task1.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "from typing import List, Tuple\n",
    "import numpy as np\n",
    "from qiskit import QuantumCircuit, BasicAer, transpile, QuantumRegister, ClassicalRegister\n",
    "from qiskit.circuit.library import StatePreparation, MCXGate\n",
    "from qiskit.quantum_info import Statevector\n",
    "from qiskit.visualization import plot_histogram"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given a positive integer and a list of prime numbers, look for the two prime numbers, that sum the positive number. Consider an appropriate number of qubits and explain why your proposal is valid for all kinds of numbers in case."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are going to assume that there are only prime numbers in the list, so no prime verification is needed after finding a pair of numbers in the list that sum the given integer. That means that we can focus in solving this: given a positive integer $n$ and a list of $m$ positive integers $a_0, \\ldots, a_{m-1}$, find a pair of numbers in the list that sum $n$. The proposed solution of Task 1 is based on a general form of Grover's algorithm, called Amplitude Amplification ([Brassard et al., 2000](https://arxiv.org/pdf/quant-ph/0005055.pdf)), which allows us to find marked elements from a set $X$ of size $m$ starting with a superposition $\\frac{1}{\\sqrt{m}}\\sum_{x\\in X} |x\\rangle$, where each $|x\\rangle$ is an element of the canonical basis in a suitable Hilbert space of dimension greater than $m$ (i.e., those elements do not neccesarily form the complete basis). The initial superposition state we consider is of the form\n",
    "$$\n",
    "\\frac{1}{\\sqrt{L}} \\sum_{i=0}^{m-2}\\sum_{j=i+1}^{m-1} |i\\rangle|j\\rangle|a_{i}+a_{j}\\rangle,\n",
    "$$\n",
    "where $L = \\binom{m}{2} = m(m-1)/2$ is the number of different pairs of indices $(i,j)$ such that $i<j$. Then, we amplify those elements such that $a_{i}+a_{j} = n$ with the help of an oracle. Let us formalize this idea.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let $N$ be the minimum number of bits neccesary to represent each integer in the list. Then each number $a$ can be written as $a = \\sum_{i=0}^{N-1} x_i2^i$, where $x_i\\in \\{0,1\\}$. Since\n",
    "$$\n",
    "a = \\sum_{i=0}^{N-1} x_i2^i \\leq \\sum_{i=0}^{N-1} 2^i = 2^{N} - 1 \\leq 2^N, \n",
    "$$\n",
    "then $\\log_2(a) \\leq \\log_2(2^N) = N$. Moreover, $N$ is the minimum integer that satisfies $a\\leq 2^N$ for each $a$ in the list. Hence, $\\lceil \\log_2(a_{max}) \\rceil = N$, where $a_{max}$ is the maximum integer in the list. Notice that if $a$ and $b$ are integers in the list, then $a+b$ is representable with $N+1$ bits. Let $N_m = \\lceil \\log_2(m-1) \\rceil$ be the number of bits neccesary to represent each position index $i\\in \\{0, \\ldots, m-1\\}$ in the list. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider $M=N+1+2N_m$ qubits. We use the first $N+1$ qubits to encode the sum of each pair of elements $|a_i + a_j\\rangle$ and the next $2*N_m$ qubits to encode the pair of indices $|i\\rangle |j\\rangle$; each encoding is given by the binary representation of each integer. For example, if the list has 4 integers such and two of them are $a_0 = 2$ and $a_3=3$, then we encode the sum of $a_0$ and $a_1$ as\n",
    "$$\n",
    "|i\\rangle|j\\rangle|a_{i}+a_{j}\\rangle = |00\\rangle |11\\rangle |101 \\rangle = |0011101 \\rangle.\n",
    "$$\n",
    "Since we use Amplitude Amplification for our solution, we need an oracle $O$ such that $O(|i\\rangle |j\\rangle |a_i+a_j\\rangle) = -|i\\rangle |j\\rangle |a_i+a_j\\rangle$ for those elements such that $a_i+a_j=n$. In our oracle implementation, we need $N+1$ ancilla qubits initialized as $|0\\rangle$ and an extra qubit initialized in $|-\\rangle$ for the [phase kickback trick](https://learn.qiskit.org/course/ch-gates/phase-kickback#kickback). In total, our quantum algorithm needs $2N+2N_m+3$ qubits."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The oracle is constructed as follows. Let $aux_0, \\ldots, aux_{N}$ be the auxiliary quantum bits, and $x_0, \\ldots, x_N$ the bits of $n$ (from less to more significant). First, we apply a $CX$ gate to flip $aux_0=|0\\rangle$ (target qubit) whenever the first qubit of $|a_i+a_j\\rangle$ (control qubit) is the same as $|x_0\\rangle$. Then, we apply a $CCX$ gate to flip $aux_1=|0\\rangle$ (target qubit) whenever the second qubit of $|a_i+a_j\\rangle$ (control qubit) is the same as $|x_1\\rangle$ and also $aux_0$ is equal $|1\\rangle$. And so on, we flip the qubit $aux_k$ whenever the $k$-th qubit of $|a_i+a_j\\rangle$ (control qubit) is the same as $|x_k\\rangle$ and also $aux_{k-1}$ is equal to $|1\\rangle$, $k=1, 2, \\ldots, N$. Hence, $aux_N = |1\\rangle$ whenever $a_i+a_j = n$ by construction (all bits of $a_i+a_j$ are the same as the bits of $n$). We then just apply a $CX$ gate with $aux_N$ as control qubit $|-\\rangle$ as target qubit to make the phase kickback trick, obtaining our oracle $O$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let $A$ be the unitary operator such that \n",
    "$$\n",
    "A|0\\rangle^{\\otimes M} = \\frac{1}{\\sqrt{L}} \\sum_{0=i<j\\leq m-1} |i\\rangle|j\\rangle|a_{i}+a_{j}\\rangle,\n",
    "$$\n",
    "and $S_0 = 2|0\\rangle^{\\otimes M}\\langle 0|^{\\otimes M} - \\mathbb{I}_M$. Then, the Amplitude Amplification algorithm is given by\n",
    "$$\n",
    "(AS_0A^\\dag O)^t(A|0\\rangle^{\\otimes M}) = (AS_0A^\\dag O)^t\\left(\\frac{1}{\\sqrt{L}} \\sum_{0=i<j\\leq m-1} |i\\rangle|j\\rangle|a_{i}+a_{j}\\rangle \\right),\n",
    "$$\n",
    "for a suitable number of iterations $t$. When we measure that final state, we should obtain with high probability the elements $|i\\rangle|j\\rangle|a_{i}+a_{j}\\rangle$ such that $a_i+a_j=n$. With the indices $i$, $j$ we can recover $a_i$ and $a_j$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below you can find the code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "01011\n",
      "13\n"
     ]
    }
   ],
   "source": [
    "# auxiliary functions\n",
    "\n",
    "def binary_repr(n: int, m: int) -> str:\n",
    "     # binary representation of a integer n as a bits string of length m\n",
    "     return bin(n)[2:].zfill(m)\n",
    "\n",
    "def bin_2_int(bin_repr: str) -> int:\n",
    "     # given a binary string, returns the integer that it represents\n",
    "     num_bits = len(bin_repr)\n",
    "     n = 0\n",
    "     for i in range(num_bits):\n",
    "          if bin_repr[-1-i] == \"1\":\n",
    "               n += 2**i\n",
    "     \n",
    "     return n\n",
    "\n",
    "print(binary_repr(11, 5))\n",
    "print(bin_2_int(\"1101\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_the_primes_numbers(n: int, list_numbers: List[int], iterations: int = 5) -> Tuple[QuantumCircuit, QuantumRegister, ClassicalRegister]:\n",
    "     \"\"\"\n",
    "     Function that receives a positive integer n, a list of positive integers list_numbers (primes, if you want), and the number of iterations for the Amplitude Amplification. \n",
    "     It returns a quantum circuit, a quantum register and a classical register (in Qiskit).\n",
    "     If you measure the quantum register (and save measurements on classical register), you will obtain with high probability a pair of integers in the list that sum n.\n",
    "     \"\"\"\n",
    "     \n",
    "     N = int(np.ceil(np.log2(max(list_numbers)))) # number of bits necessary to represent each number in the list\n",
    "     # if n is not representable with N+1 bits, then there is no solution\n",
    "     num_bits_n = int(np.ceil(np.log2(n)))\n",
    "     \n",
    "     if N+1 < num_bits_n:\n",
    "          raise Exception(\"No solution: the given integer n is not representable with N+1, where N is the minimum number of bits neccesary to represent each integer in the list (the sum of two integers in the list needs only N+1 bits).\")\n",
    "     \n",
    "     m = len(list_numbers) # number of elements in list\n",
    "     N_m = int(np.ceil(np.log2(m-1))) # number of bits necessary to represent each index in the list (0, 1, ..., m-1)\n",
    "     \n",
    "     data_quantum = QuantumRegister(2*N_m + N+1, name=\"|i>|j>|sum>\")\n",
    "     classic_register = ClassicalRegister(2*N_m+N+1)\n",
    "     aux_qreg = QuantumRegister(N+1, name=\"aux\")\n",
    "     phase_kickback = QuantumRegister(1, name=\"|->\")\n",
    "     \n",
    "     qc = QuantumCircuit(data_quantum, aux_qreg, phase_kickback, classic_register)\n",
    "     \n",
    "     init_vec = np.zeros(2**(2*N_m + N+1)) # it will be the state vector for qubits in data_quantum quantum register\n",
    "     \n",
    "     for i in range(m):\n",
    "          idx1 = binary_repr(i, N_m)\n",
    "          for j in range(i+1, m):\n",
    "               idx2 = binary_repr(j, N_m)\n",
    "               sum_i_j = list_numbers[i] + list_numbers[j]\n",
    "               sum_bin_repr = binary_repr(sum_i_j, N+1)\n",
    "               \n",
    "               state_string = idx1+idx2+sum_bin_repr # state |i>|j>|a_i + a_j> as binary string\n",
    "               num_state = bin_2_int(state_string)\n",
    "          \n",
    "               init_vec[num_state] = 1\n",
    "               \n",
    "     \n",
    "     init_vec = init_vec/np.linalg.norm(init_vec) # equal superposition of elements |i>|j>|a_i + a_j>\n",
    "     init_state = Statevector(init_vec) \n",
    "     \n",
    "     A = StatePreparation(init_state) # constructs unitary gate A such that A|0>^{(n)} is the equal superposition of elements |i>|j>|a_i+a_j>\n",
    "     A_dag = StatePreparation(init_state, inverse=True) # inverse of A, i.e., A^\\dag\n",
    "     \n",
    "     qc.append(A, data_quantum) # apply A gate to data_quantum register\n",
    "     \n",
    "     # create |-> in phase_kickback qubit\n",
    "     qc.x(phase_kickback)\n",
    "     qc.h(phase_kickback)\n",
    "     \n",
    "     qc.barrier()\n",
    "     \n",
    "     # oracle\n",
    "     # creates the quantum circuit for the oracle O\n",
    "     oracle = QuantumCircuit(data_quantum, aux_qreg, phase_kickback)\n",
    "     \n",
    "     n_bin_repr = binary_repr(n, N+1)\n",
    "     \n",
    "     for i in range(N+1):\n",
    "          if n_bin_repr[-1-i] == \"0\":\n",
    "               oracle.x(data_quantum[i])\n",
    "          \n",
    "          if i == 0:\n",
    "               oracle.cx(data_quantum[i], aux_qreg[i])\n",
    "          else:\n",
    "               oracle.ccx(data_quantum[i], aux_qreg[i-1], aux_qreg[i])\n",
    "               \n",
    "          if n_bin_repr[-1-i] == \"0\":\n",
    "               oracle.x(data_quantum[i])\n",
    "          \n",
    "     oracle.cx(aux_qreg[-1], phase_kickback)\n",
    "     \n",
    "     # diffuser\n",
    "     # creates the quantum circuit for (A)(S_0)(A^\\dag)\n",
    "     diffuser = QuantumCircuit(data_quantum)\n",
    "     diffuser = diffuser.compose(A_dag)\n",
    "     \n",
    "     for i in range(2*N_m + N +1):\n",
    "          diffuser.x(data_quantum[i])\n",
    "     diffuser.h(data_quantum[-1])\n",
    "     mcx_gate = MCXGate(2*N_m + N)\n",
    "     diffuser.append(mcx_gate, data_quantum)\n",
    "     diffuser.h(data_quantum[-1])\n",
    "     for i in range(2*N_m + N +1):\n",
    "          diffuser.x(data_quantum[i])\n",
    "          \n",
    "     diffuser = diffuser.compose(A)\n",
    "     \n",
    "\n",
    "     # iterations\n",
    "     # iterates (A)(S_0)(A^\\dag)(0) the given number of iterations\n",
    "     for _ in range(iterations):\n",
    "          qc = qc.compose(oracle)\n",
    "          qc.barrier()\n",
    "          qc = qc.compose(diffuser, data_quantum)\n",
    "          qc.barrier()\n",
    "     \n",
    "     \n",
    "     return qc, data_quantum, classic_register\n",
    "     \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Example: $n = 18$ and  list of integers $[1,3,5,7,11,13,15]$.\n",
    "\n",
    "We see that for 3 iterations, we obtain the three pairs of integers in the list such that sum $n$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'00101101010': 27, '01010110010': 166, '01110010010': 147, '00001101000': 18, '00110001110': 52, '00111010010': 148, '10111011100': 27, '00001000110': 47, '01010010000': 24, '01111010110': 50, '10011011010': 37, '00010101110': 47, '10010111000': 27, '00101001000': 18, '00011010000': 25, '01011010100': 15, '00000100100': 19, '01001101100': 28, '01110110100': 17, '00110110000': 31, '00010001100': 30}\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 201,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list_numbers = [1,3,5,7,11,13,15]\n",
    "n = 18\n",
    "qc, data_quantum, classic_register = find_the_primes_numbers(n, list_numbers, iterations=3)\n",
    "qc.measure(data_quantum, classic_register)\n",
    "\n",
    "backend = BasicAer.get_backend('qasm_simulator') # the device to run on\n",
    "\n",
    "transpiled_qc = transpile(qc, backend)\n",
    "result = backend.run(transpiled_qc, shots=1000).result()\n",
    "counts  = result.get_counts(qc)\n",
    "print(counts)   \n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 215,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5 + 13 = 18 : 166 counts\n",
      "3 + 15 = 18 : 148 counts\n",
      "7 + 11 = 18 : 147 counts\n",
      "3 + 11 = 14 : 52 counts\n",
      "7 + 15 = 22 : 50 counts\n",
      "1 + 5 = 6 : 47 counts\n",
      "1 + 13 = 14 : 47 counts\n",
      "11 + 15 = 26 : 37 counts\n",
      "3 + 13 = 16 : 31 counts\n",
      "1 + 11 = 12 : 30 counts\n",
      "5 + 7 = 12 : 28 counts\n",
      "3 + 7 = 10 : 27 counts\n",
      "13 + 15 = 28 : 27 counts\n",
      "11 + 13 = 24 : 27 counts\n",
      "1 + 15 = 16 : 25 counts\n",
      "5 + 11 = 16 : 24 counts\n",
      "1 + 3 = 4 : 19 counts\n",
      "1 + 7 = 8 : 18 counts\n",
      "3 + 5 = 8 : 18 counts\n",
      "7 + 13 = 20 : 17 counts\n",
      "5 + 15 = 20 : 15 counts\n"
     ]
    }
   ],
   "source": [
    "N = int(np.ceil(np.log2(max(list_numbers)))) # number of bits necessary to represent each number in the list\n",
    "m = len(list_numbers) # number of elements in list\n",
    "N_m = int(np.ceil(np.log2(m-1))) # number of bits necessary to represent each index in the list (0, 1, ..., m-1)\n",
    "\n",
    "sorted_counts = sorted(counts.items(), key=lambda x:x[1], reverse=True)\n",
    "\n",
    "for bin_str, val in sorted_counts:\n",
    "    print(list_numbers[bin_2_int(bin_str[:N_m])], \"+\", list_numbers[bin_2_int(bin_str[N_m:2*N_m])], \"=\", bin_2_int(bin_str[-N-1:]), \":\", val, \"counts\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The pair of integers with higher probability is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5 + 13 = 18\n"
     ]
    }
   ],
   "source": [
    "best_result = sorted_counts[0][0]\n",
    "print(list_numbers[bin_2_int(best_result[:N_m])], \"+\", list_numbers[bin_2_int(best_result[N_m:2*N_m])], \"=\", bin_2_int(best_result[-N-1:])) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Circuit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [
    {
     "data": {
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+9NJLKSkpyec+97nV7m9sbEyPHj1SUlKSN99886MN9w8flrHJoEGDUlJSkmeeeeajCfZP1jQnABu3nj175oADDkjPnj2LHQUAAAAAoNXKih2gNebMmZO33347/fr1yxZbbFHsOC1aunRpXnzxxXTu3DnbbLNNseMAQIsWLFiQu+66K3vvvXd69epV7DgAAHwEysrKsu2222bYsGHp3r17SkpKsnTp0syYMSNPPfVUli1b9qHPUVFRkd/97nf52c9+lrvvvvsjSA0AAGtmgy5DX3755XzqU5/KrrvuWuwoH2jOnDkZNGhQtt5663Tu3LnYcQCgRfPmzct5552XHXbYQRkKANCBfexjH8thhx2Wo446KiNGjEhFRcVqj6uvr8+zzz6bG264Iddcc03+93//t9kxFRUVuf322zNy5MiMGjUqX/rSlxSiAAC0Gxt0Gbrnnntm5syZxY7xoYYMGbJB5AQAAAA6toqKipx55pk5/vjjs9lmm33o8aWlpdl+++2z/fbbZ/z48bnxxhtz6qmn5o033ig8X1MRmiQrVqzIokWL1usYAABgbWzQZeiaeuihhzJo0KD069ev2FFatCFk3JB0lOv51uLXc/0f/yuPzpict955PZt165fdP31gjhz139n0Yz2LHQ8AAIANyG677ZZrr702n/rUp1bZPmvWrDz22GN54okn8vrrr6exsTE9e/bMDjvskJ122inDhg1Lp06dsskmm2Ts2LHZf//9M27cuNx6662rFKFvv/12Ro8enb/85S/FGB4AAKxWp2IHaI3q6uqUlJR86KzLX/ziF6mqqsp+++2Xm266KStWrPiIEr5n+PDhKSkpyV//+tcWjyl2xhUrVuTHP/5x9thjj2y22WYpLy9Pv379sssuu+SUU07Jq6++Wjj2pZdeSklJSfr379/i8+20004pKSnJlClTmu1ret9mzJiRRx55JAceeGC22GKLdO/ePV/84hfz9NNPF46dOnVqDj744PTt2zc9e/bMyJEjM3369A8dT7GvZ1t465038q3LPpM/PHZN/uXTX8oJYy7Lvwwdkzv+cnm+e8VeWV63tNgRAQAA2ECMGzcuU6ZMKRShK1asyHXXXZcRI0Zk0KBBOfzww/ODH/wgv/rVr/LrX/86P/nJT3L00Udn+PDhGTRoUC6++OIsWLAgSbL55pvnxhtvzAsvvKAIBQCg3dtgy9CFCxdmzpw56dKlSwYPHvyBx+68887ZdNNNM3ny5PzHf/xH+vfvn29+85uZOnXqes+5cuXK1NTUpFOnTtluu+3aZcY333wzu+yyS0466aRMnTo1W2yxRbbffvt06tQpjz/+eC655JIsWbKkcPzf/va3JO+VvKuzcuXKPPvssykpKcn222+/yr6m922TTTbJHXfckc9+9rN57LHHsuWWW6auri733ntvRo4cmQULFuQHP/hBdt999/z1r39NZWVlli9fnj/96U8ZOXJk3nnnnQ8cUzGvZ1u58d4L8vpbc/K9Q6/PuC9dlv12Oy7jvnRZvnfo9fn7q0/mlgf/v2JHBDqgrl27Zvfdd0/Xrl2LHQUAgDby3e9+N5dddlk6dXrvn4GmTp2aHXbYIUcddVQef/zxDz3/xRdfzKmnnppPfepT+e1vf1vYXlVVlUQRCgBA+7bBlqFPPvlkkmS77bYr/GG+JePGjctrr72W3/zmN9lnn32yePHiXHHFFdl1112zzTbb5MILL0xtbe16yTlz5szU1dVl4MCBH/gPy8XM+J3vfCdPP/10Dj/88NTW1ub555/PY489lldffTWvvPJKLrroomy99daF45vK0B122GG1zzd9+vTU1dXlk5/8ZLp167bKvqb3rb6+PhMmTMikSZNSW1ubJ554Is8880x69OiRN954I1/96ldz/vnn56abbirsnz59ejbbbLPMmzcvkydP/sAxFfN6tpWn/n5/Nun8sey1w2GrbP/c9oemvKwif3js2iIlAzqy6urqXH311amuri52FAAA2sARRxyRSy65pPD4ggsuyO677/6hq2ytzv/+7/9m7NixeeaZZ1bZfueddypCAQBotzbYMvSpp55K0nIh988qKipy6KGHZvLkyZk7d25++MMfZvjw4Xnuuedy+umnZ8CAARk1alQmTpyYZcuWtXnOf54h2Z4yTpo0KaWlpbnyyivTt2/fVfZVVlbmlFNOSUlJSWFbU6HZ0szQJ554Isnq35um61FfX5/f/OY3GTNmTGHfoEGDCo/vuuuu3HjjjTnwwAML+wcOHJj9998/STJ79uwPHVexrmdbWfnuipSXVaxy7ZO8d5+Wzh/LvAUvZtGS/y1SOqCjqq+vzzvvvJP6+vpiRwEAoJUqKyvz05/+tPD4jDPOyBlnnLHOf9arqKjI7bffXlj5qrGxMUly2GGH5XOf+1yr8wIAwPqwwZahTYXcmpSM/6xPnz456aST8sQTT+TZZ5/NKaeckv79++eee+7JV77ylfTr1y9HH330KveuXFdrU4YWI+O7776burq61NfX589//vManfNhM0ObytDVjbnpfTv00EML9xV5v86dOydJDjrooIwePbrZ/rKysiRJly5d1ihrk7a+nn/605+y6667pqKiIn369Mk3vvGNLFq0aK0yfZgBfYdm8bK3Mmvuk6tsnzX3ySxe9laS5I23Xm7T1wSYOXNmRowYsU4zBQAAaF+uuuqq9OjRI0ly/fXX54ILLljn52oqQt9/j9Af/ehHhf3XXHONWy0AANAulRU7wLpqKtXWdGZoS4YOHZqLLrooF154Ye67776cddZZ+etf/5pf/OIX2XTTTVf5g/26WNcy9KPKWFZWli996Uu56aabst9+++Xzn/98Dj744BxwwAGprKxsdvz8+fNTW1ubbt26rbJ07vs1laUfVIYedthhzfYlSU1NzQfuf+GFF5Ikn/rUpz54YB+gtdfzgQceyOjRozNmzJj813/9V2pra3Paaaflueeey3333ddsJue6+vfPnpRHpt+a8379H/nmAT/KJ/t9Oi+9Pj2X335Syko75936lVmxcmmbvBbQ/g0aPCh1767bLPaxY8eu8bHz5s1L8t5SZ02f52viuuuuW8tU7c+BR52Urpt2z7zX5qWqqqrZ447O+JuPd2O/Bsa/cY+/pW0dmd+BjXv8yYZ3DRoaGj5w/+c///nsvffeSZK5c+fmpJNOWufXWl0ROnr06Pz1r3/NjjvumH/913/NJz/5yZxwwgm5+OKLW3yeQYMGfeitjgAAYHX69eu3Rve7X50NsgxduXJlampq0qlTpwwbNqzVz/fGG2/kxhtvzK9+9atMmzYtSVJeXp6BAwe2+rmbZhq2pgxd3xl/+ctfZtttt83VV1+d++67L/fdd19OOOGEfO5zn8sFF1yQXXfdtXBs0z+MDxs2bLWlX0NDQ4tLGDe9b0my5557rvbcpuu1uv2NjY2F/a0twVtzPcePH59BgwblpptuKvwlbvPNN89BBx2UyZMnZ7/99mtVtibbbfXZnH7Eb/Kz276dM6/ZN0nSqVNp9t7l6AzoOzQPP/v/0mWT7m3yWkD7N+/VV7N8Hb8AsXTpmp+3fPnyws+1OW/u3Llrnau9afjHcnEN9fWZO3dus8cdnfE3H+/Gfg2Mf+Mef0vbOjK/Axv3+JOOdw2OP/74wv//7ne/m4ULF67T87RUhDbdI/TYY4/Nc889lyQ57rjj8oMf/KDForbpi3cAAPBR2iDL0BkzZqSuri6DBg1a5yVYli1blttuuy2/+tWv8sc//jHvvvtukmSnnXbK2LFj8+Uvfzmbb755q3K+/vrref3119OzZ8984hOfaJcZk/f+YnPOOefkv/7rv/Lkk0/mtttuy89//vPcf//9GTlyZGbOnFmYJfph9wudOnVqlixZkp49e2bAgAGr7Gt63wYMGJDNNtus2bkvvPBClixZksrKymyxxRbN9s+ePTuLFi1Kv379mt3bdE201fWcOnVqjjrqqFW+zTpq1Kgkya233tpmZWiS/Ov2h2SP7f49s+c9k2UrFqeqz6ey2aZ9Mu5/dklpp7J8vPfqZ+cCHU//j398nWeGrs3S4hUVFYWfa3Pe6lYT2NB0Ki0t/KysrGz2uKMz/ubj3divgfFv3ONvaVtH5ndg4x5/suFdg4aGhhbLxcrKyowZMyZJ8uqrr+bmm29ep9f4sCI0SZ5//vncdddd2XvvvbPVVltl9OjRufPOO1f7fP379zczFACAddKvX791PneDLEPXdYnchoaGPPDAA/nVr36Vm2++OYsXL07y3h/Gv/KVr+TII4/M0KFD2yznuiyR+1FnfL+SkpIMHz48w4cPz0knnZRhw4bllVdeyaOPPpoDDzwwyf8tY9tShhtuuCHJBy+R21KRuqb71+Z9Xx/Xs7S0NOXl5ats69y5c0pKSjJ9+vS1eq41er1Opdm6cofC4wVvv5ZZc/+WYVv9ayrK1+7eqcCG64XnX0hp+Ycftzprc//P6dOn55prrsk+++yzVp+P55133rpEa1cu+OnEvP3OkvTv1z+1tbXNHnd0xt98vBv7NTD+jXv8LW3ryPwObNzjTza8a7BkyZJsuummq933b//2bykre++ffH7xi18Uvgy8NtakCG1yxRVXFJbk3XfffVssQ1944QX3FQUA4CO3QZahLS3D2pLnn38+11xzTSZOnFj4C0xFRUUOPfTQHHnkkRk1alRK//GNz/WRc03K0GJlbEnPnj0LhV+fPn0K25uW1VndErmPPPJIrrjiiiSrH3PT9VjXMnRt3vf1eT0HDx6cqVOnrrLtscceS2NjYxYsWLBOz7mmGhoa8tPbvp2Gxvoc/oUz1utrARunwYMH5+GHH063bt2KHQUAgHW00047Ff7/vffeu9bnr00RmiR//vOfV/vaAADQHmyQZWhTabamMy4vuOCCXH/99UmS3XbbLUceeWQOPfTQ9OzZcz0lfM/alKHFyHj99denpqYmRx55ZLbddtvC9rfeeivf//738/e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      "text/plain": [
       "<Figure size 2388.83x6304.28 with 1 Axes>"
      ]
     },
     "execution_count": 197,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc.draw(output='mpl')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv",
   "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": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}