An Introduction to Quantum Probability Amplitude Modulation from a Compositional Perspective.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# An Introduction to Quantum Probability Amplitude Modulation (QPAM) from a Compositional Perspective"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister, Aer, execute\n",
    "from qiskit.visualization import plot_histogram\n",
    "import os"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## State initialization and measurement"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initializing the circuit with the probability amplitudes [0.5, 0.5, 0.5, 0.5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x1ea4f511fc0>"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2 quantum registers for 4 outputs\n",
    "register = QuantumRegister(2)\n",
    "circuit = QuantumCircuit(register) \n",
    "# probability amplitudes of the 4 notes\n",
    "prob_amp = np.array([0.5, 0.5, 0.5, 0.5]) \n",
    "# add 2 classical registers \n",
    "creg = ClassicalRegister(register.size, 'c') \n",
    "circuit.add_register(creg)\n",
    "# initialising the state vector\n",
    "circuit.initialize(prob_amp, register)\n",
    "# Prepare each quantum register for measurement\n",
    "circuit.measure(register, creg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 509.208x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit.draw(output = 'mpl') # Resultant circuit. The initialisation is done through a gate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 760.042x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit.decompose().decompose().decompose().decompose().decompose().draw(output = 'mpl') # Decomposing the gate reveals the resultant circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each iteration of the circuit gives a different result. Run the following code multiple times. \n",
    "\n",
    "Note: if you get the error ```IndexError: index 3 is out of bounds for axis 0 with size 3```, just run it again"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'00': 6, '10': 4, '01': 5, '11': 5}\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(0.0, 6.0)"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "shots = 20 # Any number of shots. Feel free to change\n",
    "simulator = Aer.get_backend('qasm_simulator')\n",
    "measurement = execute(circuit, simulator, shots=shots) # Execute measurement\n",
    "simulation_result = measurement.result()\n",
    "counts = simulation_result.get_counts(circuit) # dictionary for output\n",
    "print(counts)\n",
    "\n",
    "amplitudes = np.zeros(len(counts))\n",
    "index = np.array([int(key, 2) for key in counts])\n",
    "amplitudes[index] = list(counts.values())\n",
    "\n",
    "binary = ['00', '01', '10', '11']\n",
    "plt.bar(binary, amplitudes, edgecolor='black')\n",
    "plt.yticks(np.arange(0, max(amplitudes) + 1, 1))\n",
    "plt.ylabel(f'Probability / % of {shots} shots')\n",
    "plt.xlabel('Computational basis states')\n",
    "\n",
    "for ind, amp in enumerate(amplitudes):\n",
    "    # print(amplitudes)\n",
    "    plt.text(binary[ind], amp-1, str(int(amp)), ha='center', va='bottom', c='white')\n",
    "\n",
    "# ax.flat[id].text(binary[ind], amplitudes-1, str(int(amplitudes)), ha='center', va='bottom', c='white')\n",
    "plt.ylim([0,max(amplitudes)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Composing with Quantum Probability Amplitude Modulation (QPAM)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1) Prepare the circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "regsize = 2\n",
    "register = QuantumRegister(2) # 2 qubits for 4 outputs\n",
    "circuit2 = QuantumCircuit(register)\n",
    "\n",
    "creg = ClassicalRegister(register.size, 'c')\n",
    "circuit2.add_register(creg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2) Convert the amplitudes into probability amplitudes by normalizing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.43580096, 0.49805825, 0.56031553, 0.49805825])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "notes = [7,8,9,8] # intervals of the musical gesture. In the long run, this can be anything (rhythmic structures, frequencies etc..)\n",
    "prob_amp = notes/np.linalg.norm(notes)\n",
    "prob_amp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3) Initialite the circuit and measurement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x1ea4f3ecb80>"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit2.initialize(prob_amp, register)\n",
    "circuit2.measure(register, creg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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bpLQEcnJyyM7J5mz8Uev52ohTO/j5/H56tR6ByWQCIC7xDFHxP9E5fIgdqxaRWylwRRxcq7t6cOlqNP/76f+w79hGbmSmU9W7Bht2v8Hs1UMJ9GvEyN4vWdffd2wjLi6udAwbZMeqReRW6lIWcXB/HryEpLRLbD3wPlsPvA/AF/v+jtnNg37t/sCYfrPx9a5hXX/fsY20aNQt3zwRsT8FroiDq+YTwLzHtxCXeIa/ff4sB05sZt7jW2l1130FztEmpyXyU9Qe/jRokZ2qFZGiKHBFnEQd/7vIys6gtl8D2t/dr9B1fvh5Ezk52XTS+VsRh6PAFXEip2MjCG/Ypcjl3Vo+QsdmA/H18TewKhEpCQWuiJO4dPUCSWkJ+e4odStPd2883XWNpYgjUuCKOJDFT35X5LKa1YP45nWLccWISLnSZUEiIiIGUOCKiIgYQIErIiJiAAWuiIiIARS4IiIiBlDgioiIGECBKyIiYgBdhysOq88UE40CW/DHAfPp2GwAFy6d5PUPx5KUlkAVr+pMGb6SBrXDitz+n1/PZvU3s3hv0lEaBTa3zp/2Xl+upMRjMrng7VmVp4e8ReN69wCQkXWDd/89iYO/foXZ1Z3GdVszfcSaIvdR2pqKquvHE1v5x1cvkpWVgYe7N889/C4hdVvlLvvlK/6xZSY5lhyyszN5tMcU+rYbW+w+SlrXqHkNcXfzxOyWe0/m3/eaQY97hluXO9v7MfmdnpyJPcKYfnN4qMszxe5XxGgKXHFoS5/Zh5dHldyfP/0TAzr+D/3aj2NX5Ccs/uiPvPns94Vud/LCYX4+v59a1esXWPbS6I+o4lUdgL0/fc7ij8fz9nOHAXh/83RcTC6snPorJpOJxOS44usrRU1F1ZVy7Qrz141iyVO7aVC7GUdO72T+v0ayfPJPWCwWXvvXCBb9aQd31W1J/OUoxr8eStfmQ/H2rFoudb005pN8X0hu5mzvx6I/72Dh+nHF1ihiL+pSFqdwJfU3TsYcpnebUQB0a/Ew8ZfPEn85qsC6GVk3eOuzp3l26DLrQ9lvlhe2AGnXkzCZcv8bpGek8dWP/2D8A/Os2/n71imXmoqrKzbxNNWr1KJB7WYAtAq5j4tXz3HywmHrOqnXrwJw7Xoyvt7+mN08yq2uolSW90MqlsViIS0tzan+WCz2uWObjnDFKVy6Go2/b11cXXN/ZU0mE7X86vPb1fME1miYb91VX/2V+9uMok6NRkW2t2DdGI6c3gHAvMe3AhCXcBpfb3/WfvsKh09uw8Psxeg+s2jT5P4y11RcXUEBTUhKu8Txc/sJa3Ave45+RvqNVOKvRNEkqA0vjvqI2auG4unuQ2r6FV4eswGzm3u5vFcA8/81khxLDqH1O/LHB16jepWaler9kIp17do1qlSpYu8ySiU1NRUfHx/D96vAFadx69FqYd9Sj0d9z6/RP/L4gPnFtjXt96sB+PrgKt7bNIV5f9xMVk4mcZfP0KBWGI8PmM/p2CNMe683KyYft4aQLTXdri4fr2r8dcynvL95Ouk3Ughv1JUGtcNwczWTnZ3F+u2vMXvcRpo36sIv0T/y8sqHeG/S0WIfMF/SupY8uYtafvXJys7kH1tfZOGHY5n3x80Aler9EHEE6lIWp1CzejCXki6QnZ0F5H6QX7oaXeAcbeSZnZy/dILRrzVi1LyGXEq6wIzl/ThwYkuh7fZtN5Yjp3aQnJZIbb8GuJhc6NVmJAAhdVsRWKMR5y4eK1NNJamr5V3dWfzkdyx77hBPDFxIYnIs9Ws141RsBInJsTRvlPtIvruD2+PvW5czsUfK/F4B1PLLnefmamZot+f46exu67LK8n6IOAoFrjgFvyq1aFy3NdsO546Q3X30U2rXaFigq/KxXtP58KVY1syMYs3MKGpWC+K1J76iQ+gDAKRdTyYhKda6/p6jn+Hr409V7xpU8wngnsb3c/CXrwC4eOUc8ZfPElTzbiC3G3rP0c9KXVNJ6rp5MNLabXO5J6QX9QIaU6t6MAlJF4j+7RcAYhJOEZd4mqCaTQutqTR1pWekkZp+1Tq94z/raFy3tXXaGd8PEUemLmVxGs89/C6vfziOddvn4e3py9Thq6zLZr4/gLF953B3cLti20i7nsSc1Q9zIzMdF5ML1XxqMvcPX1q7Qp97+B0WfTSeFZun4WJy5bmH37MOFDoZc4iHuj5b7jUBrPzqJY6d3UN2ThbNGnRi0rD3AfCrWpu/PPwuc/75CC4mFywWC88OXUZAtXpF1lTSuny9azB79cPk5GRjwUKdGncx9bHVt7TjXO+HiCMzWew1XEucWnYG7HizYvfRZ4qJL15JsV4WZE/J1y7z6prhLPifb+xdipU9a3LE9yPPwvXjaBrc7rbX4facAK4OONZq3t/Xkpyahm8VH2Y+PbLAtKNJS0vToKkSUpeyOCy/KrV57u9d+OHnzfYuBV/vGg4XLvasyRHfD8i98cXRMzvxdDf+w1TkdtSlLA7ro5fj7V2COJlFf95h7xJEiqQjXBEREQMocEVERAygwBURETGAAldERCqVoKCgQu+jbm8K3FucPXuW5cuX88QTT9CqVSvc3NwwmUy8+OKLFbJdVFQUJpOpRH9mz55dni9VRMRhBAYGMmTIEObMmcPGjRvZsWMHO3fuZMuWLbzxxhuMHj2aZs2a3bad0NBQfvzxR1asWOFwoatRyrdYunQpS5cuNWw7T09PunTpUuTylJQUIiMjAejcuXOp2xcRcVQuLi7079+fp556igceeAAXl8KPAfv372/9+ciRIyxbtoy1a9eSlpaWb73Q0FB27NhBYGAg48eP58yZM7z66qsV+hpKQ4F7i4CAAAYNGkSHDh1o3749K1as4NNPP62w7QIDA9mzZ0+RyxcuXEhkZCRBQUHcf3/hT2kREXE27du354MPPqB588KfxVyUVq1a8e677zJ//nyef/55Vq3KvZvZzWELcOjQIZYtW1budZeFAvcWt3YBr1+/vkK3u53Vq3NvtTd69Ogiv/05onXbX+NkzGFOXjhE/OWz1PZrwJqZUfYuS0TszGw2M3v2bKZOnYqrq6t1flRUFOvXr+fAgQMcPnyY+Ph4LBYL1apVo1WrVrRt25bBgwdbe/r8/PxYuXIljzzyCAsXLuSjjz7KF7Z9+vThypUrdnmNRXGeT3AbJSQkMHnyZEJCQvD09CQ4OJhJkyaRnp7OqFGjMJlMrFixwt5lFurQoUMcO5b7ZJYxY8bYuZrS+WDLTCJObaeufwhVvfzsXY6IOAAvLy8+//xzZsyYYQ3bQ4cO8eCDDxISEsKMGTP47LPPOHfuHDdu3CAjI4NLly6xbds2FixYQJcuXWjdujXr1q2ztjlo0KACR7aOGLZQyY9wIyMj6du3LxcvXsTHx4ewsDBiYmJYsmQJUVFRnD9/HsjtonBEeV0lHTt2JDQ01M7VlM7q6aep438XAE8sak56RqqdKxIRezKbzWzYsMF6PjYjI4PZs2ezcOFCsrKyStxOREQEI0aMYN26dbz//vvUrFnTGt5Hjx512LCFShy4CQkJDBo0iIsXLzJ16lReeukl6w22X3nlFV566SXc3NxwcXEp9TkEI2RmZlq/xY0bN86+xdggL2xFRAAWLVpkDdvk5GQGDRrE7t27b7NV0U6ePMmtz95xcXEhNdVxv9xX2i7lCRMmEB0dzcSJE1mwYEG+p1m88MILhIaGkpWVRdOmTfHy8rJjpYXbtGkTCQkJeHh4MHz4cHuXIyJis+7duzNhwgQA0tPTGTBgQJnCNm+AVK1atQC4fv06AOHh4be9FNOeKmXgHj9+nA8//JBatWoxd+7cAstNJhNt27YFHLc7OW+w1ODBg/HzK3gO9MKFC0yYMIHOnTvj7e2NyWQiKirK4CpFRIrn6enJBx98YJ2eMWMGe/futbm9wkYj9+vXj8zMTABmzpxJy5Yty1Z0BamUXcpr164lJyeHUaNG4e3tXeg6Hh4egGMGbmJiIps2bQKK7k4+deoUH374IW3btuW+++5j69atZd5vu3btiI8v2RN63N28eO+Zk2Xep4i9NGnahIysdHuXUcDv/vAcPlV8iYuPIygoqMC0o8nJySl2+bBhwwgJCQFg9+7dvPmm7Q/SLixs887Zzps3j5dffhk3NzcmT55c7EDTJk2a2HzVR2BgIAcPHrRp20oZuN9++y0APXv2LHKdCxcuAI4ZuOvWrSMjI4PAwED69etX6Drdu3fn4sWLAKxcubJcAjc+Pp6YmJgSretpLvyLjIiziIuN5XrmNXuXUUBOdrb175iYmALTzuapp56y/jxt2rQC511LqriwBZg/fz7PPPMM/v7+DBs2jIkTJ5KQkFBoW3FxcTbVUFaVMnDPnTsHQMOGDQtdfuPGDX744QfAMQM3b3TyyJEj812ndrOKuCY37xe5JNzdHO+8t0hp1Klb1yGPcF3+//+8i6sr9erVKzDtaHJycooMsBYtWtCxY0cA/vOf//D999/btI/bhS3knsf94IMPmDJlCh4eHowZM4YlS5YU2l6dOnXKdIRrq0oZuHm3+8o7kX6rNWvWkJSUhL+/v8P9Av/888/W7gqjRyeXppskOwN22N4zJGJ3J389iau7vasoaN7f15KcmkadwDpcuHChwLSjSUtLyzco9WbdunWz/rxy5Uqb2i9J2N68jylTplj3XVTgnjx5Eh8fH5vqKYtKOWgq7x+msACJjo5mxowZAA55Yj3v6LZNmzYOebmSiEhJ5Q1OBdi/f3+pty9N2ELuAUtycnKBfTuKSnmE27t3b06ePMm8efPo1asXTZs2BXL/wUePHs3Vq1cBx+tOzsnJYc2aNQCMHTvWztWUzTeH/slvV3K79q+mXSIrO4O1214BwMerOg91ecae5YmIAVq3bg1AVlaW9SEsJVXasAWwWCwcPnyYHj16EBwcjL+/P4mJiba/gHJWKQN3+vTprF+/nujoaMLDwwkNDSU9PZ3Tp0/z4IMPEhwczI4dOwoN3L179zJkyBDrdN5F1EuWLOGdd96xzt+4cWO+p/zYut3Ntm3bRkxMDGazmREjRtj46h3D1gPvE3lmZ755K796CYDafg0UuCJ3gBo1agBw6dKlIk/xFcaWsM0THR2db/8K3ApWv359du/ezdSpU9m1axfnzp0jPDycGTNmMH78eOt528ICNzMzs9B/oPT0dNLT0/OtVx7b3SyvO3ngwIEEBATc5lU6tsVPfmfvEkTEzoYNG0bVqlVLPTJ5zJgxNt8befHixfzzn//k+vXrDnfOu1IGLuTecSTvWtabXb58mbi4ONzc3AgLCyuwvEePHjYNW7d1u5utXbuWtWvXlqkNERFHceDAAZu2e+GFF/Dz86N9+/alvjfykSNHbNqnESpt4Bbl6NGjQG6XRd7NL5zVJ598Avx3cNiWLVuoWbMmDRs2pF27dvYsTUTEZhaLhaeeegofHx+Hvjdyad2xgetoA6Zs8eijj+abzrvAfOzYsTYPwRcRcQQWi6VShS0ocJ1aWbuwRUTEOJXyOtzi5AWuI16DKyIildcdd4S7b98+e5cgIiJ3oDvuCFdERMQeFLgiIiIGUOCKiIgYQIErIiJiAAWuiIiIARS4IiIiBlDgioiIGECBKyIiYgAFroiIiAHuuDtNSflwMUPPCfauQsR2LmZ7V1A5eHt7l+tDBl5/dz3Jadfw9fFmyp8eKzBdHry9vculndJS4IpNTCZwdbd3FSJibyaTCR8fn3Jrz93DE/fMbNw9PPHx8Skw7czUpSwiImIABa6IiIgBFLgiIiIGUOCKiIgYQIErIiJiAAWuiIiIARS4IiIiBlDgioiIGECBKyIiYgAFroiIiAEUuCIiIgZQ4IqIiBhAgSsiImIABa6IiIgBFLgiIiIGUOCKiIgYQIErIiJiAAWuiIiIARS4IiIiBlDgioiIGECBKyIiYgAFroiIiAEUuFJir7/+Op06dcLPz4/q1avTrVs3vv76a3uXJSK3sXnzZu655x48PDxo2LAhixYtsndJhtq1axdDhgyhQYMGmEwmZs2aZZc6FLhSYtu3b2f8+PHs2LGDH374gQ4dOjBw4ED27dtn79JEpAgHDx5kyJAh9O3bl4iICGbNmsWLL77I3/72N3uXZpjU1FTCwsJYuHAhgYGBdqvDzW57FqezZcuWfNOLFy9my5YtbNiwgc6dO9upKhEpzpIlS2jdujULFy4EoFmzZhw7dowFCxbw9NNPYzKZ7FxhxRswYAADBgwAYNq0aXarQ4ErNsvOziYlJQV/f397lyLidBIuJ3E5KaXA/KzsbOvfv569UGD6Zo0b1MXFpfiOyr179zJ27Nh88/r378+iRYs4d+4cDRs2LMOrsF1GZhZRF+ILzC/N66/lX53qvlUqvthyosAVm73yyiukpKQwZswYe5ci4nRMLibWfP4NGRmZhS6/ln6dDz7aXOT0va3DaNoo6Lb7iYuLK9CNmjcdFxdnt8A1u7my79BPnDh9vtDlt3v9Vat48/z4Ryq8zvKkc7hik2XLlrFgwQI+/vhj6tWrZ+9yRJyOf3VfHuzVyaZtA/yqMaBHxzLXYM/uZJPJxMMPdMfHy9Om7R994D68bdzWXhS4UmqLFi1iypQpfPHFF/Tp08fe5Yg4rXYt76ZZ4/ql2sbFZGLYoJ64u5tLtH6dOnWIj8/fdXvx4kUAuw4gAqjq483v+ncr9Xb3tg6j6V3BFVBRxVLgSqn89a9/Zc6cOWzZsoXevXvbuxwRp2YymRjavzs+3iU/UuvRqTX169Yq8fpdunThq6++yjdv69atBAUF0aBBgxK3U1GaN21E2+ZNS7x+QI3yObq3BwWulNhzzz3H66+/zurVq2natCnx8fHEx8eTlJRk79JEnFZVH2+G9u9eonXrBQZwf+c2pWr/+eef5/Dhw0yfPp0TJ06wevVq3nrrLaZNm+YwI5Qf7N25RIOfXEwmhg8s+dF9ntTUVCIiIoiIiCAjI4P4+HgiIiI4deqUrSXbxGSxWCyG7lGcVlH/OceOHcvKlSuNLUakkvlk804OHv2lyOVubq5MGPcwtfyrl7rtTZs2MXPmTE6cOEFgYCDPPPMMU6ZMKUO15e9MdBzL//Vviguk+7u0oU/XdqVu+7vvvqNnz54F5t9333189913pW7PVgpcqRDxly7j7eWJbxVve5ci4hSu38hg6T8+5UohlwpB7lFgl7bNDa7KWJt37GfXgchClwUF1uTJUUNwdXXejlnnrVwclsVi4ZMtO1n47jqOnYyydzkiTsHTw51hA3tQWD9S4wb16NQm3PCajNa3W3sCa9YoMN/s5srwQT2dOmxBgSsV4Jcz0VyIu4QJaFC3tr3LEXEajYLr0L1jq3zzPD3ceXTAfbg4yPnWiuRWRLA+0KMjNW3oSnc0ClwnlZ2dzapVq+jTpw8BAQF4eHjQoEEDBg4cyKpVq+xWl8ViYdveQwB0ahNOFR8vu9Ui4oz6dG2X7yjvob5dqeZEd1Mqqzq1/Onb7b/naZs0DOLeSnJ0r8B1QsnJyfTp04dx48axbds2vLy8aNmyJZmZmWzZsoVx48bZrba8o1uzmyvdO7S6/QYiko+bmyuPPdgLV1cXWjUL4Z6wxvYuyXDd2rekYVAgXp4ePFKJju41aMoJDRs2jI8//pj69euzZs0aunX774XjMTExLF++3KbHT721agMpqellqi3tWjrZOTm4m814eriXqS2RO1lGZiZmNzeHuXTHaDk5OWTn5GB2c6w7EFet4sWzY4fatK0C18kcPnyYtm3bYjabiYiIICwsrNzanvf3tSSnppVbeyIilY1vFR9mPj3Spm0d66uD3NZnn30GwMCBA8s1bCH3m1tZ6OhWRCq7snxOKnCdzPHjxwG49957y71tW7tJAH45fZ5/fLIVs5srU//0mAZLiYjcQoHrZJKTkwGoXr16ubddlnO4addytzOZXHhz5YbyLEtExGGU5RyuAtfJ+Pr6AnD16tVybzslNb3M53AzMjPJyCz8+Z4iIncyBa6TCQ8PZ8OGDezfv7/c27b13ITO3YrInaIs53A1StnJRERE0Lp1a8xmM5GRkYSGhtq1npvP3U778widuxURKYJufOFk7rnnHoYNG0ZmZiYPPPAAe/fuzbc8NjaW2bNnG1KL7iolIlJyOsJ1QsnJyQwePJidO3cCEBwcTGBgIDExMcTFxWGxWDDin1VHtyIiJacjXCfk6+vLtm3bWL58Od27dyclJYXIyEjMZjMDBgxg9erVxhRiMhHgV01HtyIiJaAjXCmT7JwcsrOycXc327sUERGHpsAVERExgLqURUREDKDAFRERMYACV0RExAAKXBEREQMocEVERAygwBURETGAAldERMQAClwREREDKHBFREQMoMAVERExgAJXRETEAApcERERAyhwRUREDKDAFRERMYACV0RExAAKXBEREQMocEVERAygwBURETGAAldERMQAClwREREDKHBFREQMoMAVERExgAJXRETEAApcERERAyhwRUREDKDAFRERMYACV0RExAAKXBEREQMocEVERAygwBURETGAAldERMQAClwREREDKHBFREQMoMAVERExgAJXRETEAApcERERAyhwRUREDKDAFRERMYACV0RExAD/B3GCwXE55xIwAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 593.021x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit2.draw(output = 'mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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+fQFIS0tj5syZNm3/doErx7///e/cfsx9+/Zl2LBhmM3576ba8xx4J7LlWpnD40JXSoqlI0lhY53MmTOHy5cvU6ZMGUNOyNb47bffcm9Z3uqpxb179/Loo4/mm16nTh327t1r8/5tuV2akpKS50EFW2zbto1nnnmGmJiYfKErJiaGpKQk9u3bl2d6bGwsq1evLrBJ8nYOHDhAcHBwsWrOkZUO66baZVNF8v5f1hd7Gwd+P4C3Aa9I+eUwzMn/bARQcFPQjcY9ZLm7ceUqjFti2/7XLp9FSQNuQukYKNyCrbDpYMHzHH0MlAmBwwdtPx9ao7DzYGRkZO7rfTZs2GDTUA5FDVxg6Xryww8/0L17d0qVKkWNGjXynVPBvudAsY7HRd2cA7OgAHH8+HFeeeUVABo0cL13ROTc5WrUqNEth7K4ePEipUqVyjc9LCyMCxfc75GtZcuWkZKSwvDhw/Pc3WvcuDGtW7dmwYIFuc2JANWrV6d+/fosW7bMGeVKEVUu7bx9hwZgSOCSW6vsxBEtnHn85ch5aAts+6PWmsBV0H5u3L+4Bo8LXR06dADg7bff5vffrw+HvWXLFu6//34uXboEuF7TYnZ2NnPmzAEsr8m5HZPJlG9aQbeR3cH58+cZO3YsjRs3Zv369QwePJixY8eyatUqEhMTee211/IsHxsbS2ZmJt9++62TKpaiKBcKJZ3U8laz8HcHi4Fqlr/9Mg7btwscAzcOdbNz506r17U2cAHEx8fn/rt27dpW7VMcz+NC15gxYwgLC+P48ePUrVuX+vXrU7NmTVq0aEHt2rVp1aoVUHDoiouLo2zZsrlfOe9QnDRpUp7pcXFxdlnvRmvXruXkyZP4+vrSr1+/W37GsLCwAn/xLl26ROnSLvDn3W3Ex8fn69swdepU+vfvT1BQEJMnT2bEiBGsXbuWmJgYTp06lWfZ2NhYNm7cqFGXXZyXCVrUdM6+W0Y5Z7+SV7lQqGV79xeb+ftAk+rG7/dmqampHDlyhISEBM6ePVvk9aKiomwKXGAZHDwxMZEjR46QnJxsc+3iGB7Xp6tKlSps3LiRUaNGsWHDBo4ePUrdunV55ZVXeOKJJ3L7cRUUujIyMgoc6yotLS3PEyc3NnUVZ70b5TQtdu3albJly97yM9auXbvAvlt79+695VObrmLnzp0F/tX35Zdf8uWXX95y3dKlS9OqVStGjhzpqPLEjlrUhO/+axkzySgRJeEuJ95hkbxaRlleQm6kJtUhwPf2yznatGnTmDZtmtXr5YSm8PBwq9+luHnz5mJ19BbH8rjQBVC3bt3csa5udOHCBU6fPo2Pj0+BI/a2bdvWpiY6W9e70dy5c4v8Sohu3boxduxYjh8/TuXKlQFL8+mRI0dyXzPhqbp27YqPj4/6c7mJkkEQEwU/Gfji604NoIDWd3GSepFQKQxOGnRj2s8b2rl5q9qVK1fo1KkTEydOZMyYMbqr70E8MnQVZvfu3YClrdyW8Z1cxeDBg5k2bRo9evTg9ddf5+rVq4waNYpmzZp57KtxcixatIgVK1a45QMDAB8tHc7mvctJvHiUz1/aTfXw/A9M7Dy0nle/6EKlsrVyp019bjP+vpYOUgvXv8d3v8zEy8sHP98Anu0xjT9VbmrYZ7DWg3dbXj58wYAR6u+uYvlyNSfOHmDi/IFcTjlHSGApXu49k6oV8v7hl3DhCBPnD+LgqV+pVDaKj5+/3iH68OndTFsyjEvJZ/D29qVO1RYM6zENPx/Leazjyyaqh9fHZLL0GHm2xzTq33WfcR/wFry9oF8LeH+lMXc8u90DZUs4fj+OduXKFYYMGeLsMsTO7sjQ5Wqd6K0VGhrKDz/8wPPPP0+fPn3w8fGhW7dufPDBBx4/9srNTbbu5r4Gj9Cr7She/LjVLZerUqFOnotujkOndrI0bhozRu4h0D+EtdvnMG3JMD4c/rOjSi42f1/o2xw+/h6Kes3NGXfJmte4hATAIy6aPad8PYQu9w6mU9NBbNi1iPcXPMnU5zbnWSYoIJT/6/wmKVcvM+u7v+eZ5+sTwLM9PuSuig3Iys7inS/7sejH9+nX/vro5lOe3USgf/GGb3GUSmHQuT78Z1fR17HlGKhZAVrVuv1yIs6i0OWmatSooaf33FCDu1oXexuZ2RlcTU8h0D+E5KuXKFsy8vYrOVlUOPS6F+ZvLdrytxvD6WYBvjCknSV4uZqLyWc4cHIH/3j6OwDuq/8wHy55loQLRwgvXS13udCg0tSr3oqdh9bn20ZkuetPBnh7efOnyKYcO7sv33KurEM9OJcMP/9RtOWtPQbCS8L/3Wd5gEPEVd2RocsVx+gSudGJs/v5y+RGeJm86dT0/+geY3mdR42KDXnkvhE89k51SgSVxtfbn0lDNzi52qLJeZJxwdai3/EqimB/S+ByhXGZCnL20nHKhFbE29tyujWZTJQPq8KZS8fyhK6iSktPYeXPM3iqy4Q801/6tC1ZWRncU7M9AzuPJ9DPtQa/9DJBn3st/91yyL7bjgyDIfdbjgURV3ZHha5NmwoZHlvEhdSs1Ih5r54gOLAkZy+d4NUvulAyuCxtGvYi8eJRNu9dzqwxhygTGsHSuA9558v+dhml3Agtalr628zbbJ8+XlEVoE9zy+jjruzmcfVsffAmMyuDt+b0pnGtPxNT73r/zbljj1I+rApp6SlM+foZpn/7MsN7flysmh3Bywt632sZNHX5DriWWfxttoqCB++xNGOLuDrP7gAk4oaCA0IJDiwJQLlSkbS7py+7D28EYMPOhVQLr0eZ0AgAOjX9P3Yf3kBWdpbT6rVWVAUY3dXS98bWpqAgP0v/rb+0d/3AVa5UZc5ePkFWliVhmM1mzl46TvlS1vX4z8zK4M1/96J0iQiGxk7JM698mGVbgX7BdG8xNPd4cUUmk2UYiVFdITrC9u2UKwFD28MjzRS4xH3cUXe6RNzB+SunCQupgJeXF6lXk9iy91seaPYkAOFl7mLN9tmkXUsm0D+ELXu/oUr52nh7FfxydFfl72sJTX+uB1sOWt7Pdyn19utVLm0Ja/dUBT83OXuFhZSnZsV7WLtjDp2aDmLj7q+pULqaVU2LWVmZvDWnDyWCSvPiI5/nuXOWlHoRXx9/AvyCyM7OZv3O+dSseI8DPol9lQmBZ+6H05cg7nfYdvj2d75MJqhbyRLa/hSh/lvifkxmd313jLgEe7zw2mjJyclOe+H11MXD2Lx3GReSEigZVJZA/xBmjTnI+wufokWd7sTU7c7SuA/5dvMneHv5kJWdSesGj/JYx79jMpkwm838c+VY4v67BF8ffwL9S/Bsj2nUrFT0i2y74RjysmNrZJvhfDIcPw8nLsDG3yEjC3y9oUNdS9iqXBpKOOm1QrdSlGPg+Jn9TJw/iCup5wkKCGVU71lUC6+b5+eennmNgf+oQUbmNVKuXqZUSHk6NHqMJ7u8w/c75vKPeQO4K6IBYEkadau1ZHjPj9h7ZDOTvx6CyWQiKzuTmpUaMTR2CqFBhXdyc8VjICvbEsCOX4BTlyxhPCPLMu5Wl4aWn3+l0q4x6OnN3O08aM9zoFhHoUuKxd1ONuDc0OUKXPGCe7O/L4bLaZZ3N77e09nV3JqOAcdwp2PA3c6DCl3Ooz5dIiIiIgZQ6BIRERExgEKXiIiIiAEUukREREQMoNAlIiIiYgA3GelGXFVQUBDJycnOLsMqQUFBdtuWl6/lSTB34uWCj9y7Mx0DYs/z4MTPvuJKSiqhwUG8PKRPodOKw57nQLGOQpcUi8lkuqMfPTaZXP/Re3EsHQNiz/Ogn38AfhlZ+PkH5G6zoGnintS8KCIiImIAhS4RERERAyh0iYiIiBhAoUtERETEAApdIiIiIgZQ6BIRERExgEKXiIiIiAEUukREREQMoNAlIiIiYgCFLhEREREDKHSJiIiIGEChS0RERMQACl0iIiIiBlDoEhERETGAQpeIiIiIARS6RERERAyg0CUiIiJiAB9nFyDuzWw2k5qa6uwyrBIUFITJZCr2dsxmyM6wQ0FO4OULdvhfICJyR18HrKXQJcWSmppKSEiIs8uwSnJyMsHBwcXeTnYGrJtqh4KcoN1w8PZzdhUi4gnu5OuAtdS8KCIiImIAhS4RERERAyh0iYiIiBhAoUtERETEAApdIiIiIgZQ6BIRERExgEKXiIiIiAEUukREREQMoMFRRVzAzkPrGflpuzzTAvyCiSxXiw6NHqNHy+fw9tavq4iIO9NZXMSFtG3Ym3trd8OMmYtJCazZPptPvxnBsTO/8eIjnzu7PBERKQY1L4q4kBoV76ZD4wF0bPwYvdq+zNTntlCuVGVW/jyDS8lnnV2eiIhbqFKlirNLKJBC100OHz7M9OnTefrpp2nYsCE+Pj6YTCb++te/OmS9I0eOYDKZivT1+uuv2/OjihsI9Asmusq9mM1mTp0/5OxyREQcplatWvTv358PPviAlStX8uOPP7J+/XqWL1/Om2++yUMPPUTFihVvu52ePXty4MABnnrqKQOqto6aF28yZcoUpkyZYth6AQEBtGzZstD5SUlJ7Nq1C4CYmBirty/u7/T/wlZoUBknVyIiYl9BQUH07duXoUOH0qhRo0KXe/DBB3P/vWrVKj7++GNWrFhBdnZ2nuV69uzJV199ha+vL9OnT+fAgQP8+OOPDqvfWgpdNylbtizdunWjWbNmNG3alBkzZvD11187bL3w8HB++umnQue/++677Nq1i8jISNq3b2/VZ/FETz31FNOnTycyMpKTJ086uxy7u5qRyuWUc5jNlj5d32z+lIMnf+VPlZsSWS7K2eUZIikNMrIs/87MgvRM8NOZ6o5y5soNx0A2ZJvBy+TcmsT++vXrx9SpUylTxro/KDt37kznzp3Zt28fTzzxBJs3bwbyBi6Af/7zn2zYsMHudReHTmU3ubk58KuvvnLoercze/ZsAB577DG8vDyjNXjgwIEMGjSIdu3yPq3Xp08fRo4cSZ06dUhJSWHNmjWMGTOGY8eO5S6zfPlyPv30U7p3784nn3xidOkON3fteOauHZ9nWsu6PRje0/M+680On4UN+2HnMctFFiAlHcYtgWZ3wX1/gjIhzq1RHCfbDPFHIe4AHDpzfXrKNXh7OcREQYuaEOjnvBrFPsqVK8fnn39Ojx498kzfunUrS5cuZfv27ezcuZNLly5hMpmoUKECjRo1omnTpvTp04e77roLgOjoaH766ScmTZrEtm3bmDNnTp7A9dRTT2E2m43+eLfkGVfxWzh37hwjR46kRo0aBAQEULlyZV566SXS0tIYMGAAJpOJGTNmOLvMAm3fvp09e/YA8Pjjjzu5GscaNmwY8+bNIy0tjRdffJHJkyfTsWNHNm3aRERERO5yZ86cYevWrcTGxjqxWsfp3OxJJjy9hrefXMngrhMJDSrDxeRE/H0DnV2aQ637DaZ8B78evR64cqSmw/p9MPE/cCDBOfWJY2VmweyfYHZc3sCV41wyLP8VJq+GiynG1yf2U7VqVTZt2pQncC1atIgmTZrQvHlz/vGPf7BmzRrOnDlDeno6165d49ixYyxdupRXX32VqKgounTpwtatWwHw8vJi5MiRzJs3z+UDF3h46Nq1axf16tXj/fffJzExkTp16pCens6kSZMYMGAA+/fvB6Bhw4ZOrrRgs2bNAuDee+8lOjraydU4TunSpXnnnXfYvn07bdu25bPPPuOtt96ic+fORERE8MYbb+RZftmyZbRt25YSJUo4qWLHqVSmJo1qdaBpdGcebTuS8U98y75jW5my+C/OLs1h4n6HZTtuv9zVDJj+Ixw/7/iaxDhmM8zbAvHHbr9s4hX45AfL3S9xP5UqVWL9+vXUrFkTgMTERHr27Mmjjz7K9u3bi7SN7OxsVq5cScuWLRk1ahTp6ekAuS1Bs2bNctnABR4cus6dO0e3bt1ITExk1KhRJCQksGPHDhITExk/fjyLFy8mPj4eLy8v6tWr5+xy88nIyGDevHkADBo0yLnFOFhsbCwlSpRg6tSpZGVl5U7fvn07GzZsoFevXrl/wYAldPn7+/PAAw84o1xD1ananPaNBrAufh57j25xdjl2l5oOS4sQuHKkZ8KSop2bxU0cSITtR4q+/Jkrljuj4l68vb1ZsmQJ1apVA+C3336jcePGLFmyxKbtZWVlcejQoXzdbq5eveqygQs8OHQNHz6c48ePM2LECCZMmEBIyPXOIK+++irR0dFkZmZSq1YtAgNdr+lmxYoVnDt3Dn9/f3r37u3schyqWbNmAGzatCnfvE2bNhEaGprnTt/+/fvZt2+fxzYx3qx/h7/h5eXNrNV/c3Ypdrftj+sdpovqj7Nw6qJj6hHjxf1u/TpbDlqaJMV9jBo1iqZNmwJw6NAh7r///mI9DJXTad7Hx9I1PSMjA4AhQ4bQoUOH4hfsIB4Zuvbu3cv8+fMpX74848ePzzffZDLRuHFjwHWbFnM60Hfv3p2wsLB880+cOMHw4cOJiYkhKCgIk8nEkSNHDK7SPipVqgRYPtPNcqZFRkbmmb5s2TK6dOmS+wvnySqVrUm7hn3YcWAtu//Y6Oxy7GrbH7at97ON64lrSU2H3fl/7W8r+RrsPWX/esQxoqOjGTduHGC5Q9W3b18SEmzvoFnQU4rPP/987vwvvviCoKCgYtXsKB55xZo7dy7Z2dkMGDCg0P/x/v7+gGuGrvPnz7NixQqg8KbFgwcPMn/+fBo3bkybNm1YtWpVsffbpEkTq38Rbh4jxRY5P6Nr1/J31Lh69WqeZXIsW7aM0aNH06ZNG77//nur9hcVFWWXJ0H9fAL5/NkDxd5OUfRt/yrr4ucx67vXeO+ZdcXeXlStKNIz0+xQWfE8+Led+IdYP/7Yvxd8w7OxntvP7U5RolwNOo20bQyl5176G4c2/cvOFTnfQ//3AsEhoZxOOJ37x2ZB01zJ7a4DL730En5+lsdOJ06cyLZt22zeV0GBK2cQ1Icffpj27dtTpUoV+vfvz/Tp0wvdTnGuA+Hh4fzyyy82reuRoSvnInzzkAQ3yrmD4oqha968eaSnpxMeHk6nTp0KXKZ169YkJiYCMHPmTLuEroSEBKeMfZWamgpYgnBOyMqR0/Sbs0yOnFvJOeHZGqdPn7alzHwCfO33l1TDGm1ZM7HwfghVK9Rm9bv2a085feoUVzNSb7+gg93Yh88aaampHjlO250mLNv2MUAuXbrokcdA9v9+J7KzsnI/X0HT3EWpUqXo168fAJcvX+bNN9+0eVuFBa6cPlwvv/wyO3ZYOokOHTr0lqHLXtcBa3lk6Dp69ChAboe9m127di33cVNXDF05Ty32798fb2/vApdxxJhd4eHhVq+TnZ1d7IM35yQSGRnJwYMH88wrrOkxNjaW5ORkq+9yAURERNjtTpe7iqhY0SXudF1LSiCoZHnrV0y/mHtsiPvyCTCRnZWBl7fv7Re+iR+pHnkMeP3vnO/l7Z37+Qqa5kpudR3o169fbkvFrFmzSEmxbcyP2wUugF9//ZUtW7bQvHlz7r77bpo0aVLoHaniXAdsuVbm8MjQlfNDvfmuSY45c+Zw+fJlypQp43IH8G+//ZZ7kBj91KItt0tTUlLyPKRgi23btvHMM88QExOTL3TFxMSQlJTEvn378kyPjY1l9erVBTZJ3s6BAwcIDg4uVs0AWemwbmqxN+MUB34/gLcLDDK5YT8stuEu/RcTniHis2fsX5AYbubGog0XcaOQANi88p/4FPw3qVt7+6O5XElOISI8IvePzYKmuZJbXQfuu+++3H/PnDnTpu0XJXDduI/mzZvn7ruw65q9rgPW8siO9DkptKD/2cePH+eVV14BoEGDBobWVRQ5d7kaNWrkkkNZOMKyZctISUlh+PDhee7sNW7cmNatW7NgwYLc5kSA6tWrU79+fZYtW+aMcsWOmlYHPysvnDXKQ0Qph5QjTtCylvXrtKiBRwYuT5Tz0Fpqamrue4StYU3gAtiy5frQOjn7diUeGbpyHhd9++23+f33688jb9myhfvvv59Lly4Brte0mJ2dzZw5cwDLq3LuFOfPn2fs2LE0btyY9evXM3jwYMaOHcuqVatITEzktddey7N8bGwsmZmZfPvtt06qWOwl0A8ealL05f194CHXO49KMdQsD03vKvry4SWhXW3H1SP2ExISQlSU5Z2xO3futLoPp7WBC2DPnj25rVy3eoG2s3hk6BozZgxhYWEcP36cunXrUr9+fWrWrEmLFi2oXbs2rVq1AgoOXXFxcZQtWzb3K+cdipMmTcozPS4uzi7r3Wjt2rWcPHkSX1/f3I6Hnig+Pj7fbeapU6fSv39/goKCmDx5MiNGjGDt2rXExMRw6lTeZ8NjY2PZuHEjFy9qsCZP0KKmJUjd7n3GgX4wuB1EljakLDGIyQS9m0HjardfNqIUPHM/BFn//Iw4wY3DHR0/ftyqdW0JXACZmZm5T+EXNNySs3lkn64qVaqwceNGRo0axYYNGzh69Ch169bllVde4Yknnsjtx1VQ6MrIyOD8+fzvGUlLSyMtLS3PcvZY70Y5TYtdu3albNmyt/mU7mvnzp3s3Lkz3/Qvv/ySL7/88pbrli5dmlatWjFy5EhHlSdO0CYaqpWFjfvh12OQdcMT6MH+0LwGtKoFYcZ3wRAD+HjDgBhoUNnywuvfbxq5pnwotIyCe2tAgPV97sVJzpw5Q+vWrQkICODcuXNFXs9kMvHCCy/Y/C7FJ554Am9vb5KTk22q25E8MnQB1K1bN3esqxtduHCB06dP4+PjQ506dfLNb9u2rU2vELB1vRvNnTuXuXPnFmsbnq5r1674+PioP5cHqlrW8tWjMZy+ZHnlT6AfVC4Dvuq/4/FMJmhYxfJ1LgnOJ1vCd4kAy91N0+1uhYrLuXbtGhs3Wj+gs9lsplu3bqxevZq9e/da/S7FdeuKP5aho3hs6CrM7t27AcsIubaM8eRKFi1aBFx/YGDlypWUK1eOatWq0aSJFR1l3MiiRYtYsWIFFy5ccHYp4iAhARBl+xPZ4gHKlrB8yZ3rypUrdOjQgdTUVJd+l6K17tjQ5Wqd6G3x6KOP5vl+6NChgKUTvq2P5rq6m5trXc1HS4ezee9yEi8e5fOXdlM9PO8TqMlpl3jpk7a531/LSOX0hT9Y+PczhAYVr7PSjzsX8vO+/5CcdpGjiXvx9w2idIlwnn/4U8JLVyvWtkVEjGbrmF6uTKHLjXlS+vcU9zV4hF5tR/Hix60KnB8SWIrPRsTnfr9w/Xvs+uPHYgcugE17ltKmQS+8vX1pFv0AJpOJpXEf8sGiwUwY/F2xty8iIsVzx4YuVxyjS9xfg7taW7X86l/+xf91fuu2yyWlXmTwpPqkZ1ylbMlIMrKukXD+D/7cZBAvPPIZmVkZ7DkSx8he/8LX5/qop7WrNGfJxsnWfgwREXGAOy50bdq0ydkliACw98hmrqScp3ntbrddtkRQGPff3Y/gwFL0az+WbftXs2DdBF545DMA4g+uo07VmDyBC2DpT1NpXudBh9QvIiLW8chxukTcwapt/6Rj48fx9i7a3z4HT8VTs9I9ABw4sZ0aFe/Onbdpz1Ja1nsoz/Jffv82J88dKNKdNBERcTyFLhEnSEtP4ced8+nU7Ikir/PHqfjcoHVj6DKbzfyyfzXNoh/IXXbh+vf46b+LefuplQT4BdmzdBERsZFCl4gTbNi5kOoRDahSPjrP9AnzHuen3UvyLX/u8klMJi/KhEYA8EfCLqpH1Adg3/GfqVKhNoH+lhfOLvpxEuvi5zHh6TWEBJZy7AcREZEiU+gSsaOpi4fR981Izl4+wejPOjDwHzVz5439ogv7j1vGVFu17Qs6N3sy3/oHTm6nXKnIfNMPnvw1T3NisH8oyzd9DEDcf5cQU7cHAGcvneCzb18iOe0SIz9tx5BJd/Pc1Hvt+AlFRMRWd1xHehFHGt7zI4b3/KjAeW8/+Z/cf38wNP8ozVdSL1AmtCJ/qtw037zmdbrRvM71Dvcfv7A9999b9n7DxGcsIzCXKxXJmokaSkRExBUpdIm4iNCg0kwYvMbq9WaM3OOAakRExN7UvCgiIiJiAIUuEREREQModImIiIgYQH26pFiCgoJITk52dhlWCQqyz7hVXr7QbrhdNmU4L19nVyAinsLe14GJn33FlZRUQoODeHlIn3zf24O9rgPWUuiSYjGZTAQHBzu7DKcwmcDb7/bLiYh4MntfB/z8A/DLyMLPP4Dg4OB837szNS+KiIiIGEChS0RERMQACl0iIiIiBlDoEhERETGAQpeIiIiIARS6RERERAyg0CUiIiJiAIUuEREREQModImIiIgYQKFLRERExAAKXSIiIiIGUOgSERERMYBCl4iIiIgBFLpEREREDKDQJSIiImIAhS4RERERAyh0iYiIiBhAoUtERETEAApdIiIiIgZQ6BIRERExgEKXiIiIiAEUukREREQMoNAlRTZx4kRatGhBWFgYpUqV4r777uO7775zdlkiInIb//nPf7j77rvx9/enWrVqvPfee84uyVAbNmwgNjaWqlWrYjKZGDdunFPqUOiSIvvhhx944oknWLduHVu3bqVZs2Z07dqVTZs2Obs0EREpxC+//EJsbCx//vOfiY+PZ9y4cfz1r3/lww8/dHZphklOTqZOnTq8++67hIeHO60OH6ftWdzOypUr83z//vvvs3LlShYvXkxMTIyTqhIRkVuZNGkS99xzD++++y4AtWvXZs+ePUyYMIFhw4ZhMpmcXKHjdenShS5dugAwevRop9Wh0CU2y8rKIikpiTJlyji7FBERt3P81BnSrqXnmZaZlZX7398Pnyh0GkCAny9VKlW47X7i4uIYOHBgnmmdO3fmvffe4+jRo1SrVq04H8Nml5NSSDx3Md/0mz9vYZ8foGqlCvj7+Tq+WDtR6BKbvfnmmyQlJfH44487uxQREbdzOSmFOUvXFDgvNe0q/1zwn1tO6/Pg/UUKXadPn87XpJbz/enTp50Wuvz9fPl65Y9cTkopcP7Nn/fm76OqRVKz1wMOr9Oe1KdLbPLxxx8zYcIEFi5cSKVKlZxdjoiI26n3p+o0qhdl07oNou/i7jo1i12DM5sWA/z96NW1nU3rBgb480iXNni5WdOoQpdY7b333uPll19m+fLldOzY0dnliIi4re4dWlIqNMSqdUJDgujx51ZFXj4iIoKEhIQ80xITEwGc2qkcoEbVirRqUt/q9Xr8uRUlSwQ7oCLHUugSq7z22mu88cYbrFy5kg4dOji7HBERtxbg78ejXdtizf2aR7q0JSgwoMjLt2zZktWrV+eZtmrVKiIjI6lataoVe3aMTm2aUr5MWJGXb1i7Bg1r13BgRY6j0CVF9sILLzBx4kRmz55NrVq1SEhIICEhgcuXLzu7NBERt1WjSkVaNW1QpGVbNKpLreqRVm3/xRdfZMeOHYwZM4Z9+/Yxe/Zspk2bxujRo13iyUVfHx96P9gOb6/bR5LQkGBirbjLlyM5OZn4+Hji4+NJT08nISGB+Ph4Dh48aEvJNjOZzWazoXsUt1XYL+fAgQOZOXOmscWIiHiQjMxMPpy1pMCn+XKUK12S5wY9jJ+v9c/ArVixgrFjx7Jv3z7Cw8N59tlnefnll4tTst2t2/wrqzdsu+UyT/buQlQ160InwPr162nXLn//sTZt2rB+/Xqrt2crhS5xiISzFwgKDCA0JMjZpYiIuIVTief4aPZSsrKz883zMpn4y2OxVI4o74TKjJGdnc1nX37D0ZOJBc6PaVyP7h3ce0xINS+K3ZnNZhat/JF3P5vHngNHnF2OiIhbqFihLB3va1LgvPtjGnl04ALw8vKiV9d2Bd7JK1e6FA+0aeaEquxLoUvsbv8fxzlx+iwmoGrF248hIyIiFq2bNaDqTWNvVY4oR7sW9zipImOVCQul2/0t8kzz8jLRu1s7fG1oVnU1Cl1uKisri1mzZtGxY0fKli2Lv78/VatWpWvXrsyaNctpdZnNZtbGbQcsHT5DggOdVouIiLvx8vKiV7d2+P1vlHVfH296dWuHt/edc7lu2jCa6BpVcr9vH9OYyIhyTqzIfu6cn6IHuXLlCh07dmTQoEGsXbuWwMBAGjRoQEZGBitXrmTQoEFOqy3nLpevjzetmzV0Wh0iIu6qTKlQHvzf3Z4u7ZpTrnQp5xZkMJPJxMMPtCY4MIDKEeVp2+JuZ5dkN+pI74Z69erFwoULqVKlCnPmzOG+++7LnXfy5EmmT5/OuHHjrN7utFmLSUpOK1ZtKalpZGVn4+frS4C/X7G2JSJypzKbzaRnZOLn6+MSwzo4Q0ZmJl5eXkUaSsJIJUICeW5gT5vWVehyMzt27KBx48b4+voSHx9PnTp17Lbttz+ay5Xkgt+BJSIiIpaxwsYO62/Tuu7fK+0Os2TJEgC6du1q18AFlvReHLrLJSIinq4410qFLjezd+9eAJo3b273bdt6uxRg/6Fj/GvRKnx9vBk1pI860IuIiNxEocvNXLlyBYBSpUrZfdvF6dOVkmpZz2TyYurMxfYsS0RExGUUp0+XQpebCQ0NBeDSpUt233ZSclqx+3SlZ2SQnpFhp4pEREQ8h0KXm6lbty6LFy9my5Ytdt+2re3U6sslIiJ3iuL06dLTi24mPj6ee+65B19fX3bt2kV0dLRT67mxL9foZ/qpL5eIiEghXGvwC7mtu+++m169epGRkcEDDzxAXFxcnvmnTp3i9ddfN6QWjT4vIiJSdLrT5YauXLlC9+7d+fHHHwGoXLky4eHhnDx5ktOnT2M2mzHix6q7XCIiIkWnO11uKDQ0lLVr1zJ9+nRat25NUlISu3btwtfXly5dujB79mxjCjGZKBtWUne5REREikB3uqRYsrKzycrMyn05q4iIiBRMoUtERETEAGpeFBERETGAQpeIiIiIARS6RERERAyg0CUiIiJiAIUuEREREQModImIiIgYQKFLRERExAAKXSIiIiIGUOgSERERMYBCl4iIiIgBFLpEREREDKDQJSIiImIAhS4RERERAyh0iYiIiBhAoUtERETEAApdIiIiIgZQ6BIRERExgEKXiIiIiAEUukREREQMoNAlIiIiYgCFLhEREREDKHSJiIiIGEChS0RERMQACl0iIiIiBlDoEhERETGAQpeIiIiIARS6RERERAyg0CUiIiJiAIUuEREREQModImIiIgYQKFLRERExAAKXSIiIiIGUOgSERERMYBCl4iIiIgBFLpEREREDKDQJSIiImIAhS4RERERAyh0iYiIiBhAoUtERETEAP8P3lBY4LQsMDwAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 760.244x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit2.decompose().decompose().decompose().decompose().decompose().draw(output = 'mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'10': 21, '01': 20, '11': 11, '00': 8}\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "shots = 60 # Any number of shots\n",
    "simulator = Aer.get_backend('qasm_simulator')\n",
    "measurement = execute(circuit2, simulator, shots=shots) # Execute measurement\n",
    "simulation_result = measurement.result()\n",
    "counts = simulation_result.get_counts(circuit2) # dictionary for output\n",
    "print(counts)\n",
    "\n",
    "amplitudes = np.zeros(len(counts))\n",
    "index = np.array([int(key, 2) for key in counts])\n",
    "amplitudes[index] = list(counts.values())\n",
    "\n",
    "binary = ['00', '01', '10', '11']\n",
    "plt.bar(binary, amplitudes, edgecolor='black')\n",
    "plt.yticks(np.arange(0, max(amplitudes) + 1, 1))\n",
    "plt.ylabel(f'Probability / % of {shots} shots')\n",
    "plt.xlabel('Computational basis states')\n",
    "plt.ylim([0,max(amplitudes)])\n",
    "\n",
    "for i in range(len(binary)):\n",
    "    plt.text(binary[i], amplitudes[i]-2, str(amplitudes[i]), ha='center', va='bottom', c = 'white')\n",
    "\n",
    "plt.show()\n",
    "\n",
    "counts = {key: np.linalg.norm(notes)*np.sqrt(value/shots) for key, value in counts.items()} # Remapping the results back to the original range\n",
    "amplitudes = np.zeros(len(counts))\n",
    "index = np.array([int(key, 2) for key in counts])\n",
    "amplitudes[index] = list(counts.values())\n",
    "amplitudes = amplitudes.round(0)\n",
    "\n",
    "binary = ['00', '01', '10', '11']\n",
    "plt.bar(binary, amplitudes, edgecolor='black')\n",
    "plt.yticks(np.arange(0, max(amplitudes) + 1, 1))\n",
    "plt.ylim([0,max(amplitudes)])\n",
    "plt.ylabel('Amplitude / Half tones')\n",
    "plt.xlabel('Computational basis states')\n",
    "for i in range(len(binary)):\n",
    "    plt.text(binary[i], amplitudes[i]-1, str(amplitudes[i]), ha='center', va='bottom', c ='white')\n",
    "# plt.title('Histogram')\n",
    "# plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For quickly executing multiple sets of measurements:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'01': 5, '00': 5, '10': 6, '11': 4}\n",
      "{'01': 4, '10': 10, '11': 4, '00': 2}\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'11': 7, '10': 6, '01': 4, '00': 3}\n",
      "{'11': 7, '00': 2, '01': 5, '10': 6}\n",
      "{'00': 7, '10': 3, '01': 4, '11': 6}\n",
      "{'11': 6, '01': 8, '10': 3, '00': 3}\n",
      "{'11': 6, '01': 7, '10': 5, '00': 2}\n",
      "{'10': 7, '11': 3, '01': 4, '00': 6}\n",
      "{'10': 6, '11': 8, '00': 2, '01': 4}\n",
      "{'01': 5, '00': 7, '11': 6, '10': 2}\n"
     ]
    }
   ],
   "source": [
    "times = 10\n",
    "\n",
    "for i in range(times):\n",
    "    shots = 20 # Any number of shots\n",
    "    simulator = Aer.get_backend('qasm_simulator')\n",
    "    measurement = execute(circuit2, simulator, shots=shots) # Execute measurement\n",
    "    simulation_result = measurement.result()\n",
    "    counts = simulation_result.get_counts(circuit2) # dictionary for output\n",
    "    amplitudes = np.zeros(len(counts))\n",
    "    print(counts)"
   ]
  }
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