Part-1-3SAT-Quantum-Computing.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "ef9cc3f7",
   "metadata": {},
   "source": [
    "# Introduction\n",
    "\n",
    "This notebook is part of the bachelor's thesis *Solving the 3-SAT problem using quantum algorithms* done by *Arnau Casau* at *FIB - UPC Universitat Politècnica de Catalunya*.\n",
    "\n",
    "In this notebook, we will see an implementation of Grover's algorithm to solve the 3-SAT problem using Qiskit. We can find some explanation of the code in order to better understand the results, and for further details, I encourage the reader to go to the actual thesis document."
   ]
  },
  {
   "attachments": {
    "groverIteration_book.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "455efe85",
   "metadata": {},
   "source": [
    "# Grover's algorithm to solve 3-SAT\n",
    "\n",
    "We can break up Grover's algorithm into the following five steps:\n",
    "\n",
    "* 1) Create an equal superposition of all qubits.\n",
    "* 2) Apply the oracle O\n",
    "* 3) Apply the Hadamard transform $H^{⊗n}$\n",
    "* 4) Perform a conditional phase shift $D_4$ of -1 to all the states but the state $|0⟩^{⊗n}$ (Diffuser)\n",
    "* 5) Apply the Hadamard transform $H^{⊗n}$\n",
    "\n",
    "Steps 2, 3, 4, and 5 are repeated R times to increment the probability of obtaining a solution state at maximum. To determine R, we need to know beforehand the number of solutions that our formula has, but this is a problem because, at this point, we don't know if the problem has a solution, let alone how many there are. To solve this problem, we will use the Quantum counting algorithm later.\n",
    "\n",
    "**1) Create an equal superposition of all qubits**\n",
    "\n",
    "In this first step to create an equal superposition state, we apply the Hadamard transformation to all qubits. Our system is, initially, in the pure state $|0⟩^{⊗n}$. Assuming $N = 2^n$:\n",
    "\n",
    "$|\\psi⟩$ = $H^{⊗n}$ $|0⟩^{⊗n}$ = $1\\over{\\sqrt{N}}$ $\\sum_{x=0}^{N-1} |x⟩$\n",
    "\n",
    "Our goal with this algorithm is to find one state that satisfies the given formula. Each quantum state represents a possible assignment of the literals. In the previous state, we have a superposition of all possible assignments, but we can represent the same by splitting out the no solution states, which we will call $|\\alpha⟩$, and the solutions states, which we will call $|\\beta⟩$.\n",
    "\n",
    "$|\\alpha⟩$ = $1\\over{\\sqrt{N-M}}$ $\\sum_{x \\in No Sol}^{} |x⟩$\n",
    "\n",
    "$|\\beta⟩$ = $1\\over{\\sqrt{M}}$ $\\sum_{x \\in Sol}^{} |x⟩$\n",
    "\n",
    "Therefore, we can express $|\\psi⟩$ as:\n",
    "\n",
    "$|\\psi⟩$ = $\\sqrt{{N-M}\\over{N}}$ $|\\alpha⟩$ + $\\sqrt{{M}\\over{N}}$ $|\\beta⟩$\n",
    "\n",
    "**2) Apply the oracle O**\n",
    "\n",
    "In this step, the oracle will mark the solution states of the 3-SAT formula we are trying to solve. To do so, the oracle will perform a conditional phase shift of -1 to all solution states. We can see the oracle as the following formula:\n",
    "\n",
    "O : $|\\beta⟩$ = -$|\\beta⟩$\n",
    "\n",
    "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; $|x⟩$ = $|x⟩$ $\\forall x \\notin Sol$\n",
    "\n",
    "Analogically, we can see the same formula but using Dirac notation. The expression *I* stands for the identity matrix:\n",
    "\n",
    "O = $I -2|\\beta⟩⟨\\beta|$\n",
    "\n",
    "**3), 4), 5) Inversion about the mean**\n",
    "\n",
    "We can represent steps 3, 4, and 5 together as one transformation. Before doing that, we can represent step 4 with Dirac notation as follows:\n",
    "\n",
    "$D_4$ = $2|0⟩⟨0|^{⊗n} - I$\n",
    "\n",
    "Steps 3 and 5 are the same, so if we apply the Hadamard transformations front and back to the expression from step 4 above, we end up with the following:\n",
    "\n",
    "$D = H^{⊗n} D_4 H^{⊗n}= H^{⊗n}$ ($2|0⟩⟨0|^{⊗n} - I$) $H^{⊗n}$ = $2|\\psi⟩⟨\\psi| - I$\n",
    "\n",
    "The last equality is because, as we have seen in step 1, $H^{⊗n}$$|0⟩^{⊗n}$ = $|\\psi⟩$\n",
    "\n",
    "To summarize, in order to apply steps 2, 3, 4, and 5 to the state resulting from the first step, we need to perform the following transformations:\n",
    "\n",
    "* O = $I -2|\\beta⟩⟨\\beta|$\n",
    "* D = $2|\\psi⟩⟨\\psi| - I$\n",
    "\n",
    "We will call the application of those transformations $G = D O$\n",
    "\n",
    "We can see these two transformations, geometrically, as two reflections. The first one is over the state $|\\beta⟩$, and the second is over the state $|\\psi⟩$. As we know, two reflections are equivalent to one rotation, so we can conclude that we are rotating our state by a certain angle $\\theta$ every time we apply steps 2, 3, 4, and 5. This angle gives us information about the number of solutions we have in our problem, and we will take advantage of that when we look for it in the quantum counting algorithm.\n",
    "\n",
    "**Geometrically**\n",
    "\n",
    "In the following image, we can see a geometrical interpretation of the rotation in Grover's algorithm. We can also represent our quantum state $|\\psi⟩$ as follows:\n",
    "\n",
    "$|\\psi⟩$ = cos($\\theta \\over{2}$) $|\\alpha⟩$ + sin($\\theta \\over{2}$) $|\\beta⟩$\n",
    "\n",
    "In this image, we see the application of the two reflections as one rotation of our state:\n",
    "\n",
    "\n",
    "![groverIteration_book.png](attachment:groverIteration_book.png)\n",
    "\n",
    "*The action of a single Grover iteration. Quantum Computation and Quantum Information by Michael A. Nielsen & Isaac L. Chuang, page 253.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ce261ecf-5cc1-4d56-9c80-1ce3b6c9afe2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# imports\n",
    "import math\n",
    "\n",
    "# importing Qiskit\n",
    "from qiskit import QuantumCircuit, Aer, assemble, transpile\n",
    "from qiskit.visualization import plot_histogram"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b8aad1f",
   "metadata": {},
   "source": [
    "In order to try different formulas, we can use a text file. This text file has to contain a first line specifying the number of literals and clauses we will use, and next, we have to define all the clauses separated by an end line. The text files are similar to the DIMACS format, but we don't need a 0 at the end of each clause, although it could still appear."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2859ee5f",
   "metadata": {},
   "outputs": [],
   "source": [
    "f = open(\"cnf_test1.txt\")\n",
    "info = f.readline().split(' ')\n",
    "literals = int(info[0])\n",
    "clausulas = int(info[1])\n",
    "\n",
    "lines = [line.rstrip('\\n') for line in f]\n",
    "\n",
    "formula = []\n",
    "for i in lines:\n",
    "    l = i.split(' ')\n",
    "    formula.append([int(l[0]),int(l[1]),int(l[2])])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91beaf0f",
   "metadata": {},
   "source": [
    "In the next cell, we can see the number of qubits we will use in our circuit. We will use one qubit for each literal, one qubit for each clause, and another qubit that represents the state |-⟩ used to perform the phase shift of -1 if the assignment satisfies our formula. The last extra qubit represents a *hidden* literal used to double the state space, which I will force to be 0 in the final assignment. That has to be done to avoid the problem that the algorithm gives us no solutions states instead of solutions states if our formula has more than half of the possible assignments that satisfy it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "bd2d2cb8-0dee-4df6-b76d-740ec681bdaf",
   "metadata": {},
   "outputs": [],
   "source": [
    "n = literals + clausulas + 2 # Number of qubits in the circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5627db39",
   "metadata": {},
   "source": [
    "Step 1 of Grover's algorithm and the initialization of the state |-⟩:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "6d8dfef2-a5b6-482d-9d1f-b7cf5ac73a24",
   "metadata": {},
   "outputs": [],
   "source": [
    "def initialize_grover(qc, qubits):\n",
    "    # Superposition\n",
    "    for i in range(literals+1):\n",
    "        qc.h(qubits[i])\n",
    "        \n",
    "    # State |-⟩\n",
    "    qc.x(n-1)\n",
    "    qc.h(n-1)\n",
    "    \n",
    "    return qc"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ed6b4d2",
   "metadata": {},
   "source": [
    "Now, we are going to create a quantum gate that will represent the oracle in step 2.\n",
    "\n",
    "The SAT formulas that we use are in conjunctive normal form (CNF). This is an example of a formula where {x1,x2,x3} are the literals and {-x1,-x2,-x3} are their negations:\n",
    "\n",
    "(-x1 v -x2 v -x3) ∧ (x1 v x2 v x3) ∧ (x1 v -x2 v x3)\n",
    "\n",
    "To discover if a clause is evaluated as True, we can check if its negated version is Flase. If we do so, we will have clauses in a literal's conjunction as a result. The first clause of the previous formula will be:\n",
    "\n",
    "(-x1 v -x2 v -x3) --> (x1 ∧ x2 ∧ x3)\n",
    "\n",
    "We will negate the clauses because it is easier to implement a circuit with an and gates than one with an or gates. For its implementation, we will use a controlled Toffoli gate. In case all of the negated clauses with an assignment are evaluated as False, we will know that the same formula in CNF with that assignment is evaluated as True, and thus it's a solution. For that reason, when we will perform the phase shift of -1, we will negate all the clause's qubits to determine whether it's a solution or not using the Toffoli gate, as we can see in the following code cell:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ded58b79-71f3-4594-8370-d4bac96a324d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">          ┌───┐     ┌───┐┌───┐     ┌───┐┌───┐          ┌───┐┌───┐     ┌───┐»\n",
       "q_0: ──■──┤ X ├──■──┤ X ├┤ X ├──■──┤ X ├┤ X ├───────■──┤ X ├┤ X ├──■──┤ X ├»\n",
       "       │  ├───┤  │  ├───┤└───┘  │  └───┘└───┘       │  ├───┤└───┘  │  ├───┤»\n",
       "q_1: ──■──┤ X ├──■──┤ X ├───────■───────────────────■──┤ X ├───────■──┤ X ├»\n",
       "       │  ├───┤  │  ├───┤┌───┐  │  ┌───┐┌───┐       │  ├───┤┌───┐  │  ├───┤»\n",
       "q_2: ──■──┤ X ├──■──┤ X ├┤ X ├──■──┤ X ├┤ X ├───────■──┤ X ├┤ X ├──■──┤ X ├»\n",
       "       │  └───┘  │  └───┘└───┘  │  └───┘└───┘       │  └───┘└───┘  │  └───┘»\n",
       "q_3: ──┼─────────┼──────────────┼───────────────────┼──────────────┼───────»\n",
       "       │         │              │                   │              │       »\n",
       "q_4: ──┼─────────┼──────────────┼───────────────────┼──────────────┼───────»\n",
       "       │  ┌───┐  │              │            ┌───┐  │              │       »\n",
       "q_5: ──┼──┤ X ├──┼──────────────┼─────────■──┤ X ├──┼──────────────┼───────»\n",
       "     ┌─┴─┐├───┤  │              │         │  ├───┤  │              │       »\n",
       "q_6: ┤ X ├┤ X ├──┼──────────────┼─────────■──┤ X ├──┼──────────────┼───────»\n",
       "     └───┘└───┘┌─┴─┐┌───┐       │         │  ├───┤  │            ┌─┴─┐     »\n",
       "q_7: ──────────┤ X ├┤ X ├───────┼─────────■──┤ X ├──┼────────────┤ X ├─────»\n",
       "               └───┘└───┘     ┌─┴─┐┌───┐  │  ├───┤┌─┴─┐          └───┘     »\n",
       "q_8: ─────────────────────────┤ X ├┤ X ├──■──┤ X ├┤ X ├────────────────────»\n",
       "                              └───┘└───┘┌─┴─┐└───┘└───┘                    »\n",
       "q_9: ───────────────────────────────────┤ X ├──────────────────────────────»\n",
       "                                        └───┘                              »\n",
       "«          \n",
       "«q_0: ──■──\n",
       "«       │  \n",
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       "«q_4: ──┼──\n",
       "«       │  \n",
       "«q_5: ──┼──\n",
       "«     ┌─┴─┐\n",
       "«q_6: ┤ X ├\n",
       "«     └───┘\n",
       "«q_7: ─────\n",
       "«          \n",
       "«q_8: ─────\n",
       "«          \n",
       "«q_9: ─────\n",
       "«          </pre>"
      ],
      "text/plain": [
       "          ┌───┐     ┌───┐┌───┐     ┌───┐┌───┐          ┌───┐┌───┐     ┌───┐»\n",
       "q_0: ──■──┤ X ├──■──┤ X ├┤ X ├──■──┤ X ├┤ X ├───────■──┤ X ├┤ X ├──■──┤ X ├»\n",
       "       │  ├───┤  │  ├───┤└───┘  │  └───┘└───┘       │  ├───┤└───┘  │  ├───┤»\n",
       "q_1: ──■──┤ X ├──■──┤ X ├───────■───────────────────■──┤ X ├───────■──┤ X ├»\n",
       "       │  ├───┤  │  ├───┤┌───┐  │  ┌───┐┌───┐       │  ├───┤┌───┐  │  ├───┤»\n",
       "q_2: ──■──┤ X ├──■──┤ X ├┤ X ├──■──┤ X ├┤ X ├───────■──┤ X ├┤ X ├──■──┤ X ├»\n",
       "       │  └───┘  │  └───┘└───┘  │  └───┘└───┘       │  └───┘└───┘  │  └───┘»\n",
       "q_3: ──┼─────────┼──────────────┼───────────────────┼──────────────┼───────»\n",
       "       │         │              │                   │              │       »\n",
       "q_4: ──┼─────────┼──────────────┼───────────────────┼──────────────┼───────»\n",
       "       │  ┌───┐  │              │            ┌───┐  │              │       »\n",
       "q_5: ──┼──┤ X ├──┼──────────────┼─────────■──┤ X ├──┼──────────────┼───────»\n",
       "     ┌─┴─┐├───┤  │              │         │  ├───┤  │              │       »\n",
       "q_6: ┤ X ├┤ X ├──┼──────────────┼─────────■──┤ X ├──┼──────────────┼───────»\n",
       "     └───┘└───┘┌─┴─┐┌───┐       │         │  ├───┤  │            ┌─┴─┐     »\n",
       "q_7: ──────────┤ X ├┤ X ├───────┼─────────■──┤ X ├──┼────────────┤ X ├─────»\n",
       "               └───┘└───┘     ┌─┴─┐┌───┐  │  ├───┤┌─┴─┐          └───┘     »\n",
       "q_8: ─────────────────────────┤ X ├┤ X ├──■──┤ X ├┤ X ├────────────────────»\n",
       "                              └───┘└───┘┌─┴─┐└───┘└───┘                    »\n",
       "q_9: ───────────────────────────────────┤ X ├──────────────────────────────»\n",
       "                                        └───┘                              »\n",
       "«          \n",
       "«q_0: ──■──\n",
       "«       │  \n",
       "«q_1: ──■──\n",
       "«       │  \n",
       "«q_2: ──■──\n",
       "«       │  \n",
       "«q_3: ──┼──\n",
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       "«q_4: ──┼──\n",
       "«       │  \n",
       "«q_5: ──┼──\n",
       "«     ┌─┴─┐\n",
       "«q_6: ┤ X ├\n",
       "«     └───┘\n",
       "«q_7: ─────\n",
       "«          \n",
       "«q_8: ─────\n",
       "«          \n",
       "«q_9: ─────\n",
       "«          "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(n)\n",
    "\n",
    "# Creation of each clause.\n",
    "contador = 0\n",
    "for c in formula:\n",
    "    for i in range(3):\n",
    "        if c[i] > 0:\n",
    "            qc.x(abs(c[i])-1)\n",
    "            \n",
    "    qc.mct(list([abs(c[0])-1,abs(c[1])-1,abs(c[2])-1]), literals+1+contador)  # multi-controlled-toffoli\n",
    "    \n",
    "    for i in range(3):\n",
    "        if c[2-i] > 0:\n",
    "            qc.x(abs(c[2-i])-1)\n",
    "    \n",
    "    contador+=1\n",
    "\n",
    "\n",
    "# Checking of each clause\n",
    "qc.x(literals) # Augmented space\n",
    "for q in range(literals+1,n-1):\n",
    "    qc.x(q)\n",
    "    \n",
    "qc.mct(list(list([literals, *range(literals+1,n-1)])), n-1)\n",
    "\n",
    "for q in range(literals+1,n-1):\n",
    "    qc.x(q)\n",
    "qc.x(literals) # Augmented space\n",
    "\n",
    "\n",
    "# Creation of each clause (symmetry).    \n",
    "contador -= 1\n",
    "for c in reversed(formula):\n",
    "    for i in range(3):\n",
    "        if c[i] > 0:\n",
    "            qc.x(abs(c[i])-1)\n",
    "            \n",
    "    qc.mct(list([abs(c[0])-1,abs(c[1])-1,abs(c[2])-1]), literals+1+contador)\n",
    "    \n",
    "    for i in range(3):\n",
    "        if c[2-i] > 0:\n",
    "            qc.x(abs(c[2-i])-1)\n",
    "    \n",
    "    contador-=1\n",
    "\n",
    "oracle = qc.to_gate()\n",
    "oracle.name = \"Oracle\"\n",
    "qc.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8dff5e0",
   "metadata": {},
   "source": [
    "Once we have created the oracle gate, we can create another gate representing steps 3, 4, and 5 of Grover's algorithm. These steps, together, are also called inversion about the mean. To simplify the circuit, we will use the opposite of step 4, which is to perform a phase shift of -1 to the state $|0⟩^{⊗n}$. This simplification is equivalent because we are applying a global phase."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "367661ff-f863-4897-9709-5a3611cc52a6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">     ┌───┐┌───┐     ┌───┐┌───┐\n",
       "q_0: ┤ H ├┤ X ├──■──┤ X ├┤ H ├\n",
       "     ├───┤├───┤  │  ├───┤├───┤\n",
       "q_1: ┤ H ├┤ X ├──■──┤ X ├┤ H ├\n",
       "     ├───┤├───┤  │  ├───┤├───┤\n",
       "q_2: ┤ H ├┤ X ├──■──┤ X ├┤ H ├\n",
       "     ├───┤├───┤  │  ├───┤├───┤\n",
       "q_3: ┤ H ├┤ X ├──■──┤ X ├┤ H ├\n",
       "     ├───┤├───┤  │  ├───┤├───┤\n",
       "q_4: ┤ H ├┤ X ├──■──┤ X ├┤ H ├\n",
       "     ├───┤├───┤  │  ├───┤├───┤\n",
       "q_5: ┤ H ├┤ X ├──■──┤ X ├┤ H ├\n",
       "     └───┘└───┘  │  └───┘└───┘\n",
       "q_6: ────────────┼────────────\n",
       "                 │            \n",
       "q_7: ────────────┼────────────\n",
       "                 │            \n",
       "q_8: ────────────┼────────────\n",
       "               ┌─┴─┐          \n",
       "q_9: ──────────┤ X ├──────────\n",
       "               └───┘          </pre>"
      ],
      "text/plain": [
       "     ┌───┐┌───┐     ┌───┐┌───┐\n",
       "q_0: ┤ H ├┤ X ├──■──┤ X ├┤ H ├\n",
       "     ├───┤├───┤  │  ├───┤├───┤\n",
       "q_1: ┤ H ├┤ X ├──■──┤ X ├┤ H ├\n",
       "     ├───┤├───┤  │  ├───┤├───┤\n",
       "q_2: ┤ H ├┤ X ├──■──┤ X ├┤ H ├\n",
       "     ├───┤├───┤  │  ├───┤├───┤\n",
       "q_3: ┤ H ├┤ X ├──■──┤ X ├┤ H ├\n",
       "     ├───┤├───┤  │  ├───┤├───┤\n",
       "q_4: ┤ H ├┤ X ├──■──┤ X ├┤ H ├\n",
       "     ├───┤├───┤  │  ├───┤├───┤\n",
       "q_5: ┤ H ├┤ X ├──■──┤ X ├┤ H ├\n",
       "     └───┘└───┘  │  └───┘└───┘\n",
       "q_6: ────────────┼────────────\n",
       "                 │            \n",
       "q_7: ────────────┼────────────\n",
       "                 │            \n",
       "q_8: ────────────┼────────────\n",
       "               ┌─┴─┐          \n",
       "q_9: ──────────┤ X ├──────────\n",
       "               └───┘          "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(n)\n",
    "\n",
    "for qubit in range(literals+1):\n",
    "        qc.h(qubit)\n",
    "        \n",
    "for qubit in range(literals+1):\n",
    "        qc.x(qubit)\n",
    "        \n",
    "# Equivalent Diffuser. It gives us the opposite result in Quantum counting, therefore M will be the number of no solutions at the end.\n",
    "qc.mct(list([i for i in range(literals+1)]), n-1)\n",
    "\n",
    "########## Original Diffuser ##############################################################\n",
    "#qc.mct(list([i for i in range(literals+1)]), literals+1)\n",
    "#qc.x(literals+1)\n",
    "#qc.cx(literals+1,n-1)\n",
    "#qc.x(literals+1)\n",
    "#qc.mct(list([i for i in range(literals+1)]), literals+1)\n",
    "###########################################################################################\n",
    "\n",
    "for qubit in range(literals+1):\n",
    "        qc.x(qubit)\n",
    "        \n",
    "for qubit in range(literals+1):\n",
    "        qc.h(qubit)\n",
    "\n",
    "inversionMean = qc.to_gate()\n",
    "inversionMean.name = \"inversionMean\"\n",
    "qc.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ecd3c88a",
   "metadata": {},
   "source": [
    "At this stage, we have created all the gates to run Grover's algorithm, but we still don't know how many solutions we have. Without that information, we cannot calculate the number of repetitions of Grover's operator either. To discover it, we will use the Quantum counting algorithm, which uses the Quantum phase estimation algorithm with steps 2, 3, 4, and 5 (Grover operator) of our search algorithm to find the angle $\\theta$ that we have seen at the beginning of this notebook.\n",
    "\n",
    "Next, we will create another gate corresponding to one iteration of Grover's (steps 2, 3, 4, and 5). As we see down below, we are using the gates created previously."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "aba1e7c9-461a-494b-b4eb-58619d044b72",
   "metadata": {},
   "outputs": [],
   "source": [
    "grover_iteration = QuantumCircuit(n)\n",
    "\n",
    "grover_iteration.append(oracle, list(range(n)))\n",
    "grover_iteration.append(inversionMean, list(range(n)))\n",
    "\n",
    "gi = grover_iteration.to_gate()\n",
    "gi.label = \"GroverI\"\n",
    "cgi = gi.control()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d9a7dfa0",
   "metadata": {},
   "source": [
    "## Quantum counting"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9599d1f5",
   "metadata": {},
   "source": [
    "Quantum counting is an application of the quantum phase estimation to estimate the eigenvalues of the Grover iteration G, which in turn enables us to determine the number of solutions M to the search problem.\n",
    "\n",
    "Before using the Quantum phase estimation (QPE), we need to define the Quantum Fourier transform (QFT). This transformation is analogous to its classical discrete version. We can represent it as follows:\n",
    "\n",
    "$|\\hat{x}⟩$ = $1\\over{\\sqrt{N}}$ $\\sum_{y = 0}^{N-1} e^{{2 \\pi i x y}\\over{N}} |y⟩$ = \n",
    "\n",
    "= $1\\over{\\sqrt{N}}$ $\\sum_{y_1 = 0}^{1} \\sum_{y_2 = 0}^{1} ... \\sum_{y_n = 0}^{1} e^{2 \\pi i x (\\sum_{l = 1}^{n} y_l \\cdot 2^{-l})} |y_1y_2...y_n⟩$ =\n",
    "\n",
    "= $1\\over{\\sqrt{N}}$ $\\sum_{y_1 = 0}^{1} \\sum_{y_2 = 0}^{1} ... \\sum_{y_n = 0}^{1} ⊗_{l=1}^{n} e^{2 \\pi i x y_l \\cdot 2^{-l}} |y_1y_2...y_n⟩$ =\n",
    "\n",
    "= $1\\over{\\sqrt{N}}$ $⊗_{l=1}^{n}$ $[\\sum_{y = 0}^{1} e^{{2 \\pi i x y}\\over{2^{l}}} |y⟩]$ =\n",
    "\n",
    "= ${1}\\over{\\sqrt{N}}$ $\\cdot (|0⟩+e^{{2\\pi i x}\\over{2^1}} |1⟩)$ $\\cdot (|0⟩+e^{{2\\pi i x}\\over{2^2}} |1⟩) \\cdot$ ... $\\cdot (|0⟩+e^{{2\\pi i x}\\over{2^n}} |1⟩)$\n",
    "\n",
    "As we can see, to reach the result, we have been changing the notation of our qubit between its decimal form |y⟩ and its binary form  $|y_1y_2...y_n⟩$.\n",
    "\n",
    "In the following code cell, we have a function that creates the circuit of QFT:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "4b39c063-6b75-46a6-bd6d-8eba5216483d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def qft(n):\n",
    "    circuit = QuantumCircuit(n)\n",
    "    \n",
    "    def swap_registers(circuit, n):\n",
    "        for qubit in range(n//2):\n",
    "            circuit.swap(qubit, n-qubit-1)\n",
    "        return circuit\n",
    "    \n",
    "    def qft_rotations(circuit, n):\n",
    "        #Performs qft on the first n qubits in circuit (without swaps)\n",
    "        if n == 0:\n",
    "            return circuit\n",
    "        n -= 1\n",
    "        circuit.h(n)\n",
    "        for qubit in range(n):\n",
    "            circuit.cp(math.pi/2**(n-qubit), qubit, n)\n",
    "        qft_rotations(circuit, n)\n",
    "    \n",
    "    qft_rotations(circuit, n)\n",
    "    swap_registers(circuit, n)  # Comment this line if we use the 2 possible order of the QPE registers\n",
    "    return circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6c97d33",
   "metadata": {},
   "source": [
    "In the previous cell, we created the QFT, but to run the QPE, we will need the inverse of that circuit. To get the inverse of the QFT, we can convert our function into a gate and use the *inverse* function as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1c2cb43a-74c2-40ed-afe0-c5e2cad179c2",
   "metadata": {},
   "outputs": [],
   "source": [
    "t = literals+1  # Number of counting qubits.\n",
    "qft_dagger = qft(t).to_gate().inverse()\n",
    "qft_dagger.label = \"QFT†\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54b91bdb",
   "metadata": {},
   "source": [
    "In the next cell, we can see the Quantum phase estimation algorithm we will use to obtain the angle $\\theta$. In this algorithm, we use t qubits to predict the angle. The more qubits we use, the lower the precision error in $\\theta$.\n",
    "\n",
    "As we can see, in this algorithm, we apply the controlled version of the gate *GroverI* created before raised successively to the powers of 2. By doing that, we get the following expression:\n",
    "\n",
    "$|\\hat{x}⟩$ = ${1}\\over{\\sqrt{2^t}}$ $\\cdot (|0⟩+e^{{i \\cdot \\theta \\cdot 2^{t-1}}} |1⟩)$ $\\cdot (|0⟩+e^{{i \\cdot \\theta \\cdot 2^{t-2}}} |1⟩) \\cdot$ ... $\\cdot (|0⟩+e^{{i \\cdot \\theta \\cdot 2^{0}}} |1⟩)$\n",
    "\n",
    "This expression is similar to the one obtained in the quantum Fourier transform, and therefore, applying the inverse of QFT, we can get the angle $\\theta$ that we want. If we compare the first terms of each expression, we can see that they are only different in one exponent.\n",
    "\n",
    "QFT: $(|0⟩+e^{{2\\pi i x}\\over{2^1}} |1⟩)$\n",
    "\n",
    "QPE: $(|0⟩+e^{{i \\cdot \\theta \\cdot 2^{t-1}}} |1⟩)$\n",
    "\n",
    "If we apply the inverse of the QFT, we will obtain the *x* in the exponent because it was the input in that function. Comparing the two exponents, we can see what value will take *x* after applying the Quantum phase estimation.\n",
    "\n",
    "$e^{{2\\pi i x}\\over{2^1}}$ = $e^{{i \\cdot \\theta \\cdot 2^{t-1}}}$\n",
    "\n",
    "${2\\pi i x}\\over{2^1}$ = ${i \\cdot \\theta \\cdot 2^{t-1}}$\n",
    "\n",
    "$x$ = ${\\theta \\cdot 2^{t}}\\over{2\\pi}$\n",
    "\n",
    "With that in mind, we can extract the angle needed to determine the number of solutions later. Down below, we can see the complete circuit of the quantum counting algorithm:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "7faee44a-6106-44fc-8193-cb56b32c584c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">      ┌───┐                                                                 »\n",
       " q_0: ┤ H ├──────────■──────────────────────────────────────────────────────»\n",
       "      ├───┤          │                                                      »\n",
       " q_1: ┤ H ├──────────┼───────────■───────────■──────────────────────────────»\n",
       "      ├───┤          │           │           │                              »\n",
       " q_2: ┤ H ├──────────┼───────────┼───────────┼───────────■───────────■──────»\n",
       "      ├───┤          │           │           │           │           │      »\n",
       " q_3: ┤ H ├──────────┼───────────┼───────────┼───────────┼───────────┼──────»\n",
       "      ├───┤          │           │           │           │           │      »\n",
       " q_4: ┤ H ├──────────┼───────────┼───────────┼───────────┼───────────┼──────»\n",
       "      ├───┤          │           │           │           │           │      »\n",
       " q_5: ┤ H ├──────────┼───────────┼───────────┼───────────┼───────────┼──────»\n",
       "      ├───┤     ┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐»\n",
       " q_6: ┤ H ├─────┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├»\n",
       "      ├───┤     │          ││          ││          ││          ││          │»\n",
       " q_7: ┤ H ├─────┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├»\n",
       "      ├───┤     │          ││          ││          ││          ││          │»\n",
       " q_8: ┤ H ├─────┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├»\n",
       "      ├───┤     │          ││          ││          ││          ││          │»\n",
       " q_9: ┤ H ├─────┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├»\n",
       "      ├───┤     │          ││          ││          ││          ││          │»\n",
       "q_10: ┤ H ├─────┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├»\n",
       "      ├───┤     │  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI │»\n",
       "q_11: ┤ H ├─────┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├»\n",
       "      └───┘     │          ││          ││          ││          ││          │»\n",
       "q_12: ──────────┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├»\n",
       "                │          ││          ││          ││          ││          │»\n",
       "q_13: ──────────┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├»\n",
       "                │          ││          ││          ││          ││          │»\n",
       "q_14: ──────────┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├»\n",
       "      ┌───┐┌───┐│          ││          ││          ││          ││          │»\n",
       "q_15: ┤ X ├┤ H ├┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├»\n",
       "      └───┘└───┘└──────────┘└──────────┘└──────────┘└──────────┘└──────────┘»\n",
       " c_0: ══════════════════════════════════════════════════════════════════════»\n",
       "                                                                            »\n",
       " c_1: ══════════════════════════════════════════════════════════════════════»\n",
       "                                                                            »\n",
       " c_2: ══════════════════════════════════════════════════════════════════════»\n",
       "                                                                            »\n",
       " c_3: ══════════════════════════════════════════════════════════════════════»\n",
       "                                                                            »\n",
       " c_4: ══════════════════════════════════════════════════════════════════════»\n",
       "                                                                            »\n",
       " c_5: ══════════════════════════════════════════════════════════════════════»\n",
       "                                                                            »\n",
       "«                                                                              »\n",
       "« q_0: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_1: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_2: ─────■───────────■──────────────────────────────────────────────────────»\n",
       "«           │           │                                                      »\n",
       "« q_3: ─────┼───────────┼───────────■───────────■───────────■───────────■──────»\n",
       "«           │           │           │           │           │           │      »\n",
       "« q_4: ─────┼───────────┼───────────┼───────────┼───────────┼───────────┼──────»\n",
       "«           │           │           │           │           │           │      »\n",
       "« q_5: ─────┼───────────┼───────────┼───────────┼───────────┼───────────┼──────»\n",
       "«      ┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐»\n",
       "« q_6: ┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_7: ┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_8: ┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_9: ┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_10: ┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├»\n",
       "«      │  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI │»\n",
       "«q_11: ┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_12: ┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_13: ┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_14: ┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_15: ┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├»\n",
       "«      └──────────┘└──────────┘└──────────┘└──────────┘└──────────┘└──────────┘»\n",
       "« c_0: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_1: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_2: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_3: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_4: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_5: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "«                                                                              »\n",
       "« q_0: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_1: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_2: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_3: ─────■───────────■───────────■───────────■──────────────────────────────»\n",
       "«           │           │           │           │                              »\n",
       "« q_4: ─────┼───────────┼───────────┼───────────┼───────────■───────────■──────»\n",
       "«           │           │           │           │           │           │      »\n",
       "« q_5: ─────┼───────────┼───────────┼───────────┼───────────┼───────────┼──────»\n",
       "«      ┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐»\n",
       "« q_6: ┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_7: ┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_8: ┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_9: ┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_10: ┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├»\n",
       "«      │  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI │»\n",
       "«q_11: ┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_12: ┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_13: ┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_14: ┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_15: ┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├»\n",
       "«      └──────────┘└──────────┘└──────────┘└──────────┘└──────────┘└──────────┘»\n",
       "« c_0: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_1: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_2: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_3: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_4: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_5: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "«                                                                              »\n",
       "« q_0: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_1: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_2: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_3: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_4: ─────■───────────■───────────■───────────■───────────■───────────■──────»\n",
       "«           │           │           │           │           │           │      »\n",
       "« q_5: ─────┼───────────┼───────────┼───────────┼───────────┼───────────┼──────»\n",
       "«      ┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐»\n",
       "« q_6: ┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_7: ┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_8: ┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_9: ┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_10: ┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├»\n",
       "«      │  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI │»\n",
       "«q_11: ┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_12: ┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_13: ┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_14: ┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_15: ┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├»\n",
       "«      └──────────┘└──────────┘└──────────┘└──────────┘└──────────┘└──────────┘»\n",
       "« c_0: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_1: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_2: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_3: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_4: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_5: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "«                                                                              »\n",
       "« q_0: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_1: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_2: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_3: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_4: ─────■───────────■───────────■───────────■───────────■───────────■──────»\n",
       "«           │           │           │           │           │           │      »\n",
       "« q_5: ─────┼───────────┼───────────┼───────────┼───────────┼───────────┼──────»\n",
       "«      ┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐»\n",
       "« q_6: ┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_7: ┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_8: ┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_9: ┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_10: ┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├»\n",
       "«      │  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI │»\n",
       "«q_11: ┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_12: ┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_13: ┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_14: ┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_15: ┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├»\n",
       "«      └──────────┘└──────────┘└──────────┘└──────────┘└──────────┘└──────────┘»\n",
       "« c_0: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_1: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_2: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_3: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_4: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_5: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "«                                                                              »\n",
       "« q_0: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_1: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_2: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_3: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_4: ─────■───────────■──────────────────────────────────────────────────────»\n",
       "«           │           │                                                      »\n",
       "« q_5: ─────┼───────────┼───────────■───────────■───────────■───────────■──────»\n",
       "«      ┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐»\n",
       "« q_6: ┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_7: ┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_8: ┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_9: ┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_10: ┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├»\n",
       "«      │  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI │»\n",
       "«q_11: ┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_12: ┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_13: ┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_14: ┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_15: ┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├»\n",
       "«      └──────────┘└──────────┘└──────────┘└──────────┘└──────────┘└──────────┘»\n",
       "« c_0: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_1: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_2: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_3: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_4: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_5: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "«                                                                              »\n",
       "« q_0: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_1: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_2: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_3: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_4: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_5: ─────■───────────■───────────■───────────■───────────■───────────■──────»\n",
       "«      ┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐»\n",
       "« q_6: ┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_7: ┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_8: ┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_9: ┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_10: ┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├»\n",
       "«      │  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI │»\n",
       "«q_11: ┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_12: ┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_13: ┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_14: ┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_15: ┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├»\n",
       "«      └──────────┘└──────────┘└──────────┘└──────────┘└──────────┘└──────────┘»\n",
       "« c_0: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_1: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_2: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_3: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_4: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_5: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "«                                                                              »\n",
       "« q_0: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_1: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_2: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_3: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_4: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_5: ─────■───────────■───────────■───────────■───────────■───────────■──────»\n",
       "«      ┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐»\n",
       "« q_6: ┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_7: ┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_8: ┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_9: ┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_10: ┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├»\n",
       "«      │  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI │»\n",
       "«q_11: ┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_12: ┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_13: ┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_14: ┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_15: ┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├»\n",
       "«      └──────────┘└──────────┘└──────────┘└──────────┘└──────────┘└──────────┘»\n",
       "« c_0: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_1: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_2: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_3: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_4: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_5: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "«                                                                              »\n",
       "« q_0: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_1: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_2: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_3: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_4: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_5: ─────■───────────■───────────■───────────■───────────■───────────■──────»\n",
       "«      ┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐»\n",
       "« q_6: ┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_7: ┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_8: ┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_9: ┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_10: ┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├»\n",
       "«      │  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI │»\n",
       "«q_11: ┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_12: ┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_13: ┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_14: ┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_15: ┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├»\n",
       "«      └──────────┘└──────────┘└──────────┘└──────────┘└──────────┘└──────────┘»\n",
       "« c_0: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_1: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_2: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_3: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_4: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_5: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "«                                                                              »\n",
       "« q_0: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_1: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_2: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_3: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_4: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_5: ─────■───────────■───────────■───────────■───────────■───────────■──────»\n",
       "«      ┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐»\n",
       "« q_6: ┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_7: ┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_8: ┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_9: ┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_10: ┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├»\n",
       "«      │  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI │»\n",
       "«q_11: ┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_12: ┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_13: ┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_14: ┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_15: ┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├»\n",
       "«      └──────────┘└──────────┘└──────────┘└──────────┘└──────────┘└──────────┘»\n",
       "« c_0: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_1: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_2: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_3: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_4: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_5: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "«                                                      ┌───────┐┌─┐            »\n",
       "« q_0: ────────────────────────────────────────────────┤0      ├┤M├────────────»\n",
       "«                                                      │       │└╥┘┌─┐         »\n",
       "« q_1: ────────────────────────────────────────────────┤1      ├─╫─┤M├─────────»\n",
       "«                                                      │       │ ║ └╥┘┌─┐      »\n",
       "« q_2: ────────────────────────────────────────────────┤2      ├─╫──╫─┤M├──────»\n",
       "«                                                      │  QFT† │ ║  ║ └╥┘┌─┐   »\n",
       "« q_3: ────────────────────────────────────────────────┤3      ├─╫──╫──╫─┤M├───»\n",
       "«                                                      │       │ ║  ║  ║ └╥┘┌─┐»\n",
       "« q_4: ────────────────────────────────────────────────┤4      ├─╫──╫──╫──╫─┤M├»\n",
       "«                                                      │       │ ║  ║  ║  ║ └╥┘»\n",
       "« q_5: ─────■───────────■───────────■───────────■──────┤5      ├─╫──╫──╫──╫──╫─»\n",
       "«      ┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐└───────┘ ║  ║  ║  ║  ║ »\n",
       "« q_6: ┤0         ├┤0         ├┤0         ├┤0         ├──────────╫──╫──╫──╫──╫─»\n",
       "«      │          ││          ││          ││          │          ║  ║  ║  ║  ║ »\n",
       "« q_7: ┤1         ├┤1         ├┤1         ├┤1         ├──────────╫──╫──╫──╫──╫─»\n",
       "«      │          ││          ││          ││          │          ║  ║  ║  ║  ║ »\n",
       "« q_8: ┤2         ├┤2         ├┤2         ├┤2         ├──────────╫──╫──╫──╫──╫─»\n",
       "«      │          ││          ││          ││          │          ║  ║  ║  ║  ║ »\n",
       "« q_9: ┤3         ├┤3         ├┤3         ├┤3         ├──────────╫──╫──╫──╫──╫─»\n",
       "«      │          ││          ││          ││          │          ║  ║  ║  ║  ║ »\n",
       "«q_10: ┤4         ├┤4         ├┤4         ├┤4         ├──────────╫──╫──╫──╫──╫─»\n",
       "«      │  GroverI ││  GroverI ││  GroverI ││  GroverI │          ║  ║  ║  ║  ║ »\n",
       "«q_11: ┤5         ├┤5         ├┤5         ├┤5         ├──────────╫──╫──╫──╫──╫─»\n",
       "«      │          ││          ││          ││          │          ║  ║  ║  ║  ║ »\n",
       "«q_12: ┤6         ├┤6         ├┤6         ├┤6         ├──────────╫──╫──╫──╫──╫─»\n",
       "«      │          ││          ││          ││          │          ║  ║  ║  ║  ║ »\n",
       "«q_13: ┤7         ├┤7         ├┤7         ├┤7         ├──────────╫──╫──╫──╫──╫─»\n",
       "«      │          ││          ││          ││          │          ║  ║  ║  ║  ║ »\n",
       "«q_14: ┤8         ├┤8         ├┤8         ├┤8         ├──────────╫──╫──╫──╫──╫─»\n",
       "«      │          ││          ││          ││          │          ║  ║  ║  ║  ║ »\n",
       "«q_15: ┤9         ├┤9         ├┤9         ├┤9         ├──────────╫──╫──╫──╫──╫─»\n",
       "«      └──────────┘└──────────┘└──────────┘└──────────┘          ║  ║  ║  ║  ║ »\n",
       "« c_0: ══════════════════════════════════════════════════════════╩══╬══╬══╬══╬═»\n",
       "«                                                                   ║  ║  ║  ║ »\n",
       "« c_1: ═════════════════════════════════════════════════════════════╩══╬══╬══╬═»\n",
       "«                                                                      ║  ║  ║ »\n",
       "« c_2: ════════════════════════════════════════════════════════════════╩══╬══╬═»\n",
       "«                                                                         ║  ║ »\n",
       "« c_3: ═══════════════════════════════════════════════════════════════════╩══╬═»\n",
       "«                                                                            ║ »\n",
       "« c_4: ══════════════════════════════════════════════════════════════════════╩═»\n",
       "«                                                                              »\n",
       "« c_5: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "«         \n",
       "« q_0: ───\n",
       "«         \n",
       "« q_1: ───\n",
       "«         \n",
       "« q_2: ───\n",
       "«         \n",
       "« q_3: ───\n",
       "«         \n",
       "« q_4: ───\n",
       "«      ┌─┐\n",
       "« q_5: ┤M├\n",
       "«      └╥┘\n",
       "« q_6: ─╫─\n",
       "«       ║ \n",
       "« q_7: ─╫─\n",
       "«       ║ \n",
       "« q_8: ─╫─\n",
       "«       ║ \n",
       "« q_9: ─╫─\n",
       "«       ║ \n",
       "«q_10: ─╫─\n",
       "«       ║ \n",
       "«q_11: ─╫─\n",
       "«       ║ \n",
       "«q_12: ─╫─\n",
       "«       ║ \n",
       "«q_13: ─╫─\n",
       "«       ║ \n",
       "«q_14: ─╫─\n",
       "«       ║ \n",
       "«q_15: ─╫─\n",
       "«       ║ \n",
       "« c_0: ═╬═\n",
       "«       ║ \n",
       "« c_1: ═╬═\n",
       "«       ║ \n",
       "« c_2: ═╬═\n",
       "«       ║ \n",
       "« c_3: ═╬═\n",
       "«       ║ \n",
       "« c_4: ═╬═\n",
       "«       ║ \n",
       "« c_5: ═╩═\n",
       "«         </pre>"
      ],
      "text/plain": [
       "      ┌───┐                                                                 »\n",
       " q_0: ┤ H ├──────────■──────────────────────────────────────────────────────»\n",
       "      ├───┤          │                                                      »\n",
       " q_1: ┤ H ├──────────┼───────────■───────────■──────────────────────────────»\n",
       "      ├───┤          │           │           │                              »\n",
       " q_2: ┤ H ├──────────┼───────────┼───────────┼───────────■───────────■──────»\n",
       "      ├───┤          │           │           │           │           │      »\n",
       " q_3: ┤ H ├──────────┼───────────┼───────────┼───────────┼───────────┼──────»\n",
       "      ├───┤          │           │           │           │           │      »\n",
       " q_4: ┤ H ├──────────┼───────────┼───────────┼───────────┼───────────┼──────»\n",
       "      ├───┤          │           │           │           │           │      »\n",
       " q_5: ┤ H ├──────────┼───────────┼───────────┼───────────┼───────────┼──────»\n",
       "      ├───┤     ┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐»\n",
       " q_6: ┤ H ├─────┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├»\n",
       "      ├───┤     │          ││          ││          ││          ││          │»\n",
       " q_7: ┤ H ├─────┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├»\n",
       "      ├───┤     │          ││          ││          ││          ││          │»\n",
       " q_8: ┤ H ├─────┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├»\n",
       "      ├───┤     │          ││          ││          ││          ││          │»\n",
       " q_9: ┤ H ├─────┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├»\n",
       "      ├───┤     │          ││          ││          ││          ││          │»\n",
       "q_10: ┤ H ├─────┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├»\n",
       "      ├───┤     │  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI │»\n",
       "q_11: ┤ H ├─────┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├»\n",
       "      └───┘     │          ││          ││          ││          ││          │»\n",
       "q_12: ──────────┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├»\n",
       "                │          ││          ││          ││          ││          │»\n",
       "q_13: ──────────┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├»\n",
       "                │          ││          ││          ││          ││          │»\n",
       "q_14: ──────────┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├»\n",
       "      ┌───┐┌───┐│          ││          ││          ││          ││          │»\n",
       "q_15: ┤ X ├┤ H ├┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├»\n",
       "      └───┘└───┘└──────────┘└──────────┘└──────────┘└──────────┘└──────────┘»\n",
       " c_0: ══════════════════════════════════════════════════════════════════════»\n",
       "                                                                            »\n",
       " c_1: ══════════════════════════════════════════════════════════════════════»\n",
       "                                                                            »\n",
       " c_2: ══════════════════════════════════════════════════════════════════════»\n",
       "                                                                            »\n",
       " c_3: ══════════════════════════════════════════════════════════════════════»\n",
       "                                                                            »\n",
       " c_4: ══════════════════════════════════════════════════════════════════════»\n",
       "                                                                            »\n",
       " c_5: ══════════════════════════════════════════════════════════════════════»\n",
       "                                                                            »\n",
       "«                                                                              »\n",
       "« q_0: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_1: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_2: ─────■───────────■──────────────────────────────────────────────────────»\n",
       "«           │           │                                                      »\n",
       "« q_3: ─────┼───────────┼───────────■───────────■───────────■───────────■──────»\n",
       "«           │           │           │           │           │           │      »\n",
       "« q_4: ─────┼───────────┼───────────┼───────────┼───────────┼───────────┼──────»\n",
       "«           │           │           │           │           │           │      »\n",
       "« q_5: ─────┼───────────┼───────────┼───────────┼───────────┼───────────┼──────»\n",
       "«      ┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐»\n",
       "« q_6: ┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_7: ┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_8: ┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_9: ┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_10: ┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├»\n",
       "«      │  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI │»\n",
       "«q_11: ┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_12: ┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_13: ┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_14: ┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_15: ┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├»\n",
       "«      └──────────┘└──────────┘└──────────┘└──────────┘└──────────┘└──────────┘»\n",
       "« c_0: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_1: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_2: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_3: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_4: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_5: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "«                                                                              »\n",
       "« q_0: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_1: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_2: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_3: ─────■───────────■───────────■───────────■──────────────────────────────»\n",
       "«           │           │           │           │                              »\n",
       "« q_4: ─────┼───────────┼───────────┼───────────┼───────────■───────────■──────»\n",
       "«           │           │           │           │           │           │      »\n",
       "« q_5: ─────┼───────────┼───────────┼───────────┼───────────┼───────────┼──────»\n",
       "«      ┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐»\n",
       "« q_6: ┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_7: ┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_8: ┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_9: ┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_10: ┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├»\n",
       "«      │  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI │»\n",
       "«q_11: ┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_12: ┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_13: ┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_14: ┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_15: ┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├»\n",
       "«      └──────────┘└──────────┘└──────────┘└──────────┘└──────────┘└──────────┘»\n",
       "« c_0: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_1: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_2: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_3: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_4: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_5: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "«                                                                              »\n",
       "« q_0: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_1: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_2: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_3: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_4: ─────■───────────■───────────■───────────■───────────■───────────■──────»\n",
       "«           │           │           │           │           │           │      »\n",
       "« q_5: ─────┼───────────┼───────────┼───────────┼───────────┼───────────┼──────»\n",
       "«      ┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐»\n",
       "« q_6: ┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_7: ┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_8: ┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_9: ┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_10: ┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├»\n",
       "«      │  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI │»\n",
       "«q_11: ┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_12: ┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_13: ┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_14: ┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_15: ┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├»\n",
       "«      └──────────┘└──────────┘└──────────┘└──────────┘└──────────┘└──────────┘»\n",
       "« c_0: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_1: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_2: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_3: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_4: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_5: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "«                                                                              »\n",
       "« q_0: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_1: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_2: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_3: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_4: ─────■───────────■───────────■───────────■───────────■───────────■──────»\n",
       "«           │           │           │           │           │           │      »\n",
       "« q_5: ─────┼───────────┼───────────┼───────────┼───────────┼───────────┼──────»\n",
       "«      ┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐»\n",
       "« q_6: ┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_7: ┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_8: ┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_9: ┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_10: ┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├»\n",
       "«      │  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI │»\n",
       "«q_11: ┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_12: ┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_13: ┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_14: ┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_15: ┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├»\n",
       "«      └──────────┘└──────────┘└──────────┘└──────────┘└──────────┘└──────────┘»\n",
       "« c_0: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_1: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_2: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_3: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_4: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_5: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "«                                                                              »\n",
       "« q_0: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_1: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_2: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_3: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_4: ─────■───────────■──────────────────────────────────────────────────────»\n",
       "«           │           │                                                      »\n",
       "« q_5: ─────┼───────────┼───────────■───────────■───────────■───────────■──────»\n",
       "«      ┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐»\n",
       "« q_6: ┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_7: ┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_8: ┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_9: ┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_10: ┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├»\n",
       "«      │  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI │»\n",
       "«q_11: ┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_12: ┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_13: ┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_14: ┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_15: ┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├»\n",
       "«      └──────────┘└──────────┘└──────────┘└──────────┘└──────────┘└──────────┘»\n",
       "« c_0: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_1: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_2: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_3: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_4: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_5: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "«                                                                              »\n",
       "« q_0: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_1: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_2: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_3: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_4: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_5: ─────■───────────■───────────■───────────■───────────■───────────■──────»\n",
       "«      ┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐»\n",
       "« q_6: ┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_7: ┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_8: ┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_9: ┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_10: ┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├»\n",
       "«      │  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI │»\n",
       "«q_11: ┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_12: ┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_13: ┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_14: ┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_15: ┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├»\n",
       "«      └──────────┘└──────────┘└──────────┘└──────────┘└──────────┘└──────────┘»\n",
       "« c_0: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_1: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_2: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_3: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_4: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_5: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "«                                                                              »\n",
       "« q_0: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_1: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_2: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_3: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_4: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_5: ─────■───────────■───────────■───────────■───────────■───────────■──────»\n",
       "«      ┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐»\n",
       "« q_6: ┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_7: ┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_8: ┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_9: ┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_10: ┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├»\n",
       "«      │  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI │»\n",
       "«q_11: ┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_12: ┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_13: ┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_14: ┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_15: ┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├»\n",
       "«      └──────────┘└──────────┘└──────────┘└──────────┘└──────────┘└──────────┘»\n",
       "« c_0: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_1: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_2: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_3: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_4: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_5: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "«                                                                              »\n",
       "« q_0: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_1: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_2: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_3: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_4: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_5: ─────■───────────■───────────■───────────■───────────■───────────■──────»\n",
       "«      ┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐»\n",
       "« q_6: ┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_7: ┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_8: ┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_9: ┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_10: ┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├»\n",
       "«      │  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI │»\n",
       "«q_11: ┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_12: ┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_13: ┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_14: ┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_15: ┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├»\n",
       "«      └──────────┘└──────────┘└──────────┘└──────────┘└──────────┘└──────────┘»\n",
       "« c_0: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_1: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_2: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_3: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_4: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_5: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "«                                                                              »\n",
       "« q_0: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_1: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_2: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_3: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_4: ────────────────────────────────────────────────────────────────────────»\n",
       "«                                                                              »\n",
       "« q_5: ─────■───────────■───────────■───────────■───────────■───────────■──────»\n",
       "«      ┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐»\n",
       "« q_6: ┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├┤0         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_7: ┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├┤1         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_8: ┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├┤2         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "« q_9: ┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├┤3         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_10: ┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├┤4         ├»\n",
       "«      │  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI ││  GroverI │»\n",
       "«q_11: ┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├┤5         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_12: ┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├┤6         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_13: ┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├┤7         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_14: ┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├┤8         ├»\n",
       "«      │          ││          ││          ││          ││          ││          │»\n",
       "«q_15: ┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├┤9         ├»\n",
       "«      └──────────┘└──────────┘└──────────┘└──────────┘└──────────┘└──────────┘»\n",
       "« c_0: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_1: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_2: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_3: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_4: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "« c_5: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "«                                                      ┌───────┐┌─┐            »\n",
       "« q_0: ────────────────────────────────────────────────┤0      ├┤M├────────────»\n",
       "«                                                      │       │└╥┘┌─┐         »\n",
       "« q_1: ────────────────────────────────────────────────┤1      ├─╫─┤M├─────────»\n",
       "«                                                      │       │ ║ └╥┘┌─┐      »\n",
       "« q_2: ────────────────────────────────────────────────┤2      ├─╫──╫─┤M├──────»\n",
       "«                                                      │  QFT† │ ║  ║ └╥┘┌─┐   »\n",
       "« q_3: ────────────────────────────────────────────────┤3      ├─╫──╫──╫─┤M├───»\n",
       "«                                                      │       │ ║  ║  ║ └╥┘┌─┐»\n",
       "« q_4: ────────────────────────────────────────────────┤4      ├─╫──╫──╫──╫─┤M├»\n",
       "«                                                      │       │ ║  ║  ║  ║ └╥┘»\n",
       "« q_5: ─────■───────────■───────────■───────────■──────┤5      ├─╫──╫──╫──╫──╫─»\n",
       "«      ┌────┴─────┐┌────┴─────┐┌────┴─────┐┌────┴─────┐└───────┘ ║  ║  ║  ║  ║ »\n",
       "« q_6: ┤0         ├┤0         ├┤0         ├┤0         ├──────────╫──╫──╫──╫──╫─»\n",
       "«      │          ││          ││          ││          │          ║  ║  ║  ║  ║ »\n",
       "« q_7: ┤1         ├┤1         ├┤1         ├┤1         ├──────────╫──╫──╫──╫──╫─»\n",
       "«      │          ││          ││          ││          │          ║  ║  ║  ║  ║ »\n",
       "« q_8: ┤2         ├┤2         ├┤2         ├┤2         ├──────────╫──╫──╫──╫──╫─»\n",
       "«      │          ││          ││          ││          │          ║  ║  ║  ║  ║ »\n",
       "« q_9: ┤3         ├┤3         ├┤3         ├┤3         ├──────────╫──╫──╫──╫──╫─»\n",
       "«      │          ││          ││          ││          │          ║  ║  ║  ║  ║ »\n",
       "«q_10: ┤4         ├┤4         ├┤4         ├┤4         ├──────────╫──╫──╫──╫──╫─»\n",
       "«      │  GroverI ││  GroverI ││  GroverI ││  GroverI │          ║  ║  ║  ║  ║ »\n",
       "«q_11: ┤5         ├┤5         ├┤5         ├┤5         ├──────────╫──╫──╫──╫──╫─»\n",
       "«      │          ││          ││          ││          │          ║  ║  ║  ║  ║ »\n",
       "«q_12: ┤6         ├┤6         ├┤6         ├┤6         ├──────────╫──╫──╫──╫──╫─»\n",
       "«      │          ││          ││          ││          │          ║  ║  ║  ║  ║ »\n",
       "«q_13: ┤7         ├┤7         ├┤7         ├┤7         ├──────────╫──╫──╫──╫──╫─»\n",
       "«      │          ││          ││          ││          │          ║  ║  ║  ║  ║ »\n",
       "«q_14: ┤8         ├┤8         ├┤8         ├┤8         ├──────────╫──╫──╫──╫──╫─»\n",
       "«      │          ││          ││          ││          │          ║  ║  ║  ║  ║ »\n",
       "«q_15: ┤9         ├┤9         ├┤9         ├┤9         ├──────────╫──╫──╫──╫──╫─»\n",
       "«      └──────────┘└──────────┘└──────────┘└──────────┘          ║  ║  ║  ║  ║ »\n",
       "« c_0: ══════════════════════════════════════════════════════════╩══╬══╬══╬══╬═»\n",
       "«                                                                   ║  ║  ║  ║ »\n",
       "« c_1: ═════════════════════════════════════════════════════════════╩══╬══╬══╬═»\n",
       "«                                                                      ║  ║  ║ »\n",
       "« c_2: ════════════════════════════════════════════════════════════════╩══╬══╬═»\n",
       "«                                                                         ║  ║ »\n",
       "« c_3: ═══════════════════════════════════════════════════════════════════╩══╬═»\n",
       "«                                                                            ║ »\n",
       "« c_4: ══════════════════════════════════════════════════════════════════════╩═»\n",
       "«                                                                              »\n",
       "« c_5: ════════════════════════════════════════════════════════════════════════»\n",
       "«                                                                              »\n",
       "«         \n",
       "« q_0: ───\n",
       "«         \n",
       "« q_1: ───\n",
       "«         \n",
       "« q_2: ───\n",
       "«         \n",
       "« q_3: ───\n",
       "«         \n",
       "« q_4: ───\n",
       "«      ┌─┐\n",
       "« q_5: ┤M├\n",
       "«      └╥┘\n",
       "« q_6: ─╫─\n",
       "«       ║ \n",
       "« q_7: ─╫─\n",
       "«       ║ \n",
       "« q_8: ─╫─\n",
       "«       ║ \n",
       "« q_9: ─╫─\n",
       "«       ║ \n",
       "«q_10: ─╫─\n",
       "«       ║ \n",
       "«q_11: ─╫─\n",
       "«       ║ \n",
       "«q_12: ─╫─\n",
       "«       ║ \n",
       "«q_13: ─╫─\n",
       "«       ║ \n",
       "«q_14: ─╫─\n",
       "«       ║ \n",
       "«q_15: ─╫─\n",
       "«       ║ \n",
       "« c_0: ═╬═\n",
       "«       ║ \n",
       "« c_1: ═╬═\n",
       "«       ║ \n",
       "« c_2: ═╬═\n",
       "«       ║ \n",
       "« c_3: ═╬═\n",
       "«       ║ \n",
       "« c_4: ═╬═\n",
       "«       ║ \n",
       "« c_5: ═╩═\n",
       "«         "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qpe = QuantumCircuit(n+t, t) # Circuit with n+t qubits and t classical bits\n",
    "\n",
    "# Superposition\n",
    "for qubit in range(t+literals+1):\n",
    "    qpe.h(qubit)\n",
    "\n",
    "# State |-⟩\n",
    "qpe.x(n+t-1)\n",
    "qpe.h(n+t-1)\n",
    "    \n",
    "# Grover iterations\n",
    "iterations = 1\n",
    "for qubit in range(t):\n",
    "    for i in range(iterations):\n",
    "        qpe.append(cgi, [qubit] + [*range(t, n+t)])   # Using this line, uncomment the QFT swap.\n",
    "        #qpe.append(cgrit, [(t-1)-qubit] + [*range(t, n+t)]) # Using this line, comment the QFT swap.\n",
    "\n",
    "    iterations *= 2\n",
    "    \n",
    "# Application of QFT inverse to all counting qubits\n",
    "qpe.append(qft_dagger, range(t))\n",
    "\n",
    "# Measure the counting qubits\n",
    "qpe.measure(range(t), range(t))\n",
    "\n",
    "qpe.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9dd99c0",
   "metadata": {},
   "source": [
    "In the graphic below, we can see the results obtained after running the quantum counting circuit depicted above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "78a77abe-86d8-4a99-9f22-e420d0e1b076",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Quantum counting sinulation\n",
    "aer_sim = Aer.get_backend('aer_simulator')\n",
    "transpiled_qpe = transpile(qpe, aer_sim)\n",
    "qobj = assemble(transpiled_qpe)\n",
    "job = aer_sim.run(qobj)\n",
    "hist = job.result().get_counts()\n",
    "plot_histogram(hist)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7cbffa5b",
   "metadata": {},
   "source": [
    "After obtaining the *x* in the QFT, we can extract the angle of one Grover's iteration like this:\n",
    "\n",
    "$\\theta$ = ${2\\pi x}\\over{2^t}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "9daed31a-9a4f-4c7b-b1fb-ba9c801ddb0a",
   "metadata": {},
   "outputs": [],
   "source": [
    "measured_str = max(hist, key=hist.get)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f6e32781-3b04-48eb-810f-2175734faa1d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "101100\n",
      "Register Output = 44\n"
     ]
    }
   ],
   "source": [
    "measured_int = int(measured_str,2)\n",
    "print(measured_str)\n",
    "print(\"Register Output = %i\" % measured_int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "9b38000c-a868-4267-abf9-d7a61832fe95",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Theta = 4.31969\n"
     ]
    }
   ],
   "source": [
    "theta = (measured_int/(2**t))*math.pi*2\n",
    "print(\"Theta = %.5f\" % theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52bd25b6",
   "metadata": {},
   "source": [
    "Now, we can calculate the number of assignments that satisfy our formula with the angle $\\theta$. At the beginning of this notebook, we have defined our state as follows:\n",
    "\n",
    "$|\\psi⟩$ = $\\sqrt{N-M\\over{N}}$ $|\\alpha⟩$ + $\\sqrt{M\\over{N}}$ $|\\beta⟩$\n",
    "\n",
    "Geometrically, we have seen that we can represent our state with cosines and sines because the state $|\\psi⟩$ is normalized, and $|\\alpha⟩$ and $|\\beta⟩$ are orthogonal to each other:\n",
    "\n",
    "$|\\psi⟩$ = cos($\\theta \\over{2}$) $|\\alpha⟩$ + sin($\\theta \\over{2}$) $|\\beta⟩$\n",
    "\n",
    "Therefore, we can conclude:\n",
    "\n",
    "$\\sqrt{M\\over{N}}$ = sin($\\theta \\over{2}$)\n",
    "\n",
    "$M$ = ${sin}^{2}({{\\theta}\\over{2}}) \\cdot N$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "d63ce288-56a7-42b4-aeb0-00a196192e6f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "64 19.754130164317118\n",
      "No. of Solutions = 19.8\n"
     ]
    }
   ],
   "source": [
    "N = 2**(literals+1)\n",
    "M = N * (math.sin(theta/2)**2)\n",
    "M = N-M # Diffuser faster only\n",
    "print(N,M)\n",
    "print(\"No. of Solutions = %.1f\" % M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "580c2108-409d-45e7-b05d-2e595fd75cc2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error < 1.60\n"
     ]
    }
   ],
   "source": [
    "# Upper bound error for the number of solutions\n",
    "m = t - 1\n",
    "err = (math.sqrt(2*M*N) + N/(2**(m+1)))*(2**(-m))\n",
    "print(\"Error < %.2f\" % err)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "67c4bc41",
   "metadata": {},
   "source": [
    "## Grover's algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64b59594",
   "metadata": {},
   "source": [
    "Now, we have all the ingredients to execute Grover's algorithm. To calculate the number of iterations R in order to maximize the probability of obtaining a solution state, we can use the following upper bound:\n",
    "\n",
    "$R \\le \\lceil {{\\pi}\\over{4}} \\cdot \\sqrt{{N}\\over{M}}  \\rceil$\n",
    "\n",
    "In the worst-case scenario, our formula has only one solution, which leads us to a time complexity of $O(\\sqrt{N})$ for Grover's algorithm. We have used quantum counting before, but as we can see in *Quantum Computation and Quantum Information by Michael A. Nielsen & Isaac L. Chuang*, the time complexity is also $O(\\sqrt{N})$ thus, we have a total time complexity of $O(\\sqrt{N})$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "e33ae115",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Result: 1.4136793455054264\n",
      "Iterations R ≤ 2\n",
      "Iterations chosen: 1\n"
     ]
    }
   ],
   "source": [
    "rounds = math.pi/4.0*math.sqrt(N/M)\n",
    "print(\"Result:\",rounds)\n",
    "print(\"Iterations R ≤\",math.ceil(rounds))\n",
    "\n",
    "if math.floor(rounds) == 0:\n",
    "    rounds = round(rounds)\n",
    "else:\n",
    "    rounds = math.floor(rounds)\n",
    "\n",
    "print(\"Iterations chosen:\", rounds)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7313324c",
   "metadata": {},
   "source": [
    "In the next cell, we can see Grover's algorithm and its circuit depicted:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "b7c5f692",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">     ┌───┐     ┌─────────┐┌────────────────┐┌─┐               \n",
       "q_0: ┤ H ├─────┤0        ├┤0               ├┤M├───────────────\n",
       "     ├───┤     │         ││                │└╥┘┌─┐            \n",
       "q_1: ┤ H ├─────┤1        ├┤1               ├─╫─┤M├────────────\n",
       "     ├───┤     │         ││                │ ║ └╥┘┌─┐         \n",
       "q_2: ┤ H ├─────┤2        ├┤2               ├─╫──╫─┤M├─────────\n",
       "     ├───┤     │         ││                │ ║  ║ └╥┘┌─┐      \n",
       "q_3: ┤ H ├─────┤3        ├┤3               ├─╫──╫──╫─┤M├──────\n",
       "     ├───┤     │         ││                │ ║  ║  ║ └╥┘┌─┐   \n",
       "q_4: ┤ H ├─────┤4        ├┤4               ├─╫──╫──╫──╫─┤M├───\n",
       "     ├───┤     │  Oracle ││  inversionMean │ ║  ║  ║  ║ └╥┘┌─┐\n",
       "q_5: ┤ H ├─────┤5        ├┤5               ├─╫──╫──╫──╫──╫─┤M├\n",
       "     └───┘     │         ││                │ ║  ║  ║  ║  ║ └╥┘\n",
       "q_6: ──────────┤6        ├┤6               ├─╫──╫──╫──╫──╫──╫─\n",
       "               │         ││                │ ║  ║  ║  ║  ║  ║ \n",
       "q_7: ──────────┤7        ├┤7               ├─╫──╫──╫──╫──╫──╫─\n",
       "               │         ││                │ ║  ║  ║  ║  ║  ║ \n",
       "q_8: ──────────┤8        ├┤8               ├─╫──╫──╫──╫──╫──╫─\n",
       "     ┌───┐┌───┐│         ││                │ ║  ║  ║  ║  ║  ║ \n",
       "q_9: ┤ X ├┤ H ├┤9        ├┤9               ├─╫──╫──╫──╫──╫──╫─\n",
       "     └───┘└───┘└─────────┘└────────────────┘ ║  ║  ║  ║  ║  ║ \n",
       "c_0: ════════════════════════════════════════╩══╬══╬══╬══╬══╬═\n",
       "                                                ║  ║  ║  ║  ║ \n",
       "c_1: ═══════════════════════════════════════════╩══╬══╬══╬══╬═\n",
       "                                                   ║  ║  ║  ║ \n",
       "c_2: ══════════════════════════════════════════════╩══╬══╬══╬═\n",
       "                                                      ║  ║  ║ \n",
       "c_3: ═════════════════════════════════════════════════╩══╬══╬═\n",
       "                                                         ║  ║ \n",
       "c_4: ════════════════════════════════════════════════════╩══╬═\n",
       "                                                            ║ \n",
       "c_5: ═══════════════════════════════════════════════════════╩═\n",
       "                                                              </pre>"
      ],
      "text/plain": [
       "     ┌───┐     ┌─────────┐┌────────────────┐┌─┐               \n",
       "q_0: ┤ H ├─────┤0        ├┤0               ├┤M├───────────────\n",
       "     ├───┤     │         ││                │└╥┘┌─┐            \n",
       "q_1: ┤ H ├─────┤1        ├┤1               ├─╫─┤M├────────────\n",
       "     ├───┤     │         ││                │ ║ └╥┘┌─┐         \n",
       "q_2: ┤ H ├─────┤2        ├┤2               ├─╫──╫─┤M├─────────\n",
       "     ├───┤     │         ││                │ ║  ║ └╥┘┌─┐      \n",
       "q_3: ┤ H ├─────┤3        ├┤3               ├─╫──╫──╫─┤M├──────\n",
       "     ├───┤     │         ││                │ ║  ║  ║ └╥┘┌─┐   \n",
       "q_4: ┤ H ├─────┤4        ├┤4               ├─╫──╫──╫──╫─┤M├───\n",
       "     ├───┤     │  Oracle ││  inversionMean │ ║  ║  ║  ║ └╥┘┌─┐\n",
       "q_5: ┤ H ├─────┤5        ├┤5               ├─╫──╫──╫──╫──╫─┤M├\n",
       "     └───┘     │         ││                │ ║  ║  ║  ║  ║ └╥┘\n",
       "q_6: ──────────┤6        ├┤6               ├─╫──╫──╫──╫──╫──╫─\n",
       "               │         ││                │ ║  ║  ║  ║  ║  ║ \n",
       "q_7: ──────────┤7        ├┤7               ├─╫──╫──╫──╫──╫──╫─\n",
       "               │         ││                │ ║  ║  ║  ║  ║  ║ \n",
       "q_8: ──────────┤8        ├┤8               ├─╫──╫──╫──╫──╫──╫─\n",
       "     ┌───┐┌───┐│         ││                │ ║  ║  ║  ║  ║  ║ \n",
       "q_9: ┤ X ├┤ H ├┤9        ├┤9               ├─╫──╫──╫──╫──╫──╫─\n",
       "     └───┘└───┘└─────────┘└────────────────┘ ║  ║  ║  ║  ║  ║ \n",
       "c_0: ════════════════════════════════════════╩══╬══╬══╬══╬══╬═\n",
       "                                                ║  ║  ║  ║  ║ \n",
       "c_1: ═══════════════════════════════════════════╩══╬══╬══╬══╬═\n",
       "                                                   ║  ║  ║  ║ \n",
       "c_2: ══════════════════════════════════════════════╩══╬══╬══╬═\n",
       "                                                      ║  ║  ║ \n",
       "c_3: ═════════════════════════════════════════════════╩══╬══╬═\n",
       "                                                         ║  ║ \n",
       "c_4: ════════════════════════════════════════════════════╩══╬═\n",
       "                                                            ║ \n",
       "c_5: ═══════════════════════════════════════════════════════╩═\n",
       "                                                              "
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grover_circuit = QuantumCircuit(n,literals+1)\n",
    "\n",
    "grover_circuit = initialize_grover(grover_circuit, list(range(n)))\n",
    "for i in range(rounds):\n",
    "    grover_circuit.append(oracle, list(range(n)))\n",
    "    grover_circuit.append(inversionMean, list(range(n)))\n",
    "\n",
    "for i in range(literals+1):\n",
    "    grover_circuit.measure([i],[i])\n",
    "\n",
    "grover_circuit.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c5c6e26",
   "metadata": {},
   "source": [
    "Finally, we can see the results obtained after running the circuit. The results represent all the assignments written as binary strings that satisfy our formula. All solutions appear on the left because, as mentioned, we use the last qubit to create the augmented space, and we force it to be 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "97e7868a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Total count: {'100100': 1, '111111': 1, '100000': 1, '000000': 1, '001000': 2, '110100': 2, '101110': 1, '010010': 1, '000010': 2, '111000': 2, '011000': 1, '101111': 3, '001111': 1, '110110': 1, '011111': 2, '111011': 2, '100101': 2, '101010': 2, '011011': 42, '001001': 41, '100010': 2, '010001': 56, '000001': 47, '101100': 1, '000011': 49, '001100': 60, '000100': 45, '001010': 3, '111010': 2, '010110': 56, '100011': 4, '011100': 58, '010101': 46, '000101': 56, '011101': 46, '000110': 50, '110001': 1, '011001': 56, '010111': 1, '001101': 43, '110111': 1, '001110': 51, '010011': 42, '010100': 37, '001011': 55, '011110': 45}\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1200x500 with 1 Axes>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Grover's algorithm simulation\n",
    "aer_sim = Aer.get_backend('aer_simulator')\n",
    "transpiled_grover_circuit = transpile(grover_circuit, aer_sim)\n",
    "qobj = assemble(transpiled_grover_circuit)\n",
    "results = aer_sim.run(qobj, shots=1024).result()\n",
    "counts = results.get_counts()\n",
    "print(\"\\nTotal count:\",counts)\n",
    "plot_histogram(counts,figsize=(12,5))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.11.1"
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {},
    "version_major": 2,
    "version_minor": 0
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}