Initial_test.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Introduction to Quantum errors on Qiskit\n",
    "========================================\n",
    "\n",
    "Source:Introduction to Quantum Error Correction using Repetition Codes\n",
    "[https://qiskit.org/textbook/ch-quantum-hardware/error-correction-repetition-code.html]\n",
    "\n",
    "This is a \"pipe-cleaning\" exercise for an MSc Masters project to check that there are no issues with using the IBM Quantum experience."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculation of probabilities\n",
    "--------------------------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability of a single reply being garbled: 0.01\n",
      "Probability of a the majority of three replies being garbled: 0.0003\n"
     ]
    }
   ],
   "source": [
    "p1 = 0.01\n",
    "p3 = 3 * p1**2 * (1-p1) + p1**3 # probability of 2 or 3 errors\n",
    "print('Probability of a single reply being garbled: {}'.format(p1))\n",
    "print('Probability of a the majority of three replies being garbled: {:.4f}'.format(p3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Noise model\n",
    "-----------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.providers.aer.noise import NoiseModel\n",
    "from qiskit.providers.aer.noise.errors import pauli_error, depolarizing_error\n",
    "\n",
    "def get_noise(p_meas,p_gate):\n",
    "\n",
    "    error_meas = pauli_error([('X',p_meas), ('I', 1 - p_meas)])\n",
    "    error_gate1 = depolarizing_error(p_gate, 1)\n",
    "    error_gate2 = error_gate1.tensor(error_gate1)\n",
    "\n",
    "    noise_model = NoiseModel()\n",
    "    noise_model.add_all_qubit_quantum_error(error_meas, \"measure\") # measurement error is applied to measurements\n",
    "    noise_model.add_all_qubit_quantum_error(error_gate1, [\"x\"]) # single qubit gate error is applied to x gates\n",
    "    noise_model.add_all_qubit_quantum_error(error_gate2, [\"cx\"]) # two qubit gate error is applied to cx gates\n",
    "        \n",
    "    return noise_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "noise_model = get_noise(0.01,0.01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Call the function with 1% error for each type of noise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "noise_model = get_noise(0.01,0.01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now simulate a quantum circuit with noise of 1%."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The different states |000> etc can be counted.  The simulated result is {'000': 1001, '001': 9, '010': 9, '100': 5}\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 267.197x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import QuantumCircuit, execute, Aer\n",
    "qc0 = QuantumCircuit(3,3,name='0') # initialize circuit with three qubits in the 0 state\n",
    "qc0.measure(qc0.qregs[0],qc0.cregs[0]) # measure the qubits\n",
    "# run the circuit with th noise model and extract the counts\n",
    "counts = execute( qc0, Aer.get_backend('qasm_simulator'),noise_model=noise_model).result().get_counts()\n",
    "print ('The different states |000> etc can be counted.  The simulated result is', counts)\n",
    "qc0.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Even though there is noise the state |000> dosen't change much.  Now look at a more complicated example with parity checking of syndrome bits:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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SsLa2ZuXKlURERKDT6Xj77bcJCQnh+PHjeHp6AuWBmJKSwqhRowCIjIwkNDQUDw8P5s2bB2AyKxO3R1kZfBYLP52p+l5pGexOBZ0ORnS//bXdEVQjsnnzZgWolStXmn1/2bJlysrKSh04cMCkfd68eQpQhYWFSiml1q1bpwC1d+9ek35jxoxRgIqJiTG2bdiwQQFq7dq1Jn2joqIUoE6fPm1R7evXr1eA2r9/v0n76NGjFaDi4uKUUkqtXbtWASojI8OkX2RkpAJUbm6uUkqprKwsBajg4GBVUlJi7Hf06FEFqBUrVhjbUlJSFKB27NihlFKqpKRE6fV6NW/ePItqv5mKmlJSUn7XOPXhxXXlW2N2NOt6nTfbXlqv1IUrDV2pNjWqa4Tw8HAGDRrElClTzL7//vvv89BDDxEcHGzS7u3tDZTfKQN45513GDZsGPfdd59Jvy5dugCmi/Vz584lICCA8ePHU1JSYty6du0KwOnTpy2qfeHChQwfPrzKIrePjw+2trb4+fkBkJiYiMFgMM6aKiQmJuLu7k7Lli2B8lkXwIIFC7C2tjb269q1KzY2NuTm5hrbKu4o9urVCyif3V2+fNn4WjSMH34pn1lVp0xBQvptKeeO02jCKzMzk7S0NMaNG2f2/V9++YX09HQeeuihKu9lZGQA0KZNG7KyskhLSzOu/9woOzsbT09P42J9ZmYmx48fJyEhAVtbW5OtR48eADRr1qzG2rOyskhNTeXRRx81W5uvry/29vZAeUhVvmSE8gCqfMno6upaJajz8vIoKSnBw8PDZF83NzfjeVUEn7nj3A46na7et9t5rFvddu3/scY1LVVWSvi8vzV4rY1lq41Gs+aVnZ0NgLu7u9n3z549C5QHVGV79uzB398fg8HA999/D0Dr1q1N+ly6dIlt27Zxzz33VDnmJ598ctNZSsWMqToVMz5XV1eT9itXrhAbG8sDDzxgbEtOTjYu3lc4f/48cXFxvPrqq8a2+Ph4s+caFRWFlZUVQ4cONbZVDsTExERcXV3N7i9un+LL5ygrK8XKyvrmnXRWFF8uun1F3UEaTXi5ubkBkJqayoMPPljl/fbt2wPw008/mbTHxMSwd+9e1q5dC4CLiwtQvgB+4zjvvfceubm5JncaK2YvNjY2Zu9AWqrimCdPnjQJqsWLF5OTk2MMxgsXLlBUVGQyawJYunSp2cX63377jatXr+LgUH5PvbCwkHfffZeJEyeaXHYmJSUxY8YM4+u0tDTjZW9DULfhFtrM9bfvWLfq0M/w5Q/V99HpdGxdPZfWzebenqLuII0mvNq2bcuQIUOMazwBAQEUFBSwZ88eJk6cSHBwMCNHjmTBggU0bdoUb29vDhw4wKJFi3jmmWcIDQ0FwMvLi+7du7Nw4UKcnZ3x9vYmOjqayMhIwHS9y8PDg+HDhzN79mwKCgoICAiguLiYzMxMYmJi+Oyzzyy6S1dxzHfeeYcWLVrg7u7Opk2biImJMTmmk5MTbm5ubNy4kVGjRqGUYvXq1axYsQK4fpmXnZ3NmTNn6NChAxMmTGDatGnk5eUxf/58nJycWLZsmfHYp06doqioyCT4nJ2diY2NZfv27RgMBtq3b19lVlidTZs2Adcfkt2zZw/Hjx/H0dGRESNGWDzOH12v9rDzCJy/evNHIrp5QOuaVyaEOQ18w8BEfn6+ev7551W7du2UnZ2datOmjRozZozKy8tTSil17tw5FRYWptzc3JRer1eBgYFq1apVVcY5ceKEGjRokNLr9crFxUVNmDDBeEey4m5ehcLCQvXyyy8rb29vZW9vr1xcXFTfvn3VnDlzalX7iRMn1MCBA5Ver1eenp7qrbfeUosWLVI2Njbq8uXLxn579+5VXbp0Ufb29qpTp05q4cKF6vXXX1fNmzc39tmyZYsCVFJSknrssceUo6OjcnFxUWFhYers2bMmx920aVOVu6LHjh1T/fr1Uw4ODgpQ0dHRtToXwOzWrl27Wo1Tn7Rwt1EppX49p9Tbm03vMM5cX/7fZbuVuvJbQ1eoXTqlGvG8W+NCQ0NJTk7myJEjDV3KHafisnHpxIatwxLFJZCYfv0Ssrsn9PGCLm4gzwTfOvnW1aP4+HhN/A6lqF/2NtDvht/wmtIffD0kuH4v+fZZ4Mbnv8xt5iavFy9e5OTJk43qWatbOQ8hGisJrxqkp6dXeQas8rZmzZoq+zVp0oTS0lKmT5/eAFVXdavnIURj1WjuNjZWbm5uxo/RuZkOHTrcpmpu3Z1yHkJUkPCqgZ2d3e96BqyxuFPOQ4gKctkohNAkCS8hhCZJeAkhNEnCSwihSRJeQghNkvASQmiShJcQQpMkvIQQmiThJYTQJAkvIYQmSXgJITRJwksIoUkSXkIITZLwEkJokoSXEEKTJLyEEJok4SWE0CQJLyGEJkl4CSE0ST7DXog/gJkzZ5KUlNQgx/b392fp0qV1Pq6ElxB/AElJScTGxjZ0GXVKLhuFEJok4SWE0CQJL6EppWXwa9H112cvgFINV4+lLl69/nVGPhSXNFwtdwpZ8xKNXmkZpGTBdz/B6bNwrfT6ewu2goMtdHKFoI7Q0RWsdA1X641yz8O3P8GRDCi8fL39/Z2g04FrM+jdAf7kBU0cGq5OrZLwEo3aqVzY8D3kXbh5n6vX4Ehm+dbWABP6lQdDQ7l6DbYmwnc/37yPUpBzDrYehh1H4CF/CL678QSvFshlo2iUlILdKfDhnuqDq7KMfHgvBn48VX+1VedMESzeXn1wVXatFKIT4OP/lAefsMwdFV4pKSnodDp27NgBwKlTp9DpdGzcuNHYx1xbY5WTk4NOpyMqKqrafpXPG+Dy5cvMmTOHw4cP1+qYRUVFPPvss7Rq1Qq9Xk9QUBAHDx68pfp/j50pEHMEbmU5q7QMNhy6/QF29nx52BZcurX9T/5aHmBaXg9r2rTpbTvWHRVebm5uHDp0iMGDBwOQkJAAQEBAgLGPubbGKj4+HoDevXtX26/yeUP5cz0RERFcuGD5tEUpRUhICNHR0SxZsoStW7fi4uLC/fffX+sQ/D2O/Q92pVTfZ+nE8q06X/5gurhfn0rLYPVBuFh88z6W1JyeV37J2ZDs7Ox45JFHeP/999m3bx9Hjhzh8OHD/N///R/h4eE3/fO4bNkyvvvuO1q1anVb6ryj1rwMBgMGg8H4OiEhAWdnZ7y8vKpta6zi4+NxdnbGx8en2n6Vzxvg8OHD6HQ6/P39LT7etm3biI2NJSYmhhEjRgDQv39/fH19efPNN4mJian9SdTS1WvloVMXKmZgM4fV/1rS3jTILqybsb79CfzbQcfWdTOepezs7Hjttdd4/vnnad266sH9/f0JCQlh7ty5xMfHExERwbZt24Dy4Jo+fTrFxcX4+vqSm5tb7/XW28xr//79jBo1Ck9PTxwcHHB3d+epp56iqOj6X4UBAQGMHz+ezZs306dPH/R6PR06dODLL780O+bWrVsZMmQIzZs3R6/X4+fnx6pVq4zv9+nTh7FjxxpfJyQkVJlhVW6zpE5LlJWVsWTJEjp27IiDgwM9evQgNjaWu+++m7CwMGO/0tJS9Ho9ERERJvuXlJTg4ODAokWLTGoNDAxkw4YN+Pv7o9fr8ff35+uvvzbZt/J5+/n58cILL6CUolmzZuh0Ovr27VvjOWzZsgWDwcDw4cONbXZ2dowbN449e/Zw6dItXg/VQvxpOHe55n6WysiHn36tu/HM+a0E9h2r2zG/Plq349XE39+fxMRE5s6dS+vWrUlOTiY8PJwRI0bQo0cPAgICmDBhAh9++CH5+fkEBgby73//m7Vr1/LRRx8Zg2vUqFHs27fvttRcbzOv5ORk7r33Xp5++mmcnJw4duwYb731FgCfffYZJSUlHD16lMLCQnJycpg9ezZNmzbl7bff5sknn2TEiBEm18/h4eEsWLCASZMm8dxzz3HXXXdx8OBBCgoKgPJQSElJYdSoUcZ9EhMTefrpp03qqtxWU52WmjJlCtHR0YSHhxMQEMB3333H+PHjOXv2LLNmzTL2O378OFeuXKFnz54m+x89epTi4mKT9oSEBKytrVm5ciURERHodDrefvttQkJCOH78OJ6enmbPOzIyktDQUDw8PJg3bx5AlZmZOampqfj6+qLTmU5TunXrRklJCcePH6/3y+1vT9b9mAdPwt1t6n7cCkkZcOW3uh3zRE75M2wtnep2XHOCgoLYsWMHTk5OnDhxgmnTppkNoMTERKKionj11VeZNm0a8+fPJzQ0FMAYXDt37qz/gv+/eguvF1980fh1WVkZ99xzD8nJyezduxeAtLQ0iouL6dSpEzt27DD+wBQXFxMSEsJ///tf/Pz8APjqq6+YP38+K1euZMqUKcZxKy5tAI4dO2YSCqdPn6agoMDkh81cW011WmLDhg2sWbOG/fv3M2DAAAAGDRpEYmIiX331lcnxEhPLFzQqh1fFmlJFe3Z2Nr/++ivBwcHs3r0ba2trAHx8fPD19WXbtm1MmzatynlXjJGRkcHEiRMtmnFVKCgooGvXrlXaW7RoYXy/Pl24Cjn1sEb10xkoU/V36Xgyp37G/enX+g+vDh06sH37dpycnNiwYQNTp07l6tWr1e5z9epV/v73v9OzZ09jeB09epRdu3bVb7GV1MtlY2lpKevXr+fee++ldevWWFtbY2try0cffUSTJk2A6z+sFTOKChU/IO7u7sa28PBwBg0aZBJclVWM16tXL+D6wnxgYKCxT+U2S+q0xMKFCxk+fLgxuCr4+Phga2trDGEoDy+DwYCnp6dJ38TERNzd3WnZsqVJrQsWLDAGF0DXrl2xsbExrilUPm8on91dvnzZpM0SSqkqsy7AbFt9yMyvn3GvXqvd4xa1lVlPmV5f41bQ6XSsWrWKZs2asWXLFkJDQ2sMrgrLli0jNDSU4uJizp07R69evXj22Wfrt+BK6mXmNWnSJKKjo3nhhRd47bXXcHFxwcbGhiFDhtCtWzeg/IfO2dmZP/3pTyb7Jicn4+HhYfzbPjMzk7S0NJMZkjmHDx/Gzc3NeKejYmG+Q4cOxj6V2yypsyZZWVmkpqby0ksvVXkvIyMDX19f7O3tjW2JiYlVZl0V9Ve+ZHR1dSU4ONikX15eHiUlJXh4eJg974p9oersriYGg8Hs7KqireL/SU1uNex8Bz7FkKc+NWmr6e7czd6fud70dUDfQWQd239LddXk2X+ew15//anYuqp5w8ZtjOv78O+s7uYeeeQRBg4cyJkzZ5g6dSplZWUW7Xfj4vyoUaPQ6/Vs3ryZd999l88//5yLFy+a9I+NjbX4z4Sqxe961fnMKyUlhQ0bNrBs2TIWL17Mww8/TL9+/fjtt984f/688RLq8OHD9OrVq8pJJSQkmMwYsrOzAdOZmDmVQ6GmxXpL66xJVlYWAK6uribtV65cITY2tso4ycnJVULl/PnzxMXFmbTHx8fTpk3VhZqoqCisrKwYOnSo2fOuaHN1dTW7f3V8fX1JS0ur8gcoNTUVGxsbOnfuXKvxaqteZ3haHLueZ7zPPfccAPPmzSM/37Jpb+Xg2rlzJ1999RUHDhygadOmPP744/VZsok6n3llZmYCmKydXLt2jZdffhkov8OolCI5ObnKNLOsrIykpCSTBW43Nzeg/AfowQcfvOlxk5KSmDFjhvF1TYv1ltRpCRcXFwBOnjzJAw88YGxfvHgxOTk5JkF84cIFioqKjLOmCkuXLjW7WP/bb79x9epVHBzKf/GtsLCQd999l4kTJxovOyufN5SvJ5pbu6pJSEgIq1atYteuXcY7jteuXeOLL75gyJAhODo6WjRObf72vNGRTFh1wLSt8mykQsXs5WbvV/bDwf/g5nxLZdVo3hbIv2GyUVc1jx39IFveq5vfOh84cKDJ53m1bt2aQYMGcenSJdauXWvRGOaCq8JHH31E//79GT9+PB9//LHJfgMGDGD//v11ch43qvPw6tGjBw4ODvzlL3/hrbfeIj8/n/fff5+CggKsrKzw9/fn1KlTFBUVVQmIkydPcuHCBZMf+LZt2zJkyBDj2k9AQAAFBQXs2bOHiRMnEhwcbByv4oc/PT2d/Px8k/Ert1lSpyW8vLzo3ujLDT4AAA7ZSURBVL0777zzDi1atMDd3Z1NmzYZn4m6sQYnJyfc3NzYuHEjo0aNQinF6tWrWbFiBWC6WH/mzBk6dOjAhAkTmDZtGnl5ecyfPx8nJyeWLVsGUOW8Kzg7OxMbG8v27dsxGAy0b9++yszQnIcffpjg4GAmT57M4sWLadOmDcuXLycjI6PGp/zrgqdlV6W1ZmsNrevxdx09WpiGV52NW09hC9fXfX/44QeLHmSuLrgA4+M7vXr1wsrKyuJL0N+jzi8b3d3d2bBhAzk5OYSEhPC3v/2NV155haCgIDp37oyjo6NxkfnGxXS4vlZTeaH5yy+/ZNKkSSxfvpzhw4czffp08vPzjbOLynfqLHmy3pI6LWFlZcXGjRvx9fVl2rRpTJ48GRcXF55//nlsbGzo3r27Sf/PP/+c/Px8OnXqxNChQ7G3t2fq1Kk0b96c9u3bm9QaHR2NnZ0df/7zn5kxYwb33nsvBw8epHnz5mbPu0JERAReXl6MGTOGfv368f3331t0Ljqdjq1btzJy5EhmzZrFww8/TG5uLrt3774tv5HQXA/Oln3ba6W9C1jX4++SeNfTA+X1NS6ULxFA+TJGTWoKLihfi83OzqZJkya0bdu2zus1R6dudY4vqhUaGkpycjJHjhxp6FI0ZXcqxNT881SrS7An7oWe7X5fXdW5XAx/jTb9qB5zalNzWwPMGl5zP0tVvmzs378/gwcP5ptvvqny0PONHn30Uf71r39Z9BzXSy+9hJOTEytWrCAvL8/YrpnLRlEuPj6+Vs9YiXL9fOA/aXX36QqGJuDnUXO/30NvD3294Zs6fMB2UJe6G8ucAwcOcODAgRr7bdq0iQ8++ICdO3fW+ADq3//+97oqzyJ31C9m14eSkpJqN3MT14sXL3Ly5MlaP2dVn27lPBqCkwOMqsMr1PF9wca65n6/14P+4Kyvm7G6eYD/7bnyqpFSipkzZ97WJ+ctJeFVjfT0dGxtbavd1qxZU2W/Jk2aUFpayvTp0xug6qpu9TwaSh8vCGhffZ+Z62u+/BrmBz636ZebHWwhNKj6oLSkZkMTeOxP9f6UxB1BLhur4ebmRlxcXLV9bnwItrHS2nnodOWfhqoD4tNvbYz7fWG4X8396pJXKwgbCCtjb+0zuVo6wbT7wOmuOi/tjiThVQ07O7sqd0S1SIvnYW0FE+8p/0z66ATL18Ca3QWP9YGu1T/TXG86ucKrD0LU9/DzGcv3C+oID/csn8EJy0h4iUZLp4M+3tDVDQ79Uv4PcNzs43JaN4V7O0Fvr4YPAEMTeG4wHMsu/2yuY/8z/4mwdtbQqz0Edaq/Z9zuZBJeotFzuguGdiu/FCy4BFkF5f+UmE5XPtPyMJT/tzGx0oGvR/lWfK38gwpzz0NJGdjZgFtzaNO8fp8/u9NJeAnN0OnKZzUGyz/wo1Gwty1fD/O6PZ+O/IchuS+E0CQJLyGEJslloxB/ALX5h1gqnMoo/4hYr7ZtTL6+Hce2hPxuoxDCrL8s+icA774WZvJ1YyGXjUIITZLwEkJokoSXEEKTJLyEEJok4SWE0CQJLyGEJkl4CSE0ScJLCKFJEl5CCE2S8BJCaJKElxBCkyS8hBCaJOElhNAkCS8hhCZJeAkh6sX+/fvx9fXFx8eHp556itLS0jodX8JLCFHnysrKeOqpp9i4cSM///wz58+fZ926dXV6DAkvIUSdi4uLw83Nja5duwIwdepUNm/eXKfHkPASQtS5rKwsPD09ja/btm1LZmZmnR5DPsNeCAFAmVL8a9s+zuQVmrR/ELnZ7NdBgd0I9Lvb7FhKKXQ6ncnruiYzLyEEAFY6HcF/6k5uXiE5ufnG9spfV7z27+pz07E8PT3JyMgwvs7MzMTDw6Nu663T0YQQmube2oUh9wZU28fG2prHHhqEjbX1TfsEBgaSnZ1NWloaACtXrmT06NF1WquE1/+Xnp6OTqdj9erVDV1Kndu/fz86nY5t27bV2Ld9+/Y8+eSTxtdff/01c+bMqb/iRKPTv08P2rm3vun7w/r3xrVli2rHsLa25tNPP2XMmDF4e3vTpEkTQkND67ROWfMSJqKjo2natKnx9ddff82iRYskwP5ArK2sGPvgID6I3MRv10pM3vNq60ZQbz+LxrnvvvuMM6/6IDOvWiouLm7oEupVz5498fb2bugyRAMzODflofv6mbTZ29ky9sGBWN2wEN+QGkV4nTlzhilTpuDh4YG9vT2urq4MHTqUkydP4uvry8MPP1xln2PHjqHT6Vi1ahUAq1evRqfT8c033zB58mScnZ1p1aoVkyZN4ty5cyb7FhYW8uSTT9K8eXOcnJwYPXo02dnZVY7x5JNP4uLiwg8//MC9996LXq/ntddeA+CXX37h0UcfpUWLFjg4OODv71/lIbyKmvbt28e4ceNo1qwZLVq0YPbs2ZSVlfHjjz8SHByMo6MjXbp0YcuWLVVqSEtL45FHHsFgMODg4ECvXr3M9rPExYsXCQsLw2Aw4OjoSEhISJXb1zdeNs6ZM4dFixYBoNPpjJv4Y+jdozOdvdsaX4fcH0Tzpk0asKJKVCNw//33Kx8fH/X555+r2NhYtXnzZvXiiy+qH3/8US1fvlxZWVmp9PR0k31mzJihmjdvri5duqSUUioyMlIBysvLS73yyitq9+7d6oMPPlAODg7qiSeeMO5XWlqqgoKClF6vV0uWLFG7du1SM2fOVJ6engpQkZGRxr5PPPGEuuuuu1S7du3UBx98oP7zn/+oQ4cOqf/973+qVatWqm3btioyMlJt375djR07VgFq+fLlxv1vrCk8PFzt2bNHvfzyywpQL774ourUqZNauXKl2rlzpxo8eLCytbU1Oc/k5GTVpEkT1adPH/XFF1+onTt3qtDQUKXT6dRXX31l8fd33759ClAeHh5q3LhxKiYmRn366aeqZcuWysfHx/g9VEqpdu3aGb9fmZmZKjQ0VAHq0KFDxk38cZy/cElFfLBaff7VblVWVtbQ5ZhoFGte3333HQsWLODxxx83tlXcmejcuTOvv/46//znP1mwYAEAV65cYe3atTzxxBPo9XqTsUaPHs3ixYsBuP/++zl58iSfffYZkZGR6HQ6du7cybfffstnn33G1KlTARg6dCiXLl3i008/rVLblStXWLJkCWPGjDG2vfrqq+Tl5XH06FE6d+4MwAMPPEBubi7h4eE8/fTT2NnZGfuPHTuWuXPnAjBkyBC2b9/OBx98wLfffss999wDQMeOHfH29mbz5s3MmjULgNmzZ9O6dWv27dvHXXfdBcCwYcPIzs7mjTfe4M9//nOtvs/t27cnKirK+Lpjx44MHDiQNWvWMG3atCr9PTw8cHNzA6Bv374WH6fin4YXd47Uk6d5fXHVn4+69u5rYRb3bRSXjb179+a9995j6dKlpKSkmDzQ5uTkxKRJk1i5ciXXrl0D4IsvvuDcuXM8++yzVcaqfInp5+dHcXExZ86cASA2NhaAcePGmfSbMGGC2dp0Ol2VMffv30+vXr2MwVVh0qRJFBYWcuTIEZP2Bx54wOR1ly5daNq0qTG4ALy8vLCzszM+G3P16lX27dvHI488gq2tLSUlJcZtxIgRHD9+nNzcXLM130zlcx4wYACurq7G74kQWtIoZl7/+te/iIiIYMmSJbz00ku0atWKyZMnM2fOHBwcHHjhhRf4xz/+wVdffcVjjz3Gxx9/zH333VclPABatDC9hWtvbw+UhwFAfn4+TZo0wdHR0aSfq6ur2dqcnZ2NY1QoKCigS5cuVfq2adPGeIzKY9zIzs6uShuAra2tSZ0lJSUsXrzYOJOsLC8vj1atWpl9zxxz59i6desq9f5etfnbU4hb1SjCq2XLlixfvpzly5dz6tQp1q9fz5w5c7CxsWH+/Pl07tyZwYMH8/HHH3P33Xfz448/snHjxls6lsFg4OLFi1y6dMkkwH799Vez/c0tUBsMBrP9c3JyjO//Xs7OzlhZWfHUU0/x9NNPm+3j5eVVqzHN1XzmzBmzfwn8HnLZKG6V5i4bb+Tl5UV4eDidOnUiJSXF2P7888+zf/9+Zs2aRZs2bRg1atQtjT9gwACg/NLzRhs2bLB4jIEDB5KYmMjx48dN2tevX0+LFi3o3r37LdV2I71ez4ABA0hKSqJnz54EBgZW2RwcHGo1ZuVzjo2N5ddffzV+T8ypmHVeuXKl9ichRD1q8JlXUVERgwcPZsKECXTp0gV7e3t27drFiRMnmDFjhrHfyJEjadu2Lfv27SM8PBwbm1srffjw4QQFBTFjxgyKioro1q0bO3fuZNeuXRaPMWvWLNasWcOwYcOYO3curVq1Yu3atezdu5ePPvrIZLH+91i6dCnBwcEMGjSIsLAwPD09KSgoIDU1lZ9//pk1a9bUarz09HTGjx/PpEmTjIv+Pj4+PPHEEzfdp+IjTd577z2GDRuGtbU1gYGB1R5HLhvF7dDg4eXg4EBAQACrVq3iv//9LwDe3t784x//MLkDZm1tzejRo/nwww8JC7v1Hw4rKyv+/e9/M3PmTCIiIigrK+P+++8nKiqKoKAgi8Zo3bo13333Ha+99hozZ87k8uXLdO3alfXr19904f9WdO/enfj4eCIiInjllVfIz8/HxcWFbt26mdyZtdSSJUvYu3cvjz/+OFevXmXw4MEsX768yh3bGz3yyCM8/fTTfPjhh8yZMwelVL18QoAQtaVTGvmTWFZWRufOnfH19SU6OrqhyxFCNLAGn3nV5MKFCxw7doyNGzfy008/3ZG/OC2EqL1GH14JCQkMGjSIli1bsmTJEpNnowSUlJRU+761tbX8So+4I2nmslFUlZ6eTocOHartExkZafIRN0LcKSS8NOy3336r8jR/ZR06dKiT586EaGwkvIQQmtToHlIVQghLSHgJITRJwksIoUkSXkIITZLwEkJokoSXEEKTJLyEEJok4SWE0CQJLyGEJkl4CSE0ScJLCKFJEl5CCE2S8BJCaJKElxBCkyS8hBCaJOElhNAkCS8hhCZJeAkhNEnCSwihSRJeQghNkvASQmiShJcQQpMkvIQQmiThJYTQpP8HDBIGEf+pbrkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 382.292x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import QuantumRegister, ClassicalRegister\n",
    "cq = QuantumRegister(2,'code_qubit')     # Two code QBits\n",
    "lq = QuantumRegister(1,'ancilla_qubit')  # One Ancilla bit\n",
    "sb = ClassicalRegister(1,'syndrome_bit') # One Syndrome bit\n",
    "qc = QuantumCircuit(cq,lq,sb)\n",
    "qc.cx(cq[0],lq[0])\n",
    "qc.cx(cq[1],lq[0])\n",
    "qc.measure(lq,sb)\n",
    "qc.draw()\n",
    "#initialise circuit\n",
    "qc_init = QuantumCircuit(cq)\n",
    "(qc_init+qc).draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results: {'0': 1024}\n"
     ]
    }
   ],
   "source": [
    "counts = execute( qc_init+qc, Aer.get_backend('qasm_simulator')).result().get_counts()\n",
    "print('Results:',counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results above are always 0 for the |00> QBit input from initialisation.\n",
    "\n",
    "Moving on, we now import the necessary tools from Ingis.\n",
    "  Repetition Code sets up the gates for the Repetition code.\n",
    "    These are decoded with either:\n",
    "        Look up table decoding\n",
    "        Graph decoder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.ignis.verification.topological_codes import RepetitionCode\n",
    "from qiskit.ignis.verification.topological_codes import lookuptable_decoding\n",
    "from qiskit.ignis.verification.topological_codes import GraphDecoder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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erfZzoGrTjZyHMxgM8PBQaFoDvz4YgEeGgZtrlU1vSm6u5utTE0N0TVwhYpj56yc3lx9//LHKMCVS3yhQ1bHs7GyaNGlS6RITE1NuuxYtWlBcXMycOXOcUHV5N3oezmJsAVOGV/6Dft7bVQ9BPXgb/KptzdbW2HQ0wqTbKm9T1bV2McDk4dCuZc3WJiJSWzTkV8d8fHxISEiotI1l4mZ91hDPo68fTBsBG/5T/bv+3FwhfDAM0dxXuwz1BxcX2PKl+c//VId7E/Mctb5+VbcVEakvFKjqWNOmTcvdKdgQNdTzCPCDp8aZf9AfOWHfNl3amYcMb9Wt+9VyW1fo0hY2fQ5ZP9i3TR8fCL8NvOx/PJmISL2gQCU3HU8P+MOd8N9z8Nk35snqP5y3fX6SsQV0bQ+3+5sfkaB5PDemXSuY8xv4/iz85xvzwz/PXizTpiV094bh3cHXyzl1iog4SoFKblo+XubeEDAPAT71L/PHLzwIHs2uv51Uj8FgDqWdf557dvkqPG3+27YsnmQe4hMRaeg0KV0E2x/qClO1y6PUA1EVpkSksVCgEhEREXGQApWIiIiIgzSHSkREakVQUFC1t8k6bn7yeddOHWw+ru3jijhKgUpERGrFsmXLqr3NU0veAGDxn6fbfCxS32nIT0RERMRBClQiIiIiDlKgEhEREXGQApWIiIiIgxSoRERERBykQCUiIiLiIAUqEREREQcpUImIiIg4SIFKRERExEEKVCIiIiIOUqASERERcZAClYiIiIiDFKhEREREHOTm7AJERETqi3nz5pGamuqUYwcFBbFs2TKnHFscp0AlIiLys9TUVOLi4pxdhjRAGvITERERcZB6qEQasKJiuFYMTVzBzdXZ1TRuV4uguETXWkQqpkAl0oAUl0DGCUj+HnLOwpmLv7xmbAEd28DAzhDgC67qf3ZIUTGk5UDacfO1PnfZvN4AtGsFnYwwqAv08AYXg1NLFZF6QIFKpIE4lAPbE3/5wV7W2YvmJfU4eHrAfcHQv1Pd1tgYmEzwZRb8OxUu/lTB68Dp8+Yl8Tto1xIeHAw9O9R5qSJSjyhQidRz14rhX19Awnf2b/PjZVj7KQR3hoeHmoeppGo/XYMNn8GRE/Zv88MFeO1jCOkJ9w0EF/UMityUFKhE6rGiYlgdB5l5N7Z9Ura5l+UPd2reT1V+ugav7oPjZ29s+0+/hks/wW9vV6gSuRnpbV9GVlYWBoOBLVu2AHD48GEMBgO7d+92eF/1RV5eHgaDgU2bNlXarqJzv3z5Ms8++ywpKSl2Hy83N5e5c+dy++234+HhgcFgID09/Ybrv5nsSKk6TC2LNC/X8/VJeC+pZutqjN75vPIwVdV1BvPcto+O1GxdUr/16NGDRx99lP/3//4f69atY9WqVTz99NOMGTOG5s2bV7jNE088wYYNG3BR8m5U1ENVRlKS+SdPcHAwAD4+PsTHxzNw4MAb3tegQYNqrsAakJiYCMDgwYMrbVfRuaemphIdHc1dd91l9/G+/fZbNm/eTHBwMKGhoXzwwQc3VvhN5tgpOPB1zezr4Dfm+VTdvWtmf41N6vfmuWc14cPD0NcPfLxqZn9SPz344IPMmzeP4cOHX7dNQUEBMTExvPjii+Tm5gLmMPXyyy8DsHbtWj7++OM6qVdqnwJVGUlJSXh5edG1a1cAjEYjRqPxhvdlNBrp0qVLTZbosMTERLy8vPD396+0XUXnnpKSgsFgICgoyO7jjRgxglOnTgGwbt06BSo7xR6q4f2lwR8VqMopMcGutJrbX7HJHKqmjqi5fUr94ePjwxtvvME999wDmEPTnj17SE5O5uTJkzRt2pTevXtz++23c9tttzF37lx+97vf8T//8z+0bNnSGqb+8Ic/KEw1MupvLCMpKcnaOwUwZMgQJk2aZNMmODiYiIgI3n33XYYMGYKHhwddunRh8+bN5fZVuneqsLCQWbNm0bJlS/71r3/ZVU9JSQkvvfQS3bt3x93dnf79+xMXF0fPnj2ZPn26tV1xcTEeHh5ER0fbbF9UVIS7uztLliwpV9fGjRsJCgrCw8ODoKAgPvroI5tty557YGAgs2fPxmQy0bp1awwGA0OHDq3yHNStXX15P8Kx0zW7z+/OQG5+ze6zMfjmpHlieU06nGu+MUAal169evHll19yzz33cO7cOR5//HF8fHyYNGkSixcvZt26dbzxxhs88cQTDBkyhP79+7N9+3ZatWrFm2++aROmVq1a5eSzkZqmn3RlJCcnWwNVcXExhw8fZsCAAdbXi4qKOHLkCF988QXLly/nySefZPv27bRv357f/e53nD9/3mZflmG1rKwsbr/9dj755BO+/PLLciHteqKionjuueeYMWMGu3fvZtKkSURERJCVlWUT/DIzM7ly5YpNrQBHjhyhsLDQZn1SUhIZGRmsXr2a6Oho3nnnHQAmTJhATk7Odc997dq19OrVi1GjRhEfH098fDwbNmyw6zykeqpzl1l1ZNTSfhuy9Fq4JiUmyPxvze9XnMfb25uPPvoIX19f4uLi6NOnD6+99hqXL18/OR86dIj777+ft99+27pu586dClONlIb8Svnuu+/Iz8+3BpWvvvqqXEjJyMigsLCQHj16sHv3bgwG8xP9CgsLmTBhAt9//z2BgYHWfQ0aNIht27YRFRVFWFgYq1atokWLFnbVs3HjRmJiYti/fz+hoaEAjBw5kuTkZLZt22YTqJKTkwHKBSrL5HHL+hMnTnDy5ElCQkLYs2cPrq7mW7/8/f0JCAhg586dzJw5s8JzHzBgAMePHycyMtKunim5cTm11JNUW/ttyHJv8K6+quTkg94ljcfKlSvx9fXl008/JSwsjJ9+quAhZRV44okniIw0381QXFzM3XffzbBhw4iPj6/NcsUJFKhKKTuJ3BJGSk/KtqyLjo62himA/HzzTypfX1+bfW3cuJH33nuPpUuX8sc//rFa9SxatIiwsDBrmLLw9/enSZMmBAYGWtclJydjNBrp2LGjTdvk5GR8fX1p166dTV0LFy60himAPn364ObmxunTp6977pmZmVy+fPmGJujXhNLXuzb88S1TnRzHHhHPJ9O+s204ruoOs4pen/e27eefxB/m93f2c7A6x9Wna/37FXk097SdXFbZtb7ea2Wv9cZte5g0ZIyD1d18/rz4dcD8vVH6Y2e69957mTBhAgUFBURERFQrTJUe5uvSpQtPP/00b7zxhs3/3xZxcXFOP1cpz2Qy2dVOQ36lWCakWyaRp6Sk4OPjQ/v27a1tUlJS8PLy4rbbbrPZNi0tDT8/P9q0aWPdV6tWrXjvvfeIiIiodpjKzc0lPT2d8PDwcq8dP36cgIAAmjVrZl2XnJxcrnfKUm/Z4T5vb29CQkJs2p05c4aioiL8/Pyue+6WMFbRcaRmubjWzu86Lq5NamW/DVmtXWsX/b7aWMydOxcw/yJ94oR9Y8Rlw9SqVauIjo4mNzeXvn37MnLkyFqrV5xD7/hSyk5IryikpKSkMHDgwHK/RSQlJdn03CQlJTFixAgeeughpkyZwh133MHvf/97u2ux3GLr7W37m/OVK1eIi4vj7rvvtlmflpZmM0kd4Pz58yQkJPCnP/3Jui4xMZEOHcr/jYxNmzbh4uLC6NGjgYrPPTk5GW9v7wq3rwv2/pZwoyw9DLV9HHv8Yw9894PturI9IBaWHpPrvV7agMBerK8H51efrvVz75v/ZE9pFV3L6lxngLvH3MW7Lzj//Bqap5a8AZi/N0p/XFfuvPNO4uLirJ/7+fkxatQoLl26xJo1a+zaR0VhCuDq1au88cYb/P3vf2fq1Kl88sknNtuFhoayf//+mjkRqXPqoSolOTnZ5q681NRUm5BkMplIS0sr91ypkpISUlNTbQKIJZD89re/5dlnn2XmzJl8+OGHdtfStm1bAI4ePWqzfunSpeTl5dnUdeHCBQoKCqy9SxbLli2rcEJ6dna2TZf1uXPnWLx4MZGRkdYhw7LnDub5Y3369LH7HOTG+dbSM4xqa78Nma61VGbIkCGAeTiuoKCgyvbXC1MWO3bssNmvNB7qofpZdnY2Z8+etfZQZWVlUVBQYBNGLOtK92KBOfRcuHDBGkAs+7Js+8wzz5CVlUV4eDiffvop/fv3r7Kerl270q9fP1544QXatGmDr68vW7duJTY2FsCmhpYtW+Lj48OWLVuYOHEiJpOJdevW8eqrrwK2E9JPnTpFly5deOSRR5g5cyZnzpzh+eefp2XLlrzyyivXPXcALy8v4uLi2LVrF0ajkc6dO5frQbuerVu3Ar88VHTv3r1kZmbSvHlzxo4da9c+biad28LBo1W3q65fta35fTZ0vzKa//B0je9X17pRsPx/bbnxpzJVhSn45c7rHj164OHhUeldgtKwqIfqZ2WfkF727rjS68r2UFm2tQSqiuYavfnmmwwePJh77rnHOpxXGRcXF7Zs2UJAQAAzZ85k6tSptG3bllmzZuHm5ka/frYTizds2MDZs2fp0aMHo0ePplmzZkybNg1PT086d+5sU9f27dtp2rQp9913H3PnzuWOO+7g4MGDeHp6XvfcwTx/oGvXrjz44IMMGzaMzz//vMrzsAgPDyc8PJx//vOfAMyfP5/w8HBmzpxp9z5uJoEdwb2Gpzs1czM/LV1sDeoCLjU8D9jTA3roIaqNQnZ2Nrt27aoyUEVGRtr1nKmioiLee+893n//fZo00ZzGxsRgqg+TGMRukydPJi0tjUOHavgx2mKdG1PV3XR15b0k2J9ZdTt75/aM6An315O/glTfrvX6g+a/w1eZ6syhGhcEowIcr+tmZJk3tfjP020+ritl51DZy9PTkw8//JA333zzhp8zpTlUDZuG/BqYxMREPQPqJhHWD9KOw7kaGBFofYt5f1KxCQPhq//ClWuO76tDa7izl+P7kYblxx9/5Pbbb6e4uNjZpYiTKFA5SVFRUaWvu7q6lruT8OLFixw9epTHH3+8Nkurlhs5D7GPexN45HZYuc/89+Gup6oeExcDPDIMPJrWbH2NSWsPeGgIrDt4/Tb29Ew1dYPI28HNteq20vgoTN3cNIfKCbKzs2nSpEmlS0xMTLntWrRoQXFxMXPmzHFC1eXd6HmI/brfCo+GgOsNvlNdDTDlDujpnCddNChBvzKHqhuN/03d4A+h4NemRssSkQZCPVRO4OPjQ0JCQqVtLA8Xrc8ay3nUd/06wh9Hw8Z4OFn1XdtW7VuZe6Y6624zuw3zB2ML2PQ5nLtk/3Yd25ivdQfP2qtNROo3BSonaNq0abk7BRuixnIeDUEnIzw5Fg5+A58dhR8uXL9t25YwvDvc0QOaaOip2np4w5/vgQNfw3++gR8rmcPWwRNCesCQbjfeiygijYMClUgD4eZqnuw8oiecyIfj+eYeq0+/Nr8ePhg6Gs1DTjX9GICbjXsTGN0Xft0Hjp+F3Hx41/wINUb0BB9Pc8jt4AmaIigioEAl0uC4GMzBqaPR/LklUA3v4byaGitXF+jSzrxYAlV9efSEiNQv6qQWERERcZAClYiIiIiDNOQnIiLys6CgoGpvk3U8D4CunTrYfFwXx5b6Q4FKRETkZ8uWLav2Ns7+czlSP2jIT0RERMRBClQiIiIiDlKgEhEREXGQApWIiIiIgxSoRERERBykQCUiIiLiIAUqEREREQcpUImIiIg4SIFKRERExEEKVCIiIiIOUqASERERcZAClYiIiIiDFKhEREREHOTm7AJERKRy8+bNIzU11SnHDgoKYtmyZU45tkhDokAlIlLPpaamEhcX5+wyRKQSGvITERERcZAClYiIiIiDFKhEREREHKRAJSIiIuIgBSoRERERBylQiYiIiDhIgaoGpKWlYTAY2L17t7NLqVJeXh4Gg4FNmzZV2fbw4cM253X58mWeffZZUlJSqn3cgoICHnvsMdq3b4+HhwfDhw/n4MGD1d6PiNjP29ubgIAAevfuTcuWLSttazQaGTNmTB1VJtL4KFDVgISEBACCg4OdXEnVEhMTARg8eHCVbX18fIiPj+fXv/41YH4WTnR0NBcuXKjWMU0mExMmTGD79u289NJL7Nixg7Zt2/Kb3/zmhsKZiFTMYDAwepS9EPYAACAASURBVPRotmzZQl5eHnl5eaSnp5ORkcH58+f5+uuvWb58OX369LHZzmg08vHHH/Pvf/+bsWPHOql6kYZND/asAQkJCfj5+dG+fXtnl1KlxMREvLy88Pf3r7Kt0WjEaDRaP09JScFgMBAUFFStY+7cuZO4uDhiY2Ot/1mPGDGCgIAA/vrXvxIbG1u9k6gFJ8798vF3P0DntmAwOK8ekeoaPHgwq1evJjAw0Lruxx9/5MSJE7i6utKlSxd69OhBjx49mD17Nlu3bmXWrFkUFxfz8ccf069fP7766iv9kiNyg26aHqodO3YwatQoPD098fDwIDAwkDVr1gDmHpSVK1cycOBAPDw86NSpE/PmzePixYs2+ygpKWHp0qX4+/vj7u7O8OHDycjIICEhgUGDBpU75ltvvcXw4cNp3rw53t7eTJ06lfz8/GrVXVJSwksvvUT37t1xd3enf//+xMXF0bNnT6ZPnw5AcXExHh4eREdH22xbVFSEu7s7S5Yssa5LSkpi0KBBbNy4kaCgIDw8PAgKCuKjjz4qd+whQ4YwadIkAAIDA5k9ezYmk4nWrVtjMBgYOnSoXefw/vvvYzQaCQsLs65r2rQpDz/8MHv37uXSpUvVuiY16exF+MceeLFUpvvHHlgaC7nV+1KJOM2f/vQn4uPjCQwM5Pjx4/zlL3/B398fLy8v+vbtax3yGzJkCK+99hqXLl3iwQcfJCMjgy+++MIapu666y5Onjzp7NMRaZBuikC1YMECJk6ciJ+fH2vWrOHdd99l/Pjx5OfnU1JSQmRkJE8++STh4eHs2rWLp59+mnXr1jFt2jSb/URFRbFw4UKmT5/O7t27CQsLY/z48aSnp5cb7pszZw5RUVEMHTqU7du3s2jRIj744AMeeeSRatUeFRXFc889x4wZM9i9ezeTJk0iIiKCrKws6zEzMzO5cuUKAwYMsNn2yJEjFBYW2qxPSkoiIyOD1atXEx0dzTvvvAPAhAkTyMnJsbYrLi7m8OHD1m3Xrl1Lr169GDVqFPHx8cTHx7Nhwwa7ziE9PZ2AgAAMZbp8+vbtS1FREZmZmdW6JjWl4LI5PGX/UP61kz/C8r2Q92Pd1yVSHc888wxLlizBYDDw4osv0rNnTxYvXsyxY8ds2l27do0vv/ySxx9/nN69e7N//36MRiPdunXj+++/V5gScVCjH/Lbtm0bzz//PKtXryYqKsq63jL0tHz5cjZv3sz+/fsJCQkBYOTIkZw5c4YFCxbw+uuv4+npydtvv01MTAz79u3jrrvusrY7dOgQx44dswlUmzZtYsWKFaxfv57Jkydb199yyy1ERESQnZ1N586dq6x948aNxMTEsH//fkJDQ63HTE5OZtu2bdZjJicnA5QLVJaue8v6EydOcPLkSUJCQtizZw+urq4A+Pv7ExAQwM6dO5k5cyYAX331lU1IGzBgAMePHycyMtLunimL/Pz8cnM2ANq0aWN93Rk+yoALV8BUwWsm4GoRxKbBtNC6rkzEPnfffTfR0dEUFxcTGRnJ5s2b7dru8uXL1vcfQIsWLSgpKamtMkVuCo2+h2rBggWMHDnSJkyV9vLLLzNu3DhrmLLo1q0bALm5uQC88MILjBkzxhqmLHr37g3YTkj/+9//TnBwMBERERQVFVkXS6j47rvv7Kp90aJFhIWFWcOUhb+/P02aNLHOlUhOTsZoNNKxY0ebdsnJyfj6+tKuXTvA3DsFsHDhQmuYAujTpw9ubm6cPn3aus4SxgYOHAiYe8EuX75s/bw6TCZTud4poMJ1daWoGL44VnGYsjAB6blQcKWuqhKxX6tWrXjjjTcAeOqpp+wOU5YJ6JZhPktP1auvvlqb5Yo0eo06UOXk5JCRkcHDDz9c4evHjh0jOzubcePGlXvt+PHjAHTo0IHc3FwyMjKs84lKO3HiBB07drROSM/JySEzM5OkpCSaNGlis/Tv3x+A1q1bV1l7bm4u6enphIeHV1hbQEAAzZo1A8zBqWzvFJhDUdnhPm9v73Lh8cyZMxQVFeHn52ezrY+Pj/W8LGGsouNUxWg0VtgLZVlX+jflyhgMhhpbvNr7cbWo6mOagF79htXosWt6qY3ro5rrV81xcXHlvjd///vf4+vry+eff87LL79s13uobJi66667mDJlChcvXuSBBx4gICCg3DZxcXFOu84N5fukIdaspfpf36o06kB14sQJAHx9fSt8/YcfzJNnOnToUO61vXv3EhQUhNFotPZS3XrrrTZtLl26xM6dO216pyzHfP3110lISKhwKX0XzvVYjunt7W2z/sqVK8TFxdkcMy0trVzQOX/+PAkJCTbrExMTKzzXTZs24eLiwujRo63ryoa05ORkvL29K9y+KgEBAWRkZGAy2fYHpaen4+bmRq9evaq9T0ddK7xsd9uiq/a3FakrluH5hQsX2jVcV1GYOnnyJDk5OcTExNjsU0Sqr1EHKh8fH8D8g7sinX+ex/TNN9/YrI+NjWXfvn3Mnz8fgLZt2wLmSd6lvfjii5w+fdrmDj9LL4+bmxuDBg2qcGnSpEmVtVuOefToUZv1S5cuJS8vzzr0duHCBQoKCmx6lwCWLVtW4YT07OxsfvrpJ+u6c+fOsXjxYiIjI22GDFNTU22G9zIyMiqcB2WPCRMmcObMGT788EPrumvXrvHOO+8watQomjdvbtd+TCZTjS0/XcynSzuo6ncPr+ZwKjutRo9d00ttXB/VXL9qLjvs361bN/z9/Tl9+rRdjx25XpiyWLt2LUCFD/YMDQ112nVuKN8nDbFmLdX/+lalUU9K79SpE6NGjbLOGQoODiY/P5+9e/cSGRlJSEgI48ePZ+HChbRq1Ypu3bpx4MABlixZwowZM6wTyrt27Uq/fv1YtGgRXl5edOvWje3bt1v/EyrdW+Tn50dYWBhPPvkk+fn5BAcHU1hYSE5ODrGxsaxatcrm2U7XYznmCy+8QJs2bfD19WXr1q3W/zwtx2zZsiU+Pj5s2bKFiRMnYjKZWLdunXU+ROkJ6adOnaJLly488sgjzJw5kzNnzvD888/TsmVLXnnlFeuxs7KyKCgosAljXl5exMXFsWvXLoxGI507dy7Xe3Y99957LyEhIUydOpWlS5fSoUMHVqxYwfHjx+16Ynttuas3rK7gDr+ybVz0PCqpZyzv/y+++KLK3qmqwhSYe7mvXLmCv78/np6e/Pijbm8Vqa5G3UMFsHnzZqZMmcKKFSsICwtjzpw5nD171trbsn79eh544AGeeeYZ7rnnHv7973+zYsUKVq5cad2Hi4sLW7ZsYcCAAcybN4+HHnqI/Px8nnrqKaD8E9I3bdpEVFQUK1euZOzYsUyePJk1a9ZYhxDtYTlmQEAAM2fOZOrUqbRt25ZZs2bh5uZGv379rG03bNjA2bNn6dGjB6NHj6ZZs2ZMmzYNT09Pay+cZQ7U9u3badq0Kffddx9z587ljjvu4ODBg3h6elr3V/buQIDo6Gi6du3Kgw8+yLBhw/j888/t/RJgMBjYsWMH48ePZ/78+dx7772cPn2aPXv2OPXp8oEdYdzPzygtnZksQ+YhPeCOHnVelkiVOnXqBMDXX39daTt7whSYn1lnecxC2ZtbRMQ+BlN1+rPE6SZPnkxaWhqHDh1ydimNxvdn4OBR+OYUmEzwq7bmINX91obxtPR5b5v/XRbp3DqqQzVXz5133mkzMd3T05Nbb72VgoKCSp8dNWzYMD766CO7njPl7++PwWDg+++/5+rVq9b1oaGh7N+/v0bOwx5PLTHfubj4z9NtPq7PGmLNUvMa9ZBfY5SYmFjt50BJ5X7V1ryINBQ//vijXcNy8fHxjB49mmPHjlX50M5vv/22psoTuSkpUDlJUVHl9+y7urqWu13z4sWLHD16lMcff7w2S6uWGzkPEak7n332mbNLELkpNPo5VPVRdnZ2uWdUlV0stzGX1qJFC4qLi5kzZ44Tqi7vRs9DRESksVEPlRP4+PiQkJBQaZsuXbrUUTU3rrGch4iIiKMUqJygadOmNs+uaqgay3mIiIg4SkN+IiIiIg5SoBIRERFxkAKViIiIiIMUqEREREQcpEnpIiL1XFBQULW3yTqeB0DXTh1sPq6LY4vcjBSoRETquWXLllV7G/05FJG6pSE/EREREQcpUImIiIg4SIFKRERExEEKVCIiIiIOUqASERERcZAClYiIiIiDFKhEREREHKRAJSIiIuIgBSoRERERBylQiYiIiDhIgUpERETEQQpUIiIiIg5SoBIRERFxkJuzCxAREZEbN2/ePFJTU51y7KCgIJYtW+aUY9c3ClQiIiINWGpqKnFxcc4u46anIT8RERERBylQiYiIiDhIgUpERETEQQpUIiIiIg5SoBIRERFxkAKViIiIiIMUqERERKRKTZo0cXYJ9ZoCVQ1IS0vDYDCwe/duZ5dSpby8PAwGA5s2baqy7eHDh23O6/Llyzz77LOkpKRU65i5ubnMnTuX22+/HQ8PDwwGA+np6TdUv4iIOMbX15epU6eyYsUKYmNj+fDDD3nnnXf485//TEhICAaDodw2ffv25euvv2bEiBFOqLhh0IM9a0BCQgIAwcHBTq6kaomJiQAMHjy4yrY+Pj7Ex8czcOBAwPzwuOjoaO66665qHfPbb79l8+bNBAcHExoaygcffFD9wkVExCFBQUEsWLCA8ePH4+ZW/sf/Qw89BMDRo0f5xz/+wcqVKykpKaFv3758/PHHtGvXjtmzZ3PgwIG6Lr1BUKCqAQkJCfj5+dG+fXtnl1KlxMREvLy88Pf3r7Kt0WjEaDRaP09JScFgMBAUFFStY44YMYJTp04BsG7dOgWqGnDuEhz4Gr7M+mXde0kwoie0aeG8uipTYoKUbDhw9Jd1//wIQnpCoB9U8EuxiNQAV1dXnnnmGZ5++mnc3Ny4du0a7733Hp999hmZmZlcu3YNb29vgoODmTBhAj169OCf//wnkydPZuHChaxZs4Z27doRGxvL5MmTnX069dZNM+S3Y8cORo0ahaenJx4eHgQGBrJmzRoATCYTK1euZODAgXh4eNCpUyfmzZvHxYsXbfZRUlLC0qVL8ff3x93dneHDh5ORkUFCQgKDBg0qd8y33nqL4cOH07x5c7y9vZk6dSr5+fnVqrukpISXXnqJ7t274+7uTv/+/YmLi6Nnz55Mnz4dgOLiYjw8PIiOjrbZtqioCHd3d5YsWWJdl5SUxKBBg9i4cSNBQUF4eHgQFBTERx99VO7YQ4YMYdKkSQAEBgYye/ZsTCYTrVu3xmAwMHToULvOwcXlpvk2qxM5+bB0F3zyFVwq/GX9/kxYGgvHzzqvtuspKYENn8GG/9jW9+1pWHMA3k0Ek8l59Yk0Vm5ubmzZsoVnnnkGNzc3li9fTqdOnbjvvvt46aWX2LlzJx9++CExMTHMnTuXrl27Eh4eTm5uLkOHDuX999+3hqn777+fwsLCqg96k7opftItWLCAiRMn4ufnx5o1a3j33XcZP348+fn5lJSUEBkZyZNPPkl4eDi7du3i6aefZt26dUybNs1mP1FRUSxcuJDp06eze/duwsLCGD9+POnp6eWG++bMmUNUVBRDhw5l+/btLFq0iA8++IBHHnmkWrVHRUXx3HPPMWPGDHbv3s2kSZOIiIggKyvLeszMzEyuXLnCgAEDbLY9cuQIhYWFNuuTkpLIyMhg9erVREdH88477wAwYcIEcnJyrO2Ki4s5fPiwddu1a9fSq1cvRo0aRXx8PPHx8WzYsKFa5yKOKyqGNz+Bn65V/HphEbzxCVwrrtu6qvLJV5Dyvfnj0sHJ8vHBo7a9bSJSM1auXMl9993HuXPnuPPOO5k7dy4nT568bvvi4mK2bt1KeHg4hYWFuLi4cPXqVebNm6cwVYVGP+S3bds2nn/+eVavXk1UVJR1/dixYwFYvnw5mzdvZv/+/YSEhAAwcuRIzpw5w4IFC3j99dfx9PTk7bffJiYmhn379lnnEI0cOZJDhw5x7Ngxm0C1adMmVqxYwfr16226R2+55RYiIiLIzs6mc+fOVda+ceNGYmJi2L9/P6GhodZjJicns23bNusxk5OTAcoFKsvkccv6EydOcPLkSUJCQtizZw+urq4A+Pv7ExAQwM6dO5k5cyYAX331lU1IGzBgAMePHycyMtLunimpeWk5cP6n679uMsHFQkg7DoO61F1dlSkuMQ9PVsaAOXTd1lVDfyI15d5772XatGlcvnyZ3/zmNyQlJdm1Xd++fdmxYwfNmjXj9OnTtG/fnhUrVjBmzJharrhha/Q9VAsWLGDkyJE2Yaq0l19+mXHjxlnDlEW3bt0A8x1qAC+88AJjxowpNyG7d+/egO2E9L///e8EBwcTERFBUVGRdenTpw8A3333nV21L1q0iLCwMGuYsvD396dJkyYEBgYC5kBlNBrp2LGjTbvk5GR8fX1p164dgPXNtHDhQmuYAujTpw9ubm6cPn3aus4SxiwT0jMzM7l8+bL1c2cwGAw3/fKXxTGUFBdVep1Kiov424tvO71Wy3LrrwIpuFL519YEnCyAFm06OL3e6y0N7fuwdL0NqfaGWLeza46Liyv3nnJzc+Of//wnAH/5y1+qFaYsE9BjY2MZNGgQZ86cYfTo0Tz44IPl2sfFxTn9+tfV17cqjTpQ5eTkkJGRwcMPP1zh68eOHSM7O5tx48aVe+348eMAdOjQgdzcXDIyMqzziUo7ceIEHTt2tE5Iz8nJITMzk6SkJJo0aWKz9O/fH4DWrVtXWXtubi7p6emEh4dXWFtAQADNmjUDzMGpbO8UmENR2eE+b2/vcuHxzJkzFBUV4efnZ7Otj4+P9bwsb8aKjiN1x9WtaY22qwvVqcXVtf7ULdKQjR8/no4dO/LVV1+xfPlyu7YpG6buv/9+cnJyePbZZwGYNWtWLVbc8DXqQHXixAnA/MyNivzwww+AOTSVtXfvXoKCgjAajdZeqltvvdWmzaVLl9i5c6dN75TlmK+//joJCQkVLpaepcpYjunt7W2z/sqVK8TFxdkcMy0trVzQOX/+PAkJCTbrExMTKzzXTZs24eLiwujRo63ryoa05ORkvL29K9y+rphMppt+eWJGBC6ulY/Uu7i6Mfv34U6v1bJ8l5mEqx3/09zSBPJPfe/0eq+3NLTvw9L1NqTaG2Ldzq657CgGYJ1u8tprr9nUdT0VhSnLnKn169dz4cIF7rzzznIjIaGhoU6//nX19a1Kow5UPj4+ANd9iGTnn+cxffPNNzbrY2Nj2bdvH/Pnzwegbdu2gHmSd2kvvvgip0+ftrnDz9LL4+bmxqBBgypc7HnarOWYR48etVm/dOlS8vLyrENvFy5coKCgwKZ3CWDZsmUVTkjPzs7mp59+mYRz7tw5Fi9eTGRkpM0bJTU11WZ4LyMjwzpkKc4zpBu4VNEDbTDAsKqfilFnPJrBwF+Z50lVZqg/uLlW0UhE7HLbbbcB2PXA6crCFJh/znz22WeAfc8wvFk16knpnTp1YtSoUdY5Q8HBweTn57N3714iIyMJCQlh/PjxLFy4kFatWtGtWzcOHDjAkiVLmDFjhjXhd+3alX79+rFo0SK8vLzo1q0b27dvZ+3atYDt/Ck/Pz/CwsJ48sknyc/PJzg4mMLCQnJycoiNjWXVqlU2z3a6HssxX3jhBdq0aYOvry9bt24lNjbW5pgtW7bEx8eHLVu2MHHiREwmE+vWrePVV18FbCeknzp1ii5duvDII48wc+ZMzpw5w/PPP0/Lli155ZVXrMfOysqioKDAJox5eXkRFxfHrl27MBqNdO7cuVzvWWW2bt0K/PJg0b1795KZmUnz5s2tNwhI1Vp7wLgg2FHJw+rv7geeHnVXkz3u7g+ZeXDxJ/N8qdIMgLEFjApwRmUijY+Xlxc+Pj5cuHCBY8eOVdq2qjBlkZKSQlhYGP369WPbtm21VXqD1qh7qAA2b97MlClTWLFiBWFhYcyZM4ezZ89ae1vWr1/PAw88wDPPPMM999zDv//9b1asWMHKlSut+3BxcWHLli0MGDCAefPm8dBDD5Gfn89TTz0FlH9C+qZNm4iKimLlypWMHTuWyZMns2bNGusQoj0sxwwICGDmzJlMnTqVtm3bMmvWLNzc3OjXr5+17YYNGzh79iw9evRg9OjRNGvWjGnTpuHp6WnthbPMgdq+fTtNmzblvvvuY+7cudxxxx0cPHgQT09P6/7K3h0IEB0dTdeuXXnwwQcZNmwYn3/+ub1fAgDCw8MJDw+3TpKcP38+4eHh1rsKxX539YGHhkDrW2zXt7oFJt0Gv+nrnLoq49UcnhgDvXxs1xsM0K8j/HEMNG/mnNpEGqOVK1fy5ptvVjpk5eHhwYcffmjXc6YOHjzIqlWrSEtLq62SGzyDqToDhOJ0kydPJi0tjUOHDjm7FHGy4hI4dtrc69PCHbq1x665Ss529qL54aQG4Fdt619v2vXMe9v877JI59Zhr6eWvAHA4j9Pt/m4vmuIdTu75jvvvLPCO/3s8cADDzBlyhQmTZp0Q8+ZCg0NZf/+/Td07MamUQ/5NUaJiYl6DpQA5vDUw/5R13rD2MK8iIjzvfvuu7z77rvOLqNRaAC/zzZOpZ9PVdFSUcfhxYsXOXr0qFOfBVXWjZyHiIhIY6NA5QTZ2dnlnlFVdomJiSm3XYsWLSguLmbOnDlOqLq8Gz0PERGRxkZDfk7g4+NDQkJCpW26dKknfzekEo3lPERERBylQOUETZs2tXl2VUPVWM5DRETEURryExEREXGQApWIiIiIgxSoRERERBykQCUiIiLiIE1KFxERacCCgoJuaLus43kAdO3Uwebjujh2Y6RAJSIi0oAtW7bshrZz9p/MaWw05CciIiLiIAUqEREREQcpUImIiIg4SIFKRERExEEKVCIiIiIOUqASERERcZAClYiIiIiDFKhEREREHKRAJSIiIuIgBSoRERERBylQiYiIiDhIgUpERETEQQpUIiIiIg5yc3YBIiIicvOZN28eqampdX7coKAgli1bVuP7VaASERGROpeamkpcXJyzy6gxGvITERERcZAClYiIiIiDFKhEREREHKRAJSIiIuIgBSoRERERBylQiYiIiDhIgaoGpKWlYTAY2L17t7NLqVJeXh4Gg4FNmzZV2fbw4cM253X58mWeffZZUlJSqnXMffv28eijj9K9e3c8PDzo3LkzU6ZM4bvvvruhcxARkZtTixYtGDp0KKNHj+bOO+/E19e30vYhISGEhobWSW16DlUNSEhIACA4ONjJlVQtMTERgMGDB1fZ1sfHh/j4eAYOHAiYnxkSHR3NXXfdVa1jrly5kh9//JE//elP9OjRg5ycHJ577jmCg4NJTk6mc+fO1T4PERG5ORiNRqZOncqjjz5Knz59cHGx7Qs6efIk7733Hq+99hqHDh2yrg8JCSE2NhaDwcBtt91GRkZGrdapQFUDEhIS8PPzo3379s4upUqJiYl4eXnh7+9fZVuj0YjRaLR+npKSgsFgICgoqFrHfPXVV2nXrp3NupCQELp06cJrr73GkiVLqrU/kbp25sIvH8dlwsDO0NLdaeWI3BQMBgOPP/44S5YsoXnz5gBcvXqVI0eO8MMPP3DLLbfQt29fvL29eeyxx3jsscd4++23mTt3LgEBAcTGxtKiRQtiYmLIzMys9XpvmiG/HTt2MGrUKDw9PfHw8CAwMJA1a9YAYDKZWLlyJQMHDsTDw4NOnToxb948Ll68aLOPkpISli5dir+/P+7u7gwfPpyMjAwSEhIYNGhQuWO+9dZbDB8+nObNm+Pt7c3UqVPJz8+vVt0lJSW89NJLdO/eHXd3d/r3709cXBw9e/Zk+vTpABQXF+Ph4UF0dLTNtkVFRbi7u9sElqSkJAYNGsTGjRsJCgrCw8ODoKAgPvroo3LHHjJkCJMmTQIgMDCQ2bNnYzKZaN26NQaDgaFDh9p1DmXDFMCvfvUr2rZtS25urt3XQqSuXS2CmIPw/I5f1m1Pgv/dBv9OgRKT82oTacyaN29ObGwsK1asoHnz5nzwwQeMGzeOli1bMnDgQMaMGcOIESNo06YNgYGBvPLKK1y+fJnIyEiOHj3KBx98YA1TUVFRlJSU1HrNN0WgWrBgARMnTsTPz481a9bw7rvvMn78ePLz8ykpKSEyMpInn3yS8PBwdu3axdNPP826deuYNm2azX6ioqJYuHAh06dPZ/fu3YSFhTF+/HjS09PLDffNmTOHqKgohg4dyvbt21m0aBEffPABjzzySLVqj4qK4rnnnmPGjBns3r2bSZMmERERQVZWlvWYmZmZXLlyhQEDBthse+TIEQoLC23WJyUlkZGRwerVq4mOjuadd94BYMKECeTk5FjbFRcXc/jwYeu2a9eupVevXowaNYr4+Hji4+PZsGFDtc6ltPT0dH744Qf69u17w/sQqU0mE6w5ACnfl3+txAT7MmBn3f8ZMpFGz93dnV27dhEWFsbp06e57777GDt2LLt27eLq1avl2qenp/PHP/6Rfv36kZaWhtFoxMPDgx07dtRZmIKbYMhv27ZtPP/886xevZqoqCjr+rFjxwKwfPlyNm/ezP79+wkJCQFg5MiRnDlzhgULFvD666/j6enJ22+/TUxMDPv27bPOIRo5ciSHDh3i2LFjNoFq06ZNrFixgvXr1zN58mTr+ltuuYWIiAiys7Ptmje0ceNGYmJi2L9/v3VS3ciRI0lOTmbbtm3WYyYnJwOUC1SWyeOW9SdOnODkyZOEhISwZ88eXF1dAfD39ycgIICdO3cyc+ZMAL766iubkDZgwACOHz9OZGSk3T1T13Pt2jVmzJhB27Ztrb1sIvXNN6cgM6/yNvu/gtBe0PqWuqlJ5GawcOFCQkNDOXHiBKGhoRw7dsyu7Xx8fOjWrZv18549e9K0aVN++umn2irVRqPvoVqwYAEjR460s4G6twAAIABJREFUCVOlvfzyy4wbN84apiwsXxTLkNQLL7zAmDFjyk3I7t27N2A7If3vf/87wcHBREREUFRUZF369OkDYPfdbYsWLSIsLKzcHQr+/v40adKEwMBAwByojEYjHTt2tGmXnJyMr6+vdcgtKSkJMH+zWsIUQJ8+fXBzc+P06dPWdZYwZpmQnpmZyeXLl62f3yiTycTvf/97vvzyS95++22bOVoi9ckXx8BgqLxNiQkSs+qmHpGbwZAhQ5g3bx5FRUVMnDjR7jBlmYDeokUL3nrrLY4cOULPnj3LTYWpTY06UOXk5JCRkcHDDz9c4evHjh0jOzubcePGlXvt+PHjAHTo0IHc3FwyMjKs84lKO3HiBB07drROSM/JySEzM5OkpCSaNGlis/Tv3x+A1q1bV1l7bm4u6enphIeHV1hbQEAAzZo1A8zBqWzvFJhDUdnhPm9v73Lh8cyZMxQVFeHn52ezrY+Pj/W8LGGsouNUx+zZs3nrrbd46623GD16dLW2NRgMWrTU2bLjgwOYqpgjVVJcxPNLVzi91oqW0u+bhvQeaoh1N8Sa60PdcXFx5d5Tf/7zn3FxceHll1+23pVeldJhKiYmhkcffZSpU6cCMGvWLFq1amXTPi4u7oauU1UadaA6ceIEwHWfU/HDDz8A5tBU1t69ewkKCsJoNFp7qW699VabNpcuXWLnzp02vVOWY77++uskJCRUuFh6lipjOaa3t7fN+itXrhAXF2dzzLS0tHJB5/z58yQkJNisT0xMrPBcN23ahIuLi03AKRvSkpOT8fb2rnB7e/3P//wPr732GqtWreKhhx664f2I1IXCywWUlBRX2sbg4kLhlYI6qkikcfP19WX8+PFcvXqVl19+2a5tyoYpy5yphIQE9u3bR/PmzW2m3tSmRh2ofHx8APOEtYp0/nke0zfffGOzPjY2ln379jF//nwA2rZtC5gneZf24osvcvr0aZs7/Cy9PG5ubgwaNKjCpUmTJlXWbjnm0aNHbdYvXbqUvLw869DbhQsXKCgosOldAli2bFmFE9Kzs7NtxpPPnTvH4sWLiYyMtBkyTE1NtRney8jIsA5Z3oi//vWvvPzyyyxfvtz6m0N1mUwmLVrqbFkw615cXFwr/Z40GFzY8vpfnV5rRUvp901Deg81xLobYs31oe6y01lCQ0NxdXXlww8/5NSpU1X+TLhemLJYv349AL/+9a/LHedGrlNVGvWk9E6dOjFq1CjrnKHg4GDy8/PZu3cvkZGRhISEMH78eBYuXEirVq3o1q0bBw4cYMmSJcyYMcOaart27Uq/fv1YtGgRXl5edOvWje3bt7N27VrAdv6Un58fYWFhPPnkk+Tn5xMcHMz/b+/Oo5q88v+Bv8MWQJBVMSwCIsomioKiIoK4oCg1EMXRurQydNRDx1qVWltE7dhiXToOx1Nb9ec2bmxqhTO1p1NoB9SCWq2V6mhlxA2/IopWBwXy+4MhNSRAwhMI0PfrnByT+9zc+3lCPPnk3vvcVFdXo6ysDLm5udi+fbtG64Ya+ly3bh1sbW3h5OSEjIwM5ObmKvVpaWkJR0dHpKenY+rUqZDL5di1axe2bt0KQHlBenl5Odzd3TFz5kwsWLAA9+/fxwcffABLS0ts2bJF0fcvv/yCR48eKSVjNjY2yM/PR05ODuzs7ODm5qYyetaUjz/+GOvWrUNcXByGDBmCU6dOKY51795dUKJG1FYGuQK5F4CHT+uv+FPHSwI42bRvXERdVcPn2unTp1us21Iy9XI77bXpdpceoQKAQ4cOYc6cOUhLS0NkZCQSExNRUVGh+BDfs2cPYmNjkZycjKioKHzxxRdIS0vDp59+qmjDwMAA6enpCAgIwOLFixEXF4cHDx7gnXfeAaD6xzpw4ABef/11fPrpp5g4cSJmz56NnTt3KqYQNdHQp6+vLxYsWIDXXnsN9vb2WLRoEYyMjODv76+ou3fvXlRUVKBfv34YP348xGIx5s+fD2tra8UoXMMaqOzsbJiYmEAqleLNN99ESEgI/vWvf8Ha2lrRXuOrAwFg9erV6NOnD2QyGYYPH66UFLUkJycHQP3fYvjw4Uq3hQsXatwOUXsyNgQWRgDW/7uCr2ElRcO/bvbAnBB9REbUNTXMKrW0EF2TZAoArl69qtRuW+vSI1QAYGtri7S0NKSlpak9bmVlhW3btrXYTr9+/fDPf/5Tpfy9995TKbO2tsaGDRuwYcMG7QNu1Oc333yjVDZ79mx4e3vDzOy367THjBmjdkv9devWKe5HR0crhi4b9p5qSmxsrMowp5eXFwoLC7U+BwDIy8tr1fOI9K2HJbBiCnD2P8DZUuBpNWDdDRjWB/BxAgy7/FdSovYzd+5cLFiwAM+ePWu2Xo8ePWBqatripp21tbWwt7dvsT1d6fIJVVdTXFwseB8oItKciREQ7FF/I6K28/z5c7UbdzaWlZWFkSNHori4uMVNOysqKnQVXov4/UpPXt6fSt1N3UK4J0+e4MqVK4L3gtKl1pwHERGREN9//3277YCuKSZUelBaWqqyR1Xj2+7du1WeZ2FhgdraWiQmJuohalWtPQ8iIqKuhlN+euDo6IiioqJm67i7u7dTNK3XVc6DiIhIKCZUemBiYqK0d1Vn1VXOg4iISChO+REREREJxISKiIiISCAmVEREREQCMaEiIiIiEoiL0omIiKjdDRo0SOvn/HLjDgCgT2+J0v227lcTTKiIiIio3X3yySdaP+ed1M8AAB8lJSjd7wg45UdEREQkEBMqIiIiIoGYUBEREREJxISKiIiISCAmVEREREQCMaEiIiIiEogJFREREZFATKiIiIiIBGJCRURERCQQEyoiIiIigZhQEREREQnEhIqIiIhIICZURERERAIxoSIiIiISiAkVERERkUBMqKjTKysrQ0REBLy9veHn54cVK1boOyQi0oO8vDz4+vqib9++iI+PR21trb5DalFiYiKcnZ1hZGSk71BIICZU1OkZGRkhNTUVJSUlOHv2LAoLC3H06FF9h0VE7aiurg7x8fFIT0/H1atXUVVVhX379uk7rBbFxcXhzJkz+g6DdIAJFXV6EokEgYGBAAATExP4+/vjxo0beo6KiNpTUVERHB0d4ePjAwCYP38+MjMz9RxVy0JCQuDg4KDvMEgHOMZIXUpFRQWOHDmCr776St+hEJEGKh5WofLhY5Xyq6W31N53dXKAsbHqR9fNmzfh4uKieNy7d2+UlZXpONp6tXV1uH7jjkp5UzFbWXZDDzvrNomFOg4mVNRlVFdXQyaTYfHixfDy8tJ3OESkAZFIhL3ZJ1D9/IVS+fZDOSr3vfv2hoero9p25HI5RCKR0uO2YmhggHM//RtnLl5RKlcXs6GhARLnxrRZLNRxcMqPuoTa2lrMmjULAQEBePvtt/UdDhFpyNbKElPGjmixXjdzU8REhiolTS9zcXFRmuovKyuDs7OzzuJsbMrYEbDubtFivQmhQ9Grh22bxUEdBxMq6hISEhJgaWmJjRs36jsUItLSEL9+8PF0a7ZOTGQoLLuZN3k8MDAQt27dwqVLlwAAO3bsQExM240MmYpNMH1yONSnd/XcXSQICRrQZjFQx/K7SKjmzZsHNzc3AMBHH30Ed3f3VrdVXV2NFStWwNnZGaampggICMCRI0cUxw8ePIhu3brh6dOnWredl5cHkUiEvLw8RVlYWBjCwsJaFaubmxtkMlmTxyMjIzFv3rxWtT1v3jzY29u3WE/dOW3YsEHpNROqoKAAO3fuRHFxMQICAjBo0CBs2bJFZ+0TUdsSiUSIiRwFC3MztccDB/SHbwsJl6GhIT7//HPIZDJ4eHjAwsICs2fPboNof9PHRYJRQ/3VHhObGGN6VBgMmhhRa/DGG2/A2dkZtbW1cHZ2xqJFi9oiVGoHv7s1VDExMVixYgXOnTuHgIAArZ+fkJCAzMxMpKamwsfHB/v27UNMTAy++OILREVFISoqCrW1tfjyyy8hlUoFx7t161bBbTSl4bWoqalpsz1QBg8ejJMnTyquvAHqE6rIyEhMnTpVJ32MHDmyyfUSFZVVkMvlsLe10klfRNQ2LMzNEDsxFLszv1Qqt7WyxJSI4Rq1MWbMGMUIVXsZPyoIV67fxN3/e6BUHj12JGysLFt8/rZt29oqNGpnOh+hqq6u1nWTOtWvXz/4+PggOztb6+deuHABe/bswccff4xFixYhPDwcO3bswKhRo7Bs2TIAgKWlJSIiIlrVvjo+Pj5KyYguvfLKK3j48CG+/fbbNmkfALp3747g4GB07969zfpoTm7eKWzdewQvamr00j8Rac67ryuC/H+7oEQEYFpUGMRiE/0F1QIjI0PETQ6HoeFvH6e+/dww2M9Tj1GRPghKqFJSUiASiXD27FlERkbCwsICcXFxuHfvHl5//XU4ODhALBbDy8sLmzdvVhpF2LVrF0QiEUpLS5XaVFfeMHWVnZ2NAQMGwNzcHAMGDFC7eWN2djb8/PwgFovRr18/bN++XaWOVCptVcJz7NgxGBgYYObMmUrlc+bMQUlJCS5fvqxo//jx46jRwYd44ym/him0jIwMLFmyBD179oSNjQ2io6Nx8+bNZtuSy+VYvnw5xGIx9u/fDwcHBwwfPlxQ8ldcXIwRI0bAzMwMTk5OWLNmjdLfufGUn5ubG8rLy7F7926IRCKIRKJWTzu25Pa9Cvx0pRTDB/vCmLsQE3UKk8cEw9a6fmQndNhAuLtI9BxRyyQ97TB+VBAAwKKbGaQTRjW5eJ66Lp2MUMXGxmLUqFE4duwY/vjHPyI0NBRHjhxBcnIyjh07hoiICCxZsgTLly9vdR/ff/89UlJS8O677yIrKwsODg6IjY3F1atXFXX+8Y9/QCaTwdHREenp6Vi9ejXWr1+Pr7/+WqktqVSKixcv4t///rdWMVy8eBHOzs6wslKePvLz81McB+pHfh49eoRvvvmmNaeqkaVLl6Kqqgp79uzBpk2bUFBQgFdffbXJ+i9evMDs2bOxbds25ObmKpJCqVSKI0eOtOoS46dPnyImJgYymQxHjx6FTCbDqlWrsHLlyiafk52dDVtbW0yaNAknT57EyZMn8f7772vdtya+LjgDsYkxRnJRKFGnIRabYHpUOJwc7DEuJFDf4WhsVNAAuLtIIJs4usm1YNS16eRr+6JFi7B06VIA9Wt+Ll++jC+//BLjx48HAEyYMAFPnz7FJ598giVLlkAi0f4bR2VlJYqKihQ7yg4ePBgSiQSHDx/Gu+++CwBITk6Gq6srcnNzFWuCRowYAU9PTzg6/rZ3yZAhQ+Dq6ors7GytkrwHDx7AxsZGpdzW1lZxHAB69OiBkJAQZGdnY9y4cVqfqyaCgoKURt8qKiqwbNky3L59W+lcAeDx48eIiYnBTz/9hG+//RYDBw5UHIuJicHSpUtRVFSEoUOHahXDs2fPsGrVKsyfPx8AMH78eFRVVWHTpk1YtmyZ2tcqICAAxsbG6NGjB4KDg7Xq753Uz7Sq32DNX3e36nlEXcHL/29a+39IX97buEPfIWjtepnqhp8dXWd8j7RnzB8lJWhUTycjVK+88orifl5eHuzt7RXJVIM5c+agpqYGBQUFreojKChIaXv+nj17omfPnop9R3799VcUFxcjNjZWaYG1q6srRoxQ3eNk6tSpWk91Nd44roG6MiEjP5qYMmWK0uMBA+pHYRr/5Mq9e/cQGhqKmzdv4uTJk0rJFAC4u7tj4MCBrZ72mzFjhsrj6upqnD59ulXtERERdUY6GaHq1auX4v6DBw+UHjdoGJWqqKhoVR8No0AvE4vF+O9//wugfgRLLper7btXr14qa7WkUim2bNmidkSnKXZ2drhy5YpKecPI1MsxSqVSvPXWWzh9+rTWIzGaaPx6iMViAFC8Hg0uXbqEiooKrFy5Eq6urmrbkkqlOHDgAD788EOtYrCwsEC3bt2UyhqS3tb+nZuj6beE2/cqsOX/ZSJixGCMG9V5pgyIdKnhW/tHSQlK94kadMb3SEeOWScJ1csjNHZ2djh//rxKnTt37iiOA4CpqSkA1asCW/tBbGNjA5FIhLt376ocU1cWEhICe3t7HDlyBAsXLtSoD19fX6Snp+PRo0dK66ga1k41rKUC6kfGAgICkJWV1SYJlabCwsIQHh6OxMREGBsbY9WqVSp1pFIpUlJScOnSJa2uKHzy5Al+/fVXpaSqvLwcwG9/Z13Sdlj368Kz+LrwrM7jIOpMOuN0DrWvzvge6bJTfi8LCwvD/fv3ceLECaXyffv2wcjICCEhIQCgGC358ccfleodP368Vf1269YNgYGByMzMVLq67j//+Q8KCwtV6hsaGiI6Olqrqa7o6GjU1dXhwIEDSuV79+6Fl5cX+vfvr1QeExOjs+0ThFi0aBE+++wzrFmzBu+9957KcX9/f3h4eLQq1oMHD6o8NjU1xbBhw5p8jlgsxrNnz7Tui4iIqKPS+bXkc+fOxd/+9jfMmDEDH3zwAfr27YsvvvgCO3fuRFJSkmJKbujQofD09MTSpUtRV1cHCwsL7NmzR2VqThtr1qzBpEmTMGnSJCQmJuLJkydISUlRWnv1MqlUiqlTp6KyslLtAurGBg4ciFmzZmHZsmWoq6uDt7c39u/fj/z8fLVbOEilUrz//vu4ePGi0uiVPsTHx8PExASvv/46nj9/jvXr1ysdb9hKorkr9BozMzPD6tWrUVVVBV9fX+Tk5GDXrl149913m309fXx8kJ+fj5ycHDg4OMDe3l6xk31zNPmWsDf7BK6W3kLSgpkwNxVrfC5EXU1HnhqhjqEzvkc6csw6H6EyNzdHfn6+Yhpp8uTJ+Oqrr/DJJ58ordExNDTEsWPH4OHhgfj4eMyfPx99+/bV6gO9scjISGRkZODWrVuIjY1FcnIyli9fjoiICLX1x44dCzMzM61GxXbs2IGFCxfiL3/5CyZOnIiioiJkZGSoLBIH6qcIPT09O8QoFVB/YcC+ffuwefNmvPXWW0rHpFIpzpw5o7KovTnm5ubIyspCeno6oqOjkZ6ejpSUFKxdu7bZ561fvx4eHh6YNm0agoKCkJKS0prTUXHnf/tOhQQOYDJFRETtSiRvq8vQOom4uDg8f/68zZKepKQknDhxAufOnWuT9nVFLpfDyckJSUlJ+POf/6zvcFqlpqYWxT9ehr+3BxMq+t3ryN/kqWPojO+Rjhzz73776EOHDrVp+6mpqUhNTW3TPnRBJBLh9u3b+g5DECMjQwQHtM3P9BARETXnd59QAfWjM7W1tc3WMTQ0FPRTAi39DI3Q9nWlrq4OdXV1zdZpqx9SJiIi6qx0voaqM8rPz4exsXGzt/z8/Fa3X1pa2mL7u3d3jN2816xZ02KsREREpIxDDaj/KZqioqJm6zTeEkEbjo6OLbbv7u7e6vZ1KSEhAZMnT9Z3GERERJ0KEyoAlpaWCAxsux21TUxM2rR9XXJ0dNR453giIiKqxyk/IiIiIoGYUBEREREJxISKiIiISCAmVEREREQCMaEiIiIiEogJFREREZFATKiIiIiIBGJCRURERCQQEyoiIiIigZhQEREREQnEhIqIiIhIICZURERERAIxoSIiIiISiAkVERERkUBMqIiIiIgEYkJFREREJBATKiIiIiKBmFARERERCcSEioiIiEggJlREREREAjGhIiIiIhKICRV1CePGjcPAgQPh7+8PmUyGqqoqfYdE1Knl5eXB19cXffv2RXx8PGpra/UdEnUgiYmJcHZ2hpGRkb5D0VhZWRkiIiLg7e0NPz8/rFixQqftM6GiLiEjIwPnz5/HhQsX0Lt3b2zatEnfIRF1WnV1dYiPj0d6ejquXr2Kqqoq7Nu3T99hUQcSFxeHM2fO6DsMrRgZGSE1NRUlJSU4e/YsCgsLcfToUZ21z4SKugQrKysA9R8Ev/76K0QikZ4jIuq8ioqK4OjoCB8fHwDA/PnzkZmZqeeoqCMJCQmBg4ODvsPQikQiQWBgIADAxMQE/v7+uHHjhs7aF8nlcrnOWiPSo+joaJw6dQo+Pj44fvw4LCws9B0SUbuRy+XIyM3H7XsVAIA7//tX0tNO6X6D4AAfDBvkrbatzMxMZGVl4e9//zsAoKSkBDNnzsS5c+fa8hSojZ0vuYa8Uz8oHjf3HrG1tsSsV8bCwKD5cRcjIyPU1NS0UcTA8+cvsDvrSzx9Vt1izAAQPXYE3F0kLbZbUVGBQYMG4auvvoKXl5dOYuUIFXUZx44dw927dzF8+HBs27ZN3+EQtSuRSIRRQ/1xr6JS8UEDQOX+nXsVqKurw2A/zybbksvlSqO8/N7dNfj1d4exkaHifdCg8f27//cAoUH+LSZT7cHExBjDBnq3GPOdexWwt7GCm3OvFtusrq6GTCbD4sWLdZZMAUyoqIsxMDDAvHnzsGvXLn2HQtTuevWwRWTo0GbrGBoYYPrkcBg3s5jYxcVFaSqkrKwMzs7OOouT9EPxtzdufiF5WPBAuGqQmLQXf28PDPLp22wdSwtzTJ0Q0uJyj9raWsyaNQsBAQF4++23dRkmE6quzs3NDfPmzdN5u6WlpRCJREhLS2uxblhYGMLCwhSPi4uLkZKSgocPH+oklqqqKty5c0fxODMzE76+vjppm6izGRk0AH16Nz3lMTZkCJwc7JttIzAwELdu3cKlS5cAADt27EBMTIxO4yT9sLexwuQxwU0ed3SwQ8TIIe0YkWaix42ElWW3Jo/LJo5GNzPTFttJSEiApaUlNm7cqMvwADChonawdetWbN26VfG4uLgYq1ev1llC9ejRI0RHR2PAgAHw9/fHDz/8gL/+9a8AOFVBvz8GIhGmTQqD2MRY5ZirkwNGDxvYYhuGhob4/PPPIZPJ4OHhAQsLC8yePbstwiU9GDrQG/37uKiUGxkaIi4qHEaGhi228cYbb8DZ2Rm1tbVwdnbGokWL2iJUBXNTMaZNClN7LDjAR+35NFZQUICdO3eiuLgYAQEBGDRoELZs2aKzGDvPBhLUaTVcKdRWXFxcUFRUpPbYv4p+ROmtu5gxZUyzUxxEXYmNlSWix41Eek6eoszE2AjTo8I1XhczZswYxQgVdS0ikQiyiaOxeWe6YrE3AEwYHQSHHrYataGPdap93ZwwcogfCs5cVJTZ21hhUtgwjZ4/cuTINv2SzRGqDuDHH39EbGws7O3tYWpqCk9PT6xcuVJx/NChQxg8eDBMTU1hY2ODmJgYXL58WakNuVyOtWvXwtnZGWZmZggODkZhYaHa/srKyjBv3jz06tULYrEYPj4+2L59e6tir6mpwYoVKyCRSGBmZobw8HBcvHhRqc7LU367du3CggULAADu7u4QiUQQiUQoLS1tVf/Nef78BfJPn0d19QsmU/S7M9jXE3793BWPJ48ZDjub7nqMiDoSSwtzxEwIVTzu09sRIwMH6DEizUSOHoqedtYA6kdjp08Oh4ma0Vh9YEKlZ2fOnEFwcDBKSkqwYcMG5Obm4p133sHdu3cB1K9dmDFjBvr06YPMzExs2bIF586dw4gRI5QWja5cuRLJycmYOnUqjh49ij/84Q+YNm0aKisrlfq7ffs2hg0bhlOnTiE1NRU5OTmYMGECEhISFNNk2ti4cSPOnDmDzz77DDt27EBZWRnCwsKU1jS9LCoqCsuXLwcAZGVl4eTJkzh58iQkkpYvc9XWqR9K8OTpM4wN6XjrAYjamkgkgnTCKFh0M4OXR28EDdTd1UzUNfj1d8dgP0+ITYwxPSoMBp1g/z5jYyNMnxwOAwMRwocHoLdjT32HpMB9qPQsLCwMP//8M65cuYLu3ZW/PdbV1cHR0REeHh4oKChQlF+7dg1eXl544403kJaWhsrKSkgkEkybNg179+5V1Nu/fz9mzZqFuXPnKq56S0hIQEZGBkpKSpQ2ZZs/fz6ysrJw9+5diMXiFuMuLS2Fu7s73N3dceXKFcXPD1y7dg39+/fH22+/jdTUVMU5AvU/ZQEAn376KRYsWIDr16/Dzc1N49fqndTPNK5LRESkCx8lJWhUjyNUevT06VN89913mDFjhkoyBQA///wzysvLMXPmTKVyDw8PjBgxQpGgnDp1CtXV1ZgxY4ZSvenTp6v8zlJubi7GjRsHOzs71NTUKG6RkZF4+PAhzp8/r9U5xMbGKvXh4eGBoKAg5Ofna9UOERFRZ8aFJXpUWVmJuro6ODk5qT3+4MEDAECvXqr7gUgkEly5cgVA/Y6v6uoZGRnBzs5Oqay8vByHDx/G4cOH1fZ5//59rc5BXWwODg746aeftGpHE5p+S3j+/AXWbzuIXj1sET8jSudxEBERNcaESo9sbGxgYGCAW7duqT3ekAw1rKd62Z07dxTHm6pXU1OjSLYa2NvbIygoCMnJyWr79PRsevdkddTFVl5erpLI6YK2U35X/3OL04RERCQIp/w6AXNzc4SGhuLgwYOoqqpSOd6/f39IJBLs379fqfyXX35BYWEhwsPDAQDBwcEQi8U4ePCgUr3Dhw+r/MbSxIkTceHCBfTv3x+BgYEqt4YfGdZUZmamUh/Xrl1DUVERRo8e3eRzGtZoPXv2TKu+iIiIOiqOUOnZhg0bEBoaiuDgYCxfvhyurq64ceMGvvvuO2zfvh3r1q3Da6+9BplMhtdeew2VlZVYtWoVrK2tkZSUBKB+pGvJkiX48MMPYW1tjSlTpqCkpATr169XWZu1du1anDhxAiEhIXjzzTfh4eGBx48f4+eff0ZeXh5ycnK0iv/FixeYNGkSEhMT8fjxYyQnJ8Pa2hqLFy9u8jkN+1KlpaXh1VdfhbGxMfz9/WFiYtJsX5p8S/j2+wvI/eYU/jQrWqPfdCIiItIJOend+fPn5dHR0XJra2u5qamp3NPTU/7+++8rjh8+fFg+ePBguVgslltZWcmlUqn88uXLSm3U1tbKV69eLXd0dJSLxWL50KHWhbBCAAABnUlEQVRD5QUFBXJXV1f53LlzlereuXNH/qc//Unu4uIiNzY2lvfo0UM+atQo+aZNmzSO+fr163IA8s2bN8uTkpLkDg4OcrFYLA8LC5NfuHBBqe7o0aPlo0ePVipbuXKlXCKRyA0MDOQA5NevX9e476ZUVz+Xr92yR/75geOC2yIiItIGt02gLqP8fiX2Zp2AbNJojk4REVG7YkJFXUpdXZ3GP61BRESkK0yoSEXjheyNGRgYMGkhIiJ6CT8VSYWxsXGztzVr1ug7RCIiog6FV/mRiqKiomaPOzo6tlMkREREnQOn/IiIiIgE4pQfERERkUBMqIiIiIgEYkJFREREJBATKiIiIiKBmFARERERCcSEioiIiEggJlREREREAjGhIiIiIhKICRURERGRQEyoiIiIiARiQkVEREQkEBMqIiIiIoGYUBEREREJxISKiIiISCAmVEREREQCMaEiIiIiEogJFREREZFATKiIiIiIBGJCRURERCQQEyoiIiIigZhQEREREQnEhIqIiIhIICZURERERAIxoSIiIiIS6P8Dn5jg3fJChtYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 771.475x445.48 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 3\n",
    "T = 1\n",
    "code = RepetitionCode(n,T)\n",
    "code.circuit['0'].draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run in a simulator without any noise. Note results are shown as {'physical bits eg |000 syndrome measurement eg 00: count eg 1024."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Logical 0 : {'000 00': 1024} \n",
      "\n",
      "Logical 1 : {'111 00': 1024} \n",
      "\n"
     ]
    }
   ],
   "source": [
    "def get_raw_results(code,noise_model=None):\n",
    "\n",
    "    circuits = code.get_circuit_list()\n",
    "    raw_results = {}\n",
    "    for log in range(2):\n",
    "        job = execute( circuits[log], Aer.get_backend('qasm_simulator'), noise_model=noise_model)\n",
    "        raw_results[str(log)] = job.result().get_counts(str(log))\n",
    "    return raw_results\n",
    "\n",
    "raw_results = get_raw_results(code)\n",
    "for log in raw_results:\n",
    "    print('Logical',log,':',raw_results[log],'\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now add noise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Logical 0 : {'000 00': 674, '000 01': 59, '100 00': 59, '100 01': 4, '100 10': 7, '101 00': 2, '101 01': 1, '101 10': 1, '110 00': 3, '000 10': 67, '000 11': 1, '001 00': 44, '001 01': 7, '001 10': 5, '010 00': 49, '010 01': 32, '010 10': 4, '010 11': 1, '011 00': 2, '011 01': 2} \n",
      "\n",
      "Logical 1 : {'100 00': 6, '100 01': 2, '100 10': 1, '100 11': 1, '101 00': 43, '101 01': 22, '101 10': 2, '101 11': 18, '110 00': 58, '110 01': 29, '110 10': 3, '110 11': 1, '111 00': 604, '111 01': 60, '111 10': 54, '111 11': 15, '001 00': 6, '001 01': 1, '001 10': 4, '001 11': 1, '010 00': 2, '010 01': 1, '010 10': 2, '010 11': 2, '011 00': 57, '011 01': 4, '011 10': 20, '011 11': 5} \n",
      "\n"
     ]
    }
   ],
   "source": [
    "code = RepetitionCode(3,1)\n",
    "noise_model = get_noise(0.05,0.05)\n",
    "raw_results = get_raw_results(code,noise_model)\n",
    "for log in raw_results:\n",
    "    print('Logical',log,':',raw_results[log],'\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Error correction based on syndrome calculation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "circuits = code.get_circuit_list()\n",
    "table_results = {}\n",
    "for log in range(2):\n",
    "    job = execute( circuits[log], Aer.get_backend('qasm_simulator'), noise_model=noise_model, shots=10000 )\n",
    "    table_results[str(log)] = job.result().get_counts(str(log))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate P, the probability of error, based on using a look up table from the results above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P = {'0': 0.0233, '1': 0.0219}\n"
     ]
    }
   ],
   "source": [
    "P = lookuptable_decoding(raw_results,table_results)\n",
    "print('P =',P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Logical 0:\n",
      "raw results        {'000 00 00': 486, '000 00 01': 55, '000 00 10': 51, '000 01 00': 54, '000 10 00': 52}\n",
      "processed results  {'0 0  00 00 00': 486, '0 0  01 01 00': 55, '0 0  10 10 00': 51, '0 0  00 01 01': 54, '0 0  00 10 10': 52}\n",
      "\n",
      "Logical 1:\n",
      "raw results        {'111 00 00': 471, '111 00 01': 58, '111 10 00': 52}\n",
      "processed results  {'1 1  00 00 00': 471, '1 1  01 01 00': 58, '1 1  00 10 10': 52}\n"
     ]
    }
   ],
   "source": [
    "code = RepetitionCode(3,2)\n",
    "raw_results = get_raw_results(code,noise_model)\n",
    "results = code.process_results( raw_results )\n",
    "for log in ['0','1']:\n",
    "    print('\\nLogical ' + log + ':')\n",
    "    print('raw results       ', {string:raw_results[log][string] for string in raw_results[log] if raw_results[log][string]>=50 })\n",
    "    print('processed results ', {string:results[log][string] for string in results[log] if results[log][string]>=50 })"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "'000 00 00' has been transformed to '0 0 00 00 00', and '111 00 00' to '1 1 00 00 00', and so on.\n",
    "Real example set step_2 and step_3 to True when ready to run"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "step_2 = False \n",
    "step_3 = False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import IBMQ\n",
    "from qiskit.compiler import transpile\n",
    "from qiskit.transpiler import PassManager"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "device_name = 'ibmq_16_melbourne'\n",
    "if step_2:\n",
    "    IBMQ.load_account()\n",
    "    for provider in IBMQ.providers():\n",
    "        for potential_backend in provider.backends():\n",
    "            if potential_backend.name()==device_name:\n",
    "                backend = potential_backend\n",
    "    coupling_map = backend.configuration().coupling_map"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set up specific data for IBM Melbourne computer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "if device_name=='ibmq_16_melbourne':\n",
    "    line = [13,14,0,1,2,12,11,3,4,10,9,5,6,8,7]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create repetition code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_min = 3\n",
    "n_max = int((len(line)+1)/2)\n",
    "code = {}\n",
    "for n in range(n_min,n_max+1):\n",
    "    code[n] = RepetitionCode(n,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tell transpiler which physical links to use."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_initial_layout(code,line):\n",
    "    initial_layout = {}\n",
    "    for j in range(n):\n",
    "        initial_layout[code.code_qubit[j]] = line[2*j]\n",
    "    for j in range(n-1):\n",
    "        initial_layout[code.link_qubit[j]] = line[2*j+1]\n",
    "    return initial_layout"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Transpile QBits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "if step_2:\n",
    "    circuits = []\n",
    "    for n in range(n_min,n_max+1):\n",
    "        initial_layout = get_initial_layout(code[n],line)\n",
    "        for log in ['0','1']:\n",
    "            circuits.append( transpile(code[n].circuit[log], backend=backend, initial_layout=initial_layout) )\n",
    "            num_cx = dict(circuits[-1].count_ops())['cx']\n",
    "            assert num_cx==2*(n-1), str(num_cx) + ' instead of ' + str(2*(n-1)) + ' cx gates for n = ' + str(n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ready to run job"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "if step_2:\n",
    "    job = execute(circuits,backend,shots=8192)\n",
    "    raw_results = {}\n",
    "    j = 0\n",
    "    for d in range(n_min,n_max+1):\n",
    "        raw_results[d] = {}\n",
    "        for log in ['0','1']:\n",
    "            raw_results[d][log] = job.result().get_counts(j)\n",
    "            j += 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now decoding:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "if step_3:\n",
    "    results = {}\n",
    "    for n in range(n_min,n_max+1):\n",
    "        results[n] = code[n].process_results( raw_results[n] )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "if step_3:\n",
    "    dec = {}\n",
    "    for n in range(n_min,n_max+1):\n",
    "        dec[n] = GraphDecoder(code[n])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "if step_3:\n",
    "    logical_prob_match = {}\n",
    "    for n in range(n_min,n_max+1):\n",
    "        logical_prob_match[n] = dec[n].get_logical_prob(results[n])\n",
    "    with open('./logical_prob_match_'+device_name+'.txt', 'w') as file:\n",
    "        file.write(str(logical_prob_match))\n",
    "else:\n",
    "    with open('./logical_prob_match_'+device_name+'.txt', 'r') as file:\n",
    "        logical_prob_match = eval(file.read())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "x_axis = range(n_min,n_max+1)\n",
    "P = { log: [logical_prob_match[n][log] for n in x_axis] for log in ['0', '1'] }\n",
    "\n",
    "ax = plt.gca()\n",
    "plt.xlabel('Code distance, n')\n",
    "plt.ylabel('ln(Logical error probability)')\n",
    "ax.scatter( x_axis, P['0'], label=\"logical 0\")\n",
    "ax.scatter( x_axis, P['1'], label=\"logical 1\")\n",
    "ax.set_yscale('log')\n",
    "ax.set_ylim(ymax=1.5*max(P['0']+P['1']),ymin=0.75*min(P['0']+P['1']))\n",
    "plt.legend()\n",
    "\n",
    "plt.show()"
   ]
  }
 ],
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