Figure5.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Figure 5\n",
    "Divide-and-conquer state preparion proof of concept"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Informe seu API_TOKEN: ········\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from encoding import Encoding\n",
    "from qiskit import IBMQ, ClassicalRegister, QuantumRegister, QuantumCircuit, Aer, execute\n",
    "from qiskit.visualization import plot_histogram\n",
    "import getpass\n",
    "\n",
    "MY_API_TOKEN = getpass.getpass(\"Informe seu API_TOKEN: \")\n",
    "IBMQ.enable_account(MY_API_TOKEN)\n",
    "provider = IBMQ.get_provider(hub='ibm-q-research', group='Adenilton-Silva')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# Figure 5.b\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 490.028x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('# Figure 5.b')\n",
    "input_vector = np.array([np.sqrt(0.6), np.sqrt(0.2), np.sqrt(0.1), np.sqrt(0.1)])\n",
    "\n",
    "betas = []\n",
    "Encoding._recursive_compute_beta(input_vector, betas)\n",
    "angles = []\n",
    "for alist in betas:\n",
    "    angles = angles + alist\n",
    "    \n",
    "qr = QuantumRegister(3)\n",
    "cr = ClassicalRegister(2)\n",
    "qcircuit = QuantumCircuit(qr, cr)\n",
    "\n",
    "for k, value in enumerate(angles):\n",
    "    qcircuit.ry(value, k)\n",
    "\n",
    "qcircuit.cx(1,2)\n",
    "qcircuit.ccx(0, 2, 1)\n",
    "\n",
    "qcircuit.measure(1,0)\n",
    "qcircuit.measure(0,1)\n",
    "\n",
    "qcircuit.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit = qcircuit\n",
    "backend_sim = Aer.get_backend('qasm_simulator')\n",
    "shots = 1024\n",
    "job = execute(circuit, backend_sim, shots = shots, optimization_level=3)\n",
    "results = job.result()\n",
    "counts = results.get_counts()\n",
    "# print(counts)\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit = qcircuit\n",
    "backend = provider.get_backend('ibmq_rome')\n",
    "shots = 1024\n",
    "layout = [0, 1, 2]\n",
    "job = execute(circuit, backend, shots = shots, initial_layout=layout)\n",
    "results = job.result()\n",
    "counts_rome = results.get_counts()\n",
    "plot_histogram(counts_rome)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Figure 5.a\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('Figure 5.a')\n",
    "plot_histogram([counts, counts_rome])"
   ]
  }
 ],
 "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": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}