Qiskit-HHL.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "##HHL validate with the paper###\n",
    "\n",
    "from qiskit import Aer, transpile, assemble\n",
    "from qiskit.circuit.library import QFT\n",
    "from qiskit.aqua import QuantumInstance, aqua_globals\n",
    "from qiskit.quantum_info import state_fidelity\n",
    "from qiskit.aqua.algorithms import HHL, NumPyLSsolver\n",
    "from qiskit.aqua.components.eigs import EigsQPE\n",
    "from qiskit.aqua.components.reciprocals import LookupRotation\n",
    "from qiskit.aqua.operators import MatrixOperator\n",
    "from qiskit.aqua.components.initial_states import Custom\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "def create_eigs(matrix, num_auxiliary, num_time_slices, negative_evals):\n",
    "    ne_qfts = [None, None]\n",
    "    if negative_evals:\n",
    "        num_auxiliary += 1\n",
    "        ne_qfts = [QFT(num_auxiliary - 1), QFT(num_auxiliary - 1).inverse()]\n",
    "\n",
    "    return EigsQPE(MatrixOperator(matrix=matrix),\n",
    "                   QFT(num_auxiliary).inverse(),\n",
    "                   num_time_slices=num_time_slices,\n",
    "                   num_ancillae=num_auxiliary,\n",
    "                   expansion_mode='suzuki',\n",
    "                   expansion_order=2,\n",
    "                   evo_time=None,  # This is t, can set to: np.pi*3/4\n",
    "                   negative_evals=negative_evals,\n",
    "                   ne_qfts=ne_qfts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fidelity(hhl, ref):\n",
    "    solution_hhl_normed = hhl / np.linalg.norm(hhl)\n",
    "    solution_ref_normed = ref / np.linalg.norm(ref)\n",
    "    fidelity = state_fidelity(solution_hhl_normed, solution_ref_normed)\n",
    "    return fidelity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix:\n",
      " [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]\n",
      "Eigen Values: [1. 1. 1. 1.]\n",
      "Condition Number: 1.0\n"
     ]
    }
   ],
   "source": [
    "#https://www.sciencedirect.com/science/article/pii/S037596012030462X?via%3Dihub\n",
    "# to solve for linear equation Ax=b and comparing results with the paper\n",
    "\n",
    "matrix = [[1.5, 0.5], [0.5, 1.5]] #A \n",
    "vector = [0.707, 0.707]           #b\n",
    "\n",
    "\n",
    "matrix=[[1,0,0,0],\n",
    "[0,1,0,0],\n",
    "[0,0,1,0],\n",
    "[0,0,0,1]]\n",
    "\n",
    "vector = [0.707, 0.707, 0.707, 0.707]           #b\n",
    "\n",
    "e,v=np.linalg.eig(matrix)\n",
    "\n",
    "print('Matrix:\\n',matrix)\n",
    "print('Eigen Values:',e)\n",
    "print('Condition Number:',max(e)/min(e))\n",
    "#to find x using the HHL "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "orig_size = len(vector)\n",
    "matrix, vector, truncate_powerdim, truncate_hermitian = HHL.matrix_resize(matrix, vector)\n",
    "\n",
    "# Initialize eigenvalue finding module\n",
    "eigs = create_eigs(matrix, 3, 50, False)\n",
    "num_q, num_a = eigs.get_register_sizes()\n",
    "\n",
    "# Initialize initial state module\n",
    "init_state = Custom(num_q, state_vector=vector)\n",
    "\n",
    "# Initialize reciprocal rotation module\n",
    "reci = LookupRotation(negative_evals=eigs._negative_evals, evo_time=eigs._evo_time)\n",
    "\n",
    "algo = HHL(matrix, vector, truncate_powerdim, truncate_hermitian, eigs,\n",
    "           init_state, reci, num_q, num_a, orig_size)\n",
    "\n",
    "\n",
    "circ=algo.construct_circuit(measurement=True)\n",
    "#circ.draw(fold=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solution:\t\t [0.707-0.j 0.707-0.j 0.707-0.j 0.707-0.j]\n",
      "Classical Solution:\t [0.707 0.707 0.707 0.707]\n",
      "Probability:\t\t 0.020408\n",
      "Fidelity:\t\t 1.000000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "result = algo.run(QuantumInstance(Aer.get_backend('statevector_simulator')))\n",
    "print(\"Solution:\\t\\t\", np.round(result['solution'], 5))\n",
    "\n",
    "#print(result)\n",
    "\n",
    "result_ref = NumPyLSsolver(matrix, vector).run()\n",
    "print(\"Classical Solution:\\t\", np.round(result_ref['solution'], 5))\n",
    "\n",
    "print(\"Probability:\\t\\t %f\" % result['probability_result'])\n",
    "fid=fidelity(result['solution'], result_ref['solution'])\n",
    "print(\"Fidelity:\\t\\t %f\\n\" % fid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_hhl_fidelity(matrix,vector,condition_num):\n",
    "    orig_size = len(vector)\n",
    "    matrix, vector, truncate_powerdim, truncate_hermitian = HHL.matrix_resize(matrix, vector)\n",
    "\n",
    "    # Initialize eigenvalue finding module\n",
    "    eigs = create_eigs(matrix, 3, 50, False)\n",
    "    num_q, num_a = eigs.get_register_sizes()\n",
    "\n",
    "    # Initialize initial state module\n",
    "    init_state = Custom(num_q, state_vector=vector)\n",
    "\n",
    "    # Initialize reciprocal rotation module\n",
    "    reci = LookupRotation(negative_evals=eigs._negative_evals, evo_time=eigs._evo_time)\n",
    "\n",
    "    algo = HHL(matrix, vector, truncate_powerdim, truncate_hermitian, eigs,\n",
    "           init_state, reci, num_q, num_a, orig_size)\n",
    "\n",
    "\n",
    "    circ=algo.construct_circuit(measurement=True)\n",
    "    \n",
    "    result = algo.run(QuantumInstance(Aer.get_backend('statevector_simulator')))\n",
    "    \n",
    "    print('Matrix:\\n',matrix)\n",
    "    print('Condition Number:',condition_num)\n",
    "    print(\"Solution:\\t\\t\", np.round(result['solution'], 5))\n",
    "\n",
    "    #print(result)\n",
    "\n",
    "    result_ref = NumPyLSsolver(matrix, vector).run()\n",
    "    print(\"Classical Solution:\\t\", np.round(result_ref['solution'], 5))\n",
    "\n",
    "    print(\"Probability:\\t\\t %f\" % result['probability_result'])\n",
    "    fid=fidelity(result['solution'], result_ref['solution'])\n",
    "    \n",
    "    print(\"Fidelity:\\t\\t %f\\n\" % fid)\n",
    "    return fid\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix:\n",
      " [[1 0]\n",
      " [0 1]]\n",
      "Condition Number: 1.0\n",
      "Solution:\t\t [0.707-0.j 0.707-0.j]\n",
      "Classical Solution:\t [0.707 0.707]\n",
      "Probability:\t\t 0.020408\n",
      "Fidelity:\t\t 1.000000\n",
      "\n",
      "Matrix:\n",
      " [[1.  0.2]\n",
      " [0.2 1. ]]\n",
      "Condition Number: 1.5\n",
      "Solution:\t\t [0.58917-0.j 0.58917-0.j]\n",
      "Classical Solution:\t [0.58917 0.58917]\n",
      "Probability:\t\t 0.020408\n",
      "Fidelity:\t\t 1.000000\n",
      "\n",
      "Matrix:\n",
      " [[1.  0. ]\n",
      " [0.  0.5]]\n",
      "Condition Number: 2.0\n",
      "Solution:\t\t [0.68522-0.j 1.45625-0.j]\n",
      "Classical Solution:\t [0.707 1.414]\n",
      "Probability:\t\t 0.056291\n",
      "Fidelity:\t\t 0.999432\n",
      "\n",
      "Matrix:\n",
      " [[1.5 0. ]\n",
      " [0.  0.5]]\n",
      "Condition Number: 3.0\n",
      "Solution:\t\t [0.45231+0.j 1.46885+0.j]\n",
      "Classical Solution:\t [0.47133 1.414  ]\n",
      "Probability:\t\t 0.117814\n",
      "Fidelity:\t\t 0.999470\n",
      "\n",
      "Matrix:\n",
      " [[0.69 0.49]\n",
      " [0.49 0.92]]\n",
      "Condition Number: 4.336674861504795\n",
      "Solution:\t\t [0.72257-0.j 0.39795-0.j]\n",
      "Classical Solution:\t [0.77023 0.35825]\n",
      "Probability:\t\t 0.037255\n",
      "Fidelity:\t\t 0.995375\n",
      "\n",
      "Matrix:\n",
      " [[0.75 0.5 ]\n",
      " [0.5  0.75]]\n",
      "Condition Number: 4.999999999999998\n",
      "Solution:\t\t [0.5656-0.j 0.5656-0.j]\n",
      "Classical Solution:\t [0.5656 0.5656]\n",
      "Probability:\t\t 0.020408\n",
      "Fidelity:\t\t 1.000000\n",
      "\n",
      "Matrix:\n",
      " [[1.  0. ]\n",
      " [0.  0.1]]\n",
      "Condition Number: 10.0\n",
      "Solution:\t\t [0.87806+0.j 4.78243+0.j]\n",
      "Classical Solution:\t [0.707 7.07 ]\n",
      "Probability:\t\t 0.312914\n",
      "Fidelity:\t\t 0.993306\n",
      "\n",
      "Matrix:\n",
      " [[1.   0.  ]\n",
      " [0.   0.01]]\n",
      "Condition Number: 100.0\n",
      "Solution:\t\t [0.99985+0.j 0.05699+0.j]\n",
      "Classical Solution:\t [ 0.707 70.7  ]\n",
      "Probability:\t\t 0.010237\n",
      "Fidelity:\t\t 0.004474\n",
      "\n",
      "Matrix:\n",
      " [[1.    0.   ]\n",
      " [0.    0.001]]\n",
      "Condition Number: 1000.0\n",
      "Solution:\t\t [9.9985e-01+0.j 5.3000e-04+0.j]\n",
      "Classical Solution:\t [  0.707 707.   ]\n",
      "Probability:\t\t 0.010204\n",
      "Fidelity:\t\t 0.000002\n",
      "\n",
      "Fidelity for different condition number - HHL:\n",
      "[[1.000e+00 1.000e+00]\n",
      " [1.500e+00 1.000e+00]\n",
      " [2.000e+00 9.994e-01]\n",
      " [3.000e+00 9.995e-01]\n",
      " [4.337e+00 9.954e-01]\n",
      " [5.000e+00 1.000e+00]\n",
      " [1.000e+01 9.933e-01]\n",
      " [1.000e+02 4.500e-03]\n",
      " [1.000e+03 0.000e+00]]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 675x450 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "matlist=[np.array([[1,0],[0,1]]),\n",
    "         np.array([[1,0.2],[0.2,1]]),\n",
    "        np.array([[1,0],[0,0.5]]),\n",
    "        np.array([[1.5,0],[0,0.5]]),\n",
    "        np.array([[0.69,0.49],[0.49,0.92]]),\n",
    "        np.array([[0.75,0.5],[0.5,0.75]]),\n",
    "        np.array([[1,0],[0,0.1]]),\n",
    "        np.array([[1,0],[0,0.01]]),\n",
    "        np.array([[1,0],[0,0.001]])]\n",
    "\n",
    "result=np.zeros((len(matlist),2))\n",
    "\n",
    "for i in range(len(matlist)):\n",
    "    vector = [0.707, 0.707]\n",
    "    \n",
    "    e,v=np.linalg.eig(matlist[i])\n",
    "    k=max(e)/min(e)\n",
    "\n",
    "    fid=get_hhl_fidelity(matlist[i],vector,k)\n",
    "    \n",
    "    result[i,0]=round(k,3)\n",
    "    result[i,1]=round(fid,4)\n",
    "\n",
    "print('Fidelity for different condition number - HHL:')\n",
    "print(result)\n",
    "\n",
    "\n",
    "fig = plt.figure(figsize=(9,6),dpi=75)\n",
    "ax = plt.axes()\n",
    "\n",
    "ax.plot(result[:,0], result[:,1],color='blue');\n",
    "plt.title(\"Fidelity v/s Condition Number\")\n",
    "plt.xlabel(\"Condition Number k\")\n",
    "plt.ylabel(\"Fidelity\");\n",
    "\n",
    "plt.savefig('2_2Matrix.png')\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix:\n",
      " [[1 0 0 0]\n",
      " [0 1 0 0]\n",
      " [0 0 1 0]\n",
      " [0 0 0 1]]\n",
      "Condition Number: 1.0\n",
      "Solution:\t\t [0.707-0.j 0.707-0.j 0.707-0.j 0.707-0.j]\n",
      "Classical Solution:\t [0.707 0.707 0.707 0.707]\n",
      "Probability:\t\t 0.020408\n",
      "Fidelity:\t\t 1.000000\n",
      "\n",
      "Matrix:\n",
      " [[1.  0.  0.  0. ]\n",
      " [0.  1.  0.  0. ]\n",
      " [0.  0.  1.  0. ]\n",
      " [0.  0.  0.  0.5]]\n",
      "Condition Number: 2.0\n",
      "Solution:\t\t [0.72721-0.j 0.72721-0.j 0.72721-0.j 1.28511-0.j]\n",
      "Classical Solution:\t [0.707 0.707 0.707 1.414]\n",
      "Probability:\t\t 0.057857\n",
      "Fidelity:\t\t 0.996206\n",
      "\n",
      "Matrix:\n",
      " [[1.    0.333 0.    0.   ]\n",
      " [0.333 1.    0.333 0.   ]\n",
      " [0.    0.333 1.    0.333]\n",
      " [0.    0.    0.333 1.   ]]\n",
      "Condition Number: 3.3365634495764898\n",
      "Solution:\t\t [0.5638 -0.j 0.39753-0.j 0.39753-0.j 0.5638 -0.j]\n",
      "Classical Solution:\t [0.57851 0.38586 0.38586 0.57851]\n",
      "Probability:\t\t 0.036317\n",
      "Fidelity:\t\t 0.999329\n",
      "\n",
      "Matrix:\n",
      " [[0.97 0.   0.   0.  ]\n",
      " [0.   0.81 0.   0.  ]\n",
      " [0.   0.   0.3  0.  ]\n",
      " [0.   0.   0.   0.13]]\n",
      "Condition Number: 7.461538461538461\n",
      "Solution:\t\t [0.7262 +0.j 0.883  +0.j 2.50939-0.j 5.01425+0.j]\n",
      "Classical Solution:\t [0.72887 0.87284 2.35667 5.43846]\n",
      "Probability:\t\t 0.318373\n",
      "Fidelity:\t\t 0.996945\n",
      "\n",
      "Matrix:\n",
      " [[ 1.  -0.5  0.   0. ]\n",
      " [-0.5  1.  -0.5  0. ]\n",
      " [ 0.  -0.5  1.  -0.5]\n",
      " [ 0.   0.  -0.5  1. ]]\n",
      "Condition Number: 9.47213595499957\n",
      "Solution:\t\t [2.74582-0.j 3.78031-0.j 3.78031-0.j 2.74582-0.j]\n",
      "Classical Solution:\t [2.828 4.242 4.242 2.828]\n",
      "Probability:\t\t 0.511433\n",
      "Fidelity:\t\t 0.998386\n",
      "\n",
      "Matrix:\n",
      " [[1.  0.  0.  0. ]\n",
      " [0.  1.  0.  0. ]\n",
      " [0.  0.  1.  0. ]\n",
      " [0.  0.  0.  0.1]]\n",
      "Condition Number: 10.0\n",
      "Solution:\t\t [0.81042+0.j 0.81042+0.j 0.81042+0.j 1.70391+0.j]\n",
      "Classical Solution:\t [0.707 0.707 0.707 7.07 ]\n",
      "Probability:\t\t 0.078849\n",
      "Fidelity:\t\t 0.755189\n",
      "\n",
      "Matrix:\n",
      " [[0.99 0.37 0.31 0.  ]\n",
      " [0.37 0.32 0.15 0.15]\n",
      " [0.31 0.15 0.6  0.21]\n",
      " [0.   0.15 0.21 0.73]]\n",
      "Condition Number: 11.156596154058812\n",
      "Solution:\t\t [0.38232-0.j 0.70464-0.j 0.53377-0.j 0.7247 -0.j]\n",
      "Classical Solution:\t [-0.25037  2.01205  0.67875  0.3598 ]\n",
      "Probability:\t\t 0.053789\n",
      "Fidelity:\t\t 0.553949\n",
      "\n",
      "Matrix:\n",
      " [[1.   0.   0.   0.  ]\n",
      " [0.   1.   0.   0.  ]\n",
      " [0.   0.   1.   0.  ]\n",
      " [0.   0.   0.   0.01]]\n",
      "Condition Number: 100.0\n",
      "Solution:\t\t [0.81637+0.j 0.81637+0.j 0.81637+0.j 0.0132 +0.j]\n",
      "Classical Solution:\t [ 0.707  0.707  0.707 70.7  ]\n",
      "Probability:\t\t 0.036385\n",
      "Fidelity:\t\t 0.000710\n",
      "\n",
      "Matrix:\n",
      " [[1.    0.    0.    0.   ]\n",
      " [0.    1.    0.    0.   ]\n",
      " [0.    0.    1.    0.   ]\n",
      " [0.    0.    0.    0.001]]\n",
      "Condition Number: 1000.0\n",
      "Solution:\t\t [8.1637e-01+0.j 8.1637e-01+0.j 8.1637e-01+0.j 1.2000e-04+0.j]\n",
      "Classical Solution:\t [  0.707   0.707   0.707 707.   ]\n",
      "Probability:\t\t 0.036919\n",
      "Fidelity:\t\t 0.000003\n",
      "\n",
      "Fidelity for different condition number - HHL:\n",
      "[[1.0000e+00 1.0000e+00]\n",
      " [2.0000e+00 9.9620e-01]\n",
      " [3.3370e+00 9.9930e-01]\n",
      " [7.4620e+00 9.9690e-01]\n",
      " [9.4720e+00 9.9840e-01]\n",
      " [1.0000e+01 7.5520e-01]\n",
      " [1.1157e+01 5.5390e-01]\n",
      " [1.0000e+02 7.0000e-04]\n",
      " [1.0000e+03 0.0000e+00]]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 675x450 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "matlist=[np.array([[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]),\n",
    "         np.array([[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,0.5]]),\n",
    "         np.array([[1,0.333,0,0],[0.333,1,0.333,0],[0,0.333,1,0.333],[0,0,0.333,1]]),\n",
    "         np.array([[0.97,0,0,0],[0,0.81,0,0],[0,0,0.3,0],[0,0,0,0.13]]),\n",
    "         np.array([[1,-0.5,0,0],[-0.5,1,-0.5,0],[0,-0.5,1,-0.5],[0,0,-0.5,1]]),\n",
    "         np.array([[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,0.1]]),\n",
    "         np.array([[0.99,0.37,0.31,0],[0.37,0.32,0.15,0.15],[0.31,0.15,0.6,0.21],[0,0.15,0.21,0.73]]),\n",
    "         np.array([[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,0.01]]),\n",
    "         np.array([[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,0.001]])]\n",
    "\n",
    "result=np.zeros((len(matlist),2))\n",
    "\n",
    "for i in range(len(matlist)):\n",
    "    vector = [0.707, 0.707, 0.707, 0.707]\n",
    "    \n",
    "    e,v=np.linalg.eig(matlist[i])\n",
    "    k=max(e)/min(e)\n",
    "\n",
    "    fid=get_hhl_fidelity(matlist[i],vector,k)\n",
    "    \n",
    "    result[i,0]=round(k,3)\n",
    "    result[i,1]=round(fid,4)\n",
    "\n",
    "print('Fidelity for different condition number - HHL:')\n",
    "print(result)\n",
    "\n",
    "fig = plt.figure(figsize=(9,6),dpi=75)\n",
    "ax = plt.axes()\n",
    "\n",
    "ax.plot(result[:,0], result[:,1],color='green');\n",
    "plt.title(\"Fidelity v/s Condition Number\")\n",
    "plt.xlabel(\"Condition Number k\")\n",
    "plt.ylabel(\"Fidelity\");\n",
    "\n",
    "plt.savefig('2_2Matrix.png')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Finite Difference Matrix Simulation\n",
    "\n",
    "### Example 1 - 4*4 matrix "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix:\n",
      " [[ 2 -1  0  0]\n",
      " [-1  2 -1  0]\n",
      " [ 0 -1  2 -1]\n",
      " [ 0  0 -1  2]]\n",
      "Eigen Values: [3.61803399 2.61803399 0.38196601 1.38196601]\n",
      "Condition Number: 9.47213595499957\n"
     ]
    }
   ],
   "source": [
    "matrix = np.array([[2, -1, 0, 0], [-1, 2, -1, 0], [0, -1,  2, -1],[0, 0, -1, 2]])\n",
    "vector = [0.707, 0.707, 0.707, 0.707]\n",
    "\n",
    "e,v=np.linalg.eig(matrix)\n",
    "\n",
    "print('Matrix:\\n',matrix)\n",
    "print('Eigen Values:',e)\n",
    "print('Condition Number:',max(e)/min(e))\n",
    "#to find x using the HHL "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "orig_size = len(vector)\n",
    "matrix, vector, truncate_powerdim, truncate_hermitian = HHL.matrix_resize(matrix, vector)\n",
    "\n",
    "# Initialize eigenvalue finding module\n",
    "eigs = create_eigs(matrix, 5, 50, False)\n",
    "num_q, num_a = eigs.get_register_sizes()\n",
    "\n",
    "# Initialize initial state module\n",
    "init_state = Custom(num_q, state_vector=vector)\n",
    "\n",
    "# Initialize reciprocal rotation module\n",
    "reci = LookupRotation(negative_evals=eigs._negative_evals, evo_time=eigs._evo_time)\n",
    "\n",
    "algo = HHL(matrix, vector, truncate_powerdim, truncate_hermitian, eigs,\n",
    "           init_state, reci, num_q, num_a, orig_size)\n",
    "\n",
    "\n",
    "circ=algo.construct_circuit(measurement=True)\n",
    "#circ.draw(fold=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solution:\t\t [1.41389-0.j 2.11194-0.j 2.11194-0.j 1.41389-0.j]\n",
      "Classical Solution:\t [1.414 2.121 2.121 1.414]\n",
      "Probability:\t\t 0.105431\n",
      "Fidelity:\t\t 0.999996\n",
      "\n"
     ]
    }
   ],
   "source": [
    "result = algo.run(QuantumInstance(Aer.get_backend('statevector_simulator')))\n",
    "print(\"Solution:\\t\\t\", np.round(result['solution'], 5))\n",
    "\n",
    "#print(result)\n",
    "\n",
    "result_ref = NumPyLSsolver(matrix, vector).run()\n",
    "print(\"Classical Solution:\\t\", np.round(result_ref['solution'], 5))\n",
    "\n",
    "print(\"Probability:\\t\\t %f\" % result['probability_result'])\n",
    "fid=fidelity(result['solution'], result_ref['solution'])\n",
    "print(\"Fidelity:\\t\\t %f\\n\" % fid)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}