Shor_quantum_detail.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import *\n",
    "import numpy as np\n",
    "import math\n",
    "from qiskit.tools.visualization import plot_histogram\n",
    "%matplotlib inline\n",
    "\n",
    "N = 15\n",
    "a = 13\n",
    "\n",
    "math.gcd(a, N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1704.86x3575.88 with 1 Axes>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "if a not in [2,7,8,11,13]:\n",
    "    raise ValueError(\"'a' must be 2,7,8,11 or 13\")\n",
    "n = 4 # number of qubits needed to represent number that will be done prime factorization\n",
    "qr = QuantumRegister(2*n) # Prepare 2*n quantum registers as |x>|w> = |x3 x2 x1 x0>|w3 w2 w1 w0>\n",
    "cr = ClassicalRegister(2*n)\n",
    "qc = QuantumCircuit(qr, cr)\n",
    "# Hadamard gates\n",
    "for i in range(n):\n",
    "    qc.h(i)\n",
    "\n",
    "# |w> -> |1>\n",
    "qc.x(n)\n",
    "\n",
    "# Implement U_f (f(x) = a^x (mod N))  U_f|x>|w> = |x>|w+f(x)> (\"+\" represents \"XOR\")\n",
    "for i in range(n):\n",
    "    for j in range(2**i):\n",
    "        if a in [2,13]:\n",
    "            qc.cswap(i, n+2, n+3)\n",
    "            qc.cswap(i, n+1, n+2)\n",
    "            qc.cswap(i, n+0, n+1)\n",
    "        if a in [7,8]:\n",
    "            qc.cswap(i, n+0, n+1)\n",
    "            qc.cswap(i, n+1, n+2)\n",
    "            qc.cswap(i, n+2, n+3)\n",
    "        if a in [11]:\n",
    "            qc.cswap(i, n+0, n+2)\n",
    "            qc.cswap(i, n+1, n+3)\n",
    "        if a in [7,11,13,14]:\n",
    "            for k in range(n):\n",
    "                qc.cx(i, n+k)\n",
    "qc.barrier()\n",
    "\n",
    "# Implement QFTdagger\n",
    "for i in range(n//2): # Swap the qubits\n",
    "    qc.swap(i, n-i-1)\n",
    "    \n",
    "for i in range(n):\n",
    "    for j in range(i):\n",
    "        qc.cu1(-np.pi/(2**(i-j)), j, i) \n",
    "    qc.h(i)\n",
    "qc.barrier()\n",
    "\n",
    "# Measure\n",
    "qc.measure(range(n), range(n))\n",
    "\n",
    "# Show quantum circuit\n",
    "qc.draw(output='mpl', initial_state=True)      "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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aN27MkCFDKCoqYvPmzQAMHjyYFStW7Fg+rGfPnjRo0IDi4mIA2rZty0EHHcT06dMB2G+//Rg8eDAzZszYMU/tkCFDWLx4MZ988gkAvXv3pqysjPnz5wPQvn17OnTowIwZMwBo2rQphYWFdTZPUNXdsbpn1apVNZKn3cnYNHpmlg+sBIa5e2rT6k3Ame5+yB5e/x1CsTzD3cdH21oB7wHfc/eJ0bYngVbu/q09xVRT0+ipeTZ5lJNkUl6SRznZ1e6m0cvkleZaoAxoW2F7a3a9+txJSsE8u7xgRvoC7YAJKWvs7RO9phTo4+7zqx+6iIhIBu9puvs2YBYwssKukYRetJUys9OBZ4Fz3f2lCrv/BfQjNM2W/4wndBIaCCyukeBFRETIfO/Ze4FnzGwmMA24EMgHHgEws6cB3P3s6PkZhCvMa4DJZlZ+lbrN3de7++fA3NRfYGafAXnuvtN2ERGR6spo0XT3F8ysJXAjoVl1LjDK3ZdGh1S8I30hIcb7op9yk4CjazdaERGRnWV8EWp3fwh4qIp9R+/ueczzn7s3cYmIiOyJ5p4VERGJSUVTREQkJhVNERGRmFQ0RUREYlLRFBERiUlFU0REJCYVTRERkZhUNEVERGJS0RQREYlJRVNERCQmFU0REZGYVDRFRERiUtEUERGJSUVTREQkJhVNERGRmFQ0RUREYlLRFBERiUlFU0REJCYVTRERkZhUNEVERGJKq2ia2elmdnzK85+Z2Qoze9PM2tV8eCIiIsmR7pXmzeUPzKwA+DHwANAQ+GXNhSUiIpI8eWke3xmYHz3+NvBnd/9fM3sLeLNGIxMREUmYdK80twLNosfHAhOix/9J2S4iIlIvpXulOQX4pZlNBQqBU6PtBwPLazIwERGRpEn3SvNSYBuhWF7o7h9H209EzbMiIlLPpXWl6e4rgJMq2X5ljUUkIiKSUGmP0zSzfc3sVDO7zsz2j7Z1M7MWNR+eiIhIcqR1pWlm3Qmdf5oC+wMvAp8BF0XPz6vpAEVERJIi3SvN+4C3gDbAlpTt44ERNRWUiIhIEqXbe/ZI4Ah3LzOz1O3LgPwai0pERCSB9mbu2YaVbOtEGKspIiJSb6VbNN8Crkp57mbWHLgF+EuNRSUiIpJA6TbPXgX8w8zmA/sCLwDdgdXA6TUcm4iISKKkO07zYzMbCJwJFBCuVH8D/M7dt+z2xSIiInVculeaRMXxiehHREQkZ+yxaJrZKcCr7v5l9LhK7v7HGotMREQkYeJcab4EtAXWRI+r4kCDmghKREQkifZYNN19n8oei4iI5Jq0iqCZDTOzXQqtmTUws2E1F5aIiEjypHvl+A+gsonZ94/2iYiI1FvpFk0j3LusqCXwefXDERERSa5YQ07MbHz00IFnzawkZXcDoC/wdg3HJiIikihxx2mui/5rwAZ2XuFkGzAVeLQG4xIREUmcWEXT3b8PYGZLgHvcXU2xIiKSc9KdRu+W2gpEREQk6eLMCPQeMNzdN5jZ+1TeEQgAd+9fk8GJiIgkSZwrzZeB8o4/u5sRSEREpF6LMyPQLZU9FhERyTWaFk9ERCSmOPc0d3sfM5XuaYqISH0Wd5UTERGRnJfWPU0REZFcpnuaIiIiMWmcpoiISEwapykiIhJTxsdpmtnFwFigHfABcKW7T6ni2HbAL4ECoAfwjLufW8lxzYHbgFMJy5QtB37s7n+obrwiIiLl0pp7tpyZdQN6RU/nuftHMV/3XeB+4GLCyigXA6+bWW93X1bJSxoDa4FfAGOqOGdD4C3C6iunAyuADnx1dSwiIlIj0iqaZtYSeBwYDWz/arO9BvzA3ddV+eLgKuBJdy9fRuwyMzsBuAi4oeLB7r4EuDz6JadWcc7vA62BYe6+Ldq2JNYbEhERSUO6vWcfA7oDRwH7Rj/DgIPYw3qaZtYIOJRwVZjqLeDINONIdTIwDXjQzD4xs2Izuzm6AhUREakx6TbPfgM41t2np2ybZmYXABP28NpWQANgdYXtq4Hj0owjVVfgGOD3wDeBLsD/BZoC11Q82MzGEDX15ufnM3HixHCSrl1p1qwZc+bMAaBly5b06dOHyZMnA5CXl8fQoUOZPXs2GzduBKCwsJDVq1cD3aoRfrKU///o27cvJSUlLFy4EICOHTvSpk0bioqKAGjevDkFBQVMnTqV0tJSAIYNG8YHH3zAunWhwWHAgAFs2rSJRYsWAdClSxdatGjB7NmzATjggAMYMGAAkyZNwt0xM4YPH86cOXPYsGEDAAUFBaxfv54lS5YA8fNUn0yfPp2SknC3YejQoSxYsIA1a9YAdS9P9WmUW/lnpWnTphQWFtbZPEGn2v0flUGrVq1i/vz5ALRv354OHTowY8YMIL087Y65x5ohLxxsthQ4yd3fq7B9APCqu1f5f9/M8oGVhGbUKSnbbwLOdPdD9vC7XwPWVuwIZGYLCFe8B7l7WbRtDPAroKnv5g0WFhZ6+T/a6jj/vmqfIjEevTLbEdQM5SSZlJfkUU52ZWaz3L2wsn3pfu27FbjPzNqnnLw9oYfrrXt47VqgDGhbYXtrdr36TMcqYEF5wYzMA5oQrm5FRERqxN5M2H4QsMTMVkbP2wNbCcXvsarO4+7bzGwWMBJ4MWXXSMJY0L01Dfieme3j7uWdkw4GviAUahERkRqR6Qnb7wWeMbOZhGJ3IZAPPAJgZk8DuPvZ5S8ws4HRw+bA9uj5NncvjrY/DFwK3G9m4wj3NG8BHtpd06yIiEi6Mjphu7u/EA1buZEwucFcYJS7L40Oqeye6DsVnp8ELCUUR9x9uZkdTyjI7wKfAE8QJjsQERGpMXs1uUF1uPtDwENV7Du6km0W45z/pHrDVkRERPYorY5AZtbIzG4xswVmttXMylJ/aitIERGRJEi39+zPgXMIvWW3E+aQ/b/AOsKUeCIiIvVWukXzdOBCd/81YfjIK+5+OXAToResiIhIvZVu0WwDlPda3QzsHz1+Azi+poISERFJonSL5jLCEBGAfxOm1QMYAmypqaBERESSKN2i+Sfg2Ojx/cAtZrYYeJLdTGwgIiJSH6Q15MTdb0h5/JKZrSAM9Vjg7q/VdHAiIiJJUq1xmtH4yH/WUCwiIiKJlvY6PWZWYGZPm1lR9POMmRXURnAiIiJJku7kBv8N/IswBd5fo582wEwzO6vmwxMREUmOdJtnbwd+6u53pG40sxsIc70+W1OBiYiIJE26zbMHAn+oZPuLhKXBRERE6q10i+Y/gKMr2X40MKm6wYiIiCRZnEWoT0l5+jpwp5kV8lWv2SOAU4Cbazw6ERGRBNnbRajHRD+pHqSKJb9ERETqgziLUKc9LEVERKQ+UkEUERGJaW8mN/immU02s7Vm9qmZTTKzUbURnIiISJKkO7nBeYRJ2z8CrgOuBxYDfzKzH9R8eCIiIsmR7uQG1wFXufu4lG2Pm9ksQgF9osYiExERSZh0m2c7ERacruh1oHP1wxEREUmuvVmEemQl248HllY/HBERkeRKt3n2HuDBaFWTtwEHhgL/A1xWw7GJiIgkSrqLUP/azNYAVxNmAQKYB5zu7q/UdHAiIiJJErtomlkeoRl2srv/qfZCEhERSabY9zTdvRT4I9Cs9sIRERFJrnQ7As0ButdGICIiIkmXbtG8GfilmZ1sZh3NrEXqTy3EJyIikhjp9p79S/TfPxJ6zpaz6HmDmghKREQkidItmiNqJQoREZE6IFbRNLMmwN3AyUBDYAJwubuvrcXYREREEiXuPc1bgHMJzbPPEWYFeriWYhIREUmkuM2zpwA/dPfnAczsd8A0M2vg7mW1Fp2IiEiCxL3S7AhMKX/i7jOBUiC/NoISERFJorhFswGwrcK2UtLvSCQiIlJnxS16BjxrZiUp2/YFHjWzL8o3uPvomgxOREQkSeIWzacq2fZsTQYiIiKSdLGKprt/v7YDERERSbp0p9ETERHJWSqaIiIiMaloioiIxKSiKSIiEpOKpoiISEwqmiIiIjGpaIqIiMSkoikiIhKTiqaIiEhMKpoiIiIxqWiKiIjEpKIpIiISk4qmiIhITCqaIiIiMaloioiIxKSiKSIiEpOKpoiISEwqmiIiIjGpaIqIiMSU8aJpZheb2WIz22pms8zsqD0cPzw6bquZLTKzCyvsb2BmP08552Izu83M8mr3nYiISK7JaNE0s+8C9wN3AIOAt4HXzaxTFccfBPw1Om4QcCfwoJl9J+Ww64BLgMuBQ4Arouc31NLbEBGRHJXpq7GrgCfd/dHo+WVmdgJwEZUXuQuBj939suj5PDMbDFwDvBxtOxJ41d1fjZ4vMbPxwOBaeQciIpKzMnalaWaNgEOBtyrseotQ+CozpJLj3wQKzaxh9HwqMMLMDol+T2/gGMIVqoiISI3J5JVmK6ABsLrC9tXAcVW8pi0woZLj86LzrQLuApoBxWZWFu273d0fquyEZjYGGAOQn5/PxIkTAejatSvNmjVjzpw5ALRs2ZI+ffowefJkAPLy8hg6dCizZ89m48aNABQWFrJ69WqgW5z3XyeU///o27cvJSUlLFy4EICOHTvSpk0bioqKAGjevDkFBQVMnTqV0tJSAIYNG8YHH3zAunXrABgwYACbNm1i0aJFAHTp0oUWLVowe/ZsAA444AAGDBjApEmTcHfMjOHDhzNnzhw2bNgAQEFBAevXr2fJkiVA/DzVJ9OnT6ekpASAoUOHsmDBAtasWQPUvTzVp76H5Z+Vpk2bUlhYWGfzBJXeHauTVq1axfz58wFo3749HTp0YMaMGUB6edodc/dafAspv8gsH1gJDHP3KSnbbwLOdPdDKnnNAuAZd/95yrbhwESgnbt/YmZnAHcDY4EPgIGE+6Zj3f3x3cVUWFjo5f9oq+P8+6p9isR49MpsR1AzlJNkUl6SRznZlZnNcvfCyvZl8kpzLVBGuHpM1Zpdrz7LfVLF8aXAuuj53cA97v589Px9M+tMuEe626IpIiKSjoy1lbj7NmAWMLLCrpGE3rGVmc6uTbcjgSJ3/zJ63oRQjFOVUZ/agUREJBEy3Xv2XuAZM5sJTCP0js0HHgEws6cB3P3s6PhHgEvN7D7g18DXgXOBM1PO+SpwvZktJjTPDiL00n26tt+MiIjklowWTXd/wcxaAjcC7YC5wCh3Xxod0qnC8YvNbBTwK8KwlI+By9395ZTDLgN+DjxEaLpdBTwK3Fqb70VERHJPxmfNiXq1Vtqz1d2PrmTbJKBgN+fbBFwZ/YiIiNQa3fcTERGJSUVTREQkJhVNERGRmFQ0RUREYlLRFBERiUlFU0REJCYVTRERkZhUNEVERGJS0RQREYlJRVNERCQmFU0REZGYVDRFRERiUtEUERGJSUVTREQkJhVNERGRmFQ0RUREYlLRFBERiUlFU0REJCYVTRERkZhUNEVERGJS0RQREYlJRVNERCQmFU0REZGYVDRFRERiUtEUERGJSUVTREQkJhVNERGRmFQ0RUREYlLRFBERiUlFU0REJCYVTRERkZhUNEVERGJS0RQREYlJRVNERCQmFU0REZGYVDRFRERiUtEUERGJSUVTREQkJhVNERGRmFQ0RUREYlLRFBERiUlFU0REJCYVTRERkZhUNEVERGJS0RQREYlJRVNERCQmFU0REZGYVDRFRERiUtEUERGJSUVTREQkJhVNERGRmFQ0RUREYlLRFBERiUlFU0REJCYVTRERkZhUNEVERGLKeNE0s4vNbLGZbTWzWWZ21B6OHx4dt9XMFpnZhdU9p4iIyN7IaNE0s+8C9wN3AIOAt4HXzaxTFccfBPw1Om4QcCfwoJl9Z2/PKSIisrcyfaV5FfCkuz/q7vPc/TJgFXBRFcdfCHzs7pdFxz8KPAVcU41zioiI7JWMFU0zawQcCrxVYddbwJFVvGxIJce/CRSaWcO9PKeIiMheycvg72oFNABWV9i+Gjiuite0BSZUcnxedD5L95xmNgYYEz3dbGbz4wSfAK2AtbX9Sx77UW3/hnqn1vOinKRNn5Vkqkuflc5V7chk0SznFZ5bJdv2dHz5dtvNMZWe091/A/xmz2Emi5kVuXthtuOQnSkvyaOcJFN9yUsmi+ZaoIxw9ZiqNbteKZb7pIrjS4F1hOKY7jlFRPOj1zEAABDYSURBVET2Ssbuabr7NmAWMLLCrpGEHq+Vmc6uzawjgSJ3/3IvzykiIrJXMt08ey/wjJnNBKYResfmA48AmNnTAO5+dnT8I8ClZnYf8Gvg68C5wJlxz1mP1Lkm5RyhvCSPcpJM9SIv5r6724m18AvNLgauBdoBc4EfufvkaN9EAHc/OuX44cCvgD7Ax8Bd7v5I3HOKiIjUlIwXTRERkbpKc8+KiIjEpKIpIiISk4pmHWdmVv7f8seSXSk50ecrQZSX5CnPRV3KSZ0JVCrn7m5m+3ikfLsKaPZEOWno7tuzHYt8RXlJHnffbmb7Rf9tkO144lBHoDrMzPYHjifMv9sN+Dvwmrsvy2pgOczM8oGTCGOF2wETCfMlz3L3z6NjzPXByyjlJXnMrAdwKnAK0JwwLv/vwHR3Xxgdk7icqGjWYWb2e2AY8BGwHjiCML/jROB2d5+YteBylJm9BhwCzAA2AcOBg4F3gV+4+4tZDC9nKS/JY2aTCcXyDeAL4ETgMGAZcL+735/F8KqUjblnpQZE41ePB44C5gNNo58hwHnA02b2M3d/MmtB5hgzG0b44tLf3T9O2X4ocCnwqJkNcPcbsxVjLlJekifKSW+gh7tviDbfamYHAlcCt5nZ4cAP3X1rtuKsjO5p1l0nEpqW5rn7dnff6O4fu/vLhFmTXgb+18wOzmqUueVooBhYA2BmDaLmpVmELzI/Ay40s4LshZiTjkZ5SZpCYBFh7nDMbF8zy3P3T939J8BZhClUh2QxxkqpaNZdk4BeZjag4g53Xw3cBHxI+IMhmfEm0IMw3SPuXhZ1Pmng7mXAw8Bsdp0rWWqX8pI8fwXaE7784+5b3b3UzBpGz18BZhJa0xJFRbPumgEsBJ4zswvMrFuFbttlQBfCvU7JjPeBKcAfzewOMzs8+vZcFu1vAvQEFmctwtykvCTPv4E/Ac+a2e/N7AQza+TuXwJEzbT9gDnZDLIy6ghUh5lZT+BmoIDQ1PFPYBWho8MJwAh375S1AHNQ1KP5WsJVSwnhi81KwlJ1JwLd3L1n9iLMTcpLMpnZD4HvETowbgCWAssJTbON3D1xTeYqmnVcNLbpG8D/EG6sO6HZYxpwt7tPy2J4OSkaI3sooSt9f8IfhE6EJqkH3T1x355zgfKSTGbWmfBlpgDoDnQA/gw87u4fZTO2yqho1kFR555vAJ8SvjHPdfcSM2tOKJwfAlvcvSSLYeYMM8sjdJU/ibA4+lJgjrsvNLN9gbbuviSahEID6zNEeUkeM9uPUCBPAT4jXO3PJozR3ALs6+5bshfhnqlo1jFm9nPCVWUJYZB2E+AD4HnCt+XNWQwvJ5nZg8C3CH8E2gCNCE1MU4FH3P2DLIaXs5SX5DGzpwg9YlcShsg1JLSO/Rt4NuoAlGjqCFSHRPcwLwN+Qmjz358w/qwIuAFYYGajo2M1jV4GmNkhwDnAJcCR7p5PmHDiL4Q/2NOi+zbKSQYpL8kT/f36DmHs5Qh3Pwz4NvAY0AJ4ysx+HB2b2JzoSrMOMbOfAse4+4jo+Y5mJTP7L8Ji3f2BY939P9mLNHeY2VjgW+4+PHq+U1Ofmd1G6OhwlLuvzFKYOUd5SR4zuxQ4w92HRs8r5uRC4DZgmLsXZynMPdKVZt2yAjjQzNrBjsmOG5lZ46hI3k9o8vhONoPMMf8GOkezl6TmZN9o/68JvQLPyFaAOUp5SZ5ioLuZnQI7//2K9j9LuNWU6JyoaNYtbwIHEMY2DQFw923lHX6i3n9bgTqxWkA98f+AtYSp2EbCjpxsjR4vJ3zOEt25oR5SXpJnEqFX/y/N7CzY5e/XZsJctJ9mL8Q9U/NsHVE+2380A9D9QGtgLmFy9r8ROjtcBFwFdHT3TdmKNVek5KQDoWn8aGAJYQLqPxL+KJ9D+ObcTTnJjAp5eYAwOfsilJesSclJc+BO4GxgGyEffwL2BU4HjgR6J7lDo4pmHWRmBxGW1BlOGJPZFdiPsGLDb9394SyGl1PK78uYWStCV/oRhGEO/QhX/TOBx9z991kMM2eZWSPCkJMTgcMJQ7KUlyxIKZxG6MB4ImGavEGEpvJ/Ao+6+1+yGOYeqWjWEWbWAmhJKI6bCVN+fY3wR6AZsB1YoE4N2RXNPNMaKAX+C1iSsoqDZICZdSIMx2pHaKItcvetZtaWcEVzALDY3T/LYpg5qbxwRo8bEf6ebSFMMrG8LowtV9GsA8zsTOACQpf5tYQJDf5NuMf5V334M69Cz2UjfJY0QD7LzOwCYAzh6mUZ4fOyiXCP8w/uviA6LnGLG9dXZtYa+Mzdt2U7lpqgjkAJF125PEBoeu1J6CY/kdAseyMwLvpHKRkS3ZeZZmbXmdlBHpQX0H1SjuuS0ltTaln0WbmLsCxeC+A0whjARYSxmQ+YWR8AFczMiD4rE4B7zGyEmbWobAymmQ2Mhs0lnq40E87MLgfOcvfDK2zfDzgZ+DnRSvTuvjELIeacaLzZA4QrmQ6EKcCeAF5x9/XRMe2BpwgDuZdmK9ZcYmYXAz9w98IK2xsROmndQmgGPMxTFqOW2mNmlxA+K/MIt5LmAX8AXiXcTtocDaF7FfheeUtAkulKM/kaE1qTOsJOi7VucffnCJ0cmgJDsxlkjjkMeAQ4inAFs5zQe3aZmb1oZscTxsoOVcHMqBJg3/KrSQuLTe8TDWt4CxhFGM5wdBZjzDWDCJ+VQUAvQg/mMYSlDf9iZmMIt54OqQsFE1Q064I/EDoAnQc7LdaaFz2fR5iMulf2QswdUXPrv4GP3X25u78B/DfQB7iUMLXhH4H7gLuzFmhueoWwjuyPzKyDh8Wmt5c3B0Ydsj4HDspmkLkiusIvIkyUX+ru8939andvT+g1uxL4BfAz4JfZizQ9ap5NuOge2aWEf1RLCd/afuvu68ysJWGpoz8B/ZO4jE59FPVkPtDd51eyL4+wAs2rQBd3X5bp+HKZmZ0KPBQ9fZowy8xywpeZQ4HHgYH6rGSGmTUFDnD35dHfMk+9n2xmg4BZ1KHPiopmHWFm3QmL6I4mrAO4mDChQVvgJXf/URbDy1lRkXR3L0vZdhPhXqYWAM8CM/sacDlwFqEF5mNgI2G2mUfd/ZYshicpos/Khe7eLtuxxKWimXBRE0dnd18YPW9P+MY8kDBO8yXgvbowvqm+MLOGhFmXFlXYXj594VWE8ZkvZjy4HBZdyezj7qXR8/0JHbUGE/oGvAUs0tCgzKk4KXuFfQacSRiO8tfMRrb3VDQTysz6AVcTZjH5D2Gw/GTgd0leAaA+q5CTzwj3z6YDv3f3d1OOawxs07CGzDCzfcvnlJVkqCwnlY2NNbOG7v5lZqOrHhXNhDKzhYTu2dOBPMIiuocTZpl5A7hL3eYzq4qcFBJy8hZwu7uvyV6EucnCMl9FwBxCB62SlH1GWMCgkbt/kaUQc87ucpJyTBN3/6KuTTSRl+0AZFdm9j1Cz+azysdemlkz4BBCJ5PvA/uZ2aX1ZZaNpFNOksnMTgd+TLjy/zdhGMMk4EPgU3cvi+47P2xmd1TWeUtqVsyc7EvIyZ3u/mEWw02brjQTyMyuJxoDWNk3MDP7P8BvgJPcfWam48tFykkymdkThHmXnyLMlvVtwv3LGcBrhKWoBgC/dvfGVZ1Hak59z4nGaSbTROAY4Nroaqai8cAC4LhMBpXjJqKcJEp0BbkaWO/uU9z9IndvS+g1WwLcAfyZsJTeH7IXae7IhZzoSjOhzOwnwPnA68CThFXPt7l7iZl1JtwrGOXub2cvytyinCRL1Fu2J/A1dy8ys0apTePRVJOXEuajLXT32VkKNWfkQk5UNBPGvlqfsSFhuqmrCPNlziU0a3QEDgY+cvdvZS/S3KGcJF/KrD+eOnbWzM4Bxrl7Za0DUovqa05UNBOoYndtMxsGfJfQU/NDwgK6L7v7J1kKMecoJ8lUxdCG8i85+wC3Arj7jVkJMAfV95yoaCaIhUVyTwUKCDOZzAReSG3u05i0zFJOkqlCXnoC/wRedPd/phxjhOFAX6hHc+3LlZyoaCaImf0F6E4YC/gx8HXCROCLCJN//9bDZO1VzrIhNUs5SaZK8nIk0JcwxOEXwDOpUxtK7cuVnGicZkKY2TGEyQsGufuKaBxTY8I/unOBG4BmwL3645wZykkyxcjLzwiLUN+btSBzTC7lREUzOYYB77v7CghLgAFbgWlm9j5wGXCrmU2siz3O6ijlJJmUl+TJmZxonGZyTAD6mdkJFXdEM9DcBbwNDM90YDlMOUkm5SV5ciYnKprJMYsw/m+cmd1gZgXREkflmgK9CWtqSmYoJ8mkvCRPzuREHYESxMw6Eu6THQdsIPTUXE1YTWMI0NPde2YvwtyjnCST8pI8uZITFc0EMrP+hGmnjiTcd96fsLLGve7+fjZjy1XKSTIpL8lT33Oiopll0dqL/YFTgE3Ae0BR+SB5M+sJLEHrM2aMcpJMykvy5GJOVDSzzMweIPyDW0Xokt0F+IQwqfH/unudvwdQ1ygnyaS8JE8u5kQdgbLIzHoTxjD9ADjB3bsBbYEHgVHAh2Z2QfkcjlL7lJNkUl6SJ1dzoivNLDKzHxP+sQ2Lnue5e2nK/jsI3+KOcfePsxRmTlFOkkl5SZ5czYmuNLNrHtDOzLoDRNOx5UWzaQA8CnwBnJatAHOQcpJMykvy5GROVDSzazJQCrxmZqebWWN3Ly2f/NvdFwMNCDNrSGYoJ8mkvCRPTuZEzbNZZmb5wK+AfsAKYAbwj+jxJcD3gC7u/nnWgswxykkyKS/Jk4s5UdFMADNrCXwTOB7oSlhW5wBgEvBrd38+i+HlJOUkmZSX5Mm1nKhoZomZdSAsowPwOVAMbCH8o2tKuBew1t3XZyfC3KOcJJPykjy5nBMVzSwws4sI3bQHEP5xLQKWAxOBl9x9efaiy03KSTIpL8mT6zlRR6AMi5oy7gBeAdoBRwBPEG6ojwF+G41/Kl/lXGqZcpJMykvyKCe60sw4M7sMOMvdB1eybyhwJ9AeONzd12Y6vlyknCST8pI8yomuNLNhG9DMzPpCmLvRzBoBuPtU4L8JXbSPz16IOUc5SSblJXlyPicqmpn3ErAduNLMmrl7ibtvM7N9ANx9GfAZ0CGbQeYY5SSZlJfkyfmcqGhmUNTGvx64ERgJfGxmj5vZodH+TmZ2FmHM0x+yF2nuUE6SSXlJHuUk0D3NLDCz/YFOhPXmvg18Pdr1CeGLzNPufnN2ostNykkyKS/Jk+s5UdHMEDNrDfwPcDWwljCm6TNgCmEWjYZAN+BNYGF9WXsuyZSTZFJekkc5+YqKZoaY2ZNAH+BVQhNHC0IzxsHAGuBGd5+RtQBzkHKSTMpL8ignX1HRzIDoXsAmYJS7T07Z1okwzumHhJk0Tnf32VkLNIcoJ8mkvCSPcrIzdQTKjN7AYkJ3bQA8WOruLwAnEZo66tUSOgmnnCST8pI8ykkKFc3MWERowviVmfUo755dzt1LgKeAE7MRXI5STpJJeUke5SSFimYGuPsW4CfAfsDTwNlm1tHMvgZgZk2A4cDc7EWZW5STZFJekkc52ZnuaWZQNIvGT4HRhJUBpgOfAscBq4Dz3P397EWYe5STZFJekkc5CVQ0syDqvv1N4GTClFNzgRfd/cOsBpbDlJNkUl6SJ9dzoqKZZWa2j7tvz3Yc8hXlJJmUl+TJxZyoaIqIiMSkjkAiIiIxqWiKiIjEpKIpIiISk4qmiIhITCqaIiIiMaloioiIxKSiKSIiEtP/B9nhSBkHUjgzAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simulator = Aer.get_backend('qasm_simulator')\n",
    "result = execute(qc, backend = simulator, shots=1024).result()\n",
    "plot_histogram(result.get_counts())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}