TUT_7.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#IMPORTS\n",
    "import qiskit\n",
    "import numpy as np\n",
    "from qiskit import *\n",
    "from qiskit.visualization import plot_histogram\n",
    "from qiskit.visualization import plot_bloch_vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 173.376x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "measure_z = QuantumCircuit(1,1) #make quantum circuit with one qbit and 1 classical bit\n",
    "measure_z.measure(0,0); #map the 0th qbit to the 0th classical bit\n",
    "\n",
    "measure_z.draw(output='mpl') #draw the circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 293.776x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "measure_y = QuantumCircuit(1,1) #make quantum circuit with one qbit and 1 classical bit\n",
    "measure_y.sdg(0) #sadgoint gate on 0th qbit\n",
    "measure_y.h(0) #hadamard gate on 0th qbit\n",
    "measure_y.measure(0,0);  #map the 0th qbit to the 0th classical bit\n",
    "\n",
    "measure_y.draw(output='mpl') #draw the circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216.72x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# set up circuit (no measurements required)\n",
    "qc = QuantumCircuit(2) #quantum circuit with 2 qbits\n",
    "qc.x(0) # qubits numbered from the right, so qubit 0 is the qubit on the right\n",
    "qc.z(1) # and qubit 1 is on the left\n",
    "\n",
    "qc.draw(output='mpl') #draw the circuit\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "\\begin{pmatrix}0j&(1+0j)&0j&0j\\\\(1+0j)&0j&0j&0j\\\\0j&0j&0j&(-1+0j)\\\\0j&0j&(-1+0j)&\\end{pmatrix}"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# set up simulator that returns statevectors\n",
    "backend = Aer.get_backend('unitary_simulator')\n",
    "\n",
    "# run the circuit to get the matrix\n",
    "gate = execute(qc,backend).result().get_unitary()\n",
    "\n",
    "# now we use some fanciness to display it in latex\n",
    "from IPython.display import display, Markdown, Latex\n",
    "gate_latex = '\\\\begin{pmatrix}'\n",
    "for line in gate:\n",
    "    for element in line:\n",
    "        gate_latex += str(element) + '&'\n",
    "    gate_latex  = gate_latex[0:-1]\n",
    "    gate_latex +=  '\\\\\\\\'\n",
    "gate_latex  = gate_latex[0:-4]\n",
    "gate_latex += '\\end{pmatrix}'\n",
    "display(Markdown(gate_latex))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Mulitple qbit gates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 276.92x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#CX or controlled not or targeted x gate\n",
    "\n",
    "qc1 = QuantumCircuit(2) #quantum circuit with 2 qbits\n",
    "cr1 = ClassicalRegister(2)\n",
    "qc1.x(0) # qubits numbered from the right, so qubit 0 is the qubit on the right\n",
    "qc1.cx(0,1) # CNOT controlled on qubit 0 with qubit 1 as target\n",
    "qc1.draw(output='mpl') #draw the circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "qc1.add_register(cr1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAToAAACoCAYAAABwmyKgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAWRUlEQVR4nO3de1xUdf7H8dcMICJyEW9EmMZFEQTioouul8g0zLbdyDQMKysv6K9Vy37Vw9WyfhneKvuVLm1abuY+FPmh9DAz0SSTvKYpeUENE0xFcElRbjPM7w9WckRgxBmOfOfzfDzm4fCd7znzGZx58z3nfM8ZnclkMiGEEArTa12AEELYmgSdEEJ5EnRCCOVJ0AkhlCdBJ4RQngSdEEJ5EnRCCOVJ0AkhlCdBJ4RQngSdEEJ5EnRCCOVJ0AkhlCdBJ4RQngSdEEJ5EnRCCOVJ0AkhlCdBJ4RQngSdEEJ5EnRCCOVJ0AkhlCdBJ4RQngSdEEJ5EnRCCOVJ0AkhlCdBJ4RQngSdEEJ5EnRCCOU5al2AsEyrTRs0ed7KIcM0eV4t6XQ6TZ7XZDJp8rz2QEZ0QgjlSdAJIZQnQSeEUJ4EnRBCeRJ0QgjlSdAJIZQn00uEuEVt2rShV69eeHh4YDAYOHHiBKdOnaq3f0REBN7e3mzYoM2UIXskQSdEE3h4ePDUU08xduxYQkNDcXBwMHu8qKiIL774gsWLF7Nnz57a9oiICDIzM3F1dWXgwIHs2rWruUu3SzqTzFJsEexlwnDBBcgpgEoDdHCDyG7Q2qlZS2h0wvDYsWN599138fDwAMBgMHDo0CHOnTuHs7MzwcHBdOjQobZ/eno6SUlJ+Pj4kJmZiZeXF+np6YwaNYqqqqrafvJRtB2720dXXV3NggULCAwMpHXr1oSHh5OVlUWPHj0YP3681uVZhamsjKrHHqd623e/t1VUYJj6IoY33sJUXa1hdTdWWg4fbIIFG+Crg7DlMKzeBTPT4NujWldXw9nZmdTUVJYtW4aHhwdbt24lPj4eNzc3wsPDGTp0KIMGDaJjx44EBQWxYMECLl68yCOPPMKRI0fYunVrvSEnbMvugu6ZZ57hzTffZMKECWzYsIGRI0eSkJDAzz//TFRUlNblWYXOxQX9iEcxfv4vTCYTJqMR4/+8DU5OOLzy3+j0t9d/e6UBPtwMJwrrPlZlhP/bA9uPNX9d13J0dCQtLY0RI0ZQUlJCYmIisbGxpKenU15eXqf/0aNHeemllwgJCeH777/H09MTd3d3srKyJOQ0cHu9421s5cqVLF++nIyMDKZPn05sbCwzZsygb9++GAyG2qA7d+4cQ4cOpU2bNoSHh7Nv3z6NK795+of/BMUXMH23HeN7/4upqAiH12eha9XM24EW2HsSzpRAQxtu6/eDwdhcFdX16quvMnz4cIqKihgwYACff/65Rct17NiRHj161P7s7++Pi4uLrcoU9bCroHv77beJi4tj0KBBZu0BAQE4OTkRGhoKQFJSEkFBQRQXFzN58mRGjBiB0ajhp6wJdC6t0T/2KMb572A6cADHOW+ic22jdVk39P1xaOw0+iuVkHO6WcqpIzg4mJkzZwIwcuRIcnJyLFru6oEHLy8v1q5dy86dO/H19WX+/Pm2LFfcgN0EXUFBATk5OTz22GN1Hjt16hQhISE4Oztz6dIl1q9fz6xZs3BxcWH8+PEYjUZ27Nhhs9p0Ol2jtyYrL8dh1Eh07drZrLZbvR0+cabB0dxVz0x8oVnqud706dNxcnLio48+4ptvvrHo93ZtyKWnpzNy5EiefvppDAYDY8eO5Y477tDkd63azVJ2FXQA3t7eZu1lZWVkZWXVbrYeO3aM9u3bmx01Cw0N5dChQ81XrBVUZ26hetVqdA8MxZi+7rY+oldxpQSTqfEDJJVXfmuGasx5enry+OOPAzB37lyLlrk+5K7ukzty5Ahr167FycmJZ5991pZli+vYTdBdDa7c3Fyz9nnz5nHmzBkiIyMBuHz5Mu7u7mZ93N3dKS0ttVltJpOp0dvNqN61G+MHH+Lw2kwcJk2EkhJM326zWW23ehv9QE90uobfig562PHV0map51r9+vXDxcWFbdu28fPPPzf6+6ov5K767LPPALjvvvs0+V2rdrOU3UwY9vPzIywsjDlz5uDl5cWdd97JmjVr+PLLLwFqR3Surq5cunTJbNmLFy/Stm3bZq+5Kap/OoRxTjIOL72IPqxmn6P+sUcxrvgXugH9b7sjrgB9A2HrEaioqv+ARN8AaNu6WcsCfn9fWDKxt7GQu3Y9kZGR6HS6m/4jJprm9nvX24heryc1NZWQkBCSkpIYO3YsHTp0YPLkyTg6OhIWFgZAYGAgRUVFFBcX1y6bk5NDcHCwVqVbzJR3EuOs13GYMA79H/vVtusffgh++63Jozpb83CBiffVnRh8dQ9MaBf4S2SzlwWAj48PACdOnGiwnyUhB3D27FlKS0vx8PDA1dXVJjWLuuz+zIgxY8bw448/cuDAgdq2+Ph47rrrLpKTk1mxYgVz5szh2LFjdU7zaU72cGbElQrYlQdr99b8HNEV+gVAQGe4if3Ot+zandxOTk60adOGioqKG86Xu2rIkCFkZGSwYcOGRufJeXl5UVFRweXLl83a7fyjaFN2s+lanz179hATE2PWtmTJEhITE2nXrh2BgYGkpaVpGnL2oo0z3Bv0e9A91V/begCqqqr47bfGD4Js2rSJ/v37c+DAgUYnA1+4cMFa5QkL2XXQlZaWkpuby6RJk8zaO3fuzKZNmzSqSrRUe/fu1boEUQ+7Drq2bdu2uInAQoibZzcHI4QQ9kuCTgihPAk6IYTyJOiEEMqToBNCKE+CTgihPLueXtKSNPd3N9izmz1D4ZW5HwGQ/PJ4s/vi9iEjOiGE8iTohBDKk6ATQihPgk4IoTwJOiGE8iTohBDKk6ATQihPgk4IoTwJOiGE8iTohBDKk6ATQihPgk4IoTwJOiGE8iTohBDKk6ATQihPrkcnhAJ0Op0mz3uz1+7TiozohBDKk6ATQihPgk7cVn678vv9/AtQZdSuFqEO2UcnNFdwAbYfg58K4GL57+0LN4BeB3e2gz/4Q/Td0NpJuzpFyyVBJzRTWg5rdsP+U/X3qTbVjOzyL8D6/fBINPS+GzTa9y5aKAk6oYmTRfDxViitsHyZsipY+T0cOg2J/cDRwWblCcXIPjrR7E4Vw5LNNxdy19p/Cj7ZBsZq69YlGubh4aF1CU0mIzrRrMqr4JNvocJQf5/3nqj5d+rn9ff56TRsPgRDe1m3PnsQFRXFsGHDiIqKolu3bjg4OFBcXMy+ffvIzs4mIyODyspKs2UGDx7MmjVrSExMZP369RpV3nQSdKJZfbEP/n2l8X6W2HgQwrqAd8sdaDSrYcOGMXv2bHr37n3Dx++9916mTZtGYWEhixcvJjk5mYqKCgYPHswXX3yBi4sLDzzwQIsMOrvbdK2urmbBggUEBgbSunVrwsPDycrKokePHowfL9+ubksXy2DHCeutz1gNWw5Zb32qcnV15dNPP+XLL7+kd+/eFBcX88EHHzB69GiioqIIDw8nLi6Ov/3tb+zfv59OnTrx+uuvs2/fPiZOnFgbcikpKUyZMkXrl9Mkdjeie+aZZ0hPT2fmzJlERUWRnZ1NQkIC58+f54UXXtC6PKXtPGH9/Wo//AJ/iYQ2ztZdryrc3Nz4+uuviYmJoaysjJkzZ/Lhhx9SXl5u1u/AgQNs3LiRt956i0GDBvH3v/+dnj17snjxYnQ6HSkpKSQlJbWYU76uZ1cjupUrV7J8+XIyMjKYPn06sbGxzJgxg759+2IwGIiKigLgtddeIzg4GL1ez5o1azSuWh25Z62/ToMR8oqsv15VrF69mpiYGE6ePElkZCQLFy6sE3LXy8rK4oUXXsBgMKDT6aisrGTBggUtNuTAzoLu7bffJi4ujkGDBpm1BwQE4OTkRGhoKACBgYEsWrSIPn36aFGmkkwmKPi3bdadX2yb9bZ0EyZMIC4ujvPnzxMbG8uRI0csWm7w4MGkpaXh6OhIXl4erVq1YunSpZpdOMAa7GbTtaCggJycHKZNm1bnsVOnThESEoKzc832T2JiIgBvvfVWs9TWkt9AlnJydmXS0lKztqtHV+tT3+PXH42dv+gjhi2bcAvV3ZqXk1OAmv/Ha+9rydXVleTkZAAmTZrEyZMnLVru2gMPKSkpzJgxg5ycHAYOHMjIkSNZtWqVWX+tX6elo0y7GdEVFBQA4O3tbdZeVlZGVlZW7WarsBEbfiC0/rDdjkaPHo2npyfbt2+3ePfL9SGXlJREcXExs2fPBmoCs6WymxFdhw4dAMjNzeXBBx+sbZ83bx5nzpwhMjJSq9Ja9L4PS1Wb4JVVUHnNSfr1zZOzZB7dtab+1zgyPx53awXeglfmfgTU/D9ee785XR/2CQkJACxZssSi5W8Ucldfw4oVK5g3bx4DBw7Ex8eHX3/9tXa5lvLetZsRnZ+fH2FhYcyZM4d//vOfbN68maSkJJYtWwYgIzobu3pyvi108bLNelsqnU5X+37OzMxstH9DIQdQWlrKzp07AYiOjrZN0TZmN0Gn1+tJTU0lJCSEpKQkxo4dS4cOHZg8eTKOjo6EhYVpXaLy/DpZf506oFtH66+3JfP19cXd3Z2zZ89y7ty5Bvs2FnJX7d+/H4CQkBCb1GxrdrPpCtC9e3e++eYbs7YxY8bQs2dPXFxcatuqqqowGo1UV1dTVVVFeXk5zs7Osi/oFsUE1Jy2ZU29fMHDpfF+9uTy5cu89tprlJaWNtjP3d2d1NTURkMOYMOGDVy5coXs7GxblGxzdhV0N7Jnzx5iYmLM2saNG8fy5csB2LZtGwB5eXl069atuctTSke3mlO2DuRbb52xPa23LlVcuHCBN954o9F+Fy9eJCEhgeHDhzNlypQG97dt2bKFLVu2WLPMZmU3m643UlpaSm5ubp0DEZ9++ikmk8nsJiFnHY9Gg4uVLp75x0DbbA7bk40bN/LXv/61xRxUaCq7HtG1bdsWo1Gu1d2cPNrA6L6w7Fuo76NlydFWXy/4U4RVSxMKs+sRndBGaBd4sj84NPHdd1d7mBgrl1UXlrPrEZ3QTkRX6OwOK3fUfGeEJfQ6GBwMD4TK1YXFzZGgE5rxaQfTHqg5OPFdLpwovHG/1k7Qx69mn1xnufacaAIJOqEpB33N6C6iK1yphNMXoKi05nJOLk5wpxd0cgO97GQRt0CCTtw22rSCQG8I1LoQoRz5OymEUJ4EnRBCebLpKoQCmjLh9+qVVpJfHm92X0UyohNCKE+CTgihPAk6IYTyJOiEEMqToBNCKE+CTgihPAk6IYTyJOiEEMqToBNCKE+CTgihPAk6IYTyJOiEEMqToBNCKE+CTgihPAk6IYTyJOiEEMqToLMT+fn5DB48mJ49e9KrVy9effVVrUsS/7F161ZCQkIICAjgueeeaxFfqv7888/j6+uLo2PLuHavBJ2dcHR0ZO7cuRw+fJgffviB7Oxs1q1bp3VZdq+6uprnnnuO1NRUjh8/zsWLF1mxYoXWZTVq1KhR7N27V+syLCZBZyfuuOMOoqOjAWjVqhVhYWGcOnVK46rE7t278fHxITg4GIBnn32WtLQ0jatqXP/+/encubPWZVisZYw7hVUVFxezdu1aNm3apHUpLVKVwcAnqRsoK680a1/0SdoN78f2jSAsyO+G6yooKKBLly61P991113k5+dbueIaO/YdYuf+w3Xab1S3p3tbxsQPRa/T2aSW5iYjOjtTUVHBiBEjmDp1KkFBQVqX0yI5OToSHNiNM4XFnCksrm2//v6ZwmIqKisJDuha77pMJhO6a8KkKV9yY6nwnv78dqnUorrvCQ5QJuRAgs6uGI1GnnjiCSIiInjxxRe1LqdF6xsRQkcvj0b7PRgbg6OjQ72Pd+nSxWwXQn5+Pr6+vlap8XourZ0ZOqB3o/263tm53hFoSyVBd4309HSGDBlC+/btcXFx4e677yYhIcFmmxLNbfz48bi5ubFw4UKtS2nxHBz0DL+vb4N9/O7yISSwW4N9oqOjOX36NIcOHQJg6dKlxMfHW6vMOnqHB9G5Q7sG+/xpcD+zUaYKJOio2VyYMGEC8fHx5OXl8fjjjzNlyhQGDBhAdnY2v/zyi9Yl3rLt27ezbNky9uzZQ0REBPfccw/vv/8+YNvNJZX18OtC97tvPPrSAQ8N7ttoYDg4OPCPf/yDESNG4O/vT9u2bRkzZowNqv3P8+n1PNRAQEf26o7vHR0bXc+ECRPw9fXFaDTi6+vL5MmTrVmm1elM8i7n/fffZ8qUKUyePJlFixbh4GC+qWEwGFrMfKGm+FfGZtp7ujN0YOObNcLcuaJ/s2jZGqqv+xj1CQ8iPm6gRlU1bnnaVxw+bn7UvZWTI9PHjcLdzVWjqmzHLkZ069at46GHHqJTp044OzvTtWtXRo8ezcGDBykrK2P27Nn4+fnx3nvv1Qk5QOmQ+/VcET8ePoFebxdvBavr3KEdf4gINmtzbuXEkAHRGlVkmQdjY9DrzUeb98bco2TIgeLTSwwGA4mJiaxatQpfX1/i4+Nxd3cnNzeXtLQ0nnzySfLy8rhw4QJPP/00RqORjIwMcnNz8fT05P777ycgIEDrl2FTm7N/oLVzK/4Y3UvrUlqs+/tHse+nY5RX1Ew3ua9fBG6ubTSuqmEdvTzpF9mL7/YcBGqmkwzoHaZxVbaj9KbrxIkTSUlJYdy4cbz77ru4uv7+1yo/Px9PT0/mz5/Pm2++yUsvvcS6devIzc2t7aPX65k2bRoLFiywaZ2vzP3IpusXQlXJL4+3qJ+y2yvbtm0jJSWFuLg4UlJSzEIOag7ru7m5UVhYCMA777yDh4cHu3bt4tKlS3z77bd0796dhQsXsmTJEi1eghDCWkyKio+PNwGm/fv3N9hv3LhxJsDk4uJiOn36tNljBw8eNOn1epO/v78tS9XE6bPnTS8np5g2bdujdSnKOHf+gqm6ulrrMm6KwWg0FRb/W+sybE7ZfXSbNm2iW7duhIeHN9jPw6Nm0md0dDQ+Pj5mj/Xq1Qs/Pz+OHz9OSUkJnp6eNqlVy03XzO17ydzeck7OFuJadr3pWlJSwqVLl+jWrVujfXv06AFQb4hdbS8rK7NafUKI5qXkiM70n+MrV/e/NSQ2NhaAw4frnuxcVVXF8ePHcXV1pWPHxidRNpWlf5Ws5bP0rznxy6+8PDEBl9bOzfrcQmhByRFdu3bt8Pf35/Dhw2RmZtZ5/OjRo7X3/f39GTp0KMePH+fjjz8265ecnExJSQmPPPKIMnPpfj1XxE+5J+kfHSohJ+yGstNLVq9ezahRo3BwcODPf/4zAQEBFBYWkp2dTXBwMOnp6bV9T5w4Qb9+/SgsLGT48OEEBQWxb98+tmzZQteuXdmxYwfe3t4avhrryTmax5dbd/D8U/ESdMJuKBt0ABs3bmT+/Pns3r2b8vJyOnXqRJ8+fZg6dSoDBgww65ufn8+sWbP46quvKC4uxtvbm4cffphZs2bRqVMnjV6BbVRXV8uZEMKuKB10QggBiu6jE0KIa0nQCSGUJ0EnhFCeBJ0QQnkSdEII5UnQCSGUJ0EnhFCeBJ0QQnkSdEII5UnQCSGUJ0EnhFCeBJ0QQnkSdEII5UnQCSGUJ0EnhFCeBJ0QQnkSdEII5UnQCSGUJ0EnhFCeBJ0QQnkSdEII5UnQCSGUJ0EnhFCeBJ0QQnkSdEII5UnQCSGUJ0EnhFDe/wMotDWyGK9w5AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 397.32x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc1.measure(0,0) #MEASURE THE QUANTUM CIRCUIT (COLLAPSE THE WAVEFUNCTION) BY MAPPING TO CLASSICAL BITS\n",
    "qc1.measure(1,1)\n",
    "qc1.draw(output='mpl') #draw the circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 276.92x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#CY or controlled not or targeted Y gate\n",
    "qc2 = QuantumCircuit(2) #quantum circuit with 2 qbits\n",
    "cr2 = ClassicalRegister(2)\n",
    "qc2.h(0) # qubits numbered from the right, so qubit 0 is the qubit on the right\n",
    "qc2.cy(0,1) # CY controlled on qubit 0 with qubit 1 as target\n",
    "qc2.draw(output='mpl') #draw the circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 397.32x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc2.add_register(cr1)\n",
    "qc2.measure(0,0) #MEASURE THE QUANTUM CIRCUIT (COLLAPSE THE WAVEFUNCTION) BY MAPPING TO CLASSICAL BITS\n",
    "qc2.measure(1,1)\n",
    "qc2.draw(output='mpl') #draw the circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 276.92x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#CZ or controlled not or targeted Z gate\n",
    "qc3 = QuantumCircuit(2) #quantum circuit with 2 qbits\n",
    "cr3 = ClassicalRegister(2)\n",
    "qc3.h(0) # qubits numbered from the right, so qubit 0 is the qubit on the right\n",
    "qc3.cz(0,1) # CZ controlled on qubit 0 with qubit 1 as target\n",
    "qc3.draw(output='mpl') #draw the circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 397.32x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc3.add_register(cr3)\n",
    "qc3.measure(0,0) #MEASURE THE QUANTUM CIRCUIT (COLLAPSE THE WAVEFUNCTION) BY MAPPING TO CLASSICAL BITS\n",
    "qc3.measure(1,1)\n",
    "qc3.draw(output='mpl') #draw the circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 276.92x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#CCX or Toffoli gate\n",
    "qc4 = QuantumCircuit(3) #quantum circuit with 3 qbits\n",
    "cr4 = ClassicalRegister(3)\n",
    "qc4.h(0) # qubits numbered from the right, so qubit 0 is the qubit on the right\n",
    "qc4.ccx(0,1,2) # Toffoli controlled on qubits 0 and 1 with qubit 2 as target\n",
    "qc4.draw(output='mpl') #draw the circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWcAAADWCAYAAAANWUPpAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAd90lEQVR4nO3de1iUdf7/8ecMZwUkRVHBM6iAgIiarqbiochcs7LM0v1lefgp8nOz9upgXu5lm6lbVn53t13Nkq3sl3goTaqfZdrBbdVFTbPEJBMNUSmVgxyGmd8fLCRy1GDuG+b1uK65HD/zuW/ewwwvPvO5P/eNxeFwOBAREVOxGl2AiIhUpXAWETEhhbOIiAkpnEVETEjhLCJiQgpnERETUjiLiJiQwllExIQUziIiJqRwFhExIYWziIgJKZxFRExI4SwiYkIKZxERE1I4i4iYkMJZRMSEFM4iIiakcBYRMSGFs4iICSmcRURMSOEsImJCCmcRERNSOIuImJDCWUTEhBTOIiImpHAWETEhhbOIiAm5G12A1M/v3zTm6754vzFf10gWi8WQr+twOAz5umJOGjmLiJiQwllExIQUziIiJqRwFhExIYWziIgJKZxFRExI4SxiAHd3rWKV2ukdInKdrFYrI0aMYNCgQcTExBAQEIDNZuP48ePs27ePDz/8kOzs7CrbrVy5ki5dujBx4kRKSkoMqFyaAoWzmJLDAQadC1InDw8PkpKSmDt3Lt26dauxX0lJCRs3bmTx4sV88803QFkwJyUlUVRURGxsLHv27HFW2dLEWBwudlqS3W5nxYoV/OMf/yAzM5NevXqxcuVKZs6cyfDhw1m1apXRJVbrWs8QfGVuRwZNfJo+Ix6qaHM4HPx9RivGzEomdMAd9dqPM88QvHQGTqbB2XSwl4KPP4T0heAYcPd0Xh21nSEYFRXFP//5T/r27QvA8ePH2bp1K2lpaZw9exZPT08iIiIYOnQot956K25ubhQVFbFo0SJCQkKYO3cuRUVFTJgwgQ8++KDSvl3sR1Hq4HIj5wcffJDNmzezcOFC4uLi2L17N5MnT+bcuXPMnz/f6PIaRN5Pp8m/kEXbzjGV2i+ezaC4MJeg7v0NqqxmWV/D1+VZ9d+MunwRju2CHw9D3CTwbGFYeQAMHTqU1NRU/Pz8yMjIYN68eWzbtq1KqG7dupVly5YREhLCokWLmD59OkuXLgWoMZhFruZSBwTXrVtHcnIyW7Zs4dFHHyU+Pp4FCxYwePBgbDYbcXFxAGRnZ3PzzTfTokULYmJi2L9/v8GVX5vsjL1YrG60CYms1H7+5EFatArCr00ngyqrXt75/wazg4pgvlJ+DhwxOMt69erFtm3b8PPz46233iI6Opr33nuv1tHuqVOnmDFjBlu2bKloS01NVTBLvbhUOD/77LMkJCQwfPjwSu2hoaF4eHgQFRUFwOzZs+nduzc5OTkkJiYyceJESktLjSj5umRn7OWG9j1x9/Sp1H7u5EHadTPfqPnUAaoN5Sudz4CCC04ppwqr1cratWvx9/cnJSWFKVOmkJ+fX69tV65cyfjx4ykuLsZms3HHHXcwYsSIxi1YmgWXmdY4deoUhw8f5uGHH67y2MmTJ4mMjMTLy4vc3Fy2bdvG6dOn8fHxYebMmSxZsoQvv/ySIUOGNEpt9bkK2rw36j8fmZ2xlwvZ3/GP/x1Yqb2kKI/+v32iwWv7tV5/IoP2rWs+sFbu3rFz2Pqvlxu9nqs98MADDBo0qGIkbLfb67XdlQf/JkyYwIABA1i8eDEvv/wyERERVUbdRl0NT5yrvscWXCqcAdq3b1+p/fLly+zatYuxY8cCcOzYMdq0aUNg4C/BFhUVxZEjRxotnBta9vf7uPHOPxI+9HeV2t98IoogE46c3d3qd7Svvv0a2ty5cwF44oknuHjxYr22uTqYP/jgAz766CNmzJhB7969GTlyJB9//HFjli1NnMtMa5SHbXp6eqX25cuXk5WVRb9+/QDIz8/H39+/Uh9/f3/y8vIarTaHw1Hnrb4unPmOovyf6RJ9C35tQipupSWFFBVcoN01HgysT22/9tYrJhjqMWhc/fqLTqnnSpGRkcTGxnLu3DnWr19fr+9ZdcEMYLPZKlYDTZ061ZDvtW7G3+rLZUbO3bt3Jzo6miVLltC6dWuCg4PZsGEDqampABUHA1u2bElubm6lbS9duoSvr6/Ta74e2Rl7cfdqUWWlRtax3fi26UTLVkEGVVaz4L6Qc6L2Pt7+0LqLU8qpZODAgQDs2LGD4uLiOvvXFMzl3n//fZ5++mkGDBjQKPVK8+EyI2er1UpKSgqRkZHMnj2badOmERgYSGJiIu7u7kRHRwMQFhbG+fPnycnJqdj28OHDREREGFX6NcnO2EtQtwFY3Sr/3s367l+mnNIAaNsd2obV8KAFLFYIv8WYk1LKDxLXZ8VOXcEMcOjQIWw2G71798bDw6PB65Xmw2VGzgA9e/bkk08+qdQ2depUwsPD8fEpW9ng5+fHbbfdxtNPP83SpUt54403sFgsDBo0yIiSr9mwKSuqbR85zfkH0urLYoWocXD887KVG6VXnNHsGwg946F1Z2Nq27t3L6+88gr//ve/a+2XmJhYZzADFBcXs3r1aiwWC25ubjp9W2rkcmcIXi08PJxBgwbx2muvVbRlZ2czZcoUPv/8c8LCwkhOTiY2NtbAKl3nbwjaimHnyrL7A6eAX5DzR8zXs2qiRYsWbNq0iRdffPG61zG7+I+iXMWlRs5Xy8vLIz09nTlz5lRqDwoKYvv27QZV5dquPE3bv33N/cymoKCAhIQEo8uQZsSlw9nX17dJnVwiIq7DZQ4Iiog0JQpnERETUjiLiJiQwllExIQUziIiJqRwFhExIYWziIgJufQ656bE2WfqubJrPVPv8WVlV5pb+tjMSvdFfg2NnEVETEjhLCJiQgpnERETUjiLiJiQwllExIQUziIiJqRwFhExIYWziIgJKZxFRExI4SwiYkIKZxERE1I4i4iYkMJZRMSEFM4iIiakcBYRMSFdz1mkGbBYLIZ83Wu99rXUn0bOIiImpHAWETEhhbOIiAkpnEVETEjhLCJiQgpnERETUjiLuKgePXowcuRIxowZQ79+/fDy8qqxr5ubGw8//DAeHh5OrNC1aZ2ziAsZNmwYc+bM4ZZbbiEgIKDSYyUlJaSlpfHKK6+wbt06CgoKgLJgXrduHffccw+xsbH87ne/M6J0l+NyI2e73c5zzz1HWFgY3t7exMTEsGvXLnr16sXMmTONLs/l5Z795f6pg2ArMq6W5qRr1658/PHH7Nq1i0mTJhEQEMCZM2fYuXMn27dv5+uvv8ZqtXLjjTeyevVqMjIyuOOOOyoF88WLF/nLX/5i9FNxGS43cn7wwQfZvHkzCxcuJC4ujt27dzN58mTOnTvH/PnzjS7PZRUXwKGt8HPmL23fbof0TyB0GHTuZ1xtTd24ceN466238PX15fz58/ztb3/jtdde48SJE5X6tWzZkgkTJjBv3jwGDBjApk2bOH78OD169ODixYvcfPPN7Nmzx5gn4YJcauS8bt06kpOT2bJlC48++ijx8fEsWLCAwYMHY7PZiIuLA2DRokVERERgtVrZsGGDwVU3f6UlkLa+cjCXs9sgfUfZKFqu3dixY9m0aRO+vr6kpKQQHh7OokWLqgQzQH5+Pm+++SY33ngjSUlJ2Gw2evToQXFxsYLZAC4Vzs8++ywJCQkMHz68UntoaCgeHh5ERUUBEBYWxksvvcTAgQONKNPlnPkG8s7X3ue7z8qCWuqvY8eOvPnmm3h4ePDcc89xzz33cP58Hd9owGq1ctNNN+Hu7o7D4cDT05OYmBgnVCxXcplwPnXqFIcPH+buu++u8tjJkyeJjIysOFo9ZcoUxowZg7e3t7PLdEmnvwLquG6PrRDOHXdKOc3Gyy+/TEBAAFu3buUPf/hDvba5eo554cKFADz//PMEBwc3ZrlyFZcKZ4D27dtXar98+TK7du2qmNIwgsVicenbifQsqMfFzRJnzje81upuV76ORr2mV+vTpw/jx48nNzeXWbNm1et9eHUw33zzzTzzzDO8++67+Pn5kZiYqPduI7xWNXGZcA4MDAQgPT29Uvvy5cvJysqiXz8dcTJKXuEFHA57nf3yL190QjXNQ3kgJycnk5WVVWf/6oK5fI556dKlAEyfPl3rnJ3IZVZrdO/enejoaJYsWULr1q0JDg5mw4YNpKamAhg6cnb1a+Jm7C671cZihXd3rsGzxRrnFHUNHl+2Cih7Ha+870xXj8hGjRoFwOuvv17ntrUFM8CXX37JsWPHCAsLIyoqirS0tIrHXP2925hcZuRstVpJSUkhMjKS2bNnM23aNAIDA0lMTMTd3Z3o6GijS3RZwdHg5kmt887B0eDZwmklNWktW7akV69eFBcXc+DAgVr71hXM5crbjBzEuBqXGTkD9OzZk08++aRS29SpUwkPD8fHx6eiraSkhNLSUux2OyUlJRQWFuLl5XVN80VSf16+0G8i7N941UknFsABbcOgZ7xR1TU9HTp0wGq1kpmZSXFxcY396hvMAN999x1QtgJEnMOlwrk6+/btY9CgQZXaZsyYQXJyMgCfffYZAN9//z1du3Z1dnkuo1VHGDIDsr4uO/EEIKhX2Yj5hk6g34v1d/z4cXx9feucH/by8iIoKKheJ5gsX76cFStWVJzSLY3PZaY1qpOXl0d6enqVg4Fr167F4XBUuimYG5+HN3S+4lNz1Dho3VnBfK0cDgf5+flcuHCh1n4FBQWMHTuWYcOG1XmCSUFBAZcuXcJm02JzZ3HpkbOvry+lpaVGlyFimIKCAr766iujy5BquPTIWUTErBTOIiImpHAWETEhhbOIiAkpnEVETEjhLCJiQgpnERETcul1ziLNxfVcgKj8Ik1LH5tZ6b6Yg0bOIiImpHAWETEhhbOIiAkpnEVETEjhLCJiQgpnERETUjiLiJiQwllExIQUziIiJqRwFhExIYWziIgJKZxFRExI4SwiYkIKZxERE1I4i4iYkK7nLCKGsVgsTv+a13PtayNo5CwiYkIKZxERE1I4i6kU5f1y/1I2lNqMq0XESJpzFsPlnoVTB+DccSjO/6V9z+tgsYJfW+jQBzpEgLuXcXWKOJPCWQxTXABHP4bsozX3cdjLRtCXsuH459BzZFlIG3AcScSpFM5iiIs/woHNUHK5/tvYiuDI+5CTAZG3glXvXmnGNOcsTncxC9JSri2Yr5R9FL7aCvbShq1Lmh8fHx88PT2NLuO6aOwhTmUrgkNboLSk5j6jHy3796Pnau5z/jj8sBe6DWrY+sScWrVqxV133cXAgQOJjo7G19eX4uJi0tPT2bdvH++88w4ZGRmVtvHx8WHr1q3k5+dz9913U1xcbFD118flRs52u53nnnuOsLAwvL29iYmJYdeuXfTq1YuZM2caXV6z992nUJjbMPvK2A155xtmX2JOgYGB/P3vf+fHH39kzZo1zJo1i8GDBxMVFUVcXByTJ0/m+eef59ixY2zbto2YmBjgl2AeNWoUAwYMoGPHjgY/k2vnciPnBx98kM2bN7Nw4ULi4uLYvXs3kydP5ty5c8yfP9/o8pq1onw4fajh9uewww/7IDKh4fYp5jF+/HhWr15Nu3btAPjoo49ITU0lLS2Nn376CR8fH6KiohgxYgQTJ05k7NixjBkzhmXLljF48GBGjRpFVlYW8fHxnDhxwtgncx1cKpzXrVtHcnIyO3fuZPjw4QDEx8eTlpbGpk2biIuLo6ioiFmzZrF9+3by8/Pp168ff/3rXwkPDze4+qbvx0NlgdqQsr+BniPAw7th9yvGeuihh1i1ahVWq5UdO3aQmJjIt99+W6Xfnj17WLNmDfPmzeOPf/wjSUlJPPXUUwAVwXz0aC3LgUzMpaY1nn32WRISEiqCuVxoaCgeHh5ERUVhs9kIDQ1lz5495OTkMHr0aCZNmmRQxc3LTycbfp/2Urh4uuH3K8ZJSEioCOYFCxYwevToaoP5Sj/99BOPPfYY+/fvr2h77733mmwwgwuF86lTpzh8+DB33313lcdOnjxJZGQkXl5etGzZkqeeeorg4GDc3NxISkri0KFDFBYWGlB18+FwQG524+z7UiPtV5yvVatWvPLKK1itVhYtWsSSJUvqdaGi8jnm2NhYcnJyKC0t5aGHHmLw4MFOqLpxuFQ4A7Rv375S++XLl9m1axdxcXHVbrd79266du2Kt3fjfW62WCzN/tbC2xdbUeXnPfrR6m/1fbzc/6xYZehzu/J1bEqvqRnqvtrjjz9OcHAw//rXv/jTn/5Ur5+fKw/+ZWVlMWTIEJYvX47VauWll16q0t8s3/e6uEw4BwYGApCenl6pffny5WRlZdGvX78q2/z8888kJibyzDPPOKXG5uxa3pRm2rc4j5eXF9OnTwdg/vz52O11H6C4OpjL55gXL15MTk4OAwYMoH///o1deqNwmQOC3bt3Jzo6miVLltC6dWuCg4PZsGEDqampAFVGzpcvX2b8+PFMmjSJ++67r1FrayrXl/01HA745CWwX3Eho5rWMddnnfOV5vyfGaxImfHrCvwVHl+2Cih7Ha+8b3ZmqPvKX6yjR48mMDCQ/fv38+WXX9a5bU3BDFBYWMjatWt55JFHmDx5Mvv27avYrim8NuBCI2er1UpKSgqRkZHMnj2badOmERgYSGJiIu7u7kRHR1f0tdls3HPPPYSFhWnU3EAsFvBr1zj79gtqnP2Kc5WPcLdv315n39qCuVz5fjRybgJ69uzJJ598Uqlt6tSphIeH4+PjU9E2ffp07HY7q1atcnaJzdoNIWXX1GhQFghoeucXSDUiIyMBOHjwYK396hPMAAcOHKi036bGpcK5Ovv27WPQoF/OAf7hhx9ITk7G29ubgICAivYjR47QuXNnI0psNjpGwYk9DbvPtj3Ay7dh9ynG2LhxI0ePHiUtLa3WfosWLaozmKFsed2SJUvIy8ur9nGzc+lwzsvLIz09nTlz5lS0denSpcnMSTU1LW6AtmFw7ljD7bNL0/zEKtV4++23efvtt+vst3jxYrp27cqiRYtqXcdcUlLCggULGrJEp3LpcPb19aW0VJc2c6beo+Dnk1RZVnc9QmIgIOTX70ealoKCAu69916jy2h0Lh3O4nxevhBxK3z1LlDDB5T6rNLwC4LQ4XX3E2mqXGa1hphHu1CIuq3sT1BdD//2EHsXuDfNy/SK1ItGzmKIoN7Qsg18/cE1nNZtga4Doftg/RUUaf70FhfD+LaFAfeVHSDMPAAXTlXfz90LOkSWzTG3bOPcGkWMonAWQ1ndykbRQb2hpLDsL3FfvlB2aVF3r7IAb9n6+qdARJoqhbOYhoc3tO4MaDm5iA4IioiYkcJZRMSENK0hIoa51rNxy6+et/SxmZXuN0caOYuImJDCWUTEhBTOIiImpHAWETEhhbOIiAkpnEVETEjhLCJiQgpnERETUjiLiJiQwllExIQUziIiJqRwFhExIYWziIgJKZxFRExI4SwiYkIKZxcyZswYYmJiiI6OZuLEiVy6dMnokgTYuXMnkZGRhIaGMn36dEpLS40uqU5JSUmEhITg7t50LgmfmZnJqFGjCA8Pp0+fPjzxxBNGl1QrhbML2bBhAwcPHuSrr76ic+fOrFixwuiSXJ7dbmf69OmkpKTw3XffcenSJd544w2jy6rTpEmT+M9//mN0GdfE3d2dZcuW8c0335CWlsbu3bt59913jS6rRgpnF9KqVSugLBDy8/OxWCwGVyR79+6lY8eOREREAPDQQw+xceNGg6uq29ChQwkKCjK6jGvSoUMH+vfvD4CnpyfR0dGcPHnS4KpqpnB2MePHj6d9+/YcPXqURx55xOhyXN6pU6fo1KlTxf87d+5MZmamgRW5hpycHN555x3GjBljdCk1sjiu9Y94SZNnt9tZsGABgYGBCujrUGKz8VrK+1wuLAYg62wOAB3atal0v1z84Fiie3evdl8bNmzgnXfeqZjKOHLkCPfffz/79+9v8Lq/3H+Efx/4puL/tdUd4O/L1DtvxlrHpyt3d3dsNluD11qu4HIhr6W8j63UXmfNAONGDaZH54617rOoqIiEhATGjRtn6ve/Rs4uyGq18sADD7B27VqjS2mSPNzdiQjrStbZnIqAAKrczzqbQ1FxMRGhXWrcV6dOnSp9tM7MzCQkJKRR6o4J78HF3Lx61d03IrTOYHaGFj7edO/csV41u7tZ6dapQ637Ky0t5f777yc2NtbUwQwKZ6DsLwBv2rSJ+Ph4OnToQIsWLejVqxezZs0iIyPD6PIaxKVLl8jKyqr4/8aNG4mMjDSwoqZtcGwkbVu3qrPf2PhBuLu71fh4//79OX36NEeOHAFgzZo13HnnnQ1W55V8vL24+aYBdfbrEhxU40jfCPGDY/Ft6VNnv3GjflPnL5SZM2fi5+fH888/31DlNRqFM/Doo49y1113cfToUSZMmEBSUhLdunVj9erV9O3bl8OHDxtd4q928eJFxo8fT1RUFNHR0Rw4cICXXnrJ6LKaLDc3K7eNHFxrn+6dOxIZ1rWO/bixevVqJk6cSI8ePfD19WXq1KkNWGllA2J6ExR4Q619fjvqN3UeLJ41axYhISGUlpYSEhJCYmJiQ5ZZibeXJ7fU8Uulb0QoXYJrP0D5xRdf8Oqrr7Jv3z5iY2Pp27cvK1eubMhSG5TLzzmfOXOG4OBgOnXqxMGDBytWNAC88MILzJ8/n2nTpvHqq68aWGXjcjgcWrlxHRwOB6+lvE/696eqPGYBkqbdRccr5kPN4tj3p1izPrXax/r16ck9t41wbkH1YLfb+Z/kzZWmM8p5uLvxyIxJBPj7GlBZ43GJkfO7777LuHHjaNeuHV5eXnTp0oX77ruPQ4cOceLECex2O0OGDKkUzADjxo0D4Ny5c0aU7TT/d+sO/t+ne40uo8mxWCzcNnJwtR+lB8T0NmUwA4R1CyE8tHOVdk8PdxKG1T3tYQSr1cpvR1X/SWXYwJhmF8zQzMPZZrNx7733MmHCBA4ePMidd97JvHnziI2NZePGjZw+fZqwsDA8PT354osvqpwx99577wEwatQoI8p3ih+zz3Pwm+NYrc36rdBoggJv4MbYiEptXp4ejLmpv0EV1c/Y+EFYrZV/qYwY1Bd/v5YGVVS37p070qdnt0pt/r4tGH5jjEEVNa6mc+7ldZg7dy5vv/02M2bM4IUXXqBly1/eeJmZmQQEBODn58fSpUt55JFH6N27N7fffjv+/v4cPHiQHTt2MGfOHObOnWvgs2hcH+9Ow9vLkyH9+xhdSpM1emgc+78+RmFR2dK6kb+Jxa9lC4Orql3b1gH8pl8fPt93CChbOnfTgGiDq6rbrfE38s3xHyj979K6hOED8fT0MLiqxtFs55w/++wzhg0bRkJCAqmpqXXOqa5fv57p06eTm5tb0TZ06FCWLl3KkCFDGrXWx5etatT9i4h5LH1sZr36NdvPsi+++CIAS5curTOYFy9ezJQpU3jyySfJzMwkNzeXzz77jMLCQkaMGMGWLVucUbKISIVmO3L29/enTZs2fP/997X2+/jjjxk9ejQPP/xwlQsBnTlzhu7duxMcHMyxY8cas1yn+zH7PCvXbmL0kDhGD40zupxm4ez5n2nbJqBJrXwptdv56cIl2rYOMLqUa5J9/uc6lwQ2dc1yzvnChQvk5uYSF1d36KSmli0pio+Pr/JY+/bt6d27N/v37ycvLw9f38Y5ImzktMZHX/yHj75oWlcXE2nKXHpao/zDwNmzZ+vsW1xcdhCnpuVy586dw2q14uHRPA86iIhJOZqpHj16OCwWi2P79u1VHvv2228r7r/11lsOwBEZGem4cOFCpX4vv/yyA3AMGTKk0et1pn9u+tCx6IXXHAWXC40uRURq0GznnNevX8+kSZNwc3Pj9ttvJzQ0lLNnz7J7924iIiLYvHkzUHYhlJEjR/Lpp5/Srl07xo8fT0BAAGlpaezYsQMfHx927tzJwIEDDX5GDUNzzSJNQ7MNZ4APP/yQP//5z+zdu5fCwkLatWvHwIED+f3vf89NN91U0a+oqIgXXniB9evXc/ToUYqLiwkKCiI+Pp4nn3yS8PBwA59Fwzp89HtSd35J0v+6Ex9vL6PLEZEaNOtwlurZ7XadEShicgpnERET0vBJRMSEFM4iIiakcBYRMSGFs4iICSmcRURMSOEsImJCCmcRERNSOIuImJDCWUTEhBTOIiImpHAWETEhhbOIiAkpnEVETEjhLCJiQgpnERETUjiLiJiQwllExIQUziIiJqRwFhExIYWziIgJKZxFRExI4SwiYkIKZxERE1I4i4iYkMJZRMSEFM4iIiakcBYRMaH/D96iDHnZE7TTAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 457.52x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc4.add_register(cr4)\n",
    "qc4.measure(0,0) #MEASURE THE QUANTUM CIRCUIT (COLLAPSE THE WAVEFUNCTION) BY MAPPING TO CLASSICAL BITS\n",
    "qc4.measure(1,1)\n",
    "qc4.measure(2,2)\n",
    "qc4.draw(output='mpl') #draw the circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}