covariant-kernel-learning-T.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "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.png": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Prepare training/test data\n",
    "\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "copied from Noro-san's code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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 XZIII, ZXZZI, IZXII, IZIXZ, IIIZX\n",
    "S = np.zeros((n_qubits, 2*n_qubits))\n",
    "S[0] = np.array([1,0, 0,1, 0,0, 0,0, 0,0]) # XZIII (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, 0,0]) # ZXZZI\n",
    "S[2] = np.array([0,0, 0,1, 1,0, 0,0, 0,0]) # IZXII\n",
    "S[3] = np.array([0,0, 0,1, 0,0, 1,0, 0,1]) # IZIXZ\n",
    "S[4] = np.array([0,0, 0,0, 0,0, 0,1, 1,0]) # IIIZX\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": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#random.seed(0)\n",
    "n_data_train = 20\n",
    "epsilon = 0.01 # 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": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train = y_train.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(40, 10)"
      ]
     },
     "execution_count": 5,
     "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": 6,
   "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": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "edges= [[0,1],[1,2],[1,3],[3,4]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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": 9,
   "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": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from cvxopt import matrix, solvers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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": 12,
   "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": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.1120695696934393\n",
      "[ 1.00e+00]\n",
      "[ 1.00e+00]\n",
      "[ 3.03e-01]\n",
      "[ 1.00e+00]\n",
      "[ 1.00e+00]\n",
      "[ 8.99e-01]\n",
      "[ 1.00e+00]\n",
      "[ 1.00e+00]\n",
      "[ 1.00e+00]\n",
      "[ 1.00e+00]\n",
      "[ 1.00e+00]\n",
      "[ 1.00e+00]\n",
      "[ 1.00e+00]\n",
      "[ 1.00e+00]\n",
      "[ 7.50e-01]\n",
      "[ 1.00e+00]\n",
      "[ 1.00e+00]\n",
      "[ 1.00e+00]\n",
      "[ 1.00e+00]\n",
      "[ 1.00e+00]\n",
      "[ 1.00e+00]\n",
      "[ 1.00e+00]\n",
      "[ 9.41e-01]\n",
      "[ 1.00e+00]\n",
      "[ 1.00e+00]\n",
      "[ 1.00e+00]\n",
      "[ 1.00e+00]\n",
      "[ 1.00e+00]\n",
      "[ 1.00e+00]\n",
      "[ 1.00e+00]\n",
      "[ 5.25e-01]\n",
      "[ 1.00e+00]\n",
      "[ 1.00e+00]\n",
      "[ 4.86e-01]\n",
      "[ 1.00e+00]\n",
      "[ 1.00e+00]\n",
      "[ 1.00e+00]\n",
      "[ 1.00e+00]\n",
      "[ 1.00e+00]\n",
      "[ 1.00e+00]\n",
      "\n",
      "0.9999998673145716\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": 14,
   "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": 15,
   "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": 16,
   "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.\n",
      " -2.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.\n",
      "  0.  0.  0.  0.]\n",
      "1.0\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": 17,
   "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": 18,
   "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. -2.  0. -2.  0.  0.  0.  0. -2.  0. -2.  0.  0.  0.\n",
      "  0.  0.  0.  0.  0.  0.  0.  2.  0.  0.  0.  0.  0.  0.  2.  0.  0.  0.\n",
      "  0.  0.  0.  0.]\n",
      "6.0\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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