covariant-kernel-learning-full.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qulacs import QuantumState,QuantumCircuit\n",
    "from qulacs import ParametricQuantumCircuit\n",
    "from qulacs.gate import RY,CZ,merge\n",
    "from qulacs.state import inner_product\n",
    "import numpy as np \n",
    "import random\n",
    "\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "attachments": {
    "image-2.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Prepare training/test data\n",
    "![image-2.png](attachment:image-2.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "copied from Noro-san's code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_qubits = 5\n",
    "\n",
    "# 用いるスタビライザー群の要素を決定する\n",
    "# 生成元 XZZZZ, ZXZZZ, ZZXZZ, ZZZXZ, ZZZZX \n",
    "S = np.zeros((n_qubits, 2*n_qubits))\n",
    "S[0] = np.array([1,0, 0,1, 0,1, 0,1, 0,1]) # XZZZZ (X->1,0 Z->0,1 I->0,0としてならべる)\n",
    "S[1] = np.array([0,1, 1,0, 0,1, 0,1, 0,1]) # ZXZZZ\n",
    "S[2] = np.array([0,1, 0,1, 1,0, 0,1, 0,1]) # ZZXZZ\n",
    "S[3] = np.array([0,1, 0,1, 0,1, 1,0, 0,1]) # ZZZXZ\n",
    "S[4] = np.array([0,1, 0,1, 0,1, 0,1, 1,0]) # ZZZZX\n",
    "\n",
    "def x_generator(c, select_bin_i):\n",
    "    SS = np.copy(S)\n",
    "    \n",
    "    #select = np.random.randint(0,2,n_qubits) # i番目の生成元を使う(1)か使わない(0)かを決める行列\n",
    "    se = np.zeros(n_qubits)\n",
    "    for j in range(n_qubits):\n",
    "        se[j] = int(select_bin_i[j])\n",
    "        \n",
    "    for i in range(n_qubits):\n",
    "        SS[i] = SS[i] * se[i]\n",
    "    op = np.sum(SS, axis=0) # それぞれのビットにそれぞれのゲート(X, Z)が何回掛かるかを示す行列\n",
    "\n",
    "    # \\theta_{+-}を計算する\n",
    "    theta = np.zeros(2*n_qubits)\n",
    "\n",
    "    for i in range(n_qubits):\n",
    "        theta[2*i] = c[2*i] + np.pi/2 * op[2*i]\n",
    "        theta[2*i+1] = (-1)**op[2*i] * c[2*i+1] + np.pi/2 * op[2*i+1]\n",
    "\n",
    "    for i in range(2*n_qubits): # 0～\\piの値にする\n",
    "        theta[i] = theta[i] % np.pi\n",
    "    \n",
    "    return theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "random.seed(0)\n",
    "n_data_train = 10\n",
    "epsilon = 0.0 # エラーの分散\n",
    "\n",
    "l = [i for i in range(2**n_qubits)] # 0 = 2**n_qubits-1 のリスト\n",
    "select = random.sample(l, n_data_train)\n",
    "select_bin = [format(select[i], f'0{n_qubits}b') for i in range(n_data_train)]\n",
    "\n",
    "# c_{+-}を決める\n",
    "c_plus = np.pi/2 * np.random.rand(2*n_qubits) - np.pi/4 # - \\pi/4 ～ \\pi/4 のランダムな数\n",
    "c_minus = np.pi/2 * np.random.rand(2*n_qubits) - np.pi/4\n",
    "\n",
    "x_plus = []\n",
    "x_minus = []\n",
    "#x_plus = x_generator(c_plus, select_bin[0]).reshape((1,-1))\n",
    "#x_minus = x_generator(c_minus, select_bin[0]).reshape((1,-1))\n",
    "for i in range(n_data_train):\n",
    "    xx = x_generator(c_plus, select_bin[i]).reshape((1,-1))\n",
    "    e = np.random.normal(0, np.sqrt(epsilon), (1, 2*n_qubits))\n",
    "    x_plus.append(xx + e)\n",
    "    xx = x_generator(c_minus, select_bin[i]).reshape((1,-1))\n",
    "    e = np.random.normal(0, np.sqrt(epsilon), (1, 2*n_qubits))\n",
    "    x_minus.append(xx + e)\n",
    "x_plus = np.concatenate(x_plus)\n",
    "x_minus = np.concatenate(x_minus)\n",
    "x_train = np.concatenate([x_plus,x_minus])\n",
    "y_plus = np.ones(n_data_train)\n",
    "y_minus = -np.ones(n_data_train)\n",
    "y_train = np.concatenate([y_plus, y_minus]).reshape(1,-1)\n",
    "#print(x_train)\n",
    "#print(y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train = y_train.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20, 10)"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create helper function to get fiducial states, kernel matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_featured_gate(n_qubits,Lambda,edges,x):\n",
    "    circuit = ParametricQuantumCircuit(n_qubits)\n",
    "    for i in range(n_qubits):\n",
    "        circuit.add_parametric_RY_gate(i,-Lambda[i])\n",
    "    for control, target  in edges:\n",
    "        circuit.add_CZ_gate(control,target)\n",
    "\n",
    "    for i in range(n_qubits):\n",
    "        circuit.add_RZ_gate(i,x[2*i])\n",
    "        circuit.add_RX_gate(i,x[2*i+1])\n",
    "\n",
    "    return circuit\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "edges= [[0,1],[1,2],[2,3],[3,4],[0,3],[1,3],[1,4],[2,4],[0,2]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_kernel_value(x1,x2,Lambda):\n",
    "\n",
    "    state1 = QuantumState(n_qubits)\n",
    "    state2 = QuantumState(n_qubits)\n",
    "    state1.set_zero_state()\n",
    "    state1.set_zero_state()\n",
    "\n",
    "    circuit1 = create_featured_gate(n_qubits,Lambda,edges,x1)\n",
    "    circuit2 = create_featured_gate(n_qubits,Lambda,edges,x2)\n",
    "    \n",
    "    circuit1.update_quantum_state(state1)\n",
    "\n",
    "    circuit2.update_quantum_state(state2)\n",
    "\n",
    "    return abs(inner_product(state1,state2))**2\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "def construct_kernel_matrix(Lambda,x):\n",
    "\n",
    "    kernel_matrix = np.identity(x.shape[0])\n",
    "    for i in range(x.shape[0]):\n",
    "        for j in range(i):\n",
    "            kernel_matrix[i,j] = get_kernel_value(x[i],x[j],Lambda)\n",
    "            kernel_matrix[j,i] = kernel_matrix[i,j].conjugate()\n",
    "    \n",
    "    return kernel_matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define helper function for cvxopt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "from cvxopt import matrix, solvers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cvxopt_solver(Kernel,y,C):\n",
    "    \n",
    "    P = matrix(np.outer(y,y) * Kernel )\n",
    "    q = matrix(- np.ones(y.shape[0]))\n",
    "    n = Kernel.shape[0] \n",
    "\n",
    "    G = matrix(np.vstack(( - np.eye(n), np.eye(n)  ))) \n",
    "    h = matrix(np.vstack((np.zeros((n, 1)), np.full((n, 1),C) )))\n",
    "    A = matrix(y, (1,n))\n",
    "    b = matrix(np.zeros(1), (1, 1))\n",
    "\n",
    "    solvers.options[\"maxiters\"] = 10000\n",
    "    solvers.options[\"show_progress\"] = False\n",
    "\n",
    "    sol = solvers.qp(P,q,G,h,A,b)\n",
    "    return sol "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Kernel alignment programme"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "C = 1 \n",
    "P = 20 # the number of steps for SPSA\n",
    "### SPSA parameters. \n",
    "c = 0.1\n",
    "gamma = 0.101\n",
    "a = 0.05\n",
    "A = 1\n",
    "sigma = 0.602\n",
    "\n",
    "lam0 = .1\n",
    "lam_history = []\n",
    "F_history = []\n",
    "K_history = []\n",
    "alpha_history = []\n",
    "\n",
    "\n",
    "np.random.seed(1111)\n",
    "\n",
    "lam = np.full(n_qubits, lam0)\n",
    "for i in range(P):\n",
    "\n",
    "    c_i =  c / (i + 1)** gamma\n",
    "    a_i = a / ( i + 1 + A)** sigma\n",
    "\n",
    "    Delta = 2*np.random.randint(0, 2, 1) - 1 \n",
    "    lam_plus = lam + c_i * Delta\n",
    "    lam_minus = lam - c_i * Delta\n",
    "\n",
    "    K = construct_kernel_matrix(lam, x_train)\n",
    "    K_plus = construct_kernel_matrix(lam_plus, x_train)\n",
    "    K_minus = construct_kernel_matrix(lam_minus, x_train)\n",
    "\n",
    "    sol = cvxopt_solver(K,y_train,C)\n",
    "    sol_plus = cvxopt_solver(K_plus,y_train,C)\n",
    "    sol_minus = cvxopt_solver(K_minus,y_train,C)\n",
    "    alpha_plus = np.array(sol_plus['x']).reshape(-1)\n",
    "    alpha_minus = np.array(sol_minus['x']).reshape(-1)\n",
    "    alpha = sol['x']\n",
    "\n",
    "    F_plus = - sol_plus['primal objective']\n",
    "    F_minus = - sol_minus['primal objective']\n",
    "    F = - sol['primal objective']\n",
    "    lam = lam - (F_plus - F_minus)* Delta* a_i / (2 *c_i)\n",
    "    lam_history.append(lam[0])\n",
    "    F_history.append(F)\n",
    "    K_history.append(K)\n",
    "    alpha_history.append(alpha)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.385977270296317\n",
      "[ 6.96e-02]\n",
      "[ 6.69e-01]\n",
      "[ 5.53e-01]\n",
      "[ 1.31e-07]\n",
      "[ 7.58e-01]\n",
      "[ 1.49e-01]\n",
      "[ 1.00e+00]\n",
      "[ 1.00e+00]\n",
      "[ 1.00e+00]\n",
      "[ 3.74e-01]\n",
      "[ 1.00e+00]\n",
      "[ 3.92e-01]\n",
      "[ 1.99e-01]\n",
      "[ 8.74e-06]\n",
      "[ 7.59e-01]\n",
      "[ 6.12e-01]\n",
      "[ 1.00e+00]\n",
      "[ 1.00e+00]\n",
      "[ 3.31e-07]\n",
      "[ 6.12e-01]\n",
      "\n",
      "0.06963391960319282\n"
     ]
    }
   ],
   "source": [
    "print(lam_history[-1])\n",
    "print(alpha_history[-1])\n",
    "a = alpha_history[-1]\n",
    "print(alpha[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "x = np.arange(0,P,1)\n",
    "y = np.array(lam_history)\n",
    "plt.plot(x,y)\n",
    "plt.axhline(np.pi/2,linestyle='--')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## トレーニングデータでの確認"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict(alpha, y_train, x_train, z, Lambda):\n",
    "    kernel_value = np.zeros(len(x_train))\n",
    "    for i in range(len(x_train)):\n",
    "        kernel_value[i] = y_train[i] * alpha[i] * get_kernel_value(x_train[i], z, Lambda)\n",
    "    return np.sign(np.sum(kernel_value))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0]\n",
      "[ 1.  1.  1.  1.  1.  1.  1.  1.  1.  1. -1. -1. -1. -1. -1. -1. -1. -1.\n",
      " -1. -1.]\n",
      "[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      "0.0\n"
     ]
    }
   ],
   "source": [
    "predict_train = []\n",
    "lam_vector = np.full(n_qubits, lam_history[-1])\n",
    "for i in range(len(x_train)):\n",
    "    predict_train.append(predict(alpha_history[-1], y_train, x_train, x_train[i], lam_vector))\n",
    "print(predict_train)\n",
    "print(y_train.reshape(-1))\n",
    "print(predict_train - y_train.reshape(-1))\n",
    "print(np.sum(np.abs(predict_train - y_train.reshape(-1)))/2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## テストデータでの確認"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "テストデータ生成"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_data_test = 20\n",
    "epsilon = 0.0 # エラーの分散\n",
    "\n",
    "l = [i for i in range(2**n_qubits)] # 0 = 2**n_qubits-1 のリスト\n",
    "select = random.sample(l, n_data_test)\n",
    "select_bin = [format(select[i], f'0{n_qubits}b') for i in range(n_data_test)]\n",
    "\n",
    "x_plus = []\n",
    "x_minus = []\n",
    "for i in range(n_data_test):\n",
    "    xx = x_generator(c_plus, select_bin[i]).reshape((1,-1))\n",
    "    e = np.random.normal(0, np.sqrt(epsilon), (1, 2*n_qubits))\n",
    "    x_plus.append(xx + e)\n",
    "    xx = x_generator(c_minus, select_bin[i]).reshape((1,-1))\n",
    "    e = np.random.normal(0, np.sqrt(epsilon), (1, 2*n_qubits))\n",
    "    x_minus.append(xx + e)\n",
    "x_plus = np.concatenate(x_plus)\n",
    "x_minus = np.concatenate(x_minus)\n",
    "x_test = np.concatenate([x_plus,x_minus])\n",
    "y_plus = np.ones(n_data_test)\n",
    "y_minus = -np.ones(n_data_test)\n",
    "y_test = np.concatenate([y_plus, y_minus]).reshape(1,-1)\n",
    "#print(x_test)\n",
    "#print(y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0]\n",
      "[ 1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.  1.\n",
      "  1.  1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1. -1.\n",
      " -1. -1. -1. -1.]\n",
      "[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
      " 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      "0.0\n"
     ]
    }
   ],
   "source": [
    "predict_test = []\n",
    "lam_vector = np.full(n_qubits, lam_history[-1])\n",
    "for i in range(len(x_test)):\n",
    "    predict_test.append(predict(alpha_history[-1], y_train, x_train, x_test[i], lam_vector))\n",
    "print(predict_test)\n",
    "print(y_test.reshape(-1))\n",
    "print(predict_test - y_test.reshape(-1))\n",
    "print(np.sum(np.abs(predict_test - y_test.reshape(-1)))/2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Under construction..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "class KernelMatrix:\n",
    "\n",
    "    def __init__(self,n_qubit,Lambda,edges) -> None:\n",
    "        self.n_qubit = n_qubit\n",
    "        self.Lambda = Lambda\n",
    "        self.edges = edges\n",
    "        self.state1 = QuantumState(n_qubit)\n",
    "        self.state2 = QuantumState(n_qubit)\n",
    "\n",
    "    def make_fiducial_state(self,Lambda):\n",
    "        circuit = ParametricQuantumCircuit(self.n_qubit)\n",
    "        for i in range(self.n_qubit):\n",
    "            circuit.add_parametric_RY_gate(Lambda)\n",
    "        for control, target in self.edges:\n",
    "            circuit.add_CZ_gate(control,target)\n",
    "        return circuit\n",
    "\n",
    "    def create_featured_gate(self,theta):\n",
    "        circuit = ParametricQuantumCircuit(self.n_qubit)\n",
    "        for i in range(self.n_qubit):\n",
    "            circuit.add_parametric_RY_gate(i,self.Lambda)\n",
    "        for control, target in self.edges:\n",
    "            circuit.add_CZ_gate(control,target)\n",
    "\n",
    "        for i in range(self.n_qubit):\n",
    "            circuit.add_RZ_gate(i,theta[i,0])\n",
    "            circuit.add_RX_gate(i,theta[i,1])\n",
    "\n",
    "        return circuit\n",
    "        \n",
    "    def featured_gate(self,theta):\n",
    "        circuit = QuantumCircuit(self.n_qubit)\n",
    "        for i in range(self.n_qubit):\n",
    "            circuit.add_RZ_gate(i,theta[i,0])\n",
    "            circuit.add_RX_gate(i,theta[i,1])\n",
    "\n",
    "        return circuit\n",
    "\n",
    "    def get_kernel_value(self,x1,x2):\n",
    "        self.state1.set_zero_state()\n",
    "        self.state1.set_zero_state()\n",
    "        fiducial_gate = self.make_fiducial_state()\n",
    "\n",
    "\n",
    "        featured_gate1 = self.featured_gate(x1)\n",
    "        featured_gate2 = self.featured_gate(x2)\n",
    "        \n",
    "        circuit1 = merge(fiducial_gate,featured_gate1)\n",
    "        circuit1.update_quantum_state(state1)\n",
    "        circuit2 = merge(fiducial_gate,featured_gate2)\n",
    "        circuit2.update_quantum_state(state2)\n",
    "\n",
    "        return inner_product(state1,state2)\n",
    "    \n",
    "    def construct_kernel_matrix(self,x_data):\n",
    "        \"\"\"\n",
    "        Args:\n",
    "            x_data : MxNxD array of data where N is the number of samples,\n",
    "             N the number of qubits, D the feature dimension\n",
    "        \"\"\"\n",
    "        kernel_matrix = np.identity(x_data.shape[0])\n",
    "        for i in range(x_data.shape[0]):\n",
    "            for j in range(i):\n",
    "                kernel_matrix[i,j] = self.get_kernel_value(x_data[i],x_data[j])\n",
    "                kernel_matrix[j,i] = kernel_matrix[i,j].conjugate()\n",
    "        \n",
    "        return kernel_matrix\n",
    "\n",
    "    def spsa(self,x_data,y_label,n_step,initial_Lambda = 0.01):\n",
    "        Lambda = initial_Lambda\n",
    "        for i in n_step:\n",
    "            Delta = 2 * np.random.rand() - 1\n",
    "\n",
    "            c_i = c / ( i + 1)**gamma\n",
    "            Lambda__pm_i = Lambda + np.array([Delta*c_i, - Delta*c_i])\n",
    "            self.construct_kernel_matrix()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array([0,1 ]) + 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       " *** Quantum State ***\n",
       " * Qubit Count : 2\n",
       " * Dimension   : 4\n",
       " * State vector : \n",
       "(1,0)\n",
       "(0,0)\n",
       "(0,0)\n",
       "(0,0)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "KernelMatrix(2,np.pi,[[0,1]]).state1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "state1 = QuantumState(n)\n",
    "state2 = QuantumState(n)\n",
    "def get_kernel_value(x1,x2):\n",
    "    state1.set_zero_state()\n",
    "    create_featured_gate()"
   ]
  }
 ],
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