8GG9K7xGDOv9vBpLOwAAAAAATlTTZ3SdynsVXVAtLp6SLLywb2PePti7Cuztg6c/Zlhj8mtX9L4CAAAAAMBQUpcrulatWlV0BBgQ/9tHkje6erelPB1fe7rvc3x+oXPcasmkSZNy5513ZtIkSzwBAAAAgOpnjQZUsdKI5LeuSj549pl5/uc+klw+7cw8m2I0NzdnyZIlaW5uLjoKAAAAAEDFFF1Q5caUkqXXJHOmDNwzSyOS/3xl8isXDdwzGRr27t2bp59+Onv37i06CgAAAABAxRRdUANGn5X875/oPUtr1FmVPWvW5OSuTycfbhuQaAwx7e3tueOOO9Le3l50FAAAAACAitXlGV1QixoakoUXJrMnJ6tfTX68Odl78DTHJpn1weRjM5KLp/Q+CwAAAAAAhjpFF9SYsaOSRfOST12SrO9IXn8rad+dtO9JDr7Te09jQ3LOmKR1YtJ6TjJ3atI8ttjcAAAAAADQV4ouqFHDGpO5rb0f7+opJ+Vy7zUAAAAAAKh2ii6oI40N6d2nkLpVKpUye/bslEqloqMAAAAAAFRM0QVQR6ZNm5bHH3+86BgAAAAAAAPCBmYAAAAAAABUJUUXQB1Zv3595s2bl/Xr1xcdBQAAAACgYoougDpSLpdz5MiRlMvloqMAAAAAAFRM0QUAAAAAAEBVUnQBAAAAAABQlRRdAAAAAAAAVKXhRQcAYPBMmzYtTzzxRFpbW4uOAgAAAABQMUUXQB0plUqZMWNG0TEAAAAAAAaErQsB6khHR0fuvvvudHR0FB0FAAAAAKBiii6AOtLV1ZWVK1emq6ur6CgAAAAAABVTdAEAAAAAAFCVFF0AAAAAAABUJUUXAAAAAAAAVUnRBVBHGhsbc9lll6Wx0X/+AQAAAIDq5y+dAHWkp6cna9asSU9PT9FRAAAAAAAqpugCAAAAAACgKim6AAAAAAAAqEqKLgAAAAAAAKqSogugjowfPz6LFy/O+PHji44CAAAAAFCx4UUHAGDwTJ06Nffff3/RMQAAAAAABoQVXQB15PDhw9m2bVsOHz5cdBQAAAAAgIopugDqyObNm7No0aJs3ry56CgAAAAAABVTdAEAAAAAAFCVFF0AAAAAAABUJUUXAAAAAAAAVUnRBQAAAAAAQFUaXnQAAAbPnDlzsmHDhqJjAAAAAAAMCCu6AAAAAAAAqEqKLoA6smXLltx4443ZsmVL0VEAAAAAACpm60KgZpXLyd6DyY6fJzt2J3sOJN3v9F47+E6y5vVk6sRk0riksU5q/+7u7rz00kvp7u4uOgoAAAAAQMUUXUDNOXw0Wbs1+dGmpGPPye9551jy6I97/z22lFwxvffj7KZBiwkAAAAAQIUUXUDN6CknqzclT72UHDpy+uP2HUq+/9Pkv69LPjotuf5DyaizzlxOAAAAAAAGhqILqAm79iV//ZNk88/6/4xyOfnx5mTDG8kXLk9mf3Dg8gEAAAAAMPDq5FQaoJZt25V87enKSq5f1NWdPPRM8uwrA/O8oWTKlClZvnx5pkyZUnQUAAAAAICKWdEFVLUdu5NvrurbVoWna+Xzva+/ctHAP7soEyZMyPXXX190DAAAAACAAWFFF1C19h/qXXl1Jkqud618vncrw1qxe/fuPProo9m9e3fRUQAAAAAAKqboAqrWY2t6y66++N1FyVc/2/t6ulb8JDn4Tt/mGao6Oztzzz33pLOzs+goAAAAAAAVq4uia9euXVm2bFmmT5+eUqmU1tbW3H777Tlw4EBuueWWNDQ05MEHHyw6JtAHL21PXtze93HjRiUTRve+nq6u7uTba/s+FwAAAAAAZ1bNn9H14osv5tprr83OnTvT1NSUiy++OG+88Ua+/vWv57XXXju+fdeCBQuKDQqctnI5efrlwZ3zJ68n/+vc5OymwZ0XAAAAAIBTq+kVXbt27crixYuzc+fOfPnLX05nZ2fWrl2bnTt3Zvny5XnqqaeyZs2aNDQ0ZN68eUXHBU7TlreSzq7BnbNcTv7p1cGdEwAAAACA91bTRddtt92W9vb2LF26NA888EDGjh17/NqyZcsyf/78HD16NG1tbRk3blyBSYG+WF1Q4fTca8mxnmLmHihNTU258sor09RkaRoAAAAAUP1qtujasGFDVqxYkebm5tx7770nvefSSy9NksyfP//415599tlcc801mTx5ckaOHJmpU6fmC1/4QjZs2DAouYH3t/lnxcy771Dy5tvFzD1Q2tra8vDDD6etra3oKAAAAAAAFavZM7q+9a1vpaenJzfddFPGjBlz0ntGjRqV5MSia8+ePZk7d26+9KUv5QMf+EDa29tz77335oorrshPf/rTTJ06dVDyAyf39sFk78Hi5t+xO5k8obj5K3Xs2LEcPHgwo0aNyrBhw4qOAwAAAABQkZotulatWpUkueqqq055T3t7e5ITi67rr78+119//Qn3XXbZZbnooouycuXK3H777WcgLXC62ncXO/+O3cnCC4vNUImNGzfmhhtuyGOPPZY5c+YUHQcAAAAAoCI1W3Rt27YtSXL++eef9PrRo0ezevXqJCcWXSdzzjnnJEmGD+//t2vGjBlpbKzZnSJh0Jz34c9l4Rf+7KTXfndRMm7Ue48fV/rX169+9tT3vX0w+drTv/z1R//673L7Z5aeZtozb8mSJX26v7OzM0ny3e9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      "text/plain": [
       "<Figure size 2210.55x785.944 with 1 Axes>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "givensCircuit = get_givens_circuit([0, 1, 2], detail=True)\n",
    "givensCircuit.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2f2f021",
   "metadata": {},
   "source": [
    "### 3.2 VQC(QNN) based"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "11b4dd7d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# quantum neural networks(QNN)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "41929ba7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# https://www.researchgate.net/publication/363858547_Shuffle-QUDIO_accelerate_distributed_VQE_with_trainability_enhancement_and_measurement_reduction"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9195bd83",
   "metadata": {},
   "source": [
    "<img src=\"images/HEA.png\" width=500 align='left'>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "7ee21c41",
   "metadata": {},
   "outputs": [],
   "source": [
    "# hardware heuristic ansatze(HHA)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f98248a4",
   "metadata": {},
   "source": [
    "<img src=\"images/QNN.png\" width=600 align='left'>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "587dcd64",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_QNN_circuit(params):\n",
    "    \"\"\"\n",
    "        某种量子神经网络（QNN）线路结构，充当拟设部分\n",
    "        \n",
    "        因为没有考虑物理意义，纯粹是用神经网络的计算、拟合能力强行算，属于HHA法\n",
    "        QNN结构可以有很多中不同的可能，大体上是旋转门组成的旋转层 + 双比特门组成的纠缠层\n",
    "        \n",
    "    \"\"\"\n",
    "    circuit = QuantumCircuit(4)\n",
    "    \n",
    "    layer = len(params) // 8\n",
    "    circuit.rx(params[0], 0)\n",
    "    circuit.rz(params[1], 0)\n",
    "    circuit.rx(params[2], 1)\n",
    "    circuit.rz(params[3], 1)\n",
    "    circuit.rx(params[4], 2)\n",
    "    circuit.rz(params[5], 2)\n",
    "    circuit.rx(params[6], 3)\n",
    "    circuit.rz(params[7], 3)\n",
    "\n",
    "    for i in range(layer - 1):\n",
    "        j = (i + 1) * 8\n",
    "        \n",
    "        circuit.cx(0, 1)\n",
    "        circuit.cx(1, 2)\n",
    "        circuit.cx(2, 3)\n",
    "        \n",
    "        circuit.barrier()\n",
    "        \n",
    "        circuit.rx(params[j], 0)\n",
    "        circuit.rz(params[j + 1], 0)\n",
    "        circuit.rx(params[j + 2], 1)\n",
    "        circuit.rz(params[j + 3], 1)\n",
    "        circuit.rx(params[j + 4], 2)\n",
    "        circuit.rz(params[j + 5], 2)\n",
    "        circuit.rx(params[j + 6], 3)\n",
    "        circuit.rz(params[j + 7], 3)\n",
    "        \n",
    "        circuit.barrier()\n",
    "    \n",
    "    return circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "5bcaf7d7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 872.774x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# test - get_QNN_circuit\n",
    "\n",
    "get_QNN_circuit([0] * 16).draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "f6b03555",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1458.05x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# test - get_QNN_circuit\n",
    "\n",
    "get_QNN_circuit([0] * 24).draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "06a30d6c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2043.33x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# test - get_QNN_circuit\n",
    "\n",
    "get_QNN_circuit([0] * 32).draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cbf15f42",
   "metadata": {},
   "source": [
    "## 4. VQE"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b910c1df",
   "metadata": {},
   "source": [
    "### - Tool Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "42aa9730",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_full_circuit(ansatz, params):\n",
    "    \"\"\"\n",
    "        搭建完整线路\n",
    "        \n",
    "        :param ansatz: 构建拟设线路的函数\n",
    "        :param params: 拟设函数的参数，即ansatz(params)返回拟设线路\n",
    "        \n",
    "        1. resetCircuit 在整个线路前后用来调整端序\n",
    "        2. initCircuit 对应初始 hf_state，eg. [1, 1, 0, 0]\n",
    "        3. ansatz(params) 对应拟设（带参数）主体\n",
    "        \n",
    "    \"\"\"\n",
    "    return resetCircuit.compose(\n",
    "        initCircuit.compose(\n",
    "            ansatz(params).compose(resetCircuit)\n",
    "        )\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "d4a44558",
   "metadata": {},
   "outputs": [],
   "source": [
    "def expval(Hami, circuit):\n",
    "    \"\"\"\n",
    "        基于哈密顿量与拟设计算期望值\n",
    "        \n",
    "        1. 初始态是hf_state，eg. [1, 1, 0, 0] 记为 |φ>,\n",
    "        2. 通过拟设（例如一组Givens Rotation），态演化为 U(θ)|φ>, U(θ)对应某个拟设，记U(θ)|φ> = |Ψ(θ)>\n",
    "        3. 计算和哈密顿量间的期望：<Ψ(θ)| H |Ψ(θ)>\n",
    "        \n",
    "    \"\"\"\n",
    "    state = getStatevector(circuit) # 获取线路终态\n",
    "    size = len(state)\n",
    "    \n",
    "    right = state.reshape(size, 1)\n",
    "    left = Dag(right)\n",
    "    \n",
    "    # 计算 <Ψ(θ)| H |Ψ(θ)>\n",
    "    return (left @ Hami @ right)[0, 0].real"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "423c7f49",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "expval result:  -1.1248453246088717\n"
     ]
    }
   ],
   "source": [
    "# test - expval\n",
    "\n",
    "circuit = get_full_circuit(get_givens_circuit, [0.1, 0.2, 0.3])\n",
    "\n",
    "print('expval result: ', expval(Hami, circuit))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "b2e228be",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot(energies, color):\n",
    "    \"\"\"\n",
    "        绘制训练结果和经典计算结果的比较\n",
    "        \n",
    "    \"\"\"\n",
    "    fig = plt.figure()\n",
    "    fig.set_figheight(5)\n",
    "    fig.set_figwidth(10)\n",
    "\n",
    "    # 该经典结果数值是使用pyscf计算的，基于Full CI法\n",
    "    # Question 3：有必要装下pyscf，用pyscf跑下结果是否如下：\n",
    "    E_fci = -1.136189454088\n",
    "\n",
    "    n = len(energies)\n",
    "    plt.plot(range(n), energies, \"o\", ls=\"dashed\", color=color)\n",
    "    plt.plot(range(n), np.full(n, E_fci), color=\"#FF6666\")\n",
    "    plt.xlabel(\"Optimization step\", fontsize=13)\n",
    "    plt.ylabel(\"Energy (FCI)\", fontsize=13)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd70f9d1",
   "metadata": {},
   "source": [
    "### - Train VQE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "6b24282e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculate_grad(Hami, ansatz, params):\n",
    "    \"\"\"\n",
    "        基于参数偏移计算变分量子线路的梯度\n",
    "        \n",
    "        :param ansatz: 同get_full_circuit中，即ansatz(params)返回拟设线路\n",
    "        \n",
    "        参数偏移法：grad = [ f(θ + π/2) - f(θ - π/2) ] / 2\n",
    "        \n",
    "    \"\"\"\n",
    "    grads = []\n",
    "    \n",
    "    for i in range(len(params)):\n",
    "        params[i] += np.pi / 2\n",
    "        a = expval(Hami, get_full_circuit(ansatz, params))\n",
    "        params[i] -= np.pi\n",
    "        b = expval(Hami, get_full_circuit(ansatz, params))\n",
    "        params[i] += np.pi / 2\n",
    "        \n",
    "        grad = (a - b) / 2\n",
    "        grads.append(grad)\n",
    "        \n",
    "    return np.array(grads)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "1c9ced6c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def train_VQE(Hami, ansatz, params, *, epoch=100, lr=0.01, tol=1e-6):\n",
    "    \"\"\"\n",
    "        :param Hami: 分子哈密顿量\n",
    "        :param ansatz: 构建拟设的函数\n",
    "        :param params: 拟设的初始参数，则拟设线路为：ansatz(params)，完整线路为get_full_circuit(ansatz, params)\n",
    "        \n",
    "    \"\"\"\n",
    "    energy = None\n",
    "    energies = []\n",
    "    prev_energy = 9999\n",
    "    \n",
    "    # optimizer hyperparameters\n",
    "    beta_1 = 0.9\n",
    "    beta_2 = 0.999\n",
    "    epsilon = 1e-8\n",
    "    m = v = np.array([0.0 for i in range(len(params))])\n",
    "\n",
    "    for step in range(epoch):\n",
    "        # 1. loss(energy) calculation\n",
    "        circuit = get_full_circuit(ansatz, params)\n",
    "        energy = expval(Hami, circuit)\n",
    "        energies.append(energy)\n",
    "        print(f'Epoch {step + 1}/{epoch}: Energy: {energy}')\n",
    "        \n",
    "        # 2. grad calculation\n",
    "        grad = calculate_grad(Hami, ansatz, params)\n",
    "        \n",
    "        # 3. update parameters\n",
    "        # Adam optimizer 实现参数更新\n",
    "        m = beta_1 * m + (1 - beta_1) * grad\n",
    "        v = beta_2 * v + (1 - beta_2) * (grad ** 2)\n",
    "        m_ = m / (1 - beta_1 ** (step + 1))\n",
    "        v_ = v / (1 - beta_2 ** (step + 1))\n",
    "        params -= lr * m_ / (v_ ** 0.5 + epsilon)\n",
    "        \n",
    "        if  abs(prev_energy - energy) <= tol:\n",
    "            break\n",
    "        prev_energy = energy\n",
    "    \n",
    "    print('------- Fin -------')\n",
    "    print('Final Energy: ', energy)\n",
    "    print('Parameters: ', params)\n",
    "    \n",
    "    return energies, params"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1fa08bd",
   "metadata": {},
   "source": [
    "### 4.1 physically-motivated ansatz (PMA)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a6947612",
   "metadata": {},
   "source": [
    "### - 4.1.1 Givens Rotations "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "34289887",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/100: Energy: -1.1173489099999994\n",
      "Epoch 2/100: Energy: -1.1190968377628445\n",
      "Epoch 3/100: Energy: -1.1207579947974597\n",
      "Epoch 4/100: Energy: -1.1223308427235659\n",
      "Epoch 5/100: Energy: -1.1238141044282868\n",
      "Epoch 6/100: Energy: -1.1251968722343102\n",
      "Epoch 7/100: Energy: -1.1265080282337625\n",
      "Epoch 8/100: Energy: -1.127709584851771\n",
      "Epoch 9/100: Energy: -1.128830850645523\n",
      "Epoch 10/100: Energy: -1.1298637792618902\n",
      "Epoch 11/100: Energy: -1.130799016848608\n",
      "Epoch 12/100: Energy: -1.1316459017248117\n",
      "Epoch 13/100: Energy: -1.1324114094042566\n",
      "Epoch 14/100: Energy: -1.1330919663440135\n",
      "Epoch 15/100: Energy: -1.1336875938076498\n",
      "Epoch 16/100: Energy: -1.1342064246905987\n",
      "Epoch 17/100: Energy: -1.1346543631011987\n",
      "Epoch 18/100: Energy: -1.1350322790936966\n",
      "Epoch 19/100: Energy: -1.1353433071641137\n",
      "Epoch 20/100: Energy: -1.1355956281855957\n",
      "Epoch 21/100: Energy: -1.1357961828270136\n",
      "Epoch 22/100: Energy: -1.1359482619060646\n",
      "Epoch 23/100: Energy: -1.136056240304427\n",
      "Epoch 24/100: Energy: -1.136127989487994\n",
      "Epoch 25/100: Energy: -1.1361706496969084\n",
      "Epoch 26/100: Energy: -1.1361881920114\n",
      "Epoch 27/100: Energy: -1.1361846956243418\n",
      "Epoch 28/100: Energy: -1.1361664148929105\n",
      "Epoch 29/100: Energy: -1.136138949321443\n",
      "Epoch 30/100: Energy: -1.1361052993400387\n",
      "Epoch 31/100: Energy: -1.1360681440776708\n",
      "Epoch 32/100: Energy: -1.1360312497706873\n",
      "Epoch 33/100: Energy: -1.1359975241344322\n",
      "Epoch 34/100: Energy: -1.135968036124736\n",
      "Epoch 35/100: Energy: -1.135943752069902\n",
      "Epoch 36/100: Energy: -1.1359261013964634\n",
      "Epoch 37/100: Energy: -1.1359155038695588\n",
      "Epoch 38/100: Energy: -1.1359113195786974\n",
      "Epoch 39/100: Energy: -1.1359132694222194\n",
      "Epoch 40/100: Energy: -1.1359212847203015\n",
      "Epoch 41/100: Energy: -1.1359343932526682\n",
      "Epoch 42/100: Energy: -1.1359512504496883\n",
      "Epoch 43/100: Energy: -1.1359711457694237\n",
      "Epoch 44/100: Energy: -1.1359934384632882\n",
      "Epoch 45/100: Energy: -1.1360169103880504\n",
      "Epoch 46/100: Energy: -1.1360404819095238\n",
      "Epoch 47/100: Energy: -1.136063645765553\n",
      "Epoch 48/100: Energy: -1.1360858310699224\n",
      "Epoch 49/100: Energy: -1.1361062803006823\n",
      "Epoch 50/100: Energy: -1.136124612363297\n",
      "Epoch 51/100: Energy: -1.1361407269330897\n",
      "Epoch 52/100: Energy: -1.1361543930065143\n",
      "Epoch 53/100: Energy: -1.1361654909001784\n",
      "Epoch 54/100: Energy: -1.136174218536158\n",
      "Epoch 55/100: Energy: -1.1361807483929887\n",
      "Epoch 56/100: Energy: -1.1361851709993995\n",
      "Epoch 57/100: Energy: -1.136187790271503\n",
      "Epoch 58/100: Energy: -1.1361889959633327\n",
      "Epoch 59/100: Energy: -1.1361890135753685\n",
      "------- Fin -------\n",
      "Final Energy:  -1.1361890135753685\n",
      "Parameters:  [ 1.37834905e-04 -3.38682040e-04  2.08187026e-01]\n"
     ]
    }
   ],
   "source": [
    "init_params_Givens = np.array([0.0, 0.0, 0.0])\n",
    "energies_Givens, params_Givens = train_VQE(Hami, get_givens_circuit, init_params_Givens, epoch=100, lr=0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "cfb642a9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(energies_Givens, '#339966')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "8dd0ffbc",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1541.66x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 完整VQE（基于Givens Rotation）线路\n",
    "get_full_circuit(get_givens_circuit, params_Givens).draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe8f0144",
   "metadata": {},
   "source": [
    "### 4.2 hardware heuristic ansatze (HHA)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12fc03ee",
   "metadata": {},
   "source": [
    "### - 4.2.1 QNN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "5394f548",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/300: Energy: 0.1443937767517271\n",
      "Epoch 2/300: Energy: 0.12262062420645757\n",
      "Epoch 3/300: Energy: 0.10050768210260737\n",
      "Epoch 4/300: Energy: 0.07815218641134797\n",
      "Epoch 5/300: Energy: 0.055657556800274906\n",
      "Epoch 6/300: Energy: 0.033131675167913696\n",
      "Epoch 7/300: Energy: 0.010684719710711638\n",
      "Epoch 8/300: Energy: -0.01157339398651231\n",
      "Epoch 9/300: Energy: -0.03353587728851956\n",
      "Epoch 10/300: Energy: -0.05510211709925364\n",
      "Epoch 11/300: Energy: -0.07618075400780613\n",
      "Epoch 12/300: Energy: -0.09669260424120284\n",
      "Epoch 13/300: Energy: -0.11657321614285711\n",
      "Epoch 14/300: Energy: -0.13577484242179477\n",
      "Epoch 15/300: Energy: -0.1542676213508787\n",
      "Epoch 16/300: Energy: -0.17203980056906265\n",
      "Epoch 17/300: Energy: -0.1890969106511571\n",
      "Epoch 18/300: Energy: -0.20545989976699766\n",
      "Epoch 19/300: Energy: -0.2211623618453165\n",
      "Epoch 20/300: Energy: -0.23624710297502388\n",
      "Epoch 21/300: Energy: -0.25076236406893404\n",
      "Epoch 22/300: Energy: -0.2647580322140956\n",
      "Epoch 23/300: Energy: -0.27828213253596135\n",
      "Epoch 24/300: Energy: -0.29137782410887847\n",
      "Epoch 25/300: Energy: -0.30408106052589934\n",
      "Epoch 26/300: Energy: -0.316419033987915\n",
      "Epoch 27/300: Energy: -0.32840949027725236\n",
      "Epoch 28/300: Energy: -0.340060956279459\n",
      "Epoch 29/300: Energy: -0.35137384819922907\n",
      "Epoch 30/300: Energy: -0.3623423381881855\n",
      "Epoch 31/300: Energy: -0.37295677704276653\n",
      "Epoch 32/300: Energy: -0.38320642470199795\n",
      "Epoch 33/300: Energy: -0.39308223531270214\n",
      "Epoch 34/300: Energy: -0.4025794704109982\n",
      "Epoch 35/300: Energy: -0.41169995644140633\n",
      "Epoch 36/300: Energy: -0.420453847837573\n",
      "Epoch 37/300: Energy: -0.42886079714305136\n",
      "Epoch 38/300: Energy: -0.4369504686829368\n",
      "Epoch 39/300: Energy: -0.4447623662379412\n",
      "Epoch 40/300: Energy: -0.4523449836518821\n",
      "Epoch 41/300: Energy: -0.4597543335629956\n",
      "Epoch 42/300: Energy: -0.46705196063937504\n",
      "Epoch 43/300: Energy: -0.47430259165003025\n",
      "Epoch 44/300: Energy: -0.48157160144578937\n",
      "Epoch 45/300: Energy: -0.4889224714121112\n",
      "Epoch 46/300: Energy: -0.49641438634453394\n",
      "Epoch 47/300: Energy: -0.5041000703964182\n",
      "Epoch 48/300: Energy: -0.512023921657618\n",
      "Epoch 49/300: Energy: -0.5202204823996721\n",
      "Epoch 50/300: Energy: -0.5287132812887352\n",
      "Epoch 51/300: Energy: -0.5375140971396863\n",
      "Epoch 52/300: Energy: -0.546622707412532\n",
      "Epoch 53/300: Energy: -0.5560271852146033\n",
      "Epoch 54/300: Energy: -0.5657047869671168\n",
      "Epoch 55/300: Energy: -0.5756234257993249\n",
      "Epoch 56/300: Energy: -0.585743655551439\n",
      "Epoch 57/300: Energy: -0.5960210051137584\n",
      "Epoch 58/300: Energy: -0.6064084173761657\n",
      "Epoch 59/300: Energy: -0.6168584835578095\n",
      "Epoch 60/300: Energy: -0.6273251506908027\n",
      "Epoch 61/300: Energy: -0.6377646454221209\n",
      "Epoch 62/300: Energy: -0.6481355136600295\n",
      "Epoch 63/300: Energy: -0.6583979017803234\n",
      "Epoch 64/300: Energy: -0.6685124363421053\n",
      "Epoch 65/300: Energy: -0.6784392020500725\n",
      "Epoch 66/300: Energy: -0.6881372942736594\n",
      "Epoch 67/300: Energy: -0.6975652226625861\n",
      "Epoch 68/300: Energy: -0.7066821432992083\n",
      "Epoch 69/300: Energy: -0.7154496275216373\n",
      "Epoch 70/300: Energy: -0.7238335479812906\n",
      "Epoch 71/300: Energy: -0.731805713196081\n",
      "Epoch 72/300: Energy: -0.7393450582586101\n",
      "Epoch 73/300: Energy: -0.7464383953246718\n",
      "Epoch 74/300: Energy: -0.753080846460958\n",
      "Epoch 75/300: Energy: -0.7592760878453405\n",
      "Epoch 76/300: Energy: -0.7650364600234445\n",
      "Epoch 77/300: Energy: -0.7703829064832939\n",
      "Epoch 78/300: Energy: -0.7753446424134167\n",
      "Epoch 79/300: Energy: -0.7799584475342238\n",
      "Epoch 80/300: Energy: -0.7842675194888072\n",
      "Epoch 81/300: Energy: -0.7883199050939833\n",
      "Epoch 82/300: Energy: -0.7921666253595875\n",
      "Epoch 83/300: Energy: -0.7958596962601945\n",
      "Epoch 84/300: Energy: -0.7994502869278501\n",
      "Epoch 85/300: Energy: -0.8029872298181012\n",
      "Epoch 86/300: Energy: -0.8065160112777419\n",
      "Epoch 87/300: Energy: -0.8100782594961597\n",
      "Epoch 88/300: Energy: -0.8137116505492887\n",
      "Epoch 89/300: Energy: -0.8174500988557727\n",
      "Epoch 90/300: Energy: -0.821324090592729\n",
      "Epoch 91/300: Energy: -0.825361045426356\n",
      "Epoch 92/300: Energy: -0.8295856349232341\n",
      "Epoch 93/300: Energy: -0.8340200287395214\n",
      "Epoch 94/300: Energy: -0.8386840713975003\n",
      "Epoch 95/300: Energy: -0.8435954088103684\n",
      "Epoch 96/300: Energy: -0.8487695857759507\n",
      "Epoch 97/300: Energy: -0.854220128051282\n",
      "Epoch 98/300: Energy: -0.8599586112343645\n",
      "Epoch 99/300: Energy: -0.8659947085599347\n",
      "Epoch 100/300: Energy: -0.8723362037642831\n",
      "Epoch 101/300: Energy: -0.8789889539662705\n",
      "Epoch 102/300: Energy: -0.8859567899863335\n",
      "Epoch 103/300: Energy: -0.8932413459934933\n",
      "Epoch 104/300: Energy: -0.9008418153487854\n",
      "Epoch 105/300: Energy: -0.9087546341475625\n",
      "Epoch 106/300: Energy: -0.9169730980654351\n",
      "Epoch 107/300: Energy: -0.925486921976781\n",
      "Epoch 108/300: Energy: -0.9342817559704201\n",
      "Epoch 109/300: Energy: -0.943338676397145\n",
      "Epoch 110/300: Energy: -0.9526336769077948\n",
      "Epoch 111/300: Energy: -0.9621371923294602\n",
      "Epoch 112/300: Energy: -0.9718136975989218\n",
      "Epoch 113/300: Energy: -0.9816214342304469\n",
      "Epoch 114/300: Energy: -0.9915123266102214\n",
      "Epoch 115/300: Energy: -1.0014321575452658\n",
      "Epoch 116/300: Energy: -1.0113210738224543\n",
      "Epoch 117/300: Energy: -1.0211144843982654\n",
      "Epoch 118/300: Energy: -1.0307443928671367\n",
      "Epoch 119/300: Energy: -1.0401411701391516\n",
      "Epoch 120/300: Energy: -1.0492357236639176\n",
      "Epoch 121/300: Energy: -1.0579619607007664\n",
      "Epoch 122/300: Energy: -1.0662593836464678\n",
      "Epoch 123/300: Energy: -1.0740756068634136\n",
      "Epoch 124/300: Energy: -1.0813685591282074\n",
      "Epoch 125/300: Energy: -1.0881081436564823\n",
      "Epoch 126/300: Energy: -1.09427717283295\n",
      "Epoch 127/300: Energy: -1.099871473371823\n",
      "Epoch 128/300: Energy: -1.1048991573852862\n",
      "Epoch 129/300: Energy: -1.1093791575509435\n",
      "Epoch 130/300: Energy: -1.1133392107464715\n",
      "Epoch 131/300: Energy: -1.116813528636152\n",
      "Epoch 132/300: Energy: -1.1198404081212152\n",
      "Epoch 133/300: Energy: -1.1224600107545954\n",
      "Epoch 134/300: Energy: -1.1247124870546665\n",
      "Epoch 135/300: Energy: -1.1266365520787593\n",
      "Epoch 136/300: Energy: -1.1282685460782336\n",
      "Epoch 137/300: Energy: -1.1296419498365404\n",
      "Epoch 138/300: Energy: -1.1307872761359474\n",
      "Epoch 139/300: Energy: -1.1317322305844835\n",
      "Epoch 140/300: Energy: -1.1325020270754913\n",
      "Epoch 141/300: Energy: -1.133119752825874\n",
      "Epoch 142/300: Energy: -1.133606700505206\n",
      "Epoch 143/300: Energy: -1.1339826145341778\n",
      "Epoch 144/300: Energy: -1.134265829213947\n",
      "Epoch 145/300: Energy: -1.1344733028861553\n",
      "Epoch 146/300: Energy: -1.1346205714376822\n",
      "Epoch 147/300: Energy: -1.1347216547905825\n",
      "Epoch 148/300: Energy: -1.134788952050708\n",
      "Epoch 149/300: Energy: -1.1348331565418888\n",
      "Epoch 150/300: Energy: -1.1348632134565717\n",
      "Epoch 151/300: Energy: -1.134886332723628\n",
      "Epoch 152/300: Energy: -1.134908059912719\n",
      "Epoch 153/300: Energy: -1.1349323999353784\n",
      "Epoch 154/300: Energy: -1.1349619827201518\n",
      "Epoch 155/300: Energy: -1.1349982571411714\n",
      "Epoch 156/300: Energy: -1.1350416990293994\n",
      "Epoch 157/300: Energy: -1.1350920205271273\n",
      "Epoch 158/300: Energy: -1.1351483706059309\n",
      "Epoch 159/300: Energy: -1.1352095194819418\n",
      "Epoch 160/300: Energy: -1.1352740222982793\n",
      "Epoch 161/300: Energy: -1.1353403594311644\n",
      "Epoch 162/300: Energy: -1.1354070520402615\n",
      "Epoch 163/300: Energy: -1.1354727522006027\n",
      "Epoch 164/300: Energy: -1.1355363074328384\n",
      "Epoch 165/300: Energy: -1.1355968000002616\n",
      "Epoch 166/300: Energy: -1.1356535621631985\n",
      "Epoch 167/300: Energy: -1.1357061697044917\n",
      "Epoch 168/300: Energy: -1.1357544173303005\n",
      "Epoch 169/300: Energy: -1.1357982807651996\n",
      "Epoch 170/300: Energy: -1.1358378712246109\n",
      "Epoch 171/300: Energy: -1.1358733882340792\n",
      "Epoch 172/300: Energy: -1.135905076353428\n",
      "Epoch 173/300: Energy: -1.1359331902711358\n",
      "Epoch 174/300: Energy: -1.1359579711093892\n",
      "Epoch 175/300: Energy: -1.1359796348744928\n",
      "Epoch 176/300: Energy: -1.1359983721014073\n",
      "Epoch 177/300: Energy: -1.1360143561684108\n",
      "Epoch 178/300: Energy: -1.1360277567275487\n",
      "Epoch 179/300: Energy: -1.1360387543356079\n",
      "Epoch 180/300: Energy: -1.1360475526839735\n",
      "Epoch 181/300: Energy: -1.1360543857040548\n",
      "Epoch 182/300: Energy: -1.1360595180694264\n",
      "Epoch 183/300: Energy: -1.136063238981967\n",
      "Epoch 184/300: Energy: -1.136065850373063\n",
      "Epoch 185/300: Energy: -1.13606765157268\n",
      "Epoch 186/300: Energy: -1.1360689229745686\n",
      "Epoch 187/300: Energy: -1.1360699112208308\n",
      "------- Fin -------\n",
      "Final Energy:  -1.1360699112208308\n",
      "Parameters:  [-3.35109136e+00  1.24177914e+00  3.90824178e-04 -2.74589533e-01\n",
      "  4.97860784e-04 -2.37967762e-02 -3.05725825e+00 -2.96409433e-01\n",
      "  3.14192563e+00  1.33041678e+00 -7.17427937e-05  1.15850240e+00\n",
      " -3.13606404e+00  1.48756765e+00 -7.94408778e-02  1.33084057e+00]\n"
     ]
    }
   ],
   "source": [
    "init_params_QNN = np.random.randn(16)\n",
    "energies_QNN, params_QNN = train_VQE(Hami, get_QNN_circuit, init_params_QNN, epoch=300, lr=0.02)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "28b7b52b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(energies_QNN, '#0099CC')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "84973d3d",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1625.27x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 完整VQE（基于QNN）线路\n",
    "get_full_circuit(get_QNN_circuit, params_QNN).draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8f8188bc",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.8.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}