From 7be2573599d0420032a95ddf6459f533cbd4eb1f Mon Sep 17 00:00:00 2001
From: he-tianshen <jerryhts@163.com>
Date: Mon, 24 Jan 2022 19:44:42 +0800
Subject: [PATCH 1/2] 6_hw08624896/

---
 paper_recurrence/6_hw08624896/main.ipynb      | 989 ++++++++++++++++++
 paper_recurrence/6_hw08624896/readme.md       |  15 +
 .../6_hw08624896/src/accvqeexact.py           |  55 +
 .../6_hw08624896/src/layer recursive.py       | 111 ++
 .../6_hw08624896/src/qubit recursive.py       | 219 ++++
 .../6_hw08624896/src/random initialization.py | 105 ++
 paper_recurrence/6_hw08624896/src/readme.md   |   1 +
 7 files changed, 1495 insertions(+)
 create mode 100644 paper_recurrence/6_hw08624896/main.ipynb
 create mode 100644 paper_recurrence/6_hw08624896/readme.md
 create mode 100644 paper_recurrence/6_hw08624896/src/accvqeexact.py
 create mode 100644 paper_recurrence/6_hw08624896/src/layer recursive.py
 create mode 100644 paper_recurrence/6_hw08624896/src/qubit recursive.py
 create mode 100644 paper_recurrence/6_hw08624896/src/random initialization.py
 create mode 100644 paper_recurrence/6_hw08624896/src/readme.md

diff --git a/paper_recurrence/6_hw08624896/main.ipynb b/paper_recurrence/6_hw08624896/main.ipynb
new file mode 100644
index 000000000..45d8c6c0f
--- /dev/null
+++ b/paper_recurrence/6_hw08624896/main.ipynb
@@ -0,0 +1,989 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Accelerated variational algorithms for digital quantum simulation of the many-body ground states\n",
+    "\n",
+    "## 项目介绍"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "论文的目标是在数字量子模拟器（Digital Quantum Simulator, DQS）上制备一维链海森堡模型的基态（开放边界条件）$$H=J \\sum_{i=1}^{N-1} \\sigma^{i} \\cdot \\sigma^{i+1}$$\n",
+    "其中$J$为exchange coupling，是大于0的实数，$\\sigma^{i}=\\left(\\sigma_{x}^{i}, \\sigma_{y}^{i}, \\sigma_{z}^{i}\\right)$是第$i$个qubit上的Pauli算符组成的向量。\n",
+    "\n",
+    "### 一、绝热演化\n",
+    "针对此目标，论文首先提出了使用Suzuki-Trotter expansion来模拟绝热演化的方案，即进行如下的绝热演化$$H_{a d}(t)=H_{o d d}+\\frac{t}{T_{\\max }} H_{e v e n}$$\n",
+    "其中$H_{o d d}=J \\sum_{\\text {odd } i} \\sigma^{i} \\cdot \\sigma^{i+1}$，$H_{\\text {even }}=J \\sum_{\\text {even } i} \\sigma^{i} \\cdot \\sigma^{i+1}$，$0 \\leq t \\leq T_{\\max }$，$H_{o d d}$的基态是容易制备的$$|\\Psi(0)\\rangle=\\left|\\psi^{-}\\right\\rangle \\otimes \\cdots \\otimes\\left|\\psi^{-}\\right\\rangle$$其中$\\left|\\psi^{-}\\right\\rangle=(|01\\rangle-|10\\rangle) / \\sqrt{2}$\n",
+    "\n",
+    "当取$T_{\\max } \\sim N^{2}$时，就能满足绝热定理的条件，并且$t=T_{\\max }$时$H_{a d}\\left(T_{\\max }\\right)=H$\n",
+    "\n",
+    "实现绝热演化的线路图见论文Fig.1\n",
+    "\n",
+    "### 二、VQE\n",
+    "实现绝热演化的线路深度过高，考虑使用VQE，以在保障精度的同时降低线路深度。绝热演化的严格性由物理定律保证，因此在设计VQE所使用的参数化量子线路（Parameterized Quantum Circuit, PQC）时，论文借鉴了绝热演化的线路结构。VQE的线路图见论文Fig.3\n",
+    "\n",
+    "在此基础上，论文对如何缩短VQE参数更新的经典优化循环次数作了进一步的讨论，提出了3种策略。\n",
+    "#### 1. 随机初始化\n",
+    "#### 2. 比特数递归\n",
+    "#### 3. 层数递归\n",
+    "策略的具体内容在复现过程中详细介绍。\n",
+    "\n",
+    "### 三、其他讨论\n",
+    "论文最后讨论了以下四点：\n",
+    "#### 1. 线路的扩展性\n",
+    "相同的线路可以扩展到各向异性的海森堡模型，只需要门参数做一些微调，不用引入新的参数。\n",
+    "#### 2. 镜面对称性的作用\n",
+    "文中使用的PQC线路的结构中，每一层的PQC最后都有一层所有qubit上的相位门。由于论文中考虑的哈密顿量具有镜面对称性，在前文的讨论中，这一层相位门的参数也被强加了这一对称性。但作者发现，倘若取消相位门的镜面对称性，VQE反而能以更快的速度收敛。\n",
+    "#### 3. VQE线路设计思路\n",
+    "作者提出，VQE线路借鉴绝热演化的Suzuki-Trotter expansion这一思路是普适的。\n",
+    "#### 4. 退相干的影响\n",
+    "将线路固定为某一次VQE的最终参数，引入双量子比特门的随机的噪声扰动或失相，考察对保真度的影响。"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 复现过程"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "首先，安装、导入依赖包。"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "!pip install https://hiq.huaweicloud.com/download/mindquantum/newest/linux/mindquantum-master-cp37-cp37m-linux_x86_64.whl -i https://pypi.tuna.tsinghua.edu.cn/simple"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "from mindquantum import Circuit, X, H, RZ, RY, PhaseShift, Hamiltonian, Simulator, QubitOperator, Hamiltonian, MQAnsatzOnlyLayer\n",
+    "import mindspore as ms\n",
+    "from mindspore.common.parameter import Parameter\n",
+    "import mindspore.context as context\n",
+    "\n",
+    "context.set_context(mode=context.PYNATIVE_MODE, device_target=\"CPU\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "参考Fig.1a，自定义一个单参数双量子比特门N（论文中的$\\mathcal{N}(\\theta)$），这个门使用参数f'p{count}'，作用于 i 和 i + 1 号量子比特（也即第$i+1$和第$i+2$个量子比特）。"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def N(count, i):\n",
+    "    temp = Circuit()\n",
+    "    temp += RZ(np.pi / 2).on(i + 1)\n",
+    "    temp += X.on(i, i + 1)\n",
+    "    temp += RZ({f'p{count}' : 2}).on(i)\n",
+    "    temp += RZ(-np.pi / 2).on(i)\n",
+    "    temp += RY(np.pi / 2).on(i + 1)\n",
+    "    temp += RY({f'p{count}' : -2}).on(i + 1)\n",
+    "    temp += X.on(i + 1, i)\n",
+    "    temp += RY({f'p{count}' : 2}).on(i + 1)\n",
+    "    temp += RY(-np.pi / 2).on(i + 1)\n",
+    "    temp += X.on(i, i + 1)\n",
+    "    temp += RZ(-np.pi / 2).on(i)\n",
+    "    return temp"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Strategy 1: random initialization."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "定义模型的量子比特数num（论文中的$N$），和VQE线路的层数m（论文中的$M_{VQE}$）。根据论文Table.1，$N$取$4,8,10$时，若要达到$F=0.99$保真度，$M_{VQE}$应分别取$2,3,3$. 由于本文考虑哈密顿量的镜面对称性，因此要求$N$必须是偶数。"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "4 2\n"
+     ]
+    }
+   ],
+   "source": [
+    "NMtable = {4:2, 8:3, 10:3, 16:5, 20:6}\n",
+    "num = 4\n",
+    "m = NMtable[num]\n",
+    "assert num % 2 == 0\n",
+    "print(num, m)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "制备初态$|\\Psi(0)\\rangle=\\left|\\psi^{-}\\right\\rangle \\otimes \\cdots \\otimes\\left|\\psi^{-}\\right\\rangle$，其中$\\left|\\psi^{-}\\right\\rangle=(|01\\rangle-|10\\rangle) / \\sqrt{2}$，这个量子态是$H_{o d d}=J \\sum_{\\operatorname{odd} i} \\sigma^{i} \\cdot \\sigma^{i+1}$的基态，如前文所述，是绝热演化的起点，因此也是参数化量子线路的起点。"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "q0: ──X────H────●──\n",
+      "                │\n",
+      "q1: ──X─────────X──\n",
+      "\n",
+      "q2: ──X────H────●──\n",
+      "                │\n",
+      "q3: ──X─────────X──\n",
+      "=======Circuit Summary=======\n",
+      "|Total number of gates  : 8.|\n",
+      "|Parameter gates        : 0.|\n",
+      "|with 0 parameters are  : . |\n",
+      "|Number qubit of circuit: 4 |\n",
+      "=============================\n"
+     ]
+    }
+   ],
+   "source": [
+    "encoder = Circuit()\n",
+    "for i in range(0, num, 2):\n",
+    "    encoder += X.on(i)\n",
+    "    encoder += X.on(i + 1)\n",
+    "    encoder += H.on(i)\n",
+    "    encoder += X.on(i + 1, i)\n",
+    "    \n",
+    "print(encoder)\n",
+    "encoder.summary()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "参考Fig.3a构建ansatz线路，由于encoder中不含有参数，最后直接将其与ansatz合并。"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "q0: ──X────H────●───────────────X────RZ(2*p1)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)─────PS(p4)──────────────────────────────────────────────────────────────────────────────────────────────────────────X────────RZ(2*p6)─────RZ(-π/2)───────●───────────────────────────────────X───────RZ(-π/2)─────PS(p9)─────────────────────────────────────────────────────────────────────────\n",
+      "                │               │                             │                            │                                                                                                                                 │                                    │                                   │\n",
+      "q1: ──X─────────X────RZ(π/2)────●────RY(π/2)─────RY(-2*p1)────X────RY(2*p1)────RY(-π/2)────●───────────────────────────X────RZ(2*p3)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)────PS(p5)────RZ(π/2)─────────●────────RY(π/2)─────RY(-2*p6)───────X────────RY(2*p6)────RY(-π/2)───────●──────────X────────RZ(2*p8)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)────PS(p10)──\n",
+      "                                                                                                                       │                             │                            │                                                                                                                              │                                 │                            │\n",
+      "q2: ──X────H────●───────────────X────RZ(2*p2)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)────RZ(π/2)────●────RY(π/2)─────RY(-2*p3)────X────RY(2*p3)────RY(-π/2)────●────PS(-p5)───────X───────RZ(2*p7)─────RZ(-π/2)───────●────────────────────────────────────X────────RZ(-π/2)────RZ(π/2)───────●────────RY(π/2)─────RY(-2*p8)────X────RY(2*p8)────RY(-π/2)────●────PS(-p10)─────────────\n",
+      "                │               │                             │                            │                                                                                                         │                                   │                                    │\n",
+      "q3: ──X─────────X────RZ(π/2)────●────RY(π/2)─────RY(-2*p2)────X────RY(2*p2)────RY(-π/2)────●────PS(-p4)─────RZ(π/2)──────────────────────────────────────────────────────────────────────────────────●───────RY(π/2)─────RY(-2*p7)───────X─────────RY(2*p7)────RY(-π/2)───────●────────PS(-p9)────────────────────────────────────────────────────────────────────────────────────────────────────────────\n",
+      "==========================Circuit Summary==========================\n",
+      "|Total number of gates  : 82.                                     |\n",
+      "|Parameter gates        : 26.                                     |\n",
+      "|with 10 parameters are : p1, p2, p3, p4, p5, p6, p7, p8, p9, p10.|\n",
+      "|Number qubit of circuit: 4                                       |\n",
+      "===================================================================\n"
+     ]
+    }
+   ],
+   "source": [
+    "ansatz = Circuit()\n",
+    "count = 1\n",
+    "\n",
+    "for j in range(m):\n",
+    "    for i in range(0, num - 1, 2):\n",
+    "        ansatz += N(count, i)\n",
+    "        count += 1\n",
+    "    for i in range(1, num - 1, 2):\n",
+    "        ansatz += N(count, i)\n",
+    "        count += 1\n",
+    "    for i in range(0, num // 2):\n",
+    "        ansatz += PhaseShift('p%d' % count).on(i)\n",
+    "        ansatz += PhaseShift({'p%d' % count : -1}).on(num - i - 1)\n",
+    "        count += 1\n",
+    "\n",
+    "ansatz = encoder + ansatz\n",
+    "print(ansatz)\n",
+    "ansatz.summary()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "参考式(1)，构建哈密顿量$H=J \\sum_{i=1}^{N-1} \\sigma^{i} \\cdot \\sigma^{i+1}$，这里定义$J=1$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1 [X0 X1] +\n",
+      "1 [Y0 Y1] +\n",
+      "1 [Z0 Z1] +\n",
+      "1 [X1 X2] +\n",
+      "1 [Y1 Y2] +\n",
+      "1 [Z1 Z2] +\n",
+      "1 [X2 X3] +\n",
+      "1 [Y2 Y3] +\n",
+      "1 [Z2 Z3] \n"
+     ]
+    }
+   ],
+   "source": [
+    "J = 1\n",
+    "ham = QubitOperator('')\n",
+    "for i in range(num - 1):\n",
+    "    ham += QubitOperator('X%d X%d' % (i, i + 1), J)\n",
+    "    ham += QubitOperator('Y%d Y%d' % (i, i + 1), J)\n",
+    "    ham += QubitOperator('Z%d Z%d' % (i, i + 1), J)\n",
+    "ham = Hamiltonian(ham - QubitOperator(''))\n",
+    "\n",
+    "print(ham)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "构建参数化量子线路，对参数进行随机初始化（标准正态分布）。"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Initial energy:  -0.0997337326407433\n"
+     ]
+    }
+   ],
+   "source": [
+    "val = np.random.randn(count - 1)\n",
+    "\n",
+    "sim = Simulator('projectq', num)\n",
+    "pqc = sim.get_expectation_with_grad(ham, ansatz)\n",
+    "pqcnet = MQAnsatzOnlyLayer(pqc)\n",
+    "pqcnet.weight = Parameter(ms.Tensor(val, pqcnet.weight.dtype))\n",
+    "\n",
+    "initial_energy = pqcnet()\n",
+    "print(\"Initial energy: %20.16f\" % (initial_energy.asnumpy()))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "使用Adam算法进行梯度优化，各参数取值如论文所述。当相邻两步的能量差小于阈值时（这里设定为1e-8），判定为收敛，更新结束。"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "eps:  1e-08\n",
+      "Step   0 energy  -0.0997337326407433\n",
+      "Step 100 energy  -5.9991140365600586\n",
+      "Step 200 energy  -6.3746271133422852\n",
+      "Optimization completed at step 285\n",
+      "Optimized energy:  -6.4641013145446777\n",
+      "Optimized amplitudes: \n",
+      " [ 0.4028975   1.7767195   0.78539985 -0.44342345  0.44359204 -0.23663777\n",
+      "  0.5444191  -0.54652977 -1.57108    -1.5708411 ]\n"
+     ]
+    }
+   ],
+   "source": [
+    "optimizer = ms.nn.Adam(pqcnet.trainable_params(), learning_rate = 0.01, beta1 = 0.9, beta2 = 0.999, eps = 1e-8)\n",
+    "train_pqcnet = ms.nn.TrainOneStepCell(pqcnet, optimizer)\n",
+    "\n",
+    "eps = 1.e-8\n",
+    "print(\"eps: \", eps)\n",
+    "energy_diff = eps * 1000\n",
+    "energy_last = initial_energy.asnumpy() + energy_diff\n",
+    "iter_idx = 0\n",
+    "while (abs(energy_diff) > eps):\n",
+    "    energy_i = train_pqcnet().asnumpy()\n",
+    "    if iter_idx % 100 == 0:\n",
+    "        print(\"Step %3d energy %20.16f\" % (iter_idx, float(energy_i)))\n",
+    "    energy_diff = energy_last - energy_i\n",
+    "    energy_last = energy_i\n",
+    "    iter_idx += 1\n",
+    "\n",
+    "print(\"Optimization completed at step %3d\" % (iter_idx - 1))\n",
+    "print(\"Optimized energy: %20.16f\" % (energy_i))\n",
+    "print(\"Optimized amplitudes: \\n\", pqcnet.weight.asnumpy())"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "使用accvqeexact.py求解哈密顿量严格对角化的结果，该程序输出一个实数表示基态能量，可以与VQE的结果进行对比。\\\n",
+    "N取4,8,10时，基态能量分别为-6.464101615137754, -13.499730394751591, -17.032140829131546."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Strategy 1完整源代码见src/random initialization.py"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Strategy 2: qubit recursive.\n",
+    "\n",
+    "这个策略先在较小的系统（目标尺寸的一半，可以递归至最小的大于等于4的偶数）上进行VQE，将此步得到的最终参数作为目标系统的VQE线路参数的初猜。在本文档中，为方便进行演示，以前文Strategy 1中尺寸的两倍作为目标尺寸，以前文的参数作为新线路参数的初猜。"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "8 3\n"
+     ]
+    }
+   ],
+   "source": [
+    "num2 = 2 * num\n",
+    "m2 = NMtable[num2]\n",
+    "print(num2, m2)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "构建大系统的ansatz和哈密顿量。"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "q0: ──X────H────●───────────────X────RZ(2*p1)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)─────PS(p8)─────────────────────────────────────────────────────────────────────────────────────────────────────────────X─────────RZ(2*p12)─────RZ(-π/2)────────●────────────────────────────────────X───────RZ(-π/2)─────PS(p19)───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────X─────────RZ(2*p23)─────RZ(-π/2)────────●─────────────────────────────────────X─────────RZ(-π/2)──────PS(p30)───────────────────────────────────────────────────────────────────────────────────────────────────────────────────\n",
+      "                │               │                             │                            │                                                                                                                                    │                                       │                                    │                                                                                                                                                                      │                                       │                                     │\n",
+      "q1: ──X─────────X────RZ(π/2)────●────RY(π/2)─────RY(-2*p1)────X────RY(2*p1)────RY(-π/2)────●───────────────────────────X────RZ(2*p5)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)─────PS(p9)──────RZ(π/2)─────────●──────────RY(π/2)─────RY(-2*p12)───────X────────RY(2*p12)────RY(-π/2)───────●────────────────────────────────────X─────────RZ(2*p16)─────RZ(-π/2)────────●────────────────────────────────────X─────────RZ(-π/2)─────PS(p20)───────RZ(π/2)─────────●──────────RY(π/2)─────RY(-2*p23)───────X────────RY(2*p23)────RY(-π/2)────────●───────────────────────────────────────X─────────RZ(2*p27)─────RZ(-π/2)────────●────────────────────────────────────X───────RZ(-π/2)────PS(p31)──\n",
+      "                                                                                                                       │                             │                            │                                                                                                                                                               │                                       │                                    │                                                                                                                                                                          │                                       │                                    │\n",
+      "q2: ──X────H────●───────────────X────RZ(2*p2)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)────RZ(π/2)────●────RY(π/2)─────RY(-2*p5)────X────RY(2*p5)────RY(-π/2)────●────PS(p10)──────────────────────────────────X─────────RZ(2*p13)─────RZ(-π/2)────────●────────────────────────────────────X───────RZ(-π/2)─────RZ(π/2)─────────●──────────RY(π/2)─────RY(-2*p16)───────X────────RY(2*p16)────RY(-π/2)───────●─────────PS(p21)────────────────────────────────────X─────────RZ(2*p24)─────RZ(-π/2)────────●─────────────────────────────────────X─────────RZ(-π/2)──────RZ(π/2)─────────●──────────RY(π/2)─────RY(-2*p27)───────X────────RY(2*p27)────RY(-π/2)───────●───────PS(p32)──────────────\n",
+      "                │               │                             │                            │                                                                                                                                    │                                       │                                    │                                                                                                                                                                      │                                       │                                     │\n",
+      "q3: ──X─────────X────RZ(π/2)────●────RY(π/2)─────RY(-2*p2)────X────RY(2*p2)────RY(-π/2)────●───────────────────────────X────RZ(2*p6)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)────PS(p11)──────RZ(π/2)─────────●──────────RY(π/2)─────RY(-2*p13)───────X────────RY(2*p13)────RY(-π/2)───────●────────────────────────────────────X─────────RZ(2*p17)─────RZ(-π/2)────────●────────────────────────────────────X─────────RZ(-π/2)─────PS(p22)───────RZ(π/2)─────────●──────────RY(π/2)─────RY(-2*p24)───────X────────RY(2*p24)────RY(-π/2)────────●────────────X─────────RZ(2*p28)─────RZ(-π/2)─────────●──────────────────────────────────────X────────RZ(-π/2)────PS(p33)─────────────────────────\n",
+      "                                                                                                                       │                             │                            │                                                                                                                                                               │                                       │                                    │                                                                                                                                               │                                        │                                      │\n",
+      "q4: ──X────H────●───────────────X────RZ(2*p3)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)────RZ(π/2)────●────RY(π/2)─────RY(-2*p6)────X────RY(2*p6)────RY(-π/2)────●────PS(-p11)─────────────────────────────────X─────────RZ(2*p14)─────RZ(-π/2)────────●────────────────────────────────────X───────RZ(-π/2)─────RZ(π/2)─────────●──────────RY(π/2)─────RY(-2*p17)───────X────────RY(2*p17)────RY(-π/2)───────●─────────PS(-p22)────────X─────────RZ(2*p25)─────RZ(-π/2)─────────●──────────────────────────────────────X────────RZ(-π/2)─────RZ(π/2)─────────●──────────RY(π/2)─────RY(-2*p28)────────X────────RY(2*p28)─────RY(-π/2)────────●────────PS(-p33)────────────────────────────────────\n",
+      "                │               │                             │                            │                                                                                                                                    │                                       │                                    │                                                                                                                                           │                                        │                                      │\n",
+      "q5: ──X─────────X────RZ(π/2)────●────RY(π/2)─────RY(-2*p3)────X────RY(2*p3)────RY(-π/2)────●───────────────────────────X────RZ(2*p7)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)────PS(-p10)─────RZ(π/2)─────────●──────────RY(π/2)─────RY(-2*p14)───────X────────RY(2*p14)────RY(-π/2)───────●──────────X────────RZ(2*p18)─────RZ(-π/2)─────────●──────────────────────────────────────X────────RZ(-π/2)────PS(-p21)─────RZ(π/2)─────────●──────────RY(π/2)─────RY(-2*p25)────────X────────RY(2*p25)─────RY(-π/2)────────●───────────X────────RZ(2*p29)─────RZ(-π/2)─────────●───────────────────────────────────────X─────────RZ(-π/2)─────PS(-p32)────────────────────────────────────────────────\n",
+      "                                                                                                                       │                             │                            │                                                                                                                                     │                                       │                                      │                                                                                                                                             │                                       │                                       │\n",
+      "q6: ──X────H────●───────────────X────RZ(2*p4)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)────RZ(π/2)────●────RY(π/2)─────RY(-2*p7)────X────RY(2*p7)────RY(-π/2)────●────PS(-p9)────────X────────RZ(2*p15)─────RZ(-π/2)─────────●──────────────────────────────────────X────────RZ(-π/2)────RZ(π/2)───────●─────────RY(π/2)─────RY(-2*p18)────────X────────RY(2*p18)─────RY(-π/2)────────●────────PS(-p20)───────X────────RZ(2*p26)─────RZ(-π/2)─────────●───────────────────────────────────────X─────────RZ(-π/2)─────RZ(π/2)────────●─────────RY(π/2)─────RY(-2*p29)────────X────────RY(2*p29)──────RY(-π/2)────────●─────────PS(-p31)─────────────────────────────────────────────────────────────\n",
+      "                │               │                             │                            │                                                                                                          │                                       │                                      │                                                                                                                                         │                                       │                                       │\n",
+      "q7: ──X─────────X────RZ(π/2)────●────RY(π/2)─────RY(-2*p4)────X────RY(2*p4)────RY(-π/2)────●────PS(-p8)─────RZ(π/2)───────────────────────────────────────────────────────────────────────────────────●─────────RY(π/2)─────RY(-2*p15)────────X────────RY(2*p15)─────RY(-π/2)────────●────────PS(-p19)────RZ(π/2)──────────────────────────────────────────────────────────────────────────────────────────────────────────────●─────────RY(π/2)─────RY(-2*p26)────────X────────RY(2*p26)──────RY(-π/2)────────●─────────PS(-p30)───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────\n",
+      "===========================Circuit Summary===========================\n",
+      "|Total number of gates  : 271.                                      |\n",
+      "|Parameter gates        : 87.                                       |\n",
+      "|with 33 parameters are : p1, p2, p3, p4, p5, p6, p7, p8, p9, p10...|\n",
+      "|Number qubit of circuit: 8                                         |\n",
+      "=====================================================================\n",
+      "1 [X0 X1] +\n",
+      "1 [Y0 Y1] +\n",
+      "1 [Z0 Z1] +\n",
+      "1 [X1 X2] +\n",
+      "1 [Y1 Y2] +\n",
+      "1 [Z1 Z2] +\n",
+      "1 [X2 X3] +\n",
+      "1 [Y2 Y3] +\n",
+      "1 [Z2 Z3] +\n",
+      "1 [X3 X4] +\n",
+      "1 [Y3 Y4] +\n",
+      "1 [Z3 Z4] +\n",
+      "1 [X4 X5] +\n",
+      "1 [Y4 Y5] +\n",
+      "1 [Z4 Z5] +\n",
+      "1 [X5 X6] +\n",
+      "1 [Y5 Y6] +\n",
+      "1 [Z5 Z6] +\n",
+      "1 [X6 X7] +\n",
+      "1 [Y6 Y7] +\n",
+      "1 [Z6 Z7] \n"
+     ]
+    }
+   ],
+   "source": [
+    "encoder = Circuit()\n",
+    "for i in range(0, num2, 2):\n",
+    "    encoder += X.on(i)\n",
+    "    encoder += X.on(i + 1)\n",
+    "    encoder += H.on(i)\n",
+    "    encoder += X.on(i + 1, i)\n",
+    "\n",
+    "ansatz = Circuit()\n",
+    "count = 1\n",
+    "\n",
+    "for j in range(m2):\n",
+    "    for i in range(0, num2 - 1, 2):\n",
+    "        ansatz += N(count, i)\n",
+    "        count += 1\n",
+    "    for i in range(1, num2 - 1, 2):\n",
+    "        ansatz += N(count, i)\n",
+    "        count += 1\n",
+    "    for i in range(0, num2 // 2):\n",
+    "        ansatz += PhaseShift('p%d' % count).on(i)\n",
+    "        ansatz += PhaseShift({'p%d' % count : -1}).on(num2 - i - 1)\n",
+    "        count += 1\n",
+    "\n",
+    "ansatz = encoder + ansatz\n",
+    "print(ansatz)\n",
+    "ansatz.summary()\n",
+    "\n",
+    "J = 1\n",
+    "ham = QubitOperator('')\n",
+    "for i in range(num2 - 1):\n",
+    "    ham += QubitOperator('X%d X%d' % (i, i + 1), J)\n",
+    "    ham += QubitOperator('Y%d Y%d' % (i, i + 1), J)\n",
+    "    ham += QubitOperator('Z%d Z%d' % (i, i + 1), J)\n",
+    "ham = Hamiltonian(ham - QubitOperator(''))\n",
+    "\n",
+    "print(ham)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "调取Strategy 1得到的参数，作为新的线路参数的初猜。论文中指出，如果新的线路的层数大于先前的线路，那么旧参数只应用于原先的层数，多出的层数仍进行随机初始化。此外，对于连接上下两半的一个N门的参数也进行随机初始化。"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "5 11\n",
+      "old parameters:\n",
+      "p1 0.4028975\n",
+      "p2 1.7767195\n",
+      "p3 0.78539985\n",
+      "p4 -0.44342345\n",
+      "p5 0.44359204\n",
+      "p6 -0.23663777\n",
+      "p7 0.5444191\n",
+      "p8 -0.54652977\n",
+      "p9 -1.57108\n",
+      "p10 -1.5708411\n",
+      "new parameters:\n",
+      "p1 0.40289750695228577\n",
+      "p2 1.7767194509506226\n",
+      "p3 0.40289750695228577\n",
+      "p4 1.7767194509506226\n",
+      "p5 0.785399854183197\n",
+      "p6 -0.7981621709703667\n",
+      "p7 0.785399854183197\n",
+      "p8 -0.44342344999313354\n",
+      "p9 0.44359204173088074\n",
+      "p10 -0.44359204173088074\n",
+      "p11 0.44342344999313354\n",
+      "p12 -0.23663777112960815\n",
+      "p13 0.5444191098213196\n",
+      "p14 -0.23663777112960815\n",
+      "p15 0.5444191098213196\n",
+      "p16 -0.5465297698974609\n",
+      "p17 -0.34117606704058145\n",
+      "p18 -0.5465297698974609\n",
+      "p19 -1.571079969406128\n",
+      "p20 -1.5708410739898682\n",
+      "p21 1.5708410739898682\n",
+      "p22 1.571079969406128\n",
+      "p23 0.17239491160199313\n",
+      "p24 -0.914783228142229\n",
+      "p25 -0.590292046100649\n",
+      "p26 0.5591994325996155\n",
+      "p27 1.4652410773726405\n",
+      "p28 -0.40170510817277555\n",
+      "p29 1.2007430289046384\n",
+      "p30 -1.0807505299102804\n",
+      "p31 -0.08635083542922928\n",
+      "p32 0.6355362236237798\n",
+      "p33 -0.20765632405686124\n"
+     ]
+    }
+   ],
+   "source": [
+    "pre = pqcnet.weight.asnumpy()\n",
+    "half = num // 2\n",
+    "L1 = half * 3 - 1\n",
+    "L2 = num * 3 - 1\n",
+    "print(L1, L2)\n",
+    "val = np.random.randn(L2 * m2)\n",
+    "for j in range(m):\n",
+    "    for i in range(half):\n",
+    "        val[i + j * L2] = pre[i + j * L1]\n",
+    "        val[i + j * L2 + half] = pre[i + j * L1]\n",
+    "for j in range(m):\n",
+    "    for i in range(half - 1):\n",
+    "        val[i + j * L2 + num] = pre[i + j * L1 + half]\n",
+    "        val[i + j * L2 + num + half] = pre[i + j * L1 + half]\n",
+    "for j in range(m):\n",
+    "    for i in range(half):\n",
+    "        val[i + j * L2 + num2 - 1] = pre[i + j * L1 + num - 1]\n",
+    "        val[num - i - 2 + j * L2 + num2] = -pre[i + j * L1 + num - 1]\n",
+    "\n",
+    "print('old parameters:')\n",
+    "for i in range(L1 * m):\n",
+    "    print(f'p{i + 1}', pre[i])\n",
+    "print('new parameters:')\n",
+    "for i in range(L2 * m2):\n",
+    "    print(f'p{i + 1}', val[i])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "在新的PQC上使用Adam算法进行梯度优化。"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Initial energy:  -0.7443327307701111\n",
+      "eps:  1e-08\n",
+      "Step   0 energy  -0.7443327307701111\n",
+      "Step 100 energy -12.1580400466918945\n",
+      "Step 200 energy -12.3319196701049805\n",
+      "Step 300 energy -12.5329952239990234\n",
+      "Step 400 energy -12.8005189895629883\n",
+      "Step 500 energy -13.1239566802978516\n",
+      "Step 600 energy -13.2102670669555664\n",
+      "Step 700 energy -13.2432384490966797\n",
+      "Step 800 energy -13.2575006484985352\n",
+      "Step 900 energy -13.2690734863281250\n",
+      "Step 1000 energy -13.2739782333374023\n",
+      "Step 1100 energy -13.2763023376464844\n",
+      "Step 1200 energy -13.2777204513549805\n",
+      "Step 1300 energy -13.2787160873413086\n",
+      "Step 1400 energy -13.2794694900512695\n",
+      "Step 1500 energy -13.2800588607788086\n",
+      "Step 1600 energy -13.2805252075195312\n",
+      "Step 1700 energy -13.2808961868286133\n",
+      "Step 1800 energy -13.2811956405639648\n",
+      "Step 1900 energy -13.2814435958862305\n",
+      "Step 2000 energy -13.2816562652587891\n",
+      "Step 2100 energy -13.2818431854248047\n",
+      "Step 2200 energy -13.2820081710815430\n",
+      "Step 2300 energy -13.2821502685546875\n",
+      "Step 2400 energy -13.2822694778442383\n",
+      "Optimization completed at step 2492\n",
+      "Optimized energy: -13.2823591232299805\n",
+      "Optimized amplitudes: \n",
+      " [ 0.4028975   1.7767195   0.4028975   1.7767195   0.12742256 -1.1627834\n",
+      "  0.8583692   1.5402898   1.4963658   1.5271162   1.569726   -1.1491092\n",
+      "  0.46598285 -0.00386392  0.38710395  0.00827281  0.11402654 -0.52839077\n",
+      " -1.9126333  -2.0897553   1.5882233   1.5663463   0.06086528 -0.5167987\n",
+      " -0.05763365  0.01347558  1.5739275  -0.30428478  1.5782783  -2.7471545\n",
+      "  0.5736982   0.0340413  -0.01536573]\n"
+     ]
+    }
+   ],
+   "source": [
+    "sim = Simulator('projectq', num2)\n",
+    "pqc = sim.get_expectation_with_grad(ham, ansatz)\n",
+    "pqcnet = MQAnsatzOnlyLayer(pqc)\n",
+    "pqcnet.weight = Parameter(ms.Tensor(val, pqcnet.weight.dtype))\n",
+    "\n",
+    "initial_energy = pqcnet()\n",
+    "print(\"Initial energy: %20.16f\" % (initial_energy.asnumpy()))\n",
+    "\n",
+    "optimizer = ms.nn.Adam(pqcnet.trainable_params(), learning_rate = 0.01, beta1 = 0.9, beta2 = 0.999, eps = 1e-8)\n",
+    "train_pqcnet = ms.nn.TrainOneStepCell(pqcnet, optimizer)\n",
+    "\n",
+    "eps = 1.e-8\n",
+    "print(\"eps: \", eps)\n",
+    "energy_diff = eps * 1000\n",
+    "energy_last = initial_energy.asnumpy() + energy_diff\n",
+    "iter_idx = 0\n",
+    "while (abs(energy_diff) > eps):\n",
+    "    energy_i = train_pqcnet().asnumpy()\n",
+    "    if iter_idx % 100 == 0:\n",
+    "        print(\"Step %3d energy %20.16f\" % (iter_idx, float(energy_i)))\n",
+    "    energy_diff = energy_last - energy_i\n",
+    "    energy_last = energy_i\n",
+    "    iter_idx += 1\n",
+    "\n",
+    "print(\"Optimization completed at step %3d\" % (iter_idx - 1))\n",
+    "print(\"Optimized energy: %20.16f\" % (energy_i))\n",
+    "print(\"Optimized amplitudes: \\n\", pqcnet.weight.asnumpy())"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Strategy 2完整源代码见src/qubit recursive.py，相较本文档，源代码从目标的$N$出发，尽可能从$N$中除掉2的幂，再往上倍增至$N$。"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "值得一提的是，论文中并没有明确给出子系统的收敛的判据。论文前文在随机初始化的段落给出“对约100个不同的随机初始化参数，只有它们全部都能在50L次循环后达到保真度阈值，才判定算法成功”，这个判据显然不能应用在这个场景里，因为实际VQE的过程中目标态是未知的，无法计算保真度，只能比较更新步骤之间的能量差。从极端情形考虑，如果收敛判据取得非常严苛（阈值取得非常小），那么大量的循环都浪费在子系统PQC的收敛上，反而达不到加速的效果。\n",
+    "\n",
+    "由此考虑，可以将子系统收敛的阈值取得稍大一些，因为通过改善子系统的基态的精度来提高目标系统的精度，这件事情的效率是相对较低的。绝大部分的经典迭代应该用在最终的目标系统上。由于参数的不确定性，无法从理论上给出这一“效率”的大小，从经验上不妨试着取子系统阈值为后一步2倍大系统的10或100倍。"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 改进Strategy 2\n",
+    "\n",
+    "论文中指出，使用Strategy 2的动机是：单独考虑子系统的基态(the ground state of the local system)，与大系统的基态的子系统空间(the reduced density matrix of the subsystems from the ground state of the large system)很相似。从物理的角度分析，这个说法肯定是合理的，因为哈密顿量可以改写为$H_N=J (\\sum_{i=1}^{N/2-1} \\sigma^{i} \\cdot \\sigma^{i+1}+\\sum_{i=N/2}^{N-1} \\sigma^{i} \\cdot \\sigma^{i+1}+\\sigma^{N/2-1} \\cdot \\sigma^{N/2})$.这个式子的前两项分别对应两个子系统，把它们的和看作一个整体$H_{base}$，它的基态就是两个$H_{N/2}$的基态的张量积$|\\Psi_{base}\\rangle=|\\Psi_{N/2}\\rangle \\otimes |\\Psi_{N/2}\\rangle$，而真正的哈密顿量$H_N$可以看作是$H_{base}$上的微扰$H_N=H_{base}+\\sigma^{N/2-1} \\cdot \\sigma^{N/2}$，根据微扰论的知识，$N$越大，$|\\Psi_{base}\\rangle$与$|\\Psi_{N}\\rangle$的差距就越小。\n",
+    "\n",
+    "既然如此，为什么不从物理上认可的$H_{base}$出发作变分呢？想要制备$H_{base}$，就应该让连接上下两半的N门的参数取0，如果新增加了线路层数，那么所有的新添加的参数门的参数也应都取0.论文中将的连接的门和新添加的门的参数随机初始化，是否反而是在南辕北辙？可以做一个简单的验证：从前文中获取的子网络参数pre重新构建线路，Attempt1将连接的门的参数设置为0，Attempt2将连接的门和新添加的门的参数全都设置为0，比较这两者的能量与之前的线路的能量的高低。"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Attempt 1 better: 57.4%\n",
+      "Attempt 2 better: 74.5%\n"
+     ]
+    }
+   ],
+   "source": [
+    "pre = pqcnet.weight.asnumpy()\n",
+    "half = num // 2\n",
+    "L1 = half * 3 - 1\n",
+    "L2 = num * 3 - 1\n",
+    "\n",
+    "count1 = 0\n",
+    "count2 = 0\n",
+    "numoftests = 1000\n",
+    "for k in range(numoftests):\n",
+    "    val = np.random.randn(L2 * m2)\n",
+    "\n",
+    "    for j in range(m):\n",
+    "        for i in range(half):\n",
+    "            val[i + j * L2] = pre[i + j * L1]\n",
+    "            val[i + j * L2 + half] = pre[i + j * L1]\n",
+    "    for j in range(m):\n",
+    "        for i in range(half - 1):\n",
+    "            val[i + j * L2 + num] = pre[i + j * L1 + half]\n",
+    "            val[i + j * L2 + num + half] = pre[i + j * L1 + half]\n",
+    "    for j in range(m):\n",
+    "        for i in range(half):\n",
+    "            val[i + j * L2 + num2 - 1] = pre[i + j * L1 + num - 1]\n",
+    "            val[num - i - 2 + j * L2 + num2] = -pre[i + j * L1 + num - 1]\n",
+    "\n",
+    "    sim = Simulator('projectq', num2)\n",
+    "    pqc = sim.get_expectation_with_grad(ham, ansatz)\n",
+    "    pqcnet = MQAnsatzOnlyLayer(pqc)\n",
+    "    pqcnet.weight = Parameter(ms.Tensor(val, pqcnet.weight.dtype))\n",
+    "\n",
+    "    initial_energy1 = pqcnet()\n",
+    "    #print(\"Paper Initial energy: %20.16f\" % (initial_energy.asnumpy()))\n",
+    "\n",
+    "    for j in range(m):\n",
+    "        val[j * L2 + num + half - 1] = 0\n",
+    "    pqcnet.weight = Parameter(ms.Tensor(val, pqcnet.weight.dtype))\n",
+    "    initial_energy2 = pqcnet()\n",
+    "    #print(\"Attempt 1 Initial energy: %20.16f\" % (initial_energy.asnumpy()))\n",
+    "\n",
+    "    val = np.zeros(L2 * m2)\n",
+    "    for j in range(m):\n",
+    "        for i in range(half):\n",
+    "            val[i + j * L2] = pre[i + j * L1]\n",
+    "            val[i + j * L2 + half] = pre[i + j * L1]\n",
+    "    for j in range(m):\n",
+    "        for i in range(half - 1):\n",
+    "            val[i + j * L2 + num] = pre[i + j * L1 + half]\n",
+    "            val[i + j * L2 + num + half] = pre[i + j * L1 + half]\n",
+    "    for j in range(m):\n",
+    "        for i in range(half):\n",
+    "            val[i + j * L2 + num2 - 1] = pre[i + j * L1 + num - 1]\n",
+    "            val[num - i - 2 + j * L2 + num2] = -pre[i + j * L1 + num - 1]\n",
+    "    pqcnet.weight = Parameter(ms.Tensor(val, pqcnet.weight.dtype))\n",
+    "    initial_energy3 = pqcnet()\n",
+    "    #print(\"Attempt 2 Initial energy: %20.16f\" % (initial_energy.asnumpy()))\n",
+    "    if initial_energy2 < initial_energy1:\n",
+    "        count1 +=1\n",
+    "    if initial_energy3 < initial_energy1:\n",
+    "        count2 +=1\n",
+    "print('Attempt 1 better: %.1f' % (100.0*count1/numoftests) + '%')\n",
+    "print('Attempt 2 better: %.1f' % (100.0*count2/numoftests) + '%')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "可以看到大多数情况下，随机初始化将量子态偏离$|\\Psi_{base}\\rangle$，其得到的结果反而不如$|\\Psi_{base}\\rangle$，因此不如就将$|\\Psi_{base}\\rangle$作为大系统变分的起点。整体线路的随机性由最小的子系统的参数的随机初始化实现。\n",
+    "\n",
+    "在src/qubit recursive.py中，解除第165、166行的注释即可实现Attempt1，解除第167行的注释即可实现Attempt2."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Strategy 3: layer recursive.\n",
+    "\n",
+    "这个策略先从单层的PQC出发，达到收敛之后，增加一层PQC的层数（使用前一层的参数作为初猜），达到收敛之后再增加一层，以此类推直至总层数达到$M_{VQE}$.\n",
+    "\n",
+    "论文中没有给出使用这一策略的理论依据。个人认为这一策略的可以从几何上理解，在经过VQE的变分优化后，如果恰好初态、末态和目标态三者共面，那么下一步的参数的最优取值一定是前一步的复制，不共面时也是不错的贪心策略。这与Grover算法的思路类似。"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Current number of layers: 1\n",
+      "Initial energy:   0.0123526062816381\n",
+      "eps:  1e-08\n",
+      "Step   0 energy   0.0123526062816381\n",
+      "Optimization completed at step  94\n",
+      "Optimized energy:   0.0000000000238039\n",
+      "Optimized amplitudes: \n",
+      " [-1.8926561   0.168481   -0.78533477 -0.46012077 -1.4066193 ]\n",
+      "Current number of layers: 2\n",
+      "Initial energy:  -2.3261110782623291\n",
+      "eps:  1e-08\n",
+      "Step   0 energy  -2.3261110782623291\n",
+      "Step 100 energy  -5.9998421669006348\n",
+      "Optimization completed at step 124\n",
+      "Optimized energy:  -5.9999876022338867\n",
+      "Optimized amplitudes: \n",
+      " [-1.8926561   0.168481   -0.78522205 -0.32984713 -0.8735825  -1.8141392\n",
+      "  0.24335901 -0.78527933 -0.32926998 -1.5350333 ]\n"
+     ]
+    }
+   ],
+   "source": [
+    "num = 4\n",
+    "m = NMtable[num]\n",
+    "assert num % 2 == 0\n",
+    "#print(num, m)\n",
+    "\n",
+    "\n",
+    "encoder = Circuit()\n",
+    "for i in range(0, num, 2):\n",
+    "    encoder += X.on(i)\n",
+    "    encoder += X.on(i + 1)\n",
+    "    encoder += H.on(i)\n",
+    "    encoder += X.on(i + 1, i)\n",
+    "    \n",
+    "#print(encoder)\n",
+    "#encoder.summary()\n",
+    "\n",
+    "\n",
+    "J = 1\n",
+    "ham = QubitOperator('')\n",
+    "for i in range(num - 1):\n",
+    "    ham += QubitOperator('X%d X%d' % (i, i + 1), J)\n",
+    "    ham += QubitOperator('Y%d Y%d' % (i, i + 1), J)\n",
+    "    ham += QubitOperator('Z%d Z%d' % (i, i + 1), J)\n",
+    "ham -= QubitOperator('')\n",
+    "\n",
+    "#print(ham)\n",
+    "\n",
+    "\n",
+    "ansatz = encoder\n",
+    "count = 1\n",
+    "sim = Simulator('projectq', num)\n",
+    "val = []\n",
+    "L = num // 2 * 3 - 1\n",
+    "\n",
+    "for j in range(m):\n",
+    "    print(f'Current number of layers: {j + 1}')\n",
+    "    # print(val)\n",
+    "    for i in range(0, num - 1, 2):\n",
+    "        ansatz += N(count, i)\n",
+    "        count += 1\n",
+    "    for i in range(1, num - 1, 2):\n",
+    "        ansatz += N(count, i)\n",
+    "        count += 1\n",
+    "    for i in range(0, num // 2):\n",
+    "        ansatz += PhaseShift('p%d' % count).on(i)\n",
+    "        ansatz += PhaseShift({'p%d' % count : -1}).on(num - i - 1)\n",
+    "        count += 1\n",
+    "\n",
+    "    # print(ansatz)\n",
+    "    # ansatz.summary()\n",
+    "\n",
+    "    if j == 0:\n",
+    "        val = np.random.randn(count - 1)\n",
+    "    else:\n",
+    "        val = np.concatenate((val, val[-L:]))\n",
+    "    # print(val)\n",
+    "\n",
+    "    \n",
+    "    pqc = sim.get_expectation_with_grad(Hamiltonian(ham), ansatz)\n",
+    "    pqcnet = MQAnsatzOnlyLayer(pqc)\n",
+    "    pqcnet.weight = Parameter(ms.Tensor(val, pqcnet.weight.dtype))\n",
+    "\n",
+    "    initial_energy = pqcnet()\n",
+    "    print(\"Initial energy: %20.16f\" % (initial_energy.asnumpy()))\n",
+    "\n",
+    "\n",
+    "    optimizer = ms.nn.Adam(pqcnet.trainable_params(), learning_rate = 0.01, beta1 = 0.9, beta2 = 0.999, eps = 1e-8)\n",
+    "    train_pqcnet = ms.nn.TrainOneStepCell(pqcnet, optimizer)\n",
+    "\n",
+    "    eps = 1.e-8\n",
+    "    print(\"eps: \", eps)\n",
+    "    energy_diff = eps * 1000\n",
+    "    energy_last = initial_energy.asnumpy() + energy_diff\n",
+    "    iter_idx = 0\n",
+    "    while (abs(energy_diff) > eps):\n",
+    "        energy_i = train_pqcnet().asnumpy()\n",
+    "        if iter_idx % 100 == 0:\n",
+    "            print(\"Step %3d energy %20.16f\" % (iter_idx, float(energy_i)))\n",
+    "        energy_diff = energy_last - energy_i\n",
+    "        energy_last = energy_i\n",
+    "        iter_idx += 1\n",
+    "\n",
+    "    print(\"Optimization completed at step %3d\" % (iter_idx - 1))\n",
+    "    print(\"Optimized energy: %20.16f\" % (energy_i))\n",
+    "    print(\"Optimized amplitudes: \\n\", pqcnet.weight.asnumpy())"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Strategy 3完整源代码见src/layer recursive.py"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 项目总结"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 复现结果\n",
+    "实现了论文Sec.5中的3种不同策略的VQE线路，3种都可以复现N=4、8、10时海森堡模型的基态能量。\n",
+    "### 创新点\n",
+    "改进了Strategy 2中的参数初猜设定\n",
+    "### 未来可继续研究的方向\n",
+    "1. 论文绘制了许多与保真度相关的图表，由于mindquantum没有内置的矩阵严格对角化的功能，这些图表若要在mindquantum中重现，需要从外部导入严格对角化的结果，与ansatz.get_qs(pr = val)的结果作内积，这里由于位序的定义问题很容易引发错误。可以考虑内置矩阵严格对角化。\n",
+    "2. 由于密度矩阵模块尚不健全，无法模拟双量子比特门的失相，可以考虑引入密度矩阵，Kraus算符等模块。\n",
+    "3. 文中固定了使用Adam算法，取了一组特定的学习率等参数，可以探索不同的经典优化算法，不同参数之间的性能差异。\n",
+    "4. 可以探索绝热演化转VQE这一线路设计范式在其他模型中的应用。"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "MindQuantum",
+   "language": "python",
+   "name": "mindquantum"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.7.10"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/paper_recurrence/6_hw08624896/readme.md b/paper_recurrence/6_hw08624896/readme.md
new file mode 100644
index 000000000..75f334ec7
--- /dev/null
+++ b/paper_recurrence/6_hw08624896/readme.md
@@ -0,0 +1,15 @@
+# Accelerated variational algorithms for digital quantum simulation of the many-body ground states
+
+## 项目介绍
+
+用VQE制备一维海森堡模型的基态，线路设计由绝热演化的Suzuki-Trotter expansion启发而来，并着重探讨了优化经典参数更新循环的3种策略。
+
+## 主要结果
+
+实现了论文Sec.5中的3种不同策略的VQE线路，3种都可以复现N=4、8、10时海森堡模型的基态能量。
+
+## 创新点
+
+改进了Strategy 2中的参数初猜设定。
+
+邮箱地址：jerryhts@163.com
\ No newline at end of file
diff --git a/paper_recurrence/6_hw08624896/src/accvqeexact.py b/paper_recurrence/6_hw08624896/src/accvqeexact.py
new file mode 100644
index 000000000..74c1a318a
--- /dev/null
+++ b/paper_recurrence/6_hw08624896/src/accvqeexact.py
@@ -0,0 +1,55 @@
+# -*- coding: utf-8 -*-
+"""
+Created on Mon Jan 17 13:00:24 2022
+
+@author: Jerryhts
+"""
+
+import numpy as np
+
+X = np.array([[0, 1], [1, 0]])
+Y = np.array([[0, -1j], [1j, 0]])
+Z = np.array([[1, 0], [0, -1]])
+I = np.array([[1, 0], [0, 1]])
+'''
+def RX(t):
+    return np.array([[np.cos(t / 2), -1j * np.sin(t / 2)], [-1j * np.sin(t / 2), np.cos(t / 2)]])
+def RY(t):
+    return np.array([[np.cos(t / 2), -np.sin(t / 2)], [np.sin(t / 2), np.cos(t / 2)]])
+def RZ(t):
+    return np.array([[np.exp(-1j * t / 2), 0], [0, np.exp(1j * t / 2)]])'''
+
+def f(x):
+    if x == 'X':
+        return X
+    elif x == 'Y':
+        return Y
+    elif x == 'Z':
+        return Z
+    else:
+        return I
+    
+tot = 2
+num = 2
+    
+def QubitOperator(string, para):
+    al = ['I' for i in range(tot)]
+    tem = string.split(' ')
+    for i in tem:
+        num = eval(i[1:])
+        al[num] = i[0]
+    ini = f(al[0])
+    for i in range(1, tot):
+        ini = np.kron(f(al[i]), ini)
+    return para * ini
+
+J = 1
+ham = np.complex128(np.zeros((2 ** tot, 2 ** tot)))
+for i in range(num - 1):
+    ham += QubitOperator('X%d X%d' % (i, i + 1), J)
+    ham += QubitOperator('Y%d Y%d' % (i, i + 1), J)
+    ham += QubitOperator('Z%d Z%d' % (i, i + 1), J)
+    
+w, v = np.linalg.eig(ham)
+res = np.sort(np.real(w))
+print(res)
\ No newline at end of file
diff --git a/paper_recurrence/6_hw08624896/src/layer recursive.py b/paper_recurrence/6_hw08624896/src/layer recursive.py
new file mode 100644
index 000000000..4e27d221e
--- /dev/null
+++ b/paper_recurrence/6_hw08624896/src/layer recursive.py	
@@ -0,0 +1,111 @@
+import numpy as np
+from mindquantum import Circuit, X, H, RZ, RY, PhaseShift, Hamiltonian, Simulator, QubitOperator, Hamiltonian, MQAnsatzOnlyLayer
+import mindspore as ms
+from mindspore.common.parameter import Parameter
+import mindspore.context as context
+
+context.set_context(mode=context.PYNATIVE_MODE, device_target="CPU")
+
+
+def N(count, i):
+    temp = Circuit()
+    temp += RZ(np.pi / 2).on(i + 1)
+    temp += X.on(i, i + 1)
+    temp += RZ({f'p{count}' : 2}).on(i)
+    temp += RZ(-np.pi / 2).on(i)
+    temp += RY(np.pi / 2).on(i + 1)
+    temp += RY({f'p{count}' : -2}).on(i + 1)
+    temp += X.on(i + 1, i)
+    temp += RY({f'p{count}' : 2}).on(i + 1)
+    temp += RY(-np.pi / 2).on(i + 1)
+    temp += X.on(i, i + 1)
+    temp += RZ(-np.pi / 2).on(i)
+    return temp
+
+
+NMtable = {4:2, 8:3, 10:3, 16:5, 20:6}
+num = 4
+m = NMtable[num]
+assert num % 2 == 0
+#print(num, m)
+
+
+encoder = Circuit()
+for i in range(0, num, 2):
+    encoder += X.on(i)
+    encoder += X.on(i + 1)
+    encoder += H.on(i)
+    encoder += X.on(i + 1, i)
+    
+#print(encoder)
+#encoder.summary()
+
+
+J = 1
+ham = QubitOperator('')
+for i in range(num - 1):
+    ham += QubitOperator('X%d X%d' % (i, i + 1), J)
+    ham += QubitOperator('Y%d Y%d' % (i, i + 1), J)
+    ham += QubitOperator('Z%d Z%d' % (i, i + 1), J)
+ham -= QubitOperator('')
+
+#print(ham)
+
+
+ansatz = encoder
+count = 1
+sim = Simulator('projectq', num)
+val = []
+L = num // 2 * 3 - 1
+
+for j in range(m):
+    print(f'Current number of layers: {j + 1}')
+    # print(val)
+    for i in range(0, num - 1, 2):
+        ansatz += N(count, i)
+        count += 1
+    for i in range(1, num - 1, 2):
+        ansatz += N(count, i)
+        count += 1
+    for i in range(0, num // 2):
+        ansatz += PhaseShift('p%d' % count).on(i)
+        ansatz += PhaseShift({'p%d' % count : -1}).on(num - i - 1)
+        count += 1
+
+    # print(ansatz)
+    # ansatz.summary()
+
+    if j == 0:
+        val = np.random.randn(count - 1)
+    else:
+        val = np.concatenate((val, val[-L:]))
+    # print(val)
+
+    
+    pqc = sim.get_expectation_with_grad(Hamiltonian(ham), ansatz)
+    pqcnet = MQAnsatzOnlyLayer(pqc)
+    pqcnet.weight = Parameter(ms.Tensor(val, pqcnet.weight.dtype))
+
+    initial_energy = pqcnet()
+    print("Initial energy: %20.16f" % (initial_energy.asnumpy()))
+
+
+    optimizer = ms.nn.Adam(pqcnet.trainable_params(), learning_rate = 0.01, beta1 = 0.9, beta2 = 0.999, eps = 1e-8)
+    train_pqcnet = ms.nn.TrainOneStepCell(pqcnet, optimizer)
+
+    eps = 1.e-8
+    print("eps: ", eps)
+    energy_diff = eps * 1000
+    energy_last = initial_energy.asnumpy() + energy_diff
+    iter_idx = 0
+    while (abs(energy_diff) > eps):
+        energy_i = train_pqcnet().asnumpy()
+        if iter_idx % 100 == 0:
+            print("Step %3d energy %20.16f" % (iter_idx, float(energy_i)))
+        energy_diff = energy_last - energy_i
+        energy_last = energy_i
+        iter_idx += 1
+
+    print("Optimization completed at step %3d" % (iter_idx - 1))
+    print("Optimized energy: %20.16f" % (energy_i))
+    print("Optimized amplitudes: \n", pqcnet.weight.asnumpy())
\ No newline at end of file
diff --git a/paper_recurrence/6_hw08624896/src/qubit recursive.py b/paper_recurrence/6_hw08624896/src/qubit recursive.py
new file mode 100644
index 000000000..7066348b5
--- /dev/null
+++ b/paper_recurrence/6_hw08624896/src/qubit recursive.py	
@@ -0,0 +1,219 @@
+import numpy as np
+from mindquantum import Circuit, X, H, RZ, RY, PhaseShift, Hamiltonian, Simulator, QubitOperator, Hamiltonian, MQAnsatzOnlyLayer
+import mindspore as ms
+from mindspore.common.parameter import Parameter
+import mindspore.context as context
+
+context.set_context(mode=context.PYNATIVE_MODE, device_target="CPU")
+
+
+def N(count, i):
+    temp = Circuit()
+    temp += RZ(np.pi / 2).on(i + 1)
+    temp += X.on(i, i + 1)
+    temp += RZ({f'p{count}' : 2}).on(i)
+    temp += RZ(-np.pi / 2).on(i)
+    temp += RY(np.pi / 2).on(i + 1)
+    temp += RY({f'p{count}' : -2}).on(i + 1)
+    temp += X.on(i + 1, i)
+    temp += RY({f'p{count}' : 2}).on(i + 1)
+    temp += RY(-np.pi / 2).on(i + 1)
+    temp += X.on(i, i + 1)
+    temp += RZ(-np.pi / 2).on(i)
+    return temp
+
+
+NMtable = {4:2, 8:3, 10:3, 16:5, 20:6}
+num = 8
+
+
+temp = num
+while num % 2 == 0 and num > 4:
+    num = num // 2
+m = NMtable[num]
+assert num % 2 == 0
+
+print(f'Current N: {num}')
+
+
+encoder = Circuit()
+for i in range(0, num, 2):
+    encoder += X.on(i)
+    encoder += X.on(i + 1)
+    encoder += H.on(i)
+    encoder += X.on(i + 1, i)
+    
+# print(encoder)
+# encoder.summary()
+
+
+ansatz = Circuit()
+count = 1
+
+for j in range(m):
+    for i in range(0, num - 1, 2):
+        ansatz += N(count, i)
+        count += 1
+    for i in range(1, num - 1, 2):
+        ansatz += N(count, i)
+        count += 1
+    for i in range(0, num // 2):
+        ansatz += PhaseShift('p%d' % count).on(i)
+        ansatz += PhaseShift({'p%d' % count : -1}).on(num - i - 1)
+        count += 1
+
+ansatz = encoder + ansatz
+
+# print(ansatz)
+# ansatz.summary()
+
+
+J = 1
+ham = QubitOperator('')
+for i in range(num - 1):
+    ham += QubitOperator('X%d X%d' % (i, i + 1), J)
+    ham += QubitOperator('Y%d Y%d' % (i, i + 1), J)
+    ham += QubitOperator('Z%d Z%d' % (i, i + 1), J)
+ham -= QubitOperator('')
+
+# print(ham)
+
+
+val = np.random.randn(count - 1)
+
+sim = Simulator('projectq', num)
+pqc = sim.get_expectation_with_grad(Hamiltonian(ham), ansatz)
+pqcnet = MQAnsatzOnlyLayer(pqc)
+pqcnet.weight = Parameter(ms.Tensor(val, pqcnet.weight.dtype))
+
+initial_energy = pqcnet()
+print("Initial energy: %20.16f" % (initial_energy.asnumpy()))
+
+
+optimizer = ms.nn.Adam(pqcnet.trainable_params(), learning_rate = 0.01, beta1 = 0.9, beta2 = 0.999, eps = 1e-8)
+train_pqcnet = ms.nn.TrainOneStepCell(pqcnet, optimizer)
+
+eps = 1.e-8
+print("eps: ", eps)
+energy_diff = eps * 1000
+energy_last = initial_energy.asnumpy() + energy_diff
+iter_idx = 0
+while (abs(energy_diff) > eps):
+    energy_i = train_pqcnet().asnumpy()
+    if iter_idx % 100 == 0:
+        print("Step %3d energy %20.16f" % (iter_idx, float(energy_i)))
+    energy_diff = energy_last - energy_i
+    energy_last = energy_i
+    iter_idx += 1
+
+print("Optimization completed at step %3d" % (iter_idx - 1))
+print("Optimized energy: %20.16f" % (energy_i))
+print("Optimized amplitudes: \n", pqcnet.weight.asnumpy())
+
+
+while num < temp:
+    num2 = 2 * num
+    m2 = NMtable[num2]
+    # print(num2, m2)
+
+    print(f'Current N: {num2}')
+
+
+    encoder = Circuit()
+    for i in range(0, num2, 2):
+        encoder += X.on(i)
+        encoder += X.on(i + 1)
+        encoder += H.on(i)
+        encoder += X.on(i + 1, i)
+
+    ansatz = Circuit()
+    count = 1
+
+    for j in range(m2):
+        for i in range(0, num2 - 1, 2):
+            ansatz += N(count, i)
+            count += 1
+        for i in range(1, num2 - 1, 2):
+            ansatz += N(count, i)
+            count += 1
+        for i in range(0, num2 // 2):
+            ansatz += PhaseShift('p%d' % count).on(i)
+            ansatz += PhaseShift({'p%d' % count : -1}).on(num2 - i - 1)
+            count += 1
+
+    ansatz = encoder + ansatz
+    # print(ansatz)
+    # ansatz.summary()
+
+    J = 1
+    ham = QubitOperator('')
+    for i in range(num2 - 1):
+        ham += QubitOperator('X%d X%d' % (i, i + 1), J)
+        ham += QubitOperator('Y%d Y%d' % (i, i + 1), J)
+        ham += QubitOperator('Z%d Z%d' % (i, i + 1), J)
+    ham = Hamiltonian(ham - QubitOperator(''))
+
+    # print(ham)
+
+
+    pre = pqcnet.weight.asnumpy()
+    half = num // 2
+    L1 = half * 3 - 1
+    L2 = num * 3 - 1
+    # print(L1, L2)
+    val = np.random.randn(L2 * m2)
+    # for j in range(m):
+        # val[j * L2 + num + half - 1] = 0    # To utilize Attempt 1
+    # val = np.zeros(L2 * m2)    # To utilize Attempt 2
+
+    for j in range(m):
+        for i in range(half):
+            val[i + j * L2] = pre[i + j * L1]
+            val[i + j * L2 + half] = pre[i + j * L1]
+    for j in range(m):
+        for i in range(half - 1):
+            val[i + j * L2 + num] = pre[i + j * L1 + half]
+            val[i + j * L2 + num + half] = pre[i + j * L1 + half]
+    for j in range(m):
+        for i in range(half):
+            val[i + j * L2 + num2 - 1] = pre[i + j * L1 + num - 1]
+            val[num - i - 2 + j * L2 + num2] = -pre[i + j * L1 + num - 1]
+
+    '''print('old parameters:')
+    for i in range(L1 * m):
+        print(f'p{i + 1}', pre[i])
+    print('new parameters:')
+    for i in range(L2 * m2):
+        print(f'p{i + 1}', val[i])'''
+
+
+    sim = Simulator('projectq', num2)
+    pqc = sim.get_expectation_with_grad(ham, ansatz)
+    pqcnet = MQAnsatzOnlyLayer(pqc)
+    pqcnet.weight = Parameter(ms.Tensor(val, pqcnet.weight.dtype))
+
+    initial_energy = pqcnet()
+    print("Initial energy: %20.16f" % (initial_energy.asnumpy()))
+
+    optimizer = ms.nn.Adam(pqcnet.trainable_params(), learning_rate = 0.01, beta1 = 0.9, beta2 = 0.999, eps = 1e-8)
+    train_pqcnet = ms.nn.TrainOneStepCell(pqcnet, optimizer)
+
+    eps = 1.e-8
+    print("eps: ", eps)
+    energy_diff = eps * 1000
+    energy_last = initial_energy.asnumpy() + energy_diff
+    iter_idx = 0
+    while (abs(energy_diff) > eps):
+        energy_i = train_pqcnet().asnumpy()
+        if iter_idx % 100 == 0:
+            print("Step %3d energy %20.16f" % (iter_idx, float(energy_i)))
+        energy_diff = energy_last - energy_i
+        energy_last = energy_i
+        iter_idx += 1
+
+    print("Optimization completed at step %3d" % (iter_idx - 1))
+    print("Optimized energy: %20.16f" % (energy_i))
+    print("Optimized amplitudes: \n", pqcnet.weight.asnumpy())
+
+    num = num2
+    m = m2
\ No newline at end of file
diff --git a/paper_recurrence/6_hw08624896/src/random initialization.py b/paper_recurrence/6_hw08624896/src/random initialization.py
new file mode 100644
index 000000000..9e6eecd65
--- /dev/null
+++ b/paper_recurrence/6_hw08624896/src/random initialization.py	
@@ -0,0 +1,105 @@
+import numpy as np
+from mindquantum import Circuit, X, H, RZ, RY, PhaseShift, Hamiltonian, Simulator, QubitOperator, Hamiltonian, MQAnsatzOnlyLayer
+import mindspore as ms
+from mindspore.common.parameter import Parameter
+import mindspore.context as context
+
+context.set_context(mode=context.PYNATIVE_MODE, device_target="CPU")
+
+
+def N(count, i):
+    temp = Circuit()
+    temp += RZ(np.pi / 2).on(i + 1)
+    temp += X.on(i, i + 1)
+    temp += RZ({f'p{count}' : 2}).on(i)
+    temp += RZ(-np.pi / 2).on(i)
+    temp += RY(np.pi / 2).on(i + 1)
+    temp += RY({f'p{count}' : -2}).on(i + 1)
+    temp += X.on(i + 1, i)
+    temp += RY({f'p{count}' : 2}).on(i + 1)
+    temp += RY(-np.pi / 2).on(i + 1)
+    temp += X.on(i, i + 1)
+    temp += RZ(-np.pi / 2).on(i)
+    return temp
+
+
+NMtable = {4:2, 8:3, 10:3, 16:5, 20:6}
+num = 4
+m = NMtable[num]
+assert num % 2 == 0
+# print(num, m)
+
+
+encoder = Circuit()
+for i in range(0, num, 2):
+    encoder += X.on(i)
+    encoder += X.on(i + 1)
+    encoder += H.on(i)
+    encoder += X.on(i + 1, i)
+    
+# print(encoder)
+# encoder.summary()
+
+
+ansatz = Circuit()
+count = 1
+
+for j in range(m):
+    for i in range(0, num - 1, 2):
+        ansatz += N(count, i)
+        count += 1
+    for i in range(1, num - 1, 2):
+        ansatz += N(count, i)
+        count += 1
+    for i in range(0, num // 2):
+        ansatz += PhaseShift('p%d' % count).on(i)
+        ansatz += PhaseShift({'p%d' % count : -1}).on(num - i - 1)
+        count += 1
+
+ansatz = encoder + ansatz
+
+# print(ansatz)
+# ansatz.summary()
+
+
+J = 1
+ham = QubitOperator('')
+for i in range(num - 1):
+    ham += QubitOperator('X%d X%d' % (i, i + 1), J)
+    ham += QubitOperator('Y%d Y%d' % (i, i + 1), J)
+    ham += QubitOperator('Z%d Z%d' % (i, i + 1), J)
+ham -= QubitOperator('')
+
+# print(ham)
+
+
+val = np.random.randn(count - 1)
+
+sim = Simulator('projectq', num)
+pqc = sim.get_expectation_with_grad(Hamiltonian(ham), ansatz)
+pqcnet = MQAnsatzOnlyLayer(pqc)
+pqcnet.weight = Parameter(ms.Tensor(val, pqcnet.weight.dtype))
+
+initial_energy = pqcnet()
+print("Initial energy: %20.16f" % (initial_energy.asnumpy()))
+
+
+optimizer = ms.nn.Adam(pqcnet.trainable_params(), learning_rate = 0.01, beta1 = 0.9, beta2 = 0.999, eps = 1e-8)
+train_pqcnet = ms.nn.TrainOneStepCell(pqcnet, optimizer)
+
+eps = 1.e-8
+print("eps: ", eps)
+energy_diff = eps * 1000
+energy_last = initial_energy.asnumpy() + energy_diff
+iter_idx = 0
+while (abs(energy_diff) > eps):
+    energy_i = train_pqcnet().asnumpy()
+    if iter_idx % 100 == 0:
+        print("Step %3d energy %20.16f" % (iter_idx, float(energy_i)))
+    energy_diff = energy_last - energy_i
+    energy_last = energy_i
+    iter_idx += 1
+
+print("Optimization completed at step %3d" % (iter_idx - 1))
+print("Optimized energy: %20.16f" % (energy_i))
+print("Optimized amplitudes: \n", pqcnet.weight.asnumpy())
\ No newline at end of file
diff --git a/paper_recurrence/6_hw08624896/src/readme.md b/paper_recurrence/6_hw08624896/src/readme.md
new file mode 100644
index 000000000..5300eb462
--- /dev/null
+++ b/paper_recurrence/6_hw08624896/src/readme.md
@@ -0,0 +1 @@
+# 请将你对论文复现的源代码放置于当下src文件夹内。
\ No newline at end of file
-- 
Gitee


From 28a59f0e14f227069e1d287da485509102ba46c2 Mon Sep 17 00:00:00 2001
From: he-tianshen <jerryhts@163.com>
Date: Mon, 14 Feb 2022 10:41:26 +0800
Subject: [PATCH 2/2] 6_hw08624896

---
 paper_recurrence/6_hw08624896/main.ipynb | 175 +++++++++++++++++------
 1 file changed, 135 insertions(+), 40 deletions(-)

diff --git a/paper_recurrence/6_hw08624896/main.ipynb b/paper_recurrence/6_hw08624896/main.ipynb
index 45d8c6c0f..6423505d2 100644
--- a/paper_recurrence/6_hw08624896/main.ipynb
+++ b/paper_recurrence/6_hw08624896/main.ipynb
@@ -156,20 +156,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "q0: ──X────H────●──\n",
-      "                │\n",
-      "q1: ──X─────────X──\n",
-      "\n",
-      "q2: ──X────H────●──\n",
-      "                │\n",
-      "q3: ──X─────────X──\n",
       "=======Circuit Summary=======\n",
       "|Total number of gates  : 8.|\n",
       "|Parameter gates        : 0.|\n",
@@ -177,6 +170,42 @@
       "|Number qubit of circuit: 4 |\n",
       "=============================\n"
      ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
+      ],
+      "text/plain": []
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<pre style=\"white-space: pre;\"><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">q0: ──X────H────●──</span>\n",
+       "<span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">                │</span>\n",
+       "<span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">q1: ──X─────────X──</span>\n",
+       "\n",
+       "<span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">q2: ──X────H────●──</span>\n",
+       "<span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">                │</span>\n",
+       "<span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">q3: ──X─────────X──</span>\n",
+       "</pre>\n"
+      ],
+      "text/plain": [
+       "q0: ──X────H────●──\n",
+       "                │\n",
+       "q1: ──X─────────X──\n",
+       "\n",
+       "q2: ──X────H────●──\n",
+       "                │\n",
+       "q3: ──X─────────X──"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
     }
    ],
    "source": [
@@ -187,8 +216,8 @@
     "    encoder += H.on(i)\n",
     "    encoder += X.on(i + 1, i)\n",
     "    \n",
-    "print(encoder)\n",
-    "encoder.summary()"
+    "encoder.summary()\n",
+    "encoder"
    ]
   },
   {
@@ -200,20 +229,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 10,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "q0: ──X────H────●───────────────X────RZ(2*p1)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)─────PS(p4)──────────────────────────────────────────────────────────────────────────────────────────────────────────X────────RZ(2*p6)─────RZ(-π/2)───────●───────────────────────────────────X───────RZ(-π/2)─────PS(p9)─────────────────────────────────────────────────────────────────────────\n",
-      "                │               │                             │                            │                                                                                                                                 │                                    │                                   │\n",
-      "q1: ──X─────────X────RZ(π/2)────●────RY(π/2)─────RY(-2*p1)────X────RY(2*p1)────RY(-π/2)────●───────────────────────────X────RZ(2*p3)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)────PS(p5)────RZ(π/2)─────────●────────RY(π/2)─────RY(-2*p6)───────X────────RY(2*p6)────RY(-π/2)───────●──────────X────────RZ(2*p8)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)────PS(p10)──\n",
-      "                                                                                                                       │                             │                            │                                                                                                                              │                                 │                            │\n",
-      "q2: ──X────H────●───────────────X────RZ(2*p2)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)────RZ(π/2)────●────RY(π/2)─────RY(-2*p3)────X────RY(2*p3)────RY(-π/2)────●────PS(-p5)───────X───────RZ(2*p7)─────RZ(-π/2)───────●────────────────────────────────────X────────RZ(-π/2)────RZ(π/2)───────●────────RY(π/2)─────RY(-2*p8)────X────RY(2*p8)────RY(-π/2)────●────PS(-p10)─────────────\n",
-      "                │               │                             │                            │                                                                                                         │                                   │                                    │\n",
-      "q3: ──X─────────X────RZ(π/2)────●────RY(π/2)─────RY(-2*p2)────X────RY(2*p2)────RY(-π/2)────●────PS(-p4)─────RZ(π/2)──────────────────────────────────────────────────────────────────────────────────●───────RY(π/2)─────RY(-2*p7)───────X─────────RY(2*p7)────RY(-π/2)───────●────────PS(-p9)────────────────────────────────────────────────────────────────────────────────────────────────────────────\n",
       "==========================Circuit Summary==========================\n",
       "|Total number of gates  : 82.                                     |\n",
       "|Parameter gates        : 26.                                     |\n",
@@ -221,6 +243,42 @@
       "|Number qubit of circuit: 4                                       |\n",
       "===================================================================\n"
      ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
+      ],
+      "text/plain": []
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<pre style=\"white-space: pre;\"><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">q0: ──X────H────●───────────────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p1)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────●────────────────────────────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">PS</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(p4)──────────────────────────────────────────────────────────────────────────────────────────────────────────X────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p6)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)───────●───────────────────────────────────X───────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">PS</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(p9)─────────────────────────────────────────────────────────────────────────</span>\n",
+       "<span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">                │               │                             │                            │                                                                                                                                 │                                    │                                   │</span>\n",
+       "<span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">q1: ──X─────────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────●────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">-2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p1)────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p1)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────●───────────────────────────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p3)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────●────────────────────────────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">PS</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(p5)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────────●────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">-2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p6)───────X────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p6)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)───────●──────────X────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p8)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────●────────────────────────────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">PS</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(p10)──</span>\n",
+       "<span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">                                                                                                                       │                             │                            │                                                                                                                              │                                 │                            │</span>\n",
+       "<span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">q2: ──X────H────●───────────────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p2)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────●────────────────────────────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────●────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">-2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p3)────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p3)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────●────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">PS</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-p5)───────X───────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p7)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)───────●────────────────────────────────────X────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)───────●────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">-2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p8)────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p8)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────●────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">PS</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-p10)─────────────</span>\n",
+       "<span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">                │               │                             │                            │                                                                                                         │                                   │                                    │</span>\n",
+       "<span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">q3: ──X─────────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────●────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">-2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p2)────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p2)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────●────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">PS</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-p4)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)──────────────────────────────────────────────────────────────────────────────────●───────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">-2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p7)───────X─────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p7)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)───────●────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">PS</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-p9)────────────────────────────────────────────────────────────────────────────────────────────────────────────</span>\n",
+       "</pre>\n"
+      ],
+      "text/plain": [
+       "q0: ──X────H────●───────────────X────RZ(2*p1)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)─────PS(p4)──────────────────────────────────────────────────────────────────────────────────────────────────────────X────────RZ(2*p6)─────RZ(-π/2)───────●───────────────────────────────────X───────RZ(-π/2)─────PS(p9)─────────────────────────────────────────────────────────────────────────\n",
+       "                │               │                             │                            │                                                                                                                                 │                                    │                                   │\n",
+       "q1: ──X─────────X────RZ(π/2)────●────RY(π/2)─────RY(-2*p1)────X────RY(2*p1)────RY(-π/2)────●───────────────────────────X────RZ(2*p3)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)────PS(p5)────RZ(π/2)─────────●────────RY(π/2)─────RY(-2*p6)───────X────────RY(2*p6)────RY(-π/2)───────●──────────X────────RZ(2*p8)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)────PS(p10)──\n",
+       "                                                                                                                       │                             │                            │                                                                                                                              │                                 │                            │\n",
+       "q2: ──X────H────●───────────────X────RZ(2*p2)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)────RZ(π/2)────●────RY(π/2)─────RY(-2*p3)────X────RY(2*p3)────RY(-π/2)────●────PS(-p5)───────X───────RZ(2*p7)─────RZ(-π/2)───────●────────────────────────────────────X────────RZ(-π/2)────RZ(π/2)───────●────────RY(π/2)─────RY(-2*p8)────X────RY(2*p8)────RY(-π/2)────●────PS(-p10)─────────────\n",
+       "                │               │                             │                            │                                                                                                         │                                   │                                    │\n",
+       "q3: ──X─────────X────RZ(π/2)────●────RY(π/2)─────RY(-2*p2)────X────RY(2*p2)────RY(-π/2)────●────PS(-p4)─────RZ(π/2)──────────────────────────────────────────────────────────────────────────────────●───────RY(π/2)─────RY(-2*p7)───────X─────────RY(2*p7)────RY(-π/2)───────●────────PS(-p9)────────────────────────────────────────────────────────────────────────────────────────────────────────────"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
     }
    ],
    "source": [
@@ -240,8 +298,8 @@
     "        count += 1\n",
     "\n",
     "ansatz = encoder + ansatz\n",
-    "print(ansatz)\n",
-    "ansatz.summary()"
+    "ansatz.summary()\n",
+    "ansatz"
    ]
   },
   {
@@ -253,7 +311,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 11,
    "metadata": {},
    "outputs": [
     {
@@ -392,7 +450,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 12,
    "metadata": {},
    "outputs": [
     {
@@ -418,28 +476,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 14,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "q0: ──X────H────●───────────────X────RZ(2*p1)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)─────PS(p8)─────────────────────────────────────────────────────────────────────────────────────────────────────────────X─────────RZ(2*p12)─────RZ(-π/2)────────●────────────────────────────────────X───────RZ(-π/2)─────PS(p19)───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────X─────────RZ(2*p23)─────RZ(-π/2)────────●─────────────────────────────────────X─────────RZ(-π/2)──────PS(p30)───────────────────────────────────────────────────────────────────────────────────────────────────────────────────\n",
-      "                │               │                             │                            │                                                                                                                                    │                                       │                                    │                                                                                                                                                                      │                                       │                                     │\n",
-      "q1: ──X─────────X────RZ(π/2)────●────RY(π/2)─────RY(-2*p1)────X────RY(2*p1)────RY(-π/2)────●───────────────────────────X────RZ(2*p5)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)─────PS(p9)──────RZ(π/2)─────────●──────────RY(π/2)─────RY(-2*p12)───────X────────RY(2*p12)────RY(-π/2)───────●────────────────────────────────────X─────────RZ(2*p16)─────RZ(-π/2)────────●────────────────────────────────────X─────────RZ(-π/2)─────PS(p20)───────RZ(π/2)─────────●──────────RY(π/2)─────RY(-2*p23)───────X────────RY(2*p23)────RY(-π/2)────────●───────────────────────────────────────X─────────RZ(2*p27)─────RZ(-π/2)────────●────────────────────────────────────X───────RZ(-π/2)────PS(p31)──\n",
-      "                                                                                                                       │                             │                            │                                                                                                                                                               │                                       │                                    │                                                                                                                                                                          │                                       │                                    │\n",
-      "q2: ──X────H────●───────────────X────RZ(2*p2)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)────RZ(π/2)────●────RY(π/2)─────RY(-2*p5)────X────RY(2*p5)────RY(-π/2)────●────PS(p10)──────────────────────────────────X─────────RZ(2*p13)─────RZ(-π/2)────────●────────────────────────────────────X───────RZ(-π/2)─────RZ(π/2)─────────●──────────RY(π/2)─────RY(-2*p16)───────X────────RY(2*p16)────RY(-π/2)───────●─────────PS(p21)────────────────────────────────────X─────────RZ(2*p24)─────RZ(-π/2)────────●─────────────────────────────────────X─────────RZ(-π/2)──────RZ(π/2)─────────●──────────RY(π/2)─────RY(-2*p27)───────X────────RY(2*p27)────RY(-π/2)───────●───────PS(p32)──────────────\n",
-      "                │               │                             │                            │                                                                                                                                    │                                       │                                    │                                                                                                                                                                      │                                       │                                     │\n",
-      "q3: ──X─────────X────RZ(π/2)────●────RY(π/2)─────RY(-2*p2)────X────RY(2*p2)────RY(-π/2)────●───────────────────────────X────RZ(2*p6)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)────PS(p11)──────RZ(π/2)─────────●──────────RY(π/2)─────RY(-2*p13)───────X────────RY(2*p13)────RY(-π/2)───────●────────────────────────────────────X─────────RZ(2*p17)─────RZ(-π/2)────────●────────────────────────────────────X─────────RZ(-π/2)─────PS(p22)───────RZ(π/2)─────────●──────────RY(π/2)─────RY(-2*p24)───────X────────RY(2*p24)────RY(-π/2)────────●────────────X─────────RZ(2*p28)─────RZ(-π/2)─────────●──────────────────────────────────────X────────RZ(-π/2)────PS(p33)─────────────────────────\n",
-      "                                                                                                                       │                             │                            │                                                                                                                                                               │                                       │                                    │                                                                                                                                               │                                        │                                      │\n",
-      "q4: ──X────H────●───────────────X────RZ(2*p3)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)────RZ(π/2)────●────RY(π/2)─────RY(-2*p6)────X────RY(2*p6)────RY(-π/2)────●────PS(-p11)─────────────────────────────────X─────────RZ(2*p14)─────RZ(-π/2)────────●────────────────────────────────────X───────RZ(-π/2)─────RZ(π/2)─────────●──────────RY(π/2)─────RY(-2*p17)───────X────────RY(2*p17)────RY(-π/2)───────●─────────PS(-p22)────────X─────────RZ(2*p25)─────RZ(-π/2)─────────●──────────────────────────────────────X────────RZ(-π/2)─────RZ(π/2)─────────●──────────RY(π/2)─────RY(-2*p28)────────X────────RY(2*p28)─────RY(-π/2)────────●────────PS(-p33)────────────────────────────────────\n",
-      "                │               │                             │                            │                                                                                                                                    │                                       │                                    │                                                                                                                                           │                                        │                                      │\n",
-      "q5: ──X─────────X────RZ(π/2)────●────RY(π/2)─────RY(-2*p3)────X────RY(2*p3)────RY(-π/2)────●───────────────────────────X────RZ(2*p7)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)────PS(-p10)─────RZ(π/2)─────────●──────────RY(π/2)─────RY(-2*p14)───────X────────RY(2*p14)────RY(-π/2)───────●──────────X────────RZ(2*p18)─────RZ(-π/2)─────────●──────────────────────────────────────X────────RZ(-π/2)────PS(-p21)─────RZ(π/2)─────────●──────────RY(π/2)─────RY(-2*p25)────────X────────RY(2*p25)─────RY(-π/2)────────●───────────X────────RZ(2*p29)─────RZ(-π/2)─────────●───────────────────────────────────────X─────────RZ(-π/2)─────PS(-p32)────────────────────────────────────────────────\n",
-      "                                                                                                                       │                             │                            │                                                                                                                                     │                                       │                                      │                                                                                                                                             │                                       │                                       │\n",
-      "q6: ──X────H────●───────────────X────RZ(2*p4)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)────RZ(π/2)────●────RY(π/2)─────RY(-2*p7)────X────RY(2*p7)────RY(-π/2)────●────PS(-p9)────────X────────RZ(2*p15)─────RZ(-π/2)─────────●──────────────────────────────────────X────────RZ(-π/2)────RZ(π/2)───────●─────────RY(π/2)─────RY(-2*p18)────────X────────RY(2*p18)─────RY(-π/2)────────●────────PS(-p20)───────X────────RZ(2*p26)─────RZ(-π/2)─────────●───────────────────────────────────────X─────────RZ(-π/2)─────RZ(π/2)────────●─────────RY(π/2)─────RY(-2*p29)────────X────────RY(2*p29)──────RY(-π/2)────────●─────────PS(-p31)─────────────────────────────────────────────────────────────\n",
-      "                │               │                             │                            │                                                                                                          │                                       │                                      │                                                                                                                                         │                                       │                                       │\n",
-      "q7: ──X─────────X────RZ(π/2)────●────RY(π/2)─────RY(-2*p4)────X────RY(2*p4)────RY(-π/2)────●────PS(-p8)─────RZ(π/2)───────────────────────────────────────────────────────────────────────────────────●─────────RY(π/2)─────RY(-2*p15)────────X────────RY(2*p15)─────RY(-π/2)────────●────────PS(-p19)────RZ(π/2)──────────────────────────────────────────────────────────────────────────────────────────────────────────────●─────────RY(π/2)─────RY(-2*p26)────────X────────RY(2*p26)──────RY(-π/2)────────●─────────PS(-p30)───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────\n",
       "===========================Circuit Summary===========================\n",
       "|Total number of gates  : 271.                                      |\n",
       "|Parameter gates        : 87.                                       |\n",
@@ -468,6 +511,58 @@
       "1 [Y6 Y7] +\n",
       "1 [Z6 Z7] \n"
      ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
+      ],
+      "text/plain": []
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<pre style=\"white-space: pre;\"><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">q0: ──X────H────●───────────────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p1)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────●────────────────────────────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">PS</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(p8)─────────────────────────────────────────────────────────────────────────────────────────────────────────────X─────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p12)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────────●────────────────────────────────────X───────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">PS</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(p19)───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────X─────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p23)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────────●─────────────────────────────────────X─────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)──────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">PS</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(p30)───────────────────────────────────────────────────────────────────────────────────────────────────────────────────</span>\n",
+       "<span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">                │               │                             │                            │                                                                                                                                    │                                       │                                    │                                                                                                                                                                      │                                       │                                     │</span>\n",
+       "<span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">q1: ──X─────────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────●────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">-2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p1)────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p1)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────●───────────────────────────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p5)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────●────────────────────────────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">PS</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(p9)──────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────────●──────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">-2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p12)───────X────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p12)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)───────●────────────────────────────────────X─────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p16)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────────●────────────────────────────────────X─────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">PS</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(p20)───────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────────●──────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">-2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p23)───────X────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p23)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────────●───────────────────────────────────────X─────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p27)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────────●────────────────────────────────────X───────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">PS</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(p31)──</span>\n",
+       "<span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">                                                                                                                       │                             │                            │                                                                                                                                                               │                                       │                                    │                                                                                                                                                                          │                                       │                                    │</span>\n",
+       "<span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">q2: ──X────H────●───────────────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p2)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────●────────────────────────────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────●────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">-2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p5)────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p5)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────●────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">PS</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(p10)──────────────────────────────────X─────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p13)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────────●────────────────────────────────────X───────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────────●──────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">-2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p16)───────X────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p16)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)───────●─────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">PS</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(p21)────────────────────────────────────X─────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p24)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────────●─────────────────────────────────────X─────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)──────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────────●──────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">-2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p27)───────X────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p27)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)───────●───────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">PS</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(p32)──────────────</span>\n",
+       "<span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">                │               │                             │                            │                                                                                                                                    │                                       │                                    │                                                                                                                                                                      │                                       │                                     │</span>\n",
+       "<span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">q3: ──X─────────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────●────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">-2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p2)────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p2)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────●───────────────────────────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p6)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────●────────────────────────────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">PS</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(p11)──────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────────●──────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">-2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p13)───────X────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p13)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)───────●────────────────────────────────────X─────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p17)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────────●────────────────────────────────────X─────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">PS</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(p22)───────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────────●──────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">-2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p24)───────X────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p24)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────────●────────────X─────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p28)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────────●──────────────────────────────────────X────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">PS</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(p33)─────────────────────────</span>\n",
+       "<span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">                                                                                                                       │                             │                            │                                                                                                                                                               │                                       │                                    │                                                                                                                                               │                                        │                                      │</span>\n",
+       "<span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">q4: ──X────H────●───────────────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p3)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────●────────────────────────────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────●────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">-2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p6)────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p6)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────●────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">PS</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-p11)─────────────────────────────────X─────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p14)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────────●────────────────────────────────────X───────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────────●──────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">-2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p17)───────X────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p17)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)───────●─────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">PS</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-p22)────────X─────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p25)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────────●──────────────────────────────────────X────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────────●──────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">-2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p28)────────X────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p28)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────────●────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">PS</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-p33)────────────────────────────────────</span>\n",
+       "<span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">                │               │                             │                            │                                                                                                                                    │                                       │                                    │                                                                                                                                           │                                        │                                      │</span>\n",
+       "<span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">q5: ──X─────────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────●────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">-2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p3)────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p3)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────●───────────────────────────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p7)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────●────────────────────────────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">PS</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-p10)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────────●──────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">-2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p14)───────X────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p14)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)───────●──────────X────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p18)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────────●──────────────────────────────────────X────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">PS</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-p21)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────────●──────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">-2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p25)────────X────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p25)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────────●───────────X────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p29)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────────●───────────────────────────────────────X─────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">PS</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-p32)────────────────────────────────────────────────</span>\n",
+       "<span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">                                                                                                                       │                             │                            │                                                                                                                                     │                                       │                                      │                                                                                                                                             │                                       │                                       │</span>\n",
+       "<span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">q6: ──X────H────●───────────────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p4)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────●────────────────────────────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────●────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">-2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p7)────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p7)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────●────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">PS</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-p9)────────X────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p15)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────────●──────────────────────────────────────X────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)───────●─────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">-2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p18)────────X────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p18)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────────●────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">PS</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-p20)───────X────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p26)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────────●───────────────────────────────────────X─────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────────●─────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">-2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p29)────────X────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p29)──────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────────●─────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">PS</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-p31)─────────────────────────────────────────────────────────────</span>\n",
+       "<span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">                │               │                             │                            │                                                                                                          │                                       │                                      │                                                                                                                                         │                                       │                                       │</span>\n",
+       "<span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">q7: ──X─────────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────●────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">-2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p4)────X────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p4)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────●────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">PS</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-p8)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)───────────────────────────────────────────────────────────────────────────────────●─────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">-2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p15)────────X────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p15)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────────●────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">PS</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-p19)────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RZ</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)──────────────────────────────────────────────────────────────────────────────────────────────────────────────●─────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)─────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">-2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p26)────────X────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">*p26)──────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">RY</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-π/</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">2</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">)────────●─────────</span><span style=\"color: #800080; text-decoration-color: #800080; font-weight: bold\">PS</span><span style=\"color: #000080; text-decoration-color: #000080; font-weight: bold\">(-p30)───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────</span>\n",
+       "</pre>\n"
+      ],
+      "text/plain": [
+       "q0: ──X────H────●───────────────X────RZ(2*p1)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)─────PS(p8)─────────────────────────────────────────────────────────────────────────────────────────────────────────────X─────────RZ(2*p12)─────RZ(-π/2)────────●────────────────────────────────────X───────RZ(-π/2)─────PS(p19)───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────X─────────RZ(2*p23)─────RZ(-π/2)────────●─────────────────────────────────────X─────────RZ(-π/2)──────PS(p30)───────────────────────────────────────────────────────────────────────────────────────────────────────────────────\n",
+       "                │               │                             │                            │                                                                                                                                    │                                       │                                    │                                                                                                                                                                      │                                       │                                     │\n",
+       "q1: ──X─────────X────RZ(π/2)────●────RY(π/2)─────RY(-2*p1)────X────RY(2*p1)────RY(-π/2)────●───────────────────────────X────RZ(2*p5)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)─────PS(p9)──────RZ(π/2)─────────●──────────RY(π/2)─────RY(-2*p12)───────X────────RY(2*p12)────RY(-π/2)───────●────────────────────────────────────X─────────RZ(2*p16)─────RZ(-π/2)────────●────────────────────────────────────X─────────RZ(-π/2)─────PS(p20)───────RZ(π/2)─────────●──────────RY(π/2)─────RY(-2*p23)───────X────────RY(2*p23)────RY(-π/2)────────●───────────────────────────────────────X─────────RZ(2*p27)─────RZ(-π/2)────────●────────────────────────────────────X───────RZ(-π/2)────PS(p31)──\n",
+       "                                                                                                                       │                             │                            │                                                                                                                                                               │                                       │                                    │                                                                                                                                                                          │                                       │                                    │\n",
+       "q2: ──X────H────●───────────────X────RZ(2*p2)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)────RZ(π/2)────●────RY(π/2)─────RY(-2*p5)────X────RY(2*p5)────RY(-π/2)────●────PS(p10)──────────────────────────────────X─────────RZ(2*p13)─────RZ(-π/2)────────●────────────────────────────────────X───────RZ(-π/2)─────RZ(π/2)─────────●──────────RY(π/2)─────RY(-2*p16)───────X────────RY(2*p16)────RY(-π/2)───────●─────────PS(p21)────────────────────────────────────X─────────RZ(2*p24)─────RZ(-π/2)────────●─────────────────────────────────────X─────────RZ(-π/2)──────RZ(π/2)─────────●──────────RY(π/2)─────RY(-2*p27)───────X────────RY(2*p27)────RY(-π/2)───────●───────PS(p32)──────────────\n",
+       "                │               │                             │                            │                                                                                                                                    │                                       │                                    │                                                                                                                                                                      │                                       │                                     │\n",
+       "q3: ──X─────────X────RZ(π/2)────●────RY(π/2)─────RY(-2*p2)────X────RY(2*p2)────RY(-π/2)────●───────────────────────────X────RZ(2*p6)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)────PS(p11)──────RZ(π/2)─────────●──────────RY(π/2)─────RY(-2*p13)───────X────────RY(2*p13)────RY(-π/2)───────●────────────────────────────────────X─────────RZ(2*p17)─────RZ(-π/2)────────●────────────────────────────────────X─────────RZ(-π/2)─────PS(p22)───────RZ(π/2)─────────●──────────RY(π/2)─────RY(-2*p24)───────X────────RY(2*p24)────RY(-π/2)────────●────────────X─────────RZ(2*p28)─────RZ(-π/2)─────────●──────────────────────────────────────X────────RZ(-π/2)────PS(p33)─────────────────────────\n",
+       "                                                                                                                       │                             │                            │                                                                                                                                                               │                                       │                                    │                                                                                                                                               │                                        │                                      │\n",
+       "q4: ──X────H────●───────────────X────RZ(2*p3)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)────RZ(π/2)────●────RY(π/2)─────RY(-2*p6)────X────RY(2*p6)────RY(-π/2)────●────PS(-p11)─────────────────────────────────X─────────RZ(2*p14)─────RZ(-π/2)────────●────────────────────────────────────X───────RZ(-π/2)─────RZ(π/2)─────────●──────────RY(π/2)─────RY(-2*p17)───────X────────RY(2*p17)────RY(-π/2)───────●─────────PS(-p22)────────X─────────RZ(2*p25)─────RZ(-π/2)─────────●──────────────────────────────────────X────────RZ(-π/2)─────RZ(π/2)─────────●──────────RY(π/2)─────RY(-2*p28)────────X────────RY(2*p28)─────RY(-π/2)────────●────────PS(-p33)────────────────────────────────────\n",
+       "                │               │                             │                            │                                                                                                                                    │                                       │                                    │                                                                                                                                           │                                        │                                      │\n",
+       "q5: ──X─────────X────RZ(π/2)────●────RY(π/2)─────RY(-2*p3)────X────RY(2*p3)────RY(-π/2)────●───────────────────────────X────RZ(2*p7)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)────PS(-p10)─────RZ(π/2)─────────●──────────RY(π/2)─────RY(-2*p14)───────X────────RY(2*p14)────RY(-π/2)───────●──────────X────────RZ(2*p18)─────RZ(-π/2)─────────●──────────────────────────────────────X────────RZ(-π/2)────PS(-p21)─────RZ(π/2)─────────●──────────RY(π/2)─────RY(-2*p25)────────X────────RY(2*p25)─────RY(-π/2)────────●───────────X────────RZ(2*p29)─────RZ(-π/2)─────────●───────────────────────────────────────X─────────RZ(-π/2)─────PS(-p32)────────────────────────────────────────────────\n",
+       "                                                                                                                       │                             │                            │                                                                                                                                     │                                       │                                      │                                                                                                                                             │                                       │                                       │\n",
+       "q6: ──X────H────●───────────────X────RZ(2*p4)─────RZ(-π/2)────●────────────────────────────X────RZ(-π/2)────RZ(π/2)────●────RY(π/2)─────RY(-2*p7)────X────RY(2*p7)────RY(-π/2)────●────PS(-p9)────────X────────RZ(2*p15)─────RZ(-π/2)─────────●──────────────────────────────────────X────────RZ(-π/2)────RZ(π/2)───────●─────────RY(π/2)─────RY(-2*p18)────────X────────RY(2*p18)─────RY(-π/2)────────●────────PS(-p20)───────X────────RZ(2*p26)─────RZ(-π/2)─────────●───────────────────────────────────────X─────────RZ(-π/2)─────RZ(π/2)────────●─────────RY(π/2)─────RY(-2*p29)────────X────────RY(2*p29)──────RY(-π/2)────────●─────────PS(-p31)─────────────────────────────────────────────────────────────\n",
+       "                │               │                             │                            │                                                                                                          │                                       │                                      │                                                                                                                                         │                                       │                                       │\n",
+       "q7: ──X─────────X────RZ(π/2)────●────RY(π/2)─────RY(-2*p4)────X────RY(2*p4)────RY(-π/2)────●────PS(-p8)─────RZ(π/2)───────────────────────────────────────────────────────────────────────────────────●─────────RY(π/2)─────RY(-2*p15)────────X────────RY(2*p15)─────RY(-π/2)────────●────────PS(-p19)────RZ(π/2)──────────────────────────────────────────────────────────────────────────────────────────────────────────────●─────────RY(π/2)─────RY(-2*p26)────────X────────RY(2*p26)──────RY(-π/2)────────●─────────PS(-p30)───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
     }
    ],
    "source": [
@@ -494,7 +589,6 @@
     "        count += 1\n",
     "\n",
     "ansatz = encoder + ansatz\n",
-    "print(ansatz)\n",
     "ansatz.summary()\n",
     "\n",
     "J = 1\n",
@@ -505,7 +599,8 @@
     "    ham += QubitOperator('Z%d Z%d' % (i, i + 1), J)\n",
     "ham = Hamiltonian(ham - QubitOperator(''))\n",
     "\n",
-    "print(ham)"
+    "print(ham)\n",
+    "ansatz"
    ]
   },
   {
-- 
Gitee