community/algorithms/grover_algorithm.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"../../images/qiskit-heading.gif\" alt=\"Note: In order for images to show up in this jupyter notebook you need to select File => Trusted Notebook\" width=\"500 px\" align=\"left\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Grover Search for Combinatorial Problems\n",
    "\n",
    "\n",
    "The latest version of this notebook is available on https://github.com/qiskit/qiskit-tutorial.\n",
    "\n",
    "***\n",
    "### Contributors\n",
    "Giacomo Nannicini and Rudy Raymond (based on [this paper](https://arxiv.org/abs/1708.03684)) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "Grover search is one of the most popular algorithms used for searching a solution among many possible candidates using Quantum Computers. If there are $N$ possible solutions among which there is exactly one solution (that can be verified by some function evaluation), then Grover search can be used to find the solution with $O(\\sqrt{N})$ function evaluations. This is in contrast to classical computers that require $\\Omega(N)$ function evaluations: the Grover search is a quantum algorithm that provably can be used search the correct solutions quadratically faster than its classical counterparts.  \n",
    "\n",
    "Here, we are going to illustrate the use of Grover search to solve a combinatorial problem called [Exactly-1 3-SAT problem](https://en.wikipedia.org/wiki/Boolean_satisfiability_problem#Exactly-1_3-satisfiability). The Exactly-1 3-SAT problem is a NP-complete problem, namely, it is one of the most difficult problems that are interconnected (meaning that if we solve any one of them, we essentially can solve all of them). Unfortunately, there are many natural problems that are NP-complete, such as, the Traveling Salesman Problem (TSP), the Maximum Cut (MaxCut) and so on. Up to now, there is no classical and quantum algorithm that can efficiently solve such NP-hard problems. \n",
    "\n",
    "We begin with an example of the Exactly-1 3-SAT problem. Then, we show how to design an evaluation function which is also known as the oracle (or, blackbox) which is essential to Grover search. Finally, we show the circuit of Grover search using the oracle and present their results on simulator and real-device backends."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exactly-1 3-SAT problem\n",
    "\n",
    "The Exactly-1 3-SAT problem is best explained with the following concrete problem. Let us consider a Boolean function $f$ with three Boolean variables $x_1, x_2, x_3$ as below.\n",
    "\n",
    "$$\n",
    "f(x_1, x_2, x_3) = (x_1 \\vee x_2 \\vee \\neg x_3) \\wedge (\\neg x_1 \\vee \\neg x_2 \\vee \\neg x_3) \\wedge (\\neg x_1 \\vee x_2 \\vee x_3) \n",
    "$$\n",
    "\n",
    "In the above function, the terms on the right-hand side equation which are inside $()$ are called clauses. Each clause has exactly three literals. Namely, the first clause has $x_1$, $x_2$ and $\\neg x_3$ as its literals. The symbol $\\neg$ is the Boolean NOT that negates (or, flips) the value of its succeeding literal. The symbols $\\vee$ and $\\wedge$ are, respectively, the Boolean OR and AND. The Boolean $f$ is satisfiable if there is an assignment of $x_1, x_2, x_3$ that evaluates to $f(x_1, x_2, x_3) = 1$ (or, $f$ evaluates to True). The Exactly-1 3-SAT problem requires us to find an assignment such that $f = 1$ (or, True) and there is *exactly* one literal that evaluates to True in every clause of $f$. \n",
    "\n",
    "A naive way to find such an assignment is by trying every possible combinations of input values of $f$. Below is the table obtained from trying all possible combinations of $x_1, x_2, x_3$. For ease of explanation, we interchangably use $0$ and False, as well as $1$ and True.  \n",
    "\n",
    "|$x_1$ | $x_2$ | $x_3$ | $f$ | Comment | \n",
    "|------|-------|-------|-----|---------|\n",
    "| 0    |  0    |  0    |  1  | Not a solution because there are three True literals in the second clause     | \n",
    "| 0    |  0    |  1    |  0  | Not a solution because $f$ is False          | \n",
    "| 0    |  1    |  0    |  1  | Not a solution because there are two True literals in the first clause        | \n",
    "| 0    |  1    |  1    |  1  | Not a solution because there are three True literals in the third clause        | \n",
    "| 1    |  0    |  0    |  0  | Not a solution because $f$ is False        | \n",
    "| 1    |  0    |  1    |  1  | **Solution**. BINGO!!       | \n",
    "| 1    |  1    |  0    |  1  | Not a soluton because there are three True literals in the first clause        | \n",
    "| 1    |  1    |  1    |  0  | Not a solution because $f$ is False        | \n",
    "\n",
    "\n",
    "From the table above, we can see that the assignment $x_1x_2x_3 = 101$ is the solution fo the Exactly-1 3-SAT problem to $f$. In general, the Boolean function $f$ can have many clauses and more Boolean variables. \n",
    "\n",
    "## A blackbox function to check the assignment of Exactly-1 3-SAT problem\n",
    "\n",
    "Here, we describe a method to construct a circuit to check the assignment of Exactly-1 3-SAT problem. The circuit can then be used as a blackbox (or, oracle) in Grover search. To design the blackbox, we do not need to know the solution to the problem in advance: it suffices to design a blackbox that checks if the assignment results in $f$ evaluates to True or False. It turns out that we can design such a blackbox efficiently (in fact, any NP-complete problem has the property that although finding the solution is difficult, checking the solution is easy). \n",
    "\n",
    "For each clause of $f$, we design a sub-circuit that outputs True if and only if there is exactly one True literal in the clause. Combining all sub-circuits for all clauses, we can then obtain the blackbox that outputs True if and only if all clauses are satisfied with exactly one True literal each.   \n",
    "\n",
    "For example, let us consider the clause $(x_1 \\vee \\neg x_2 \\vee x_3)$. It is easy to see that $y$ defined as \n",
    "\n",
    "$$\n",
    "y = x_1 \\oplus \\neg x_2 \\oplus x_3 \\oplus ( x_1 \\wedge \\neg x_2 \\wedge x_3), \n",
    "$$\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import numpy as npis True if and only if exactly one of $x_1$, $\\neg x_2$, and $x_3$ is True. Using two working qubits, $y$ can be computed by the following sub-circuit. Below, $x_1x_2x_3$ is renamed as $q_1q_2q_3$, $q_4$ is used as a working qubit, and $q_5$ is used to store the value of $y$.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-25T17:34:42.934376Z",
     "start_time": "2018-09-25T17:34:42.923743Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "# importing Qiskit\n",
    "from qiskit import BasicAer, IBMQ\n",
    "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister, execute, compile\n",
    "from qiskit.tools.visualization import plot_histogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-25T17:32:05.667148Z",
     "start_time": "2018-09-25T17:32:03.983610Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgkAAAEzCAYAAAC7a5CuAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAAIABJREFUeJzt3XtYVPW+P/D3DKiYcjHFK4KGlkohIxLmVnFrim4xSry0a1toKlpn79NB3bLT1MpDmJeTtcsiC7xR2mULpaK1t+J1U4qoeUuUS3QR8TgMooLOfH5/dJif6GIYZGbWDLxfz7Oep+A76/t2uVi8XWvNGo2ICIiIiIhuo1U7ABERETknlgQiIiJSxJJAREREilgSiIiISBFLAhERESliSSAiIiJFLAlERESkiCWBiIiIFLEkEBERkSKWBCIiIlLEkkBERESKWBKIiIhIEUsCERERKWJJICIiIkUsCURERKSIJYGIiIgUsSQQERGRIpYEIiIiUsSSQERERIpYEoiIiEgRSwIREREpYkkgIiIiRSwJREREpIglgYiIiBSxJBAREZEilgQiIiJSxJJAREREilgSiIiISBFLAhERESliSSAiIiJFLAlERESkiCWBiIiIFLEkEBERkSKWBCIiIlLEkkBERESKWBKIiIhIEUsCERERKWJJICIiIkUsCURERKSIJYGIiIgUNdmSkJqaiqFDh9brNaGhodixY4d9AhERETkZpyoJRqMRc+fOha+vLzw9PRETE4PS0lKnmTs6OhoZGRkOyUNERKQ2pyoJSUlJSE9PR3Z2NoqLiwEAkydPdpq5WRKIiKgpcXhJ2Lx5M3r06IHWrVtj5MiRmD17NiZMmAAASE5Oxrx583DffffB29sbb7zxBjIzM1FYWGj3XNbM3bdvX7i5ueHw4cN2z0NERKQ2h5aEtWvXYvbs2di4cSPKy8sRFRWFVatWQafTQa/Xo6ioCKGhoebxgYGB8PLywtGjR+s1T1JSEoKDg60eX5+5o6OjkZ6eXq88RERELkkcpKKiQu69917Ztm1bja8BkG3btklRUZEAkPPnz9d4nb+/v6xfv15ERNavXy8DBgyQAQMGyL/+9a8G5UlJSZGIiAgREavmrrZjxw7p169fg+a2BgAuXLhw4cLFLou13OEgWVlZMJlMGD16tPlrFy9eBADodDp4eHgAAMrKymq8Tq/Xw8vLC3q9HsuXL8e///1vXLlyBY8++ihycnKg1Tb8ZIinp6fFuW9VWFgIf3//Bs9Zl996AhERkXocdrmhpKQE7du3r/G1tLQ0dOjQAR07doSPjw/8/f2Rk5Nj/v758+dhMBgQHByM7OxsREREwMPDA+3atUPnzp1RUFBgk2x1zX2rjIwMREdH22ReIiIiZ+awktCnTx/k5eUhKysLVVVVSEtLQ1JSEnQ6nXnMjBkzsHTpUuTn58NgMGDevHmIjIxEt27dcOnSJbRp08Y8tk2bNrh06ZLN8lmau1pFRQV27dqFqKgom81LRETkrBxWEsLCwjB//nyMGzcOfn5+yM7ORnh4eI2SkJCQgLFjxyIsLAxdunSB0WjEhg0bAABt27bF5cuXzWP1ej3atm2rOFdiYiKCgoLqlc/S3NV27twJnU6Hdu3a1WvdRERErkgjKl787tatG5YtW2Z+C6Qler0ew4YNw8GDB1FRUYFhw4Y16J6E1NRUpKamYvfu3Va/ZsqUKQgKCsKcOXPuak4iIiJX4rAbF29nMBhQWFhY40yCJT4+PnjxxRfNj1JesWKFTW5arI+AgACrCg0REVFjoNqZhAMHDmDUqFEoKyuDRqNx+Py5ubnIzc1FbGysw+cmIiJyBapebiAiIiLn5VSf3UBERETOgyWBiIiIFLEkEBERkSKWBCIiIlLEkkBERESKWBKIiIhIEUsCERERKWJJICIiIkUsCURERKSIJYGIiIgUsSQQERGRIpYEIiIiUsSSQERERIpYEoiIiEgRSwIREREpYkkgIiIiRSwJREREpIglgYiIiBSxJBAREZEilgQiIiJSxJJAREREilgSiIiISBFLAhERESliSSAiIiJFLAlERESkiCWBiIiIFLEkEBERkSKWBCIiIlLEkkBERESKWBKIiIhIEUsCERERKXJXO4BaUlNTkZqait27d1v9mtDQUCQmJiIyMtJ+wcghrl+/jszMTJSUlMDX1xejR4+Gh4eH2rEapStXrmDbtm3Q6/Xw8/PDiBEj0KxZM7VjkZMQEezZswc//PADWrZsiZEjR6J9+/Zqx6L/41RnEoxGI+bOnQtfX194enoiJiYGpaWlTjN3dHQ0MjIyHJKH7ENEsHLlSnTu3BlPPPEE4uLiMG7cOHTq1AkrVqyAiKgdsdEwGo14+eWX0bFjR0yaNAlxcXEYM2YMunbtipSUFLXjkRP4+uuv8cADD2Do0KGYMWMGJk+ejC5duuC5555DRUWF2vEIAMSJLFmyRHr27Cnnzp0TvV4v48aNk1GjRtllrpSUFImIiKjX3Lm5ueLn52eXPOQYCxcuFAC1LgsWLFA7YqMxffp0i9v6nXfeUTsiqWjHjh3i5uYmWq1Wcf+IiIiQyspKtWM2eQ4vCZs2bZLAwEBp1aqVjBgxQuLj42X8+PEiIuLv7y9r1qwxj83LyxMAUlBQYPMct5cEa+cOCAiQQ4cO2TwP2V9BQUGtB6TqRaPRSH5+vtpRXd63335rcTsDEA8PD9Hr9WpHJRUYjUYJDAys8+dx7dq1akdt8hx6uWHt2rWYPXs2Nm7ciPLyckRFRWHVqlXQ6XTQ6/UoKipCaGioeXxgYCC8vLxw9OjRes2TlJSE4OBgq8fXZ+7o6Gikp6fXKw85hw8//BAmk8niGBHBhx9+6KBEjVdycjK0WsuHl+vXr2Pjxo0OSkTOJCsrC+fOnbP486jVavHee+85MBUpcVhJuHr1KuLj45GcnIzw8HBoNBpMmzYNRqMROp0O5eXlAABvb+8ar/Px8YHBYAAAPProo/D19cWSJUsszpWQkIBjx45Znc2auauNGTMGW7dutXrd5DzOnDkDNzc3i2Pc3Nxw+vRpByVqvM6cOVNnIdNqtdzWTdSZM2fqHGMymXDq1CkHpCFLHPbuhqysLJhMJowePdr8tYsXLwIAdDqd+c7ysrKyGq/T6/Xw8vIC8Ns7Er755hsUFxfbNJunp2edc1crLCyEv7+/TedXotFo7D4H3cloNOKzzz7j9ncAk8mEt99+G2+//bbaUchJ6fV6/izaiVh5k7bDziSUlJTc8baWtLQ0dOjQAR07doSPjw/8/f2Rk5Nj/v758+dhMBjMlw78/Pzsks2auatlZGQgOjraLjluJb/dL8LFhsunn35q1bbfvHmz6lldfXnrrbes2tZ79+5VPSsXxy8///xznWf1NBoNZs6cqXrWxrpYy2EloU+fPsjLy0NWVhaqqqqQlpaGpKQk6HQ685gZM2Zg6dKlyM/Ph8FgwLx58xAZGYlu3brZPZ81c1dUVGDXrl2Iioqyex6yvejoaPj7+9d6rVyr1aJr1654/PHHHZys8XnmmWfg4+NjcVv369cPv/vd7xycjJxBp06d8NRTT9V6lkCj0UCr1eKFF15wcDK6ncNKQlhYGObPn49x48bBz88P2dnZCA8Pr1ESEhISMHbsWISFhaFLly4wGo3YsGFDvedKTExEUFBQvV5jzdw7d+6ETqdDu3bt6p2J1NesWTNs377d/Pd3+wGqbdu22L59Ox/0YwPe3t7YunUrWrVqVePr1ds8ICAA//jHP3gquQl799138cgjjwBAjTJZXRDWr1+PBx98UK14VE1UFBAQIJs3b67Xa1JSUuS1115r8Ny3vwXSGrGxsbJs2bIGz03qunDhgrz66qty3333SevWrQWAvPLKK/Lrr7+qHa3RKSwslISEBOnatasAkF69esny5cvl8uXLakcjJ3Dt2jX58MMPJSwsTDw9PQWAxMXFybFjx9SORv9HI1KPixM2ZDAY4O3tjbNnz6JHjx5WvWbq1KnIzs5GZWUlevfujS+//PKu57+bxzIvXrwYU6ZMQUBAwF3PS85Ho9HU6xod3R1uZ6oL9xHno1pJOHDgAEaNGoWysjJVTjnm5uYiNzcXsbGxDp+bnAsPTI7B7Ux14T7ifFQrCUTOggcmx+B2prpwH3E+TvUBT0REROQ8WBKIiIhIEUsCERERKWJJICIiIkUsCURERKSIJYGIiIgUsSQQERGRIpYEIiIiUsSSQERERIpYEoiIiEgRSwIREREpYkkgIiIiRSwJREREpIglgYiIiBSxJBAREZEilgQiIiJSxJJAREREilgSiIiISBFLAhERESliSSAiIiJFLAlERESkyF3tAOQ8XnzxReTm5qoyd0hICN58801V5iaipovHPct4JoHMcnNzVflhUWteIiIe9yzjmQSqISQkBLt373bonEOHDnXofEREt+Jxr3Y8k0BERESKWBKIiIhIEUsCERERKWJJICIiIkUsCURERKSIJYGIiIgUsSQQERGRoiZbElJTU+v9PtXQ0FDs2LHDPoGIiIicjFOVBKPRiLlz58LX1xeenp6IiYlBaWmp08wdHR2NjIwMh+RxBVeuXIGvry8+++wz89euXbuGgQMHYvz48TCZTCqma1xEBFu2bMGIESPg5eUFb29vREdH4+uvv1Y7mkWFhYX461//ii5dugAA7r//frzxxhu4fPmyysnIGVy/fh0ffPABQkND4enpCQCYPn06jh49qnKy2jW54544kSVLlkjPnj3l3LlzotfrZdy4cTJq1Ci7zJWSkiIRERH1mjs3N1f8/PzskscZRERE1Ngm1khKSpKHHnpITCaT3Lx5U6KiomTo0KFy/fp1u85rS072Y3AHo9EoU6ZMEQCi1WoFQI3//utf/yomk0ntmHfYu3evtG7dWjQajTlz9X8HBARIQUGB2hFJRQaDQQYMGKC4X2u1WtmwYYNDcjTV4561HH503LRpkwQGBkqrVq1kxIgREh8fL+PHjxcREX9/f1mzZo15bF5engCwy8Hk9pJg7dwBAQFy6NAhm+dxBnez0165ckV8fX3l008/lalTp0pISIiUlZXZfV5bcvaSsHLlSvMBtLYlLS1N7Zg1XL58Wby9vWsc/G9dtFqt6HQ6pyw35Bh/+tOfahTIWxeNRiNubm5y7Ngxu+doqsc9azn0csPatWsxe/ZsbNy4EeXl5YiKisKqVaug0+mg1+tRVFSE0NBQ8/jAwEB4eXnV+9RTUlISgoODrR5fn7mjo6ORnp5erzyNWatWrTB37lzExsZi9+7dyMzMhJeXl9qxGg2j0YiVK1dCo9HUOkar1WLFihUOTFW3devWoaysrNZTryaTCUeOHMG+ffscnIycwc8//4yPP/4YIqL4fRGByWTCO++84+Bk1mlKxz2HlYSrV68iPj4eycnJCA8Ph0ajwbRp02A0GqHT6VBeXg4A8Pb2rvE6Hx8fGAwGnDt3DkOGDMHgwYMxaNAgHDp0qNa5EhIScOzYMauz1TX3rcaMGYOtW7dave6moqKiAgkJCejQoYPaURqVEydOoLi4uNaDKfDbL9zDhw+jpKTEgcks++qrrywWGwDQaDT48ssvHZSInMnOnTthNBotjhERp/8HWZM47jnqlMW2bdvEx8enxtcKCgoEgPzyyy9y+fJlASBHjhypMcbLy0vS09OltLRUSktLRUTkxIkTMmjQoAblufVyQ11z3yo5OVkef/zxBs1tDdRxetleS31Pf61fv17atGkjU6dOlaCgoLs6fRwREaHan5cLFy5cmuJxz1oOO5NQUlKC9u3b1/haWloaOnTogI4dO8LHxwf+/v7Iyckxf//8+fMwGAwIDg5G27Zt0bZtWwBAixYt4ObmZrNsdc19q4yMDERHR9ts7trIb/eLOHSJiIioV8Zt27bh+eefx5YtW/DWW2+hpKQEn3766V39eSMiIlT5M8v//QtdrbnrWi5evAh397o/0d3LywvXr19XPW/1Mn36dGi1dR9e3nnnHdWzcnH8smvXrjr3Da1Wi0ceecTuWZrycc8aDisJffr0QV5eHrKyslBVVYW0tDQkJSVBp9OZx8yYMQNLly5Ffn4+DAYD5s2bh8jISHTr1s08xmg04i9/+QsSEhJsms+auSsqKrBr1y5ERUXZdG5XdODAATz55JNYt24dhgwZYr5G9+qrrza+twCpqF27dhg/frzFX7gajQZTp05FixYtHJjMsri4uDr3g5YtW+Lpp592UCJyJhEREejRo4fF/dpkMmHWrFkOTFW3pnjcc1hJCAsLw/z58zFu3Dj4+fkhOzsb4eHhNUpCQkICxo4di7CwMHTp0gVGoxEbNmwwf19EMHXqVERFRWHUqFG1zpWYmIigoKB65atrbuC362g6nQ7t2rWr17obm++//x5RUVFYuXIlHn/8cfPXX3jhBVy8ePGuWzUpW7JkCXx8fBQPqFqtFn5+fjYvzQ0VGhqKuLg4xe9V36uwYsWKO+4DoqZBo9Fg9erV0Gg0tRaFoUOHYtKkSQ5OVrsme9wTFQUEBMjmzZutHv/CCy/Iq6++apO5b38LpDViY2Nl2bJlNpnfGan1lhy13wqk8o+BVc6cOSNDhgy547riqFGjpLi4WO14ioxGoyxatEg8PT1rZO7UqZOkpqaqHY+cwDfffCO9evWqsX80a9ZMpk+fLhUVFQ7J0FSPe9ZS7YmLBoMBhYWFNc4kWLJ7924kJyfjn//8J4YOHYpx48bZOeGdAgICMGHCBIfPS3T//fcjKysLx48fR0pKCgDg7Nmz2L59u/lphs5Gq9Vi8eLF+OWXX8xPp9u+fTuKiorw7LPPqpyOnMHw4cNx8uRJ7N27F2vWrAEA/PTTT0hOTsY999yjcjoCAI1IPe5gsKEDBw5g1KhRKCsrq/OtUvaQm5uL3NxcxMbGOnxuZ1X9WRa7d+9uEvNW02g09bqRxxkwMzVGauwjTfW4Z626b5u2k4EDB97xDAJHCgkJQUhIiGrzExEROTun+oAnIiIich4sCURERKSIJYGIiIgUsSQQERGRIpYEIiIiUsSSQERERIpUewskOafc3Fzz+3cdOSffjkpEauFxr3YsCWSm1g7LZ1YQkVp43LNMtScuEjkLV3wSIDNTY8R9xPnwngQiIiJSxJJAREREilgSiIiISBFLAhERESliSSAiIiJFLAlERESkiCWBiIiIFLEkEBERkSKWBCIiIlLEkkBERESKWBKIiIhIEUsCERERKWJJICIiIkUsCURERKSIJYGIiIgUsSQQERGRIpYEIiIiUsSSQERERIpYEoiIiEgRSwIREREpYkkgIiIiRSwJREREpIglgYiIiBS5qx1ALampqUhNTcXu3butfk1oaCgSExMRGRlpv2BEpLqbN2/iq6++wvHjx9GsWTOMGDECoaGhaseq07lz57BlyxZcuXIF9913H2JiYnDPPfeoHYtcmFOdSTAajZg7dy58fX3h6emJmJgYlJaWOs3c0dHRyMjIcEgeIlJHZmYm/P398cQTT2DhwoX429/+hv79+2PgwIEoKipSO54ig8GAmJgY9OjRA3PmzMHixYvxzDPPoFOnTkhOTlY7HrkwpyoJSUlJSE9PR3Z2NoqLiwEAkydPdpq5WRKIGrddu3YhKioKFy5cuON72dnZGDx4MC5evKhCstpVVVVh9OjR+Mc//nHH9wwGA+Li4lgU6O6Jg23atEkCAwOlVatWMmLECImPj5fx48eLiIi/v7+sWbPGPDYvL08ASEFBgc1zpKSkSEREhPn/rZ07ICBADh06ZPM8pB4VfgwajJnto1+/fqLVagVArcvChQvVjlnDxx9/bDEvAPHx8ZGrV6+qHbVOrrCPNDUOPZOwdu1azJ49Gxs3bkR5eTmioqKwatUq6HQ66PV6FBUV1bjuFxgYCC8vLxw9erRe8yQlJSE4ONjq8fWZOzo6Gunp6fXKQ0TO7+jRo8jJyYHJZLI47v3333dQIuusWbMGWq3lQ7ler8eWLVsclIgaE4eVhKtXryI+Ph7JyckIDw+HRqPBtGnTYDQaodPpUF5eDgDw9vau8TofHx8YDAZcuHABAwcOxNChQxEeHo5//vOftc6VkJCAY8eOWZ2trrlvNWbMGGzdutXqdRORaygoKLBq3IULF1BVVWXfMPWQl5dXZ7EBrP/zEd3KYe9uyMrKgslkwujRo81fq762p9Pp4OHhAQAoKyur8Tq9Xg8vLy+0a9cOe/fuhZubG86fP49Jkybhu+++s0k2T09Pi3PfqrCwEP7+/jaZ1xKNRmP3Oej/c8XtzczqadGihdoR6u2ll17CSy+9pHaMOjWWfcTZiYhV4xxWEkpKStC+ffsaX0tLS0OHDh3QsWNHAIC/vz9ycnIQEhICADh//jwMBgOCg4Ph5uZmfp1er6/X5YS6+Pj4WJz7VhkZGYiJibHZ3LWx9i+QGk6j0bjc9mZm26usrETnzp3xv//7v7WO0Wq1ePLJJ7Fx40YHJrNsyZIlePnlly2O0Wq1KCgoQNeuXR2U6u44+z7SFDnsckOfPn2Ql5eHrKwsVFVVIS0tDUlJSdDpdOYxM2bMwNKlS5Gfnw+DwYB58+YhMjIS3bp1AwDk5+dj0KBBiIyMxBNPPGHTfHXNDQAVFRXmu5+JqHFp0aIFZs+eXev3q/+F++KLLzoqklWmTZsGLy8vi/clPPXUU05fEMg5OawkhIWFYf78+Rg3bhz8/PyQnZ2N8PDwGiUhISEBY8eORVhYGLp06QKj0YgNGzaYv9+9e3fs27cP2dnZ+I//+I9a50pMTERQUFC98tU1NwDs3LkTOp0O7dq1q9e6icg1JCQkYNq0aQBQ45euRqOBm5sbNmzYgLCwMLXiKerYsSO2b9+O1q1bA/j/ZaY6/7Bhw/Dee++plo9cm0ZUPLfTrVs3LFu2DBMmTKhzbGVlpfk6YGlpKYYOHYrvv//+rue+mycuTpkyBUFBQZgzZ85dz0vOxxVPcTKz/YgI9u7di9WrV+PIkSM4c+YM5s6di7i4OAQGBqodr1YlJSX46KOP8Nlnn+Hw4cP4wx/+gOnTpyMqKgru7q7xcF1X2UeaEtVKgsFggLe3N86ePYsePXrUOX7fvn146aWX4Obmhhs3buCVV17B8OHD73r+uykJixcvxpQpUxAQEHDX85LzccUDEzM7jivmdsXMgOvmbsxUKwkHDhzAqFGjUFZWpsrdrLm5ucjNzUVsbKzD5ybn4ooHJmZ2HFfM7YqZAdfN3ZipermByBm44oGJmR3HFXO7YmbAdXM3Zk712Q1ERETkPFgSiIiISBFLAhERESliSSAiIiJFLAlERESkiCWBiIiIFLEkEBERkSKWBCIiIlLEkkBERESKWBKIiIhIEUsCERERKWJJICIiIkUsCURERKSIJYGIiIgUsSQQERGRIpYEIiIiUsSSQERERIpYEoiIiEgRSwIREREpYkkgIiIiRSwJREREpIglgYiIiBSxJBAREZEilgQiIiJSxJJAREREilgSiIiISBFLAhHZnIhg//79+POf/4xHHnkEbdq0gVarRfv27TF8+HC89NJLOH36tNoxSUU//fQTEhMTERUVhS5duuCee+6BVquFTqfDtGnT8OWXX8JoNKods8ljSSAim9q7dy90Oh0GDRqEjz76CO7u7vjjH/8Ik8mExx57DGVlZVi2bBl69+6NyMhInD17Vu3I5EAXL17E5MmTERAQgPnz5yM/Px/Dhg3D888/D5PJBF9fX3z++ed47LHHEBgYiE2bNkFE1I7ddAlRE+eKPwbOmPnmzZsye/Zs0Wg00r17d0lOTpby8nLz92/N/Ouvv8qSJUvEx8dHWrZsKcnJyWpEtoozbuu6OGvmzMxM8fX1lWbNmkl8fLzk5eXV+H517qqqKvn0008lNDRUAMiECRPkypUrakRu8pxzTyJyIGc9oFribJmNRqNMnjxZAMisWbMUD+hKmYuLiyUyMlIAyPLlyx0Rtd6cbVtbwxkzb9myRdzd3aVv375y/PhxxTG3575x44a8/vrrotVqZdCgQSwKKnC+PYnIwZzxgFoXZ8v8+uuvCwB59dVXax1TW+YbN27IxIkTBYBs377dXhHvmrNta2s4W+bTp0+Lh4eHPPzww1JWVlbruNpyb9q0SbRarTzzzDP2iki10Ig0zYs9qampSE1Nxe7du61+TWhoKBITExEZGWm/YORwGo3G5a55OlPmkydPQqfT4bHHHsPmzZuh0WgUx1nKXFlZiX79+sFgMOD777+Ht7e3PSPXizNta2sYjUa4u7vDZDLV+nfh6DyDBw/G6dOnceLECXTq1KnWsZa29cKFC/Haa68hIyMDY8eOtVdcuo1T3bhoNBoxd+5c+Pr6wtPTEzExMSgtLXWauaOjo5GRkeGQPESuYsmSJWjZsiXeeeedu/6l1KJFC3z00UcoLi5GcnKyjRM2Dfv27UNMTAxatGgBAGjfvj3mz5+Pixcvqppr+/btOHjwIFasWGGxINRlwYIF6N27N15++WWXKm2uzqlKQlJSEtLT05GdnY3i4mIAwOTJk51mbpYEopouXLiAzz77DLGxsWjfvn2D1hUeHo4hQ4Zg9erVMJlMNkrYNKSkpGDIkCHYsmWL+W2DpaWlSExMRGhoKIqKilTL9u6776JTp07405/+1KD1NG/eHP/5n/+Jo0eP4uDBgzZKR3Vy9PWNTZs2SWBgoLRq1UpGjBgh8fHxMn78eBER8ff3lzVr1pjH5uXlCQApKCiweY6UlBSJiIgw/7+1cwcEBMihQ4dsnofUo8KPQYM5S+a0tDQBYNXPhDWZ16xZIwDk1KlTtohnE86yrWtz8uRJ0Wq1AkBxqb7pTw2VlZXSvHlziY+Pt2p8XdvaYDCIVquVBQsW2CIeWcGhZxLWrl2L2bNnY+PGjSgvL0dUVBRWrVoFnU4HvV6PoqIihIaGmscHBgbCy8sLR48erdc8SUlJCA4Otnp8feaOjo5Genp6vfIQNVaHDh1CixYt6vXzZsnDDz9sXi9ZZ/Xq1RZPv5tMJuzbt6/ex1Fb+P7771FVVYXw8HCbrM/T0xN9+vTB4cOHbbI+qpvDSsLVq1cRHx+P5ORkhIeHQ6PRYNq0aTDSbNc8AAAViklEQVQajdDpdCgvLweAO25Y8vHxgcFgMP//pUuX0KZNG2zYsKHWuRISEnDs2DGrs1k7NwCMGTMGW7dutXrdRI3Zjz/+iO7du6NZs2Y2WV/Pnj0BQNXT465mx44dVl2j/+abbxyQpqbqv8fqv1db6NmzJ/cPB3J31ERZWVkwmUwYPXq0+WvVN9TodDp4eHgAAMrKymq8Tq/Xw8vLy/z/S5YswaBBg2yazdPT06q5AaCwsBD+/v42nV+JM9yV3JS44vZ2pszWZrF23Pz58zF//vyGRLIpZ9rWd2vOnDmYM2eOKnP369fP6rG23pdImTXFEnDgmYSSkpI7bmxKS0tDhw4d0LFjR/j4+MDf3x85OTnm758/fx4Gg8F8KjMvLw+XLl2qcVnAFqyZu1pGRgaio6NtOr8S+e0ZFlwcsLji9naWzHFxcfDx8YHJZLJJ5vz8fADAe++9p/qfzdm2dW3L+PHjodXWfSjfvn27w7Pt2bMHALB161abbetHHnkEgwcPVn27u/piLYeVhD59+iAvLw9ZWVmoqqpCWloakpKSoNPpzGNmzJiBpUuXIj8/HwaDAfPmzUNkZCS6desG4Lf3yS5atMgu+eqaGwAqKiqwa9cuREVF2SUDkavp168f9Ho9zp8/b5P1VV9rrs+/PJu6WbNmWXw3iFarRUBAAEaOHOnAVL/p27cvANjsHoKbN28iNzeX+4cDOawkhIWFYf78+Rg3bhz8/PyQnZ2N8PDwGiUhISEBY8eORVhYGLp06QKj0Wi+9+DAgQNo27YtAgMD65wrMTERQUFB9cpnae5qO3fuhE6nQ7t27eq1bqLGasiQIQCAL774wibr+/zzz+Ht7W2zGyGbgt///veYNm2a4ve0Wi3c3d2Rmppq1dkGW/Py8kK/fv3w+eef1+tfr7XJzMzEtWvXEBERYYN0ZBVRUUBAgGzevNmqsatWrZIhQ4ZIZGSkBAYGSnBwsBw4cOCu5779LZDWiI2NlWXLlt31nOScVP4xuCvOlDkiIkK6d+8ulZWVFsfVlbm4uFiaNWsmL774oi3jNZgzbevaGI1GSUpKknbt2tV4++PAgQNl//79qmZ7//33BYDs3r27zrGWtrXJZJIRI0ZI586dpaqqypYRyQLV9v6ysjIBIGfPnq33axctWiTr169v0Px3UxIWLVpkl2c2kLpc4ZfA7Zwp87Zt2wSALFy40OK4un4BjB07Vjw8POTcuXO2jtggzrSt61JZWSlZWVkCQE6ePKl2HBERKS8vly5dukifPn3k+vXrFsda2tYff/yxAJAVK1bYOiJZoNrev3//fvH09BSTyaTK/EeOHJGUlBRV5ibn4kq/BKo5W+bJkyeLu7u77Nixo9YxljKvXLlSAMjKlSvtEa9BnG1bW8PZMlcXyWnTplk85teW+8SJE9KmTRsJDw+Xmzdv2ismKXCuPYlIBc52QLWGs2XW6/XSt29f8fDwkI8//lhxjFLmmzdvyquvvioAJCYmxil/ATjbtraGM2aeP3++AJDY2NhaP/JZKfe+ffvE19dXOnbs6HRnmZoC59uTiBzMGQ+odXHGzBcvXpQBAwYIAJkwYcIdj1a+NbPJZJK9e/dKeHi4AJCnn366znsa1OKM27ouzpjZZDLJwoULBYAEBgbKli1b7iiFt+YuLi6Wv/zlL6LRaKR79+5y5swZR0cmacIfFU1UzdU+Chhw3sw3b97EG2+8gVdeeQVVVVUYMmQIhgwZgoceegiTJk3C+vXrceTIEXz99dc4fvw42rZti7fffhtPPvmk0z4cx1m3tSXOnHn37t147rnncP78eQQEBGDMmDHo168f2rdvj8ceewxLlizBwYMHkZmZCaPRiFmzZmHp0qXmh96RY7EkUJPnzAfU2jh75gsXLuCjjz7CJ598ghMnTpg/mRAAPDw80K9fP8TGxuKpp55Cq1atVExaN2ff1kqcPfONGzeQnp6ONWvW4MCBA+ZH41fr2bMnoqOjMXPmTKve9k72w5JATZ6zH1CVuFLma9euIS8vD9evX4enpyd69OgBd3eHPRG+wVxpW1dzpcwmkwn5+fm4fPky3N3d0b179zs+R4fUw5JATZ4rHVCruWJmV+WK29oVM5NzcvwjuIiIiMglsCQQERGRIpYEIiIiUsSSQERERIpYEoiIiEgRSwIREREpYkkgIiIiRSwJREREpIglgYiIiBSxJBAREZEilgQiIiJSxJJAREREilgSiIiISBFLAhERESliSSAiIiJFLAlERESkiCWBiIiIFLEkEBERkSKWBCIiIlLEkkBERESKWBKIiIhIkbvaAYgc7ZdffsF3332HEydO4Nq1awCAjIwM9O/fH507d1Y5nbLKykrk5ubi8OHDuHDhAgAgOTkZ/fv3x0MPPYRmzZqpnLDxuHr1KnJycpCTk4PS0lIAQEpKCvr3748+ffrAzc1N5YR3EhGcO3cOhw4dwtmzZwEAy5cvR0hICPr37w8fHx+VE5LLEqImwGQyyRdffCHDhg0TALUuw4YNky+++EJMJpPakUVEpKCgQOLj46VNmza1Zu7QoYMsWLBAfv31V7XjurRTp07JzJkzpVWrVrVu64CAAElMTJTLly+rHVdERCorK+W9996T4ODgWjO7u7vLxIkT5cCBA2rHJRfEkkCN3o8//iijRo0SAOLv7y+vvfaa7Nu3T8rLy0VEBIDs379flixZIgEBAQJAIiMjpaioSLXMRqNR3nnnHWnVqpW4u7vLpEmT5LPPPpPCwkIxmUwCQPLy8uTjjz+WsWPHikajkXvvvVc2btzoNAXHVdy4cUOWLFkizZo1Ew8PD5kyZYpkZGTITz/9ZN7Wp06dktTUVHPJ7Ny5s2zdulXV3IcPH5YHH3xQAIhOp5O///3vkpOTI5WVlQJALl26JF9//bX813/9l7lkzpw5UwwGg6q5ybWwJFCjlpubK+3bt5d77rlH3nrrLbl58+YdY249oXbz5k35+9//Lvfcc4/4+vrKkSNHHBnXnOGZZ54RADJy5EgpKCi4Y8ztJwFPnjwpAwYMEAAyZ84cFgUrXbt2TcaMGSMAZOLEiXLhwoU7xty+rb/99lsJCgoSALJs2TJHRa3hiy++kObNm0vnzp0lIyPjjr/v2zNfuXJF4uPjRaPRSHBwsOKfk0gJSwI1WgUFBeLr6yt+fn5y8uTJWscpXXU7deqUdO3aVXx9fSU/P9+OKe/0/PPPCwBZvHhxrb/slTLfvHlTXnjhBQEgr7zyir1jujyTySRPPPGEAJDVq1fXOk5pW1+/fl0mTpwoACQ5OdmeMe+wa9cuadasmQwYMEAuXbqkOKa2K8mZmZnSsmVLCQkJkatXr9ozJjUSLAnUKJlMJhk+fLi0bt1aTp8+bXFsbQfUM2fOiKenpwwbNkyMRqM9Yt7hq6++EgASHx9vcVxtmU0mkzz99NOi1WolOzvbHhEbjTVr1lh1NqC2bX3jxg0ZOXKktGzZUs6ePWuPiHcoKyuTrl27yv3332/xvghLt5tV72OzZ8+2R0RqZJpsSUhJSZGIiIh6vaZfv36SmZlpn0BkU2lpaQJA3nvvvTrHWjqgvv/++wJANmzYYMt4iqqqqqRr164SFBQk169ftzjWUma9Xi9+fn4SEhLCyw610Ov14uXlJREREXUWQEvburi4WLy9vWX06NG2jqhozpw5otVq5eDBgxbH1XVPelxcnGg0Gjl+/Lgt41Ej5FTPSTAajZg7dy58fX3h6emJmJgY81uQnGHu6OhoZGRkOCQPNcxbb72FBx54ADNmzGjQeqZPn45evXrh7bfftlGy2qWnp+PHH3/E66+/jhYtWtz1ery9vbFw4ULk5uZi//79NkzYeKxbtw4GgwHLly+HVnv3h8EuXbogPj4e27dvN7/10F4qKirwwQcfYOLEiRgwYECD1vXf//3faNGiBd59910bpaPGyqlKQlJSEtLT05GdnY3i4mIAwOTJk51mbpYE1/DDDz/g3//+N2bOnAmNRtOgdWk0GsycORPZ2dk4c+aMjRIqW7duHfz9/fGHP/yhwet66qmn4OXlhbVr19ogWeOzbt069O/fH/3792/wuqZPnw43NzesX7/eBslq99VXX6GsrAyzZs1q8Lratm2LiRMnYsOGDTAajTZIR42Vw0vC5s2b0aNHD7Ru3RojR47E7NmzMWHCBAC/PRxm3rx5uO++++Dt7Y033ngDmZmZKCwstHsua+bu27cv3NzccPjwYbvnobv37bffAgAeffRRm6yvej3V67UHEUF2djaGDRtmk4f1tGrVCgMHDrRrZld1/fp15ObmYsSIETZZX6dOnRAUFGT3bZ2dnY2WLVti4MCBNlnfo48+ivLycpw+fdom66PGyaElYe3atZg9ezY2btyI8vJyREVFYdWqVdDpdNDr9SgqKkJoaKh5fGBgILy8vHD06NF6zZOUlITg4GCrx9dn7ujoaKSnp9crDznW8ePH0bx5c/Tq1csm6+vVqxdatGiBY8eO2WR9SkpLS1FSUoKQkBCbrTMkJAQnTpzgvxRv88MPP+DmzZs23dY6nQ7Hjx+32fqUHD9+HA8++CDc3W3zoFydTgcAdt2vyfU5rCRcvXoV8fHxSE5ORnh4ODQaDaZNmwaj0QidTofy8nIAv11PvZWPjw8MBgMAoGXLlhg6dCiGDh2K5OTkWudKSEio145vzdzVxowZg61bt1q9bnK8K1euwNPT02YHUzc3N3h6eqKiosIm61Ny5coVAHfugw3h7e0No9GIyspKm62zMaje1rZ8VLG3t7d5vfZy5coVm2cGYNf9mhoBR90huW3bNvHx8anxtYKCAgEgv/zyi1y+fFkA3PHwGi8vL0lPTxcRkcDAQJvlufXdDdbMXS05OVkef/xxm+WoDSw8OpgLFy5cuHBpyGIth51JKCkpQfv27Wt8LS0tDR06dEDHjh3h4+MDf39/5OTkmL9//vx5GAwG86WDX3/9FREREXj88cdx/vx5m2WzZu5qGRkZiI6OttnctZHf3p7K5S6WDz74AMBvp5WtGV/X9s7LywPw230r9spsMpng7e2NuLg4m2QWEURHR+P+++9X/e/D2Zby8nJoNBosXrzYZtv64YcfRkREhF1zz5o1C56enjAajTbJvHnzZgDAoUOHVP874eL4xVoOKwl9+vRBXl4esrKyUFVVhbS0NCQlJZmviwHAjBkzsHTpUuTn58NgMGDevHmIjIxEt27dAAAFBQXIysrCn//8Z0ydOtWm+eqaG/jttNyuXbsQFRVl07nJtsLCwgAAe/bsscn6qtdjizvha6PRaNC/f3/s2bOnXj/Atblx4wYOHjxo18yuqnXr1ujdu7fN9o+ysjLk5ubafVuHhYWhvLy83vdo1WbPnj1o3rw5HnzwQZusjxonh5WEsLAwzJ8/H+PGjYOfnx+ys7MRHh5eoyQkJCRg7NixCAsLQ5cuXWA0GrFhwwbz99u1awcAGD58uPltikoSExMRFBRUr3x1zQ0AO3fuhE6nM+cg5xQcHIxevXqZzyg0VHJyMh544AGb3uim5Mknn8SpU6ds8myD9PR0lJSU4I9//KMNkjU+Tz75JP71r3/Z5NkG69atQ1VVld239WOPPQYPDw+b7NcVFRVYv349YmJiGvRMDmoCREUBAQGyefNmq8aWl5ebP5zn+PHjEhYW1qC57+aJi7Gxsap9oAvVz9tvvy0AJCMjo86xln4MvvzySwEgb731li3jKbpy5Yq0adOmwU8BrKyslAcffFC6deum+IFWJPLzzz9Ls2bNZNKkSXWOtbStq59uGR4ebst4tZoyZYp4eHjIDz/8YHFcXYf2V155RQDIvn37bBmPGiHVSkJZWZkAsPqZ59nZ2RISEiKDBw+WwYMHS05OToPmv5uSsGjRIsVP5CPnU1lZKcHBwdKxY8c6P/GutgNqSUmJdOrUSR566CGprKy0R8w7VH+ewP/8z/9YHGfpl0BCQoIAkK+++srW8RqV1157TQDIJ598YnFcbdvaZDLJs88+69DPyfjpp5/Ex8dHBg4caHGftLR/HDp0SNzd3eWpp56yR0RqZFQrCfv37xdPT0/Vni1/5MgRSUlJUWVucowjR46YP/GupKSk1nFKB9SLFy+KTqcTDw8POXz4sD1j1mAymSQqKkq0Wq1s3Lix1nG1/RJ48803BYA899xz9orYaFRVVUl4eLh4eHhY/EwWpW1tMpnMZezll1+2Z8w7VH8uSUxMTK1Fobb94/jx49KhQwfx8/OT0tJSe8akRkLVyw1E9rZ9+3bx8PAQPz8/2b59u+KY2w+omZmZ4ufnJx4eHrJt2zZHxKzhypUrEhERIQDkhRdekPLy8jvG3J750qVL8vTTTwsAeeKJJ6SqqspRcV3axYsXpW/fvuLm5iYLFixQ/GCt27d1cXGxjBkzRgBIXFycKv/QWblypQCQ0NBQxQ9puj2zyWSS1atXS+vWraVTp05y6tQpR0UlF8eSQI3ed999J7179xYA8vvf/142bdpU4xIEACkpKZFNmzbJsGHDBID07t1bvv32W9UyX716VV588UXRaDTSoUMHWbBggRw7dkxu3LhhzlxZWSmHDh2S+Ph4adOmjbi7u8uiRYvMY8g6er1enn32WQEg/v7+kpiYKKdPnzbfFwJArl27JgcOHJC4uDhp1aqVtGzZUt58801VP2Xz888/F19fX3F3d5eJEyfKjh07pKyszJzZZDJJQUGBrF69Wh566CEBII8++qgUFhaqlplcD0sCNQnXrl2TpUuXSkBAgPlhIp06dZL777+/xgNGAgICJCkpSa5du6Z2ZBH57bLc2LFjRaPRCABp2bKl9OzZUwBI8+bNBYC4u7vLpEmTJDc3V+24Li0zM1OGDx9u3hc8PT3N29rd3V0AiIeHh0yZMsXqe6nsraSkxFwSAYhGozHv4/fee6/5z6LT6WTt2rX86HCqN42IDd6UTeQijEYj9u/fj++++w7ff/89rl27hk2bNmH58uUICwvD7373O5t8wJKtFRUVYc+ePTh8+DB+/fVXfPLJJ5gzZw769++PiIgIdOzYUe2IjUZeXh727t2LnJwclJaW4pNPPsHf/vY39O/fH0OHDsW9996rdsQ7XLt2Dbt27cLhw4fxww8/YMOGDZgxYwZCQkLwyCOPoG/fvg3+RFRqmlgSiIiISJHDPyqaiIiIXANLAhERESliSSAiIiJFLAlERESkiCWBiIiIFLEkEBERkSKWBCIiIlLEkkBERESKWBKIiIhIEUsCERERKWJJICIiIkUsCURERKSIJYGIiIgUsSQQERGRIpYEIiIiUsSSQERERIpYEoiIiEgRSwIREREpYkkgIiIiRSwJREREpIglgYiIiBT9P4fp+tS+rxAaAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa19505e48>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q = QuantumRegister(6)\n",
    "qc = QuantumCircuit(q)\n",
    "qc.x(q[2])\n",
    "qc.cx(q[1], q[5])\n",
    "qc.cx(q[2], q[5])\n",
    "qc.cx(q[3], q[5])\n",
    "qc.ccx(q[1], q[2], q[4])\n",
    "qc.ccx(q[3], q[4], q[5])\n",
    "qc.ccx(q[1], q[2], q[4])\n",
    "qc.x(q[2])\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the sub-circuit above, the three `ccx` gates on the right are used to compute $( q_1 \\wedge \\neg q_2 \\wedge q_3)$ and write the result to $q_5$, while the three `cx` gates on the left are used to compute $q_1 \\oplus \\neg q_2 \\oplus q_3$ and write the result to $q_5$. Notice that the right-most `ccx` gate is used to reset the value of $q_4$ so that it can be reused in the succeeding sub-circuits. \n",
    "\n",
    "From the above sub-circuit, we can define a blackbox function to check the solution of the Exactly-1 3-SAT problem as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-25T17:32:05.678916Z",
     "start_time": "2018-09-25T17:32:05.669852Z"
    }
   },
   "outputs": [],
   "source": [
    "def black_box_u_f(circuit, f_in, f_out, aux, n, exactly_1_3_sat_formula):\n",
    "    \"\"\"Circuit that computes the black-box function from f_in to f_out.\n",
    "\n",
    "    Create a circuit that verifies whether a given exactly-1 3-SAT\n",
    "    formula is satisfied by the input. The exactly-1 version\n",
    "    requires exactly one literal out of every clause to be satisfied.\n",
    "    \"\"\"\n",
    "    num_clauses = len(exactly_1_3_sat_formula)\n",
    "    for (k, clause) in enumerate(exactly_1_3_sat_formula):\n",
    "        # This loop ensures aux[k] is 1 if an odd number of literals\n",
    "        # are true\n",
    "        for literal in clause:\n",
    "            if literal > 0:\n",
    "                circuit.cx(f_in[literal-1], aux[k])\n",
    "            else:\n",
    "                circuit.x(f_in[-literal-1])\n",
    "                circuit.cx(f_in[-literal-1], aux[k])\n",
    "        # Flip aux[k] if all literals are true, using auxiliary qubit\n",
    "        # (ancilla) aux[num_clauses]\n",
    "        circuit.ccx(f_in[0], f_in[1], aux[num_clauses])\n",
    "        circuit.ccx(f_in[2], aux[num_clauses], aux[k])\n",
    "        # Flip back to reverse state of negative literals and ancilla\n",
    "        circuit.ccx(f_in[0], f_in[1], aux[num_clauses])\n",
    "        for literal in clause:\n",
    "            if literal < 0:\n",
    "                circuit.x(f_in[-literal-1])\n",
    "    # The formula is satisfied if and only if all auxiliary qubits\n",
    "    # except aux[num_clauses] are 1\n",
    "    if (num_clauses == 1):\n",
    "        circuit.cx(aux[0], f_out[0])\n",
    "    elif (num_clauses == 2):\n",
    "        circuit.ccx(aux[0], aux[1], f_out[0])\n",
    "    elif (num_clauses == 3):\n",
    "        circuit.ccx(aux[0], aux[1], aux[num_clauses])\n",
    "        circuit.ccx(aux[2], aux[num_clauses], f_out[0])\n",
    "        circuit.ccx(aux[0], aux[1], aux[num_clauses])\n",
    "    else:\n",
    "        raise ValueError('We only allow at most 3 clauses')\n",
    "    # Flip back any auxiliary qubits to make sure state is consistent\n",
    "    # for future executions of this routine; same loop as above.\n",
    "    for (k, clause) in enumerate(exactly_1_3_sat_formula):\n",
    "        for literal in clause:\n",
    "            if literal > 0:\n",
    "                circuit.cx(f_in[literal-1], aux[k])\n",
    "            else:\n",
    "                circuit.x(f_in[-literal-1])\n",
    "                circuit.cx(f_in[-literal-1], aux[k])\n",
    "        circuit.ccx(f_in[0], f_in[1], aux[num_clauses])\n",
    "        circuit.ccx(f_in[2], aux[num_clauses], aux[k])\n",
    "        circuit.ccx(f_in[0], f_in[1], aux[num_clauses])\n",
    "        for literal in clause:\n",
    "            if literal < 0:\n",
    "                circuit.x(f_in[-literal-1])\n",
    "# -- end function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inversion about the average\n",
    "\n",
    "Another important procedure in Grover search is to have an operation that perfom the *inversion-about-the-average* step, namely, it performs the following transformation:\n",
    "\n",
    "$$\n",
    "\\sum_{j=0}^{2^{n}-1} \\alpha_j |j\\rangle \\rightarrow \\sum_{j=0}^{2^{n}-1}\\left(2 \\left( \\sum_{k=0}^{k=2^{n}-1} \\frac{\\alpha_k}{2^n} \\right) - \\alpha_j  \\right) |j\\rangle \n",
    "$$\n",
    "\n",
    "The above transformation can be used to amplify the probability amplitude $\\alpha_s$ when s is the solution and $\\alpha_s$ is negative (and small), while $\\alpha_j$ for $j \\neq s$ is positive. Roughly speaking, the value of $\\alpha_s$ increases by twice the average of the amplitudes, while others are reduced. The inversion-about-the-average can be realized with the sequence of unitary matrices as below:\n",
    "\n",
    "$$\n",
    "H^{\\otimes n} \\left(2|0\\rangle \\langle 0 | - I \\right) H^{\\otimes n}\n",
    "$$\n",
    "\n",
    "The first and last $H$ are just Hadamard gates applied to each qubit. The operation in the middle requires us to design a sub-circuit that flips the probability amplitude of the component of the quantum state corresponding to the all-zero binary string. The sub-circuit can be realized by the following function, which is a multi-qubit controlled-Z which flips the probability amplitude of the component of the quantum state corresponding to the all-one binary string. Applying X gates to all qubits before and after the function realizes the sub-circuit. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-25T17:32:08.246809Z",
     "start_time": "2018-09-25T17:32:08.236159Z"
    }
   },
   "outputs": [],
   "source": [
    "def n_controlled_Z(circuit, controls, target):\n",
    "    \"\"\"Implement a Z gate with multiple controls\"\"\"\n",
    "    if (len(controls) > 2):\n",
    "        raise ValueError('The controlled Z with more than 2 ' +\n",
    "                         'controls is not implemented')\n",
    "    elif (len(controls) == 1):\n",
    "        circuit.h(target)\n",
    "        circuit.cx(controls[0], target)\n",
    "        circuit.h(target)\n",
    "    elif (len(controls) == 2):\n",
    "        circuit.h(target)\n",
    "        circuit.ccx(controls[0], controls[1], target)\n",
    "        circuit.h(target)\n",
    "# -- end function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, the inversion-about-the-average circuit can be realized by the following function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-25T17:32:09.200728Z",
     "start_time": "2018-09-25T17:32:09.196905Z"
    }
   },
   "outputs": [],
   "source": [
    "def inversion_about_average(circuit, f_in, n):\n",
    "    \"\"\"Apply inversion about the average step of Grover's algorithm.\"\"\"\n",
    "    # Hadamards everywhere\n",
    "    for j in range(n):\n",
    "        circuit.h(f_in[j])\n",
    "    # D matrix: flips the sign of the state |000> only\n",
    "    for j in range(n):\n",
    "        circuit.x(f_in[j])\n",
    "    n_controlled_Z(circuit, [f_in[j] for j in range(n-1)], f_in[n-1])\n",
    "    for j in range(n):\n",
    "        circuit.x(f_in[j])\n",
    "    # Hadamards everywhere again\n",
    "    for j in range(n):\n",
    "        circuit.h(f_in[j])\n",
    "# -- end function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is a circuit of the inversion about the average on three qubits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-25T17:32:11.403205Z",
     "start_time": "2018-09-25T17:32:10.138028Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa1ba83dd8>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qr = QuantumRegister(3)\n",
    "qInvAvg = QuantumCircuit(qr)\n",
    "inversion_about_average(qInvAvg, qr, 3)\n",
    "qInvAvg.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Grover Search: putting all together\n",
    "\n",
    "The complete steps of Grover search is as follow.\n",
    "\n",
    "1. Create the superposition of all possible solutions as the initial state (with working qubits initialized to zero)\n",
    "$$  \\sum_{j=0}^{2^{n}-1} \\frac{1}{2^n} |j\\rangle |0\\rangle$$\n",
    "2. Repeat for $T$ times:\n",
    "\n",
    "    Apply the blackbox function\n",
    "    \n",
    "    Apply the inversion-about-the-average function\n",
    "    \n",
    "3. Measure to obtain the solution\n",
    "\n",
    "The code for the above steps is as below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-25T17:37:05.873175Z",
     "start_time": "2018-09-25T17:34:42.936448Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa190dc860>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "Grover search implemented in Qiskit.\n",
    "\n",
    "This module contains the code necessary to run Grover search on 3\n",
    "qubits, both with a simulator and with a real quantum computing\n",
    "device. This code is the companion for the paper\n",
    "\"An introduction to quantum computing, without the physics\",\n",
    "Giacomo Nannicini, https://arxiv.org/abs/1708.03684. \n",
    "\"\"\"\n",
    "\n",
    "def input_state(circuit, f_in, f_out, n):\n",
    "    \"\"\"(n+1)-qubit input state for Grover search.\"\"\"\n",
    "    for j in range(n):\n",
    "        circuit.h(f_in[j])\n",
    "    circuit.x(f_out)\n",
    "    circuit.h(f_out)\n",
    "# -- end function\n",
    "\n",
    "# Make a quantum program for the n-bit Grover search.\n",
    "n = 3\n",
    "\n",
    "# Exactly-1 3-SAT formula to be satisfied, in conjunctive\n",
    "# normal form. We represent literals with integers, positive or\n",
    "# negative, to indicate a Boolean variable or its negation.\n",
    "exactly_1_3_sat_formula = [[1, 2, -3], [-1, -2, -3], [-1, 2, 3]]\n",
    "\n",
    "# Define three quantum registers: 'f_in' is the search space (input\n",
    "# to the function f), 'f_out' is bit used for the output of function\n",
    "# f, aux are the auxiliary bits used by f to perform its\n",
    "# computation.\n",
    "f_in = QuantumRegister(n)\n",
    "f_out = QuantumRegister(1)\n",
    "aux = QuantumRegister(len(exactly_1_3_sat_formula) + 1)\n",
    "\n",
    "# Define classical register for algorithm result\n",
    "ans = ClassicalRegister(n)\n",
    "\n",
    "# Define quantum circuit with above registers\n",
    "grover = QuantumCircuit()\n",
    "grover.add_register(f_in)\n",
    "grover.add_register(f_out)\n",
    "grover.add_register(aux)\n",
    "grover.add_register(ans)\n",
    "\n",
    "input_state(grover, f_in, f_out, n)\n",
    "T = 2\n",
    "for t in range(T):\n",
    "    # Apply T full iterations\n",
    "    black_box_u_f(grover, f_in, f_out, aux, n, exactly_1_3_sat_formula)\n",
    "    inversion_about_average(grover, f_in, n)\n",
    "\n",
    "# Measure the output register in the computational basis\n",
    "for j in range(n):\n",
    "    grover.measure(f_in[j], ans[j])\n",
    "\n",
    "# Execute circuit\n",
    "backend = BasicAer.get_backend('qasm_simulator')\n",
    "job = execute([grover], backend=backend, shots=1000)\n",
    "result = job.result()\n",
    "\n",
    "# Get counts and plot histogram\n",
    "counts = result.get_counts(grover)\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Running the circuit in real devices\n",
    "\n",
    "We have seen that the simulator can find the solution to the combinatorial problem. We would like to see what happens if we use the real quantum devices that have noise and imperfect gates. \n",
    "\n",
    "However, due to the restriction on the length of strings that can be sent over the network to the real devices (there are more than sixty thousands charactes of QASM of the circuit), at the moment the above circuit cannot be run on real-device backends. We can see the compiled QASM on real-device `ibmqx5` backend as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "IBMQ.load_accounts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-25T18:41:39.542516Z",
     "start_time": "2018-09-25T18:41:28.052236Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of gates for ibmq_16_melbourne is 1911\n"
     ]
    }
   ],
   "source": [
    "# get ibmq_16_melbourne configuration and coupling map\n",
    "backend = IBMQ.get_backend('ibmq_16_melbourne')\n",
    "\n",
    "# compile the circuit for ibmq_16_rueschlikon\n",
    "grover_compiled = compile(grover, backend=backend, seed=1)\n",
    "\n",
    "grover_compiled_qasm = grover_compiled.experiments[0].header.compiled_circuit_qasm\n",
    "print(\"Number of gates for\", backend.name(), \"is\", len(grover_compiled_qasm.split(\"\\n\")) - 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The number of gates is in the order of thousands which is above the limits of decoherence time of the current near-term quantum computers. It is a challenge to design a quantum circuit for Grover search to solve large optimization problems. \n",
    "\n",
    "### Future Work\n",
    "\n",
    "In addition to using too many gates, the circuit in this notebook uses auxiliary qubits. It is left as future work to improve the efficiency of the circuit as to make it possible to run it in the real devices. Below is the original circuit. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-25T18:42:03.016728Z",
     "start_time": "2018-09-25T18:41:52.288291Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa1e01a240>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grover.draw(output='mpl', scale=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "[1] \"[A fast quantum mechanical algorithm for database search](https://arxiv.org/abs/quant-ph/9605043)\", L. K. Grover, Proceedings of the 28th Annual ACM Symposium on the Theory of Computing (STOC 1996)\n",
    "\n",
    "[2] \"[Tight bounds on quantum searching](https://arxiv.org/abs/quant-ph/9605034)\", Boyer et al., Fortsch.Phys.46:493-506,1998"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [default]",
   "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": "3.6.4"
  },
  "latex_envs": {
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 0
  },
  "nav_menu": {},
  "toc": {
   "navigate_menu": true,
   "number_sections": true,
   "sideBar": true,
   "threshold": 6,
   "toc_cell": false,
   "toc_section_display": "block",
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}