01_grover_sat.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import qiskit\n",
    "from qiskit import QuantumCircuit\n",
    "from qiskit import QuantumRegister, ClassicalRegister\n",
    "from qiskit.visualization import plot_distribution\n",
    "from qiskit.primitives import StatevectorEstimator, StatevectorSampler\n",
    "import math\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quick revision of the Grover's algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Idea"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Geometric interpretation of the states relevant to the algorithm from wikipedia.org"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"https://upload.wikimedia.org/wikipedia/commons/1/16/Grovers_algorithm_geometry.png\" style=\"background-color:white;\" />"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For n qubits problem with $\\omega$ as the solution, the followings are defined.\n",
    "\n",
    "\\begin{align*}\n",
    "N &= 2^n                                                    \\\\\n",
    "\n",
    "|\\omega\\rangle \\; &\\textrm{where} \\; \\omega \\in \\{0..N-1\\}  \\\\\n",
    "\n",
    "|s\\rangle &= \\frac{1}{\\sqrt{N}}\\sum_{x=0}^{N-1} |x\\rangle   \\\\\n",
    "\n",
    "|s'\\rangle &= \\frac{1}{\\sqrt{N-1}}\\sum_{x\\neq \\omega, x=0}^{N-1} |x\\rangle\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The goal is to move the state from $|s\\rangle$ as close as to $|\\omega\\rangle$.  Then, the measured value is likely $\\omega$.  \n",
    "\n",
    "The algorithm is to start with $|s\\rangle$ and flip it along $|s'\\rangle$.  And then, flip along $|s\\rangle$.  Iterate a number of times such that the resulting state is approximately $|\\omega\\rangle$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The operators"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Grover's algorithm uses 2 operators: $\\operatorname{U_\\omega}$ and $\\operatorname{U_s}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider the projection operator $|\\omega\\rangle \\langle \\omega |$.  For any state $|\\phi\\rangle$, \n",
    "$|\\omega\\rangle \\langle \\omega |\\phi\\rangle$ is the component along $|\\omega\\rangle$.  Therefore, $\\operatorname{U_\\omega}$ can be expressed as $ \\operatorname{I} - 2 |\\omega\\rangle \\langle\\omega| $ (effectivley, multiple -1 to the component $|\\omega\\rangle$).\n",
    "\n",
    "$ \\operatorname{U_\\omega} = \\operatorname{I} - 2 |\\omega\\rangle \\langle\\omega| $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider the projection operator $|s\\rangle \\langle s|$.  For any state $|\\phi\\rangle$, \n",
    "$|s\\rangle \\langle s|\\phi\\rangle$ is the component along $|s\\rangle$ and zero the component perpendicular to $|s\\rangle$.  Therefore, $\\operatorname{U_s}$ can be expressed as $ 2 |s \\rangle \\langle s| - \\operatorname{I}$ (effectivley, multiple -1 to the component perpendicular to $|s\\rangle$).\n",
    "\n",
    "$\\operatorname{U_s} = 2 |s \\rangle \\langle s| - \\operatorname{I}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After the first iteration, the resulting state becomes $\\operatorname{U_sU_\\omega} |s\\rangle$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Number of iterations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align*}\n",
    "\\cos \\frac{\\theta}{2} &= \\langle s'|s \\rangle   \\\\\n",
    "                      &= \\sqrt \\frac{N-1}{N}    \\\\\n",
    "\\end{align*}\n",
    "\n",
    "Therefore,\n",
    "\n",
    "\\begin{align*}\n",
    "\\sin \\frac{\\theta}{2} &= \\frac{1}{\\sqrt{N}}     \\\\\n",
    "\\theta                &= \\frac{2}{\\sqrt{N}} \\; \\textrm{for large N, hence small} \\; \\theta    \\\\\n",
    "\\end{align*}\n",
    "\n",
    "The number of iteration r is an integer such that,\n",
    "\n",
    "\\begin{align*}\n",
    "r \\theta &\\approx \\frac{\\pi}{2}                 \\\\\n",
    "r        &\\approx \\frac{\\pi}{4} \\sqrt{N} = \\frac{\\pi}{4} 2^\\frac{n}{2} \\approx 2^\\frac{n}{2}\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If there are m matches out of N, say $\\omega_0$ .. $\\omega_{m-1}$, $|\\omega \\rangle$ is replaced by $|\\psi\\rangle = \\frac{1}{\\sqrt{m}} \\sum_{i=0}^{m-1} |\\omega_i \\rangle$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align*}\n",
    "\\cos \\frac{\\theta}{2} &= \\langle s'|s \\rangle   \\\\\n",
    "                      &= \\sqrt \\frac{N-m}{N}    \\\\\n",
    "\\end{align*}\n",
    "\n",
    "Therefore,\n",
    "\n",
    "\\begin{align*}\n",
    "\\sin \\frac{\\theta}{2} &= \\sqrt{\\frac{m}{N}}     \\\\\n",
    "\\theta                &= 2\\sqrt{\\frac{m}{N}} \\; \\textrm{for} \\; m \\ll N \\textrm{, hence small} \\; \\theta    \\\\\n",
    "\\end{align*}\n",
    "\n",
    "The number of iteration r is an integer such that,\n",
    "\n",
    "\\begin{align*}\n",
    "r \\theta &\\approx \\frac{\\pi}{2}                 \\\\\n",
    "r        &\\approx \\frac{\\pi}{4} \\sqrt{\\frac{N}{m}} = \\frac{\\pi 2^\\frac{n}{2}}{4 \\sqrt{m}} \n",
    "                \\approx \\frac{2^\\frac{n}{2}}{\\sqrt{m}}\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The circuits $\\operatorname{U_\\omega}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Phase kickback can be used to negate the coefficient of a specific state component.  For example $\\omega = 100$ (binary), $\\operatorname{U_\\omega}$ can be implemented as the circuit below.  Therefore, the implemented circuit has an extra qubits y for phase kickback."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 871.572x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qreg1_x = QuantumRegister(3, 'x')\n",
    "qreg1_y = QuantumRegister(1, 'y')\n",
    "qc1 = QuantumCircuit(qreg1_x, qreg1_y)\n",
    "\n",
    "# prepare |s>\n",
    "qc1.h(qreg1_x)\n",
    "# prepare |-> state for phase kickback\n",
    "qc1.x(qreg1_y)\n",
    "qc1.h(qreg1_y)\n",
    "\n",
    "qc1.barrier()\n",
    "\n",
    "# U_w, flip the coefficient sign of |100> by phase kickback\n",
    "qc1.x(qreg1_x[0])\n",
    "qc1.x(qreg1_x[1])\n",
    "qc1.mcx(qreg1_x, qreg1_y)\n",
    "qc1.x(qreg1_x[1])\n",
    "qc1.x(qreg1_x[0])\n",
    "\n",
    "qc1.barrier()\n",
    "\n",
    "# restore y from |-> to |0> so that only the coefficients of |0xxx> are non-zeros\n",
    "qc1.h(qreg1_y)\n",
    "qc1.x(qreg1_y)\n",
    "\n",
    "qc1.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3.53553391e-01+0.j,  3.53553391e-01+0.j,  3.53553391e-01+0.j,\n",
       "        3.53553391e-01+0.j, -3.53553391e-01+0.j,  3.53553391e-01+0.j,\n",
       "        3.53553391e-01+0.j,  3.53553391e-01+0.j,  3.36731597e-18+0.j,\n",
       "        3.36731597e-18+0.j,  3.36731597e-18+0.j,  3.36731597e-18+0.j,\n",
       "       -3.36731597e-18+0.j,  3.36731597e-18+0.j,  3.36731597e-18+0.j,\n",
       "        3.36731597e-18+0.j])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.quantum_info import Statevector\n",
    "sv1 = Statevector(qc1)\n",
    "sv1.data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.3536+0.0000j |0000>\n",
      "+ 0.3536+0.0000j |0001>\n",
      "+ 0.3536+0.0000j |0010>\n",
      "+ 0.3536+0.0000j |0011>\n",
      "+ -0.3536+0.0000j |0100>\n",
      "+ 0.3536+0.0000j |0101>\n",
      "+ 0.3536+0.0000j |0110>\n",
      "+ 0.3536+0.0000j |0111>\n"
     ]
    }
   ],
   "source": [
    "firstline = True\n",
    "for i, amp in enumerate(sv1.data):\n",
    "    if np.absolute(amp.real) > 1e-10:\n",
    "        if not firstline:\n",
    "            print(\"+ \", end=\"\")\n",
    "        print(f\"{amp:.4f} |{i:04b}>\")\n",
    "        firstline = False"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the coefficients of $|0xxx\\rangle$ are $\\frac{1}{\\sqrt{8}}$, except $-\\frac{1}{\\sqrt{8}}|0100\\rangle$.  The rest coefficients of $|1xxx\\rangle$ are all zeros ($10^{-18}$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The circuits $\\operatorname{U_s}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align*}\n",
    "\\operatorname{U_s} &= 2 |s\\rangle \\langle s| - \\operatorname{I}         \\\\\n",
    "&= \\operatorname{H^{\\otimes n}} (2 |0\\rangle \\langle 0| - \\operatorname{I}) \\operatorname{H^{\\otimes n}} \\\\\n",
    "\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The part between $\\operatorname{H}^{\\otimes n}$ can be implemented as $\\operatorname{U_\\omega}$ with $\\omega=0$ because the global phase -1 does not affect the measured result."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The overall operation (before measure) is,\n",
    "\n",
    "\\begin{align*}\n",
    "(\\operatorname{U_s}\\operatorname{U_\\omega})^r \\operatorname{H^{\\otimes n}} |0..0\\rangle\n",
    "\\end{align*}\n",
    "\n",
    "where the n qubits are initialized as 0.  In the actual circuit, there is an additional qubit for phase kickback."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: [Boolean Satisfiability Problem](https://en.wikipedia.org/wiki/Boolean_satisfiability_problem)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Apply Grover's algorithm to find $(x_0, x_1, x_2)$ such that the expression return true.\n",
    "\n",
    "$ (x_0 \\lor \\neg x_1) \\land (\\neg x_0 \\lor x_1 \\lor x_2) \\land \\neg x_2 \\land (x_0 \\lor x_1) $\n",
    "\n",
    "$ = \\neg (\\neg x_0 \\land x_1) \\land \\neg (x_0 \\land \\neg x_1 \\land \\neg x_2) \\land \\neg x_2 \\land \\neg (\\neg x_0 \\land \\neg x_1) $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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6d4qxr8+K4cduESPvmRhvTJ7XZs8/dcqUiMLiNnu+VqvuGtGndafOnzcn5k/vIJmvB4piLgC0Rw6YCxSnw8wFoqrV/+0WzJ8XC6Z2kMzXA0UxF8A4UJpy5kDHGQciYkhdROfST2tqWNxx/r4bB4qW28+GgKKYC5QmmbnA4IURXUo/rbmxseNkvrlA0cwFWE7XpojS9wNGRMSc2bNizvuudyXJ61zAuqni5bUHzAVWUc+GiE6ln1a/aEHHGff1QNHyOh+stLHAOECHss78Vq4fLfz/9aNUkryOA+YCq6C6ttXrR+fNnRPzZnSQHNADRbFmBMjtewLjQOtVdWr9+tF5c2PBtA6S+Yn1wPTp01v9urnfHH7cccfFLbfcEltuuWWceeaZMWzYsPjd734Xxx13XPTtW4ZVBf+jf//+JZ/TvQyb1MttnXXWcefwDPTo0aOk4z8YvLt3717SuQMHDizpdcjW/K4NMacV53VqnhX9B67T5vVQXqX8Xa6kDGiOzjG1DZ/v+MM2i89tu0784o/PxK0PTYrRN+wXl4/YJT57zF1t9hoD1lmng/zaU8S05vnRXN2z5HNXr22MHh0k8/VAccwFgPbIAXOB4nSUuUBExLSmWdHUqfRv+3p3b4ieHSTz9UBxzAUwDhSv3DnQkcaB2Z3rorSv/5boWj0v1uwgf9+NA8XL62dDQHHMBYqX0lxgTpe6mN+K87pUzY21OkjmmwsUz1yA/9UcXWNqoTGiqvTlQGus1hzdurvelSSvcwHrpoqX1x4wF1g171bNjcWxZsnn9eiyKFbvIOO+HiheXueDlTYWGAfoSOZ1WxxzW3FeTWFW9HO9K05exwFzgdYrRFVMbV4Yheraks/t06MxajtIDuiB4lgzAuT1PYFxYNVMbZ4TzdWl/4ps79pG60dXQak90NzcHFOnLvm37Nev9T9ol+vN4WeccUZcfPHFMWTIkLjrrruif//+sfvuu8d9990XZ599dpxzzjllr+GZZ54p+ZzCokXRePBRZaimfF599dWo6taan5pjVTz99NMlHT9u3Li47rrrYtiwYbHJJpsUfd75559fYmVk6d3362LQ7tfH4obSPnA+/cdfip9/46QyVUW5lJIDlZQBCxY2RM/tr26T59pg8Gpx1gnbxFMvvhu/vfyFaG4uxKkXj46zThgaxx+2WVxw7dg2eZ0Jr74aPWpbcWu2Mjj5D0/H2Ze9UNI5vXp0jrce/0f06tGKW8qUgR4ojrkA0B45YC5QnI40Fzj9kjFxyoWjSzqnW9dO8fojf481Vu8Y7+31QHHMBTAOFKc9cqAjjQPPjp0Z23z11pLPu/bC78ZXdvttGSoqnXGgeHn9bAgojrlAcVKbC7zyxuzYbL9/lHzepeccGUfsfVoZKiqduUDxzAVYkSN/8XD87Y7XSjpn8IAe8caYh6JTp8raiJW6vM4FrJsqXl57wFxg1Vx75+tx+Mn/Lvm8J+48Jz6x4aVtX1Ar6IHi5XU+WGljgXGAjmTazIUx+Is3RENjaetHz/rpnvGTo39epqool7yOA+YCq+anv3sqzrvqxZLO6d2rS7z9xC0d5t9BDxTHmhEgr+8JjAOr5tSLRsdv/jympHO6d+sUbz56fay+WtcyVVWaFHpgwYIF0bPnkhtCPvroo61+3dx+q3PVVVfF8OHDo2/fvnH33XcvvYP3iBEjIiLiwgsvXLq7HlKxwQYbxD333BMbbLBB1qVQRmv17R4Hf2ndks7p0rk6jtlvozJVREeRYgZUVUVcedqu0am6Ko4a/nA0NxciIuKcK16Mp196N846YZtYb1CvjKtse98+cJOorq4q6Zwj996gw2wMb0up9kBLUswBYFmp5UCq48A3v7JxdK4p7SOfQ760XofZGN6WUu2BlqSWASwvxR5IMQe23mzN2PYTa5V0zsC1a2Ofzw4uU0XZSfH6r0yKGQAsK8UcSHEs2HS91eNzQweUdM4aq3eNg75Y2ndLlSDF678yKWZAqr53yKYln/Odgza1MTwBcoDUeiDVucABuw+JtfuW9nn/Llv1i09s2LdMFWUn1R5oSWoZwPL0QBr6r1kbB+w2pKRzunbpFF/fb8PyFESHkWIGpDoX+M7Bm0RVactH4+h9NuwwG9raUqo90JIUcwBYVmo5kOo48K0DNo5OnUqbDBz+5fU7zMbwtpRCD+Tym5177rknvvnNb0a3bt3i1ltvXebXLLbffvvYY489oq6uLk47rWP88jm0l5qamujTp0/U1NRkXQplds6Pto3BA3oUffyFJ+8Qa6/RvYwV0RGkmAEnHvXJ2GnLfvGri0bHuIlzlv55c3Mhjj7lkajpVB2Xj9glwwrLY8jAXnHOj4YWffzGQ3rHiO9vXcaKspNqD7QkxRwAlpVaDqQ6DvRfszb++PPtiz5+yDo94+wfblPGirKTag+0JLUMYHkp9kCqOfDXU3eOXj2KW8BR06kqrjx916gp8YdFKkGq178lKWYAsKwUcyDVseDi4TtG397FLeCorq6KK0bsGt265q8vUr3+LUkxA1K1/afXjh8dsXnxx39qrfjh14o/nsolB0itB1KdC3Tt0imuOG3Xon9QfvVeXeLPp+xU5qqykWoPtCS1DGB5eiAd5524bQzqV/z60YuH75jLHxJnWSlmQKpzgfU/tlqc+YPi14Bsut7q8evvblnGirKTag+0JMUcAJaVWg6kOg4M7Ncjzj+p+PWj63+sV0lzh0qSQg/kbrXX6NGj48ADD4zm5ua45pprYuedd17umA/uHn7ppZfGG2+80d4lQmYmT54cJ554YkyePDnrUiizAWvVxoOXfjk2/PhqKz2uuroqLvzFDvGtAzdZ6XHkQ2oZsMm6veO0728Vjz8/I3531UvLPT729dlx6sWj4zPbDIjjD9ssgwrL68dHfqKoTV6f3LBP3H/JsKIXClaS1HtgRVLLAWB5KeVA6uPAdw7eNP748+0/8tegNx7SOx64dFj0X7O2fQprR6n3wIqklAGsWGo9kHIOfGqjvnHfX/aINfusfDFXbbeauPn/dovdth/YTpW1n5Svf0tSywBgeanlQMpjwcbrrh73X7JH9F9z5T8M3LVLdVx/zudi788ObqfK2k/K178lqWVA6s47cbuiNnzvunX/uPNPX4ru3dJYDJg6OUBKPZD6XODLu3wsbjzv89Gta6eVHtdvje5x3yV7xGbr92mnytpP6j2wIillACumB9IxsF+PePDSYbH+x1Z+B7zq6qr48yk7xdf326idKiNLqWVA6nOBnx3zqTjtuK0+8rhPb9w37r9kj+iTwzuFpt4DK5JaDgDLSykHUh8Hjjt0s/j9T7f7yPWjm663ejzw12GxVt/83Ww0lR7I3bc7W221VcybN2+lxwwdOjQKhUI7VZSdz6y5dize++CVHvNRj5Mv8+fPj1GjRsW3vvWtrEuhHaz/sdVi9A37xTV3vBZ/uv6VeOm1WUsfq6qK+O7Bm8b3Dtk0Nt8gf1/wsGKpZcC4iXOi+9CrVnrM2Ze9EGdf9kI7VdS+qqqq4mfHfDq+uMPAuOiGV+Lvd70edYualj6+1aZrxPe/ull8dY/1orZ77qaEEaEHViS1HACWl1IOGAcijj9s8/jc0AFx0Q2vxN/ueC3mL2xc+tinNuob3ztk0zh8z/WjZ21xd5atNHpgeSllACuWWg+kngPbfWrtGPvPr8Rl/3w1/nzjuJg0Zf7Sx6qrIn7+jU/Htw/aJAYP6JlhleWT+vVfkdQyAFheajmQ+liw5aZrxsv/PCCuuOXVuHjkK/H62x9+h15dFfGToz8Z3z5ok1hv0Mp/aLhSpX79VyS1DEhddXVV/N9J28cBuw2Ji254JW66781oaGxe+viuW/eP7x2yaXzlC0Oic+fc3VeCFqSWA9ZNLS+lHjAXiPjKbkPilU0PiD/fOC4uvXl8vDe7fulj6w7sFd89eJM4Zv+NcnunWD2wvJQy4APGgmWl2AMp2/DjvWPMyP3ib7e/Fhfd8Eq8/PrspY9VVUV8/6ubxXcP3iSXPxDCiqWWAanPBaqqqmL4sVvGl3f+WFx0wytx7d3Lrh/dZvM14/tf3TQO+dJ6uf3BuNR7YEVSywFgeSnlgHEg4kdHfCK+sN06cdENr8Q1d7wWC+o+XD/66Y37xvcP2TQO+/L60cP60XaqqDzyOZNbBTfddFNERIwdO3aZ/3/IkCGxzTYfffdNgI6kZ23n+M7Bm8a3D9okJr4zL7Y//LZ4d1Z99F+je/zplztmXR7QDrbcdM3466m7xO9+sl1suNeNMeP9RdFvjW7xzPX7RtVH/RQUAFDxPrFh37ho+E5xzo+3jfW/PHLpXOC5G/czFwBIwFp9u8fPv/Hp+OnRn4zX3pobuxx9x5LPhtbsHmf8wOfdAJB3fXt3jROP+mT86IhPxGtvzY2dj7p96Vzgtz/aNuvygHaw81b9Y+et+seFv6iPTfe9KWa8vyj6r9EtHr5iz6xLA6AdDBnYK87+4dA49btbxse/dEPMeH9RrN23W7x250FRXe07AoC869WjS3zvq5vFdw/ZNN6YPC92+NptSz8XuODkHbIuD2gHW222Zlz6m13i9z9ddv3o09ftm3VpAEA7+NRGfePPp+wU5/54aGyw54dzgTEjrR/NC5vD/8dBBx20wv//qKOOiiuvvDKDigBWXVVVVaw3aLXo0rlTRIQveCBBq/XsEp1rltz5oaZTtck8ACSmZ21ncwGAhHXqVB0br7v60s+GjAMAkJbq6qrYaEhvcwFIWN/eXZd+NtSpkzuFA6SmW9eapeNA55pq64YAElNVVRXrf+y/1o/6XACS87/rRwGAtPTqYS9JXtkc/j8KhULWJQAAAAAAAAAAAAAAAAAAACzHz/5AQtZaa6044YQTYq211sq6FCADMgCQA4AcgLTJAPQApE0GAHIA0iYDADmAHoC0yQD0AKRNBgByAJADkD/uHA4JWWONNeLwww/PugwgIzIAkAOAHIC0yQD0AKRNBgByANImAwA5gB6AtMkA9ACkTQYAcgCQA5A/7hwOCZk7d27cf//9MXfu3KxLATIgAwA5AMgBSJsMQA9A2mQAIAcgbTIAkAPoAUibDEAPQNpkACAHADkA+WNzOCRkypQp8Ytf/CKmTJmSdSlABmQAIAcAOQBpkwHoAUibDADkAKRNBgByAD0AaZMB6AFImwwA5AAgByB/bA4HAAAAAAAAAAAAAAAAAACoADaHAwAAAAAAAAAAAAAAAAAAVACbwwEAAAAAAAAAAAAAAAAAACqAzeGQkK5du8bGG28cXbt2zboUIAMyAJADgByAtMkA9ACkTQYAcgDSJgMAOYAegLTJAPQApE0GAHIAkAOQPzVZFwC0n3XXXTf+9re/ZV0GkBEZAMgBQA5A2mQAegDSJgMAOQBpkwGAHEAPQNpkAHoA0iYDADkAyAHIH3cOBwAAAAAAAAAAAAAAAAAAqAA2h0NCxo8fHzvttFOMHz8+61KADMgAQA4AcgDSJgPQA5A2GQDIAUibDADkAHoA0iYD0AOQNhkAyAFADkD+2BwOCSkUCtHQ0BCFQiHrUoAMyABADgByANImA9ADkDYZAMgBSJsMAOQAegDSJgPQA5A2GQDIAUAOQP7UZF0AK9C1a9SMvCrrKkrTtWvWFQCQI7Xda2L+E0dmXUZJarubVrUlPQCQNuMAegDSJgPQAwBpMw6gBwASZ91U8swF0ANU3FhgHABoU+YC6AGAtBkH0APF03kdUFVVVUS3blmXAQCZqaqqih61nbMugwzpAYC0GQfQA5A2GYAeAEibcQA9AJA266YwF0APYCwASJu5AHoAIG3GAfRA8aqzLgAAAAAAAAAAAAAAAAAAAICP5s7hkJAhQ4bEddddFwMHDsy6FCADMgCQA4AcgLTJAPQApE0GAHIA0iYDADmAHoC0yQD0AKRNBgByAJADkD82h0NCunXrFuuvv37WZQAZkQGAHADkAKRNBqAHIG0yAJADkDYZAMgB9ACkTQagByBtMgCQA4AcgPypzroAoP1MnTo1Tj/99Jg6dWrWpQAZkAGAHADkAKRNBqAHIG0yAJADkDYZAMgB9ACkTQagByBtMgCQA4AcgPyxORwSMmfOnLjttttizpw5WZcCZEAGAHIAkAOQNhmAHoC0yQBADkDaZAAgB9ADkDYZgB6AtMkAQA4AcgDyx+ZwAAAAAAAAAAAAAAAAAACACmBzOAAAAAAAAAAAAAAAAAAAQAWwORwAAAAAAAAAAAAAAAAAAKAC2BwOCamuro4tt9wyqqv91YcUyQBADgByANImA9ADkDYZAMgBSJsMAOQAegDSJgPQA5A2GQDIAUAOQP742wwJaW5ujjFjxkRzc3PWpQAZkAGAHADkAKRNBqAHIG0yAJADkDYZAMgB9ACkTQagByBtMgCQA4AcgPyxORwAAAAAAAAAAAAAAAAAAKAC2BwOAAAAAAAAAAAAAAAAAABQAWwOBwAAAAAAAAAAAAAAAAAAqAA2h0NCevXqFXvssUf06tUr61KADMgAQA4AcgDSJgPQA5A2GQDIAUibDADkAHoA0iYD0AOQNhkAyAFADkD+1GRdANB+Bg4cGCNGjMi6DCAjMgCQA4AcgLTJAPQApE0GAHIA0iYDADmAHoC0yQD0AKRNBgByAJADkD/uHA4Jqa+vj7fffjvq6+uzLgXIgAwA5AAgByBtMgA9AGmTAYAcgLTJAEAOoAcgbTIAPQBpkwGAHADkAOSPzeGQkIkTJ8YBBxwQEydOzLoUIAMyAJADgByAtMkA9ACkTQYAcgDSJgMAOYAegLTJAPQApE0GAHIAkAOQPzVZF8DyCoVCRKX9CkfXrlFVVZV1FQDkRKFQiIV1jVmXUZLa7jXGwjakB9Lm+qMHAAAgbd4TUGk94Pq3rUq7/hF6oK3pAYC0WTeFuQB6gIobC4wDAG3KXAA9kDbXHz0AUDybwzui+vpoPPiorKsoSc3IqyK6dcu6DAByYmFdY/Tc/uqsyyjJ/CeOjB61nbMuIzf0QNpcf/QAAACkzXsCKq0HXP+2VWnXP0IPtDU9AJA466aSZy6AHqDSxgLjAEDbMhdAD6TN9UcPABSvOusCAAAAAAAAAAAAAAAAAAAA+Gg2hwMAAAAAAAAAAAAAAAAAAFSAmqwLANrPJptsEk899VTWZQAZkQGAHADkAKRNBqAHIG0yAJADkDYZAMgB9ACkTQagByBtMgCQA4AcgPxx53AAAAAAAAAAAAAAAAAAAIAKYHM4JGTSpElxzDHHxKRJk7IuBciADADkACAHIG0yAD0AaZMBgByAtMkAQA6gByBtMgA9AGmTAYAcAOQA5I/N4ZCQurq6eOmll6Kuri7rUoAMyABADgByANImA9ADkDYZAMgBSJsMAOQAegDSJgPQA5A2GQDIAUAOQP7YHA4AAAAAAAAAAAAAAAAAAFABbA4HAAAAAAAAAAAAAAAAAACoADaHAwAAAAAAAAAAAAAAAAAAVACbwyEhAwYMiN/85jcxYMCArEsBMiADADkAyAFImwxAD0DaZAAgByBtMgCQA+gBSJsMQA9A2mQAIAcAOQD5U5N1AUD76d27dwwbNizrMoCMyABADgByANImA9ADkDYZAMgBSJsMAOQAegDSJgPQA5A2GQDIAUAOQP64czgkZNasWXHjjTfGrFmzsi4FyIAMAOQAIAcgbTIAPQBpkwGAHIC0yQBADqAHIG0yAD0AaZMBgBwA5ADkj83hkJDp06fHueeeG9OnT8+6FCADMgCQA4AcgLTJAPQApE0GAHIA0iYDADmAHoC0yQD0AKRNBgByAJADkD82hwMAJKJQKGRdApCxhobmaG6WBQAAAClqamqOxsbmrMsAMuQzYgCAdJkLAgCkzXwQWNzQJAsAcsbm8Bx7eOaM6HL7yPj96+NaPKbL7SNjvydHtWNVANB+zvjB1lF44Rvx9f02XOHjD1325Vj0zNGx+QZ92rmy9jNn3uK44NqX4xP7/yOmvFsXERFT3l0Yx/zqkXjm5Xczrq789AB6IOLpl96Nr5/ySKy2w9XRZesrovNWV8Qnv3Jz/On6sTF3/uKsyysr1x8AANLmPUHEtJkL4/RLxsSQPW6Imi2XvCdc+zN/jx+f+0S8+uacrMsrOz1A6j3Q3FyI+x5/J/b/4f3RfeiVSz8jfnfWovj7na9F/eKmjCssr9SvP0DqrJvCXCCifnFTXHvn67HzUXcsnQu+M2Nh7PuD++Kexybn/kel9QDGAoC0mQtEzJ5bH3/8+8ux+f+sH/3Gr0fF6LEzM66u/PQAqfdAoVCIJ1+YEUf98uHotf3V0XXrK6NmyyviUwfcHBddPzbmLbB+NM/XH0hDrjeHn3XWWVFVVRWbb755NDcvfyeEkSNHRnV1day22mrx3HPPtX+BAEBZnXrRmHhxwvvx+59sFwP71S7z2A+/tnl8duiA+PVFo+Pl12ZlVGF53f7vt+JjX7w+fnD2E/Hy67OX/nmhEHHFLRNi6KG3xYE/fiAW1jVmV2SZpd4DpN0DCxY2xP4/vD+2Pey2uPLWCTFvQUNELFkU/NJrs+K4Mx+PQbtfH3eNejvjSssn5esPAAB4T/Cn68fGx3a/Pk65cHRMmjJ/6Z+/O2tR/N/fXo6N97kpfnTOE9HUlN+7iafeA6TdA9NmLowdj7g9vvjtf8UtD06KRfUfbgRf3NAcXzv54Vj/yyNzvQg05esPAJgLPDfuvdhwrxvj8JP/HY+Nmb7MY7f9+63Y47v3xHaH3xZT312YUYXll3oPAEDqUp8L3PLgmzFo9+vjhN8+EWP/Z/3o5f98Nbb+6q1xyE8fjLpF1o/mtQdIuwfmL2yIfX9wf2z/tdvj6ttfi/kLP1w/+uKEWfH9Mx+Pj33xhvjXo5MzrrR8Ur7+QDpyvTn8hBNOiH79+sXYsWPjhhtuWOaxUaNGxZFHHhk1NTVx8803xxZbbJFNkdCOamtrY7vttova2tqPPhjInRQzoKGxOY4a/kj06N45Ljt1l6V/vtGQ3nHG8dvEEy/MiHOvfDHDCsvntocmxX4/vH/pZtCW/OP+N2OfH9wXixvyeYeYlHtgReRAOj1Qv7gp9jr+vrjlwUkrPW7egobY5wf3xR0Pv9VOlbWvVK//yqSYA8CHZAB6ANKWYgak/J7g//72Uhx35uPR2LTyu8Cdf83L8Z3THotCIZ93i0u5B1ZEDqTTA+/NXhSfPeauePLFd1d63DszFsZnv3FXPD/+vXaqrH2lev1bkmIGAMuSA6TWAynPBV589f34zDF3xtvTFqz0uGdenhm7fv3OePf9unaqrH2l3AMrkloGsDw9AGlLMQNSngvcfP+b8ZUfPRALPuLGQSPvmRj7/fD+aGjI54/IptwDKyIH0umBRfWN8eXv3RO3f8S60DnzFsdex9+b2w3iqV7/lUkxByDvcr05vLa2NoYPHx4RESNGjFh69/BXXnkl9t1331i8eHFcccUVsdtuu2VZJrSbwYMHxwUXXBCDBw/OuhQgA6lmwJhX3ouzLns+vrTToPjWARtHdXVVXH3GrlFVFXHU8EeiuTl/C1/fm70oDvv5v4v+d3vgySlx9mUvlLmq7KTYAy2RA+n0wJl/fT7+/fTUoo5tairEoT97KGbNrS9zVdlI8fqvTKo5ACwhA9ADkLZUMyDF9wTPj38vTjzvyaKPv/TmV+OGf71RxoqylWIPtEQOpNMDx535eIx/c05Rx85b0BAH/PiBaGrK5wLQFK9/S1LNAOBDcoAUeyDFuUBzcyEO+smDMXf+yn9I/gOvvTU3vnv6f8pcVXZS7IGWpJgBLEsPQNpSzYAU5wIz3quLr5387yj2N2Hv/c87ce6V1o+mQA6k0wOn/eW5GDV6elHHNjUV4pCTHow58xaXuapspHj9VybVHIA8y/Xm8IiIY489NoYMGRLjxo2La6+9NqZNmxbDhg2LWbNmxdlnnx2HH3541iWW3cKmpphZX7/Cf0hLU1NTzJ8/P5qa8nl3WGDlUs6A0y4ZE8+Ney/OO3HbuODkHWK7T64dv7zg2Xi1yMVxlebKWyd85C8+/q8/3zgut7/+GJFeD7REDqTRA4sbmuLPN75S0jnzFzbGVbdOKFNF2Uvp+n+UlHMAkAHoAUhdyhmQ2nuCP13/StGLvj5w4fWlvY+sNKn1QEvkQBo9MGXGgrjpvoklnfP62/Pinv+8U6aKspfS9V+ZlDMAWCLVHLBu6kOp9kBqc4H7n3in6B8K+sA/H5wUkz/iLuOVLLUeaEmqGRBhLPhAyj0ApJ0Bqc0FLr/l1airL+06XzxyXDQ2Wj+ad3IgjR5YVN8Yl/xjfEnnzJ3fEH+747UyVZS9lK7/R0k5ByCvcr85vEuXLnHqqadGxJK7h++5554xadKkOP744+Okk05a5tibbropDjjggPj4xz8etbW1sckmm8Qvf/nLmD9/fgaVt50R41+Ode69dYX/kJYJEybE5z//+ZgwIb8bf4CWpZwBjY2FOGr4I9Gta6f43iGbxqjR0+L8a17KuqyyKBQKcfHI0hfzTn13Ydz270llqKhjSKkHVkYOpNEDtzw4KWa8v6jk8y4eOa4M1XQMKV3/j5JyDgAyAD0AqUs5A1J6TzB3/uL4+52vl3zeY2Omx4uvvl+GijqGlHpgZeRAGj1w2T9fjcam0u90cfEN+f2RiJSu/8qknAHAEqnmgHVTH0q1B1KbC7TmO7/m5kL8tcTNA5UktR5oSaoZEGEs+EDKPQCknQEpzQUKhUL8+cbS54OTpy+IO0e9XYaKOoaUemBl5EAaPfCP+9+MmbNas37UdwQpSDkHIK9qsi6gPRxxxBHx29/+Nl55ZclgdcABB8T555+/3HHnnXdeDB48OM4888wYNGhQPPfcc/Gb3/wmHn744XjkkUeiurr0vfTbbLNNTJs2raRzuldXx9gtdij5tVryzcHrxQHrfGyFjw174uE2eY2NNtoo6prz+2tRHdWBBx5Y0vEzZsyIiIi77747nn322aLP23///Ut6HTquqav/OKK6d0ydNjUGDRqUdTm0gVJyoJIyoDk6R/Qd3qbPOWf+4qhf3BRdOneKu0a9XfLdkz7KhhttFNXR0LZP2grN0TmmtvK/3de/96s4oe6hNq6odfRAcfI6FyjH9Y8obw90lAyIiJjb/fMR3T9T8nmvTpoTAwd9PKoi+18ElAHFa48c8H4gP7wfyJ+8zgUonnGAUhkL8sdnQ8XL63uC/7W4U/9Y2Pu7rTr3M3scHrWLX2zjilqn0nrAe8K25bOhVfNez4Mjumxe8nl3P/RCDBp0TBkqKl2lZUBEZeRAJc0FKA/vB/Inr3MB66aKl9ceMBdYNdN6nxDRqW/J551zwd/jsrP2KUNFpdMDxcvrfLDSxgLjAJXCe4L8yes4YC7Qes3RNab2/UWrzj3iW7+I1Ra1zXukVaUHipPXNSO+I1g1c7rvHtF955LPG/v67Bg4aHBURfb7wmRA8bwnoBTeD3Qszf/1OcLOO+8cY8aMadXzJLE5vL6+Pnr16hUREZ06dYqLL754hRu9b7/99lhrrbWW/v+f+cxnYq211orDDz88Hn300dh1111Lfu1p06bFO++8U9I5tZ06RWxR8ku1aIOePeMLa/VruydcgSlTpsTCpuw3kaRmwYIFJR1fV1e39H9LObfUHqYD69UUUR3R3NTkuuZEKX+XKyoDqrpElP5d5UpdMWKX6NK5U4x9fVYMP3aLGHnPxHhj8rw2e/6pU6ZEFBa32fO1Wqcerf5vN29+Xcyb1kGyQQ8UJbdzgTJc/4jy9kCHyYCIiP71Ed1bd+qUqe9GNNe1bT2tIQOK1h45YN6YI94P5E5u5wIUzThAyYwFueOzoeLl9T3Bcmq7RvRu3amzZs+PWbM6SDZUWA94T9jGfDa0aj7eGNGl9NOamqs7zvygwjIgojJyoKLmApSH9wO5k9e5gHVTxctrD5gLrKJeVRGdSj9tUX0HGh/0QNHyOh+stLHAOEDF8J4gd/I6DpgLrIKa1VZt/ej0DpINeqAouV0z4juCVTNgUevXj06Z3jH+PWRA0bwnoCTeD3RY06dPb/W5ud8c3tzcHIcddlg89dRTUVNTE42NjXHxxRfHr371q+WO/e+N4R/YZpttIqL1Yda/f/+Sz+neijuUZ22dddZx5/AM9OjRo6TjPxi8u3fvXtK5AwcOLOl16LimduoUzRFR3alTDHBdc6GUv8uVlAHN0TmmtuHzHX/YZvG5bdeJX/zxmbj1oUkx+ob94vIRu8Rnj7mrzV5jwDrrdIhffStEVUwpNEdUlT6fWK1HTfTqINmgB4qT17lAW1//iPL3QEfJgIiIed2qY25rTiw0xToD1oiqaOOfRGwFGVC89sgB7wfyw/uB/MnrXIDiGQcolbEgf3w2VJw8vyf4Xw3VPWNGREShEFFVVdK5fXt3je61HSMbKq0HvCdsWz4bWjWzujbHwlacV1NdH/06yPyg0jIgojJyoJLmApSH9wP5k9e5gHVTxctrD5gLrJrpVfXR2Irzundpjr4dZHzQA8XL63yw0sYC4wCVwnuC/MnrOGAu0HqF6NT69aM9a6JXTcfIBj1QnLyuGfEdwaqZ2606WrXludAQ66yzVpT27WJ5yIDieU9AKbwf6Fiam5tj6tQladevX+t/0C73m8OPO+64uOWWW2LLLbeMM888M4YNGxa/+93v4rjjjou+fT/6p0QeeuihiIjYdNNNW/X6zzzzTMnnFBYtisaDj2rV62Xl1Vdfjapu3bIuIzlPP/10ScePGzcurrvuuhg2bFhssskmRZ93/vnnl1gZHdWg3a6Ld2YsjAH9B8TklyZnXQ5toJQcqKQMWLCwIXpuf3WbPNcGg1eLs07YJp568d347eUvRHNzIU69eHScdcLQOP6wzeKCa8e2yetMePXV6FHbuU2ea1Xt/8P745YHJ5V83lP3/Tk2Xnf1ti+oFfRAcfI6F2jL6x/RPj3QkTLg5ddmxSe+cnPJ5x2w+/px0+/fLkNFpZMBxWuPHPB+ID+8H8ifvM4FKJ5xgFIZC/LHZ0MfLe/vCf5XoVCIT3zl5hj7+uySzutZWxNvPn5X9OrRitsNl0Gl9YD3hG3LZ0Or5pYH34z9f/hAyef99Njd48wTTi5DRaWrtAyIqIwcqKS5AOXh/UD+5HUuYN1U8fLaA+YCq+ZXf3o2TvvLcyWfd/UFP4oDv/jHti+oFfRA8fI6H6y0scA4QKXwniB/8joOmAusmr2OuzfufKT0NWDPPnhpbDB4tTJUVDo9UJy8rhnxHcGqeX78e7HFQbeUfN4hwzaK68/pGPMDGVA87wkohfcDHcuCBQuiZ8+eERHx6KOPtvp5Kuvn9Up0xhlnxMUXXxxDhgyJu+66K/bYY4/YfffdY+7cuXH22Wd/5PnvvPNOnHLKKbHHHnvEFltsUf6Cocw22GCDuOeee2KDDTbIuhQgAylmQFVVxJWn7RqdqqviqOEPR3PzkrvhnnPFi/H0S+/GWSdsE+sN6pVxlW3ve4eU/qM2X9hunQ6zMbwtpdoDLZEDafTA5hv0ic9s07/k81qTHR1ditf/o6SYA8CHZAB6ANKWYgak+J6gqqoqvntw6e/vjthrgw6zMbwtpdgDKyMH0uiBvXYdHIP6lXaniKqqiG8ftHGZKspOitd/ZVLMAGBZcoDUeiDVucCxB2wSnTqVdq+3AWvVxr6f+3iZKspOqj3QktQygOXpAUhbihmQ6lygNWvAvrTjwA6zMbwtpdoDLZEDafTApzdeI3basvQ70H6vFd8vdnQpXv+PkmIOQN7ldnP4VVddFcOHD4++ffvG3XffHf37L9kcMWLEiIiIuPDCC5feen1F5s+fH/vuu2906dIlLr/88napGcqtpqYm+vTpEzU1NVmXAmQgxQw48ahPxk5b9otfXTQ6xk2cs/TPm5sLcfQpj0RNp+q4fMQuGVZYHl/Ybp3YdeviN4bWdKqKU769RfkKylCqPdASOZBOD/z6O1uWtOjjs0MHxOe2HVDGirKR6vVfmRRzAPiQDEAPQNpSzIBU3xMcufcGJS3i6t2zS/z4yE+WsaLspNoDLZEDafRATU11nPrdLUs651sHbBwfXyd/C6BSvP4rk2IGAMuSA6TWA6nOBQb17xHfPrD4uwBGLPlusXPn/C0lTbUHWpJaBrA8PQBpSzEDUp0LfGnHgbHjFmsXfXznmuo45dulfZ5YKVLtgZbIgXR64NTvbhnV1cWvH91t+3VilxLWnVeKVK//yqSYA5B3+ftELyLuueee+OY3vxndunWLW2+9NTbZ5MMPO7fffvvYY489oq6uLk477bQVnl9XVxd77713TJw4Me69994YMCB/myRI0+TJk+PEE0+MyZMnZ10KkIHUMmCTdXvHad/fKh5/fkb87qqXlnt87Ouz49SLR8dnthkQxx+2WQYVlk91dVX88/zdYstN1vjIYzt1qoorT981PrNN/uY7KfdAS+TAsvLcA5/bdp24/De7FLVBfOvN1oyb/+8LUVVV2h0EOrqUr//KpJYDwLJkAHoA0pZaBqT8nmC1nl3irj99MT7W/6PvHNyrR+e49Y+75fKOICn3QEvkwLLy3APf+MrG8evvFLegc5/PDo4LT96xzBW1v5Svf0tSywBgeXKAlHog9bnA+SdtH/t/obg7gf/yW5+Obx9U2mbySpB6D6xIShnAiukBSFtqGZDyXKBTp+q49Q+7x6c26vuRx9Z0qoqrz9i1VXcZ7uhS7oGWyIFl5bkHdtt+YPz11zsXtUF86CfWjJt+Z/1oKlLLAUhB7n7qYfTo0XHggQdGc3NzXHPNNbHzzjsvd8yIESPiX//6V1x66aXxk5/8JNZbb72ljzU0NMSBBx4YzzzzTDzwwAOx2WaVG/KfWXPtWLz3wSs95qMeJ1/mz58fo0aNim9961tZlwJkILUMGDdxTnQfetVKjzn7shfi7MteaKeK2lff3l3jkSv3jF/+8Zm48rYJMXd+w3LH7Lxlv/jN97aKz2+3TgYVll/qPbAicmB5ee6BI/fZMNZZuzZ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      "text/plain": [
       "<Figure size 5136.54x1622.06 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qreg2_x = QuantumRegister(3, 'x')\n",
    "qreg2_a = QuantumRegister(4, 'a')\n",
    "qreg2_y = QuantumRegister(1, 'y')\n",
    "creg2 = ClassicalRegister(3, name='c')\n",
    "qc2 = QuantumCircuit(qreg2_x, qreg2_a, qreg2_y, creg2)\n",
    "\n",
    "def append_U_w(qc):\n",
    "    # Oracle\n",
    "\n",
    "    # a_0 = !(!x_0 & x_1)\n",
    "    # then, restore x_0 to original value\n",
    "    qc.x(qreg2_x[0])\n",
    "    qc.ccx(qreg2_x[0], qreg2_x[1], qreg2_a[0])\n",
    "    qc.x(qreg2_a[0])\n",
    "    qc.x(qreg2_x[0])\n",
    "    qc.barrier()\n",
    "\n",
    "    # a_1 = !(x_0 & !x_1 & !x_2)\n",
    "    qc.x(qreg2_x[1])\n",
    "    qc.x(qreg2_x[2])\n",
    "    qc.mcx(qreg2_x, qreg2_a[1])\n",
    "    qc.x(qreg2_a[1])\n",
    "    qc.x(qreg2_x[2])\n",
    "    qc.x(qreg2_x[1])\n",
    "    qc.barrier()\n",
    "\n",
    "    # a_2 = !x_2\n",
    "    qc.x(qreg2_x[2])\n",
    "    qc.cx(qreg2_x[2], qreg2_a[2])\n",
    "    qc.x(qreg2_x[2])\n",
    "    qc.barrier()\n",
    "\n",
    "    # a_3 = !(!x_0 & !x_1)\n",
    "    qc.x(qreg2_x[0])\n",
    "    qc.x(qreg2_x[1])\n",
    "    qc.ccx(qreg2_x[0], qreg2_x[1], qreg2_a[3])\n",
    "    qc.x(qreg2_a[3])\n",
    "    qc.x(qreg2_x[1])\n",
    "    qc.x(qreg2_x[0])\n",
    "    qc.barrier()\n",
    "\n",
    "    # phase kickback\n",
    "    qc.mcx(qreg2_a, qreg2_y)\n",
    "    qc.barrier()\n",
    "\n",
    "    # restore a_0 to a_3\n",
    "    qc.x(qreg2_x[0])\n",
    "    qc.x(qreg2_x[1])\n",
    "    qc.x(qreg2_a[3])\n",
    "    qc.ccx(qreg2_x[0], qreg2_x[1], qreg2_a[3])\n",
    "    qc.x(qreg2_x[1])\n",
    "    qc.x(qreg2_x[0])\n",
    "    qc.barrier()\n",
    "\n",
    "    qc.x(qreg2_x[2])\n",
    "    qc.cx(qreg2_x[2], qreg2_a[2])\n",
    "    qc.x(qreg2_x[2])\n",
    "    qc.barrier()\n",
    "\n",
    "    qc.x(qreg2_x[1])\n",
    "    qc.x(qreg2_x[2])\n",
    "    qc.x(qreg2_a[1])\n",
    "    qc.mcx(qreg2_x, qreg2_a[1])\n",
    "    qc.x(qreg2_x[2])\n",
    "    qc.x(qreg2_x[1])\n",
    "    qc.barrier()\n",
    "\n",
    "    qc.x(qreg2_x[0])\n",
    "    qc.x(qreg2_a[0])\n",
    "    qc.ccx(qreg2_x[0], qreg2_x[1], qreg2_a[0])\n",
    "    qc.x(qreg2_x[0])\n",
    "    qc.barrier()\n",
    "\n",
    "def append_U_s(qc):\n",
    "# Amplification\n",
    "    qc.h(qreg2_x)\n",
    "    qc.barrier()\n",
    "\n",
    "    qc.x(qreg2_x)\n",
    "    qc.mcx(qreg2_x, qreg2_y)\n",
    "    qc.x(qreg2_x)\n",
    "    qc.barrier()\n",
    "\n",
    "    qc.h(qreg2_x)\n",
    "    qc.barrier()\n",
    "\n",
    "# prepare |s> \n",
    "qc2.h(qreg2_x)\n",
    "\n",
    "# prepare |-> state for phase kickback\n",
    "qc2.x(qreg2_y)\n",
    "qc2.h(qreg2_y)\n",
    "qc2.barrier()\n",
    "\n",
    "# iterate 2 times for 3 qubits (~sqrt(2^3))\n",
    "append_U_w(qc2)\n",
    "append_U_s(qc2)\n",
    "append_U_w(qc2)\n",
    "append_U_s(qc2)\n",
    "\n",
    "qc2.measure(qreg2_x, creg2)\n",
    "qc2.draw('mpl', fold=60)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'011': 976, '100': 9, '001': 9, '010': 8, '000': 6, '111': 8, '101': 7, '110': 1}\n"
     ]
    }
   ],
   "source": [
    "sampler = StatevectorSampler()\n",
    "job = sampler.run([qc2])\n",
    "result = job.result()[0]\n",
    "samp_dist = result.data.c.get_counts()\n",
    "print(samp_dist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_distribution(samp_dist)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Solution is $(x_0, x_1, x_2) = (1, 1, 0)$.  Note that qiskit convention is $|x_2 x_1 x_0 \\rangle$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'1.0.2'"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qiskit.__version__"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "qiskit1_env",
   "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": "3.11.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}