sampler_lab_exercise_w_state.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "6196753d",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Sampler lab exercise solution with W state"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4de54c99-ae01-416b-a826-2192e8a68c89",
   "metadata": {},
   "source": [
    "This program samples one piece of candy from a box that contains three chocolate candies. The circuit that chooses the piece of candy should be a three qubit [W state](https://en.wikipedia.org/wiki/W_state)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3710db96",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### 1. Initialize the account"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "dac21228",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from qiskit_ibm_runtime import QiskitRuntimeService\n",
    "\n",
    "service = QiskitRuntimeService(channel=\"ibm_quantum\")\n",
    "backend = service.backend(\"ibmq_qasm_simulator\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "00356482",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### 2. Create a circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "820a1bc7",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZS3Y1adKEEydOnNXesWPH/H7fb38RYoO4jq6f5yNDJ8UDkpvDRS4uLW0B+rSrl3IM5bDbqXj6GbDbCZp6f9USXdYx12NJScY+fwGOQ4HzNnFKSgrr1q2r6uQwq8plJw8fPuzWu4d1DbOVvvzyy7OuLeJL/DbQJiQksGbNGoYNG4bNZmPfvn1ER0fzyiuvsHTpUnbt2gWcHWg7dOhQ41jZjIwMOnTo4JXa5cK16gHBYec/rlLkRXCRuf++yWksFhje1bVzereDmMjzH2c29vcX4cjYjvWWP2A5bbKrJSiIoAfuB3sFFX/9Gw5H7RNK/UlISAjR0dGEhHhyhLJ3tWzZsmoJrU2bXH9XydUwe+Z1FGjFF/ltoAVnOP3444/Jz88nPz+f9evXM2HCBAoLC9m3bx9Wq5VOnTpVO2f48OGsXbu2akkvgPXr17Nnzx5GjBjh7acgbgpvAl2vqVuojWgKXa8FA94plXqUlgjXdXf2vNbp2B71XpLXOQ4cwP7GW1g6tMd63bVnPW5JaoX1D2NxbP0R+2JzL0tYVwcOHODOO+/kwAEXFyr2IS1atKj6d2XnTF25E2bBueFC5aoLcXGem0go4ikB+Sd827ZtOBwOUlJSzpoUMGHCBJ577jlGjRrFY489RnFxMdOmTaNnz56MGuWZcWbiHY0ToMdNsGcdHMl0bod7uuAwiEuFNn2cwxTE/1x2sbPX9bMf4acaZlhFRziPGXAx+OM8FkvLloQs/fCcxwT9/gaCfn+DlyoyXn5+PqtWreKuu+4yuhS3ZWdnM2PGDBo0aMDXX39d5/NsNhvvv/++y2EWnBNnn3zyScrLy039YkD8V0AG2q1btwJnDzcAiIqKYuXKlUyePJkbb7yR4OBghg8fzt/+9jfN3DShiKaQNhJKCuDwTtiz1rnebHAYXHYHPjORTepPhxbOj+zjkJENn22D0nIID4UZI/0zyIp/O3jwII8//rjL5xUXFzNmzBiWL1/OunXr6hxmK82YMcPla4p4iwJtDdq2bcvHH3/szZIuyAuLJ/FNxhIOH9/PS/dupl1817OOsdvtvLZ0Ght3rqDCXk5qUl8mXfsSIcGhnCop4LE3r2N31iYq7OUs/ssJrz+H+hbWEFp2g/0bnIE2KERhNtDEN3F+rN3lDLQhQQqzEnjWrl3LZZddxo4dO1wKsyK+LiB/nZ8v0JrNZWnX87c719K8Sc27ogGs2PBPMrO/58V7v+efU7djsVj5z9p/ABAUFMINg6Yze8Ln3ipZREQMkp6erjArficgA+3KlStxOBwMGzbM6FI8Iq1Nf5o1TjjnMXsObeGS5MGEBIdisVjo0X4on296C4DQ4DAuaXc5DRs09kK1IiLGad68OdOnT6d58+ZGlyIiHhSQgTYQJSd045uMJRQWn6S8ooyvtrzH4eP7jC5LRMSrYmJiGDduXNWyVyLiHwJyDG0gurL7OH4+vp8pLw0gLKQBlyQPJmjXp0aXJSLiVXl5eXzzzTf07t2bRo0aGV2OiHiIemgDhMVi4Y+/e5SX79vMP+7+mlbNO9Iqtu7bPoqI+IOsrCzuu+++amuNi4j5KdAGiNKyYvKLjgOQV3iUf698ijEDpxlclYiIiMiF05ADP/D39+9g/Y6lHMvP5aF5VxIeFskbD2by1//7E707jqRP6kgKi/OY8vJArBYrdoeda/pNpnfH/+58NuGvaeQVHqGo5CS/n5VAl7aDePD3bxn4rERERETqRoHWD9x7/Ss13j9l9LyqfzeJbM78qdtrbePVKT94vC4RERERb9CQAxERCRg2m40OHTpgs2m/axF/oh5aEREJGG3btmXRokVGlyEiHqYeWhERERExNQVaEREJGBkZGaSlpZGRkWF0KSLiQQq0IiISMBwOB2VlZTgcDqNLEREP0hhaH2UNgUGTjK6i7qwhRlcg4l/CrUEcv/wKo8twSbg1yOgS/Ep4eDgFBQUea+/pV/7NycIioiLCmXrHjWfd9oTw8HCPtCPiKgVaH2WxQFCo0VWIiFEsFgsRQfoVHcgsFgsREREeay80zEZoWQWhYTYiIiLOui1iZhpyICIiIiKmppf/IiISMNq2bcuSJUtITEw0uhQR8SAFWhERCRg2m43k5GSjyxARD9OQAxERCRjZ2dnMmDGD7Oxso0sREQ9SoBURkYBx4sQJPvjgA06cOGF0KSLiQQq0IiIiImJqCrQiIiIiYmoKtCIiIiJiagq0IiISMKxWKz169MBq1Z8/EX+in2gREQkYdrudDRs2YLfbjS5FRDxIgVZERERETE2BVkRERERMTYFWRERERExNgVZERAJGo0aNGDFiBI0aNTK6FBHxoGCjCxAREfGWhIQE5syZY3QZIuJh6qEVEZGAUVJSwv79+ykpKTG6FBHxIAVaEREJGJmZmQwZMoTMzEyjSxERD1KgFRERERFT0xha8UkOB9jL6qfdys8VpZ5t2xoCFotn2xQRCVQOh4OioiKjy3BJeHg4Fv0hMIQCrfgkexmserb+2i8t9Hz7gyZBUKhn2xQRCVRFRUU0bNjQ6DJcUlBQQEREhNFlBCQNORARERERU1MPrYiIBIzU1FS2b99udBki4mHqoRURERERU1OgFRGRgLF3715uvPFG9u7da3QpIuJBGnIgIn6vsASyjsGxQigpd95XVgG/FEB0hFanCCRFRUVs2bLFdLPnReTcFGhFxC/l5sG63bAtyxlkz1RUCn/5EMJDoV1z6JMMKbFgVbgVETEdBVoR8SsHf4Elm2H34bodX1QKPxx0fjSLhN91gu6t1WsrImImCrQi4hfKK+CTrfBFBtgd7rVxJB/+9Q1s3g839IJG4Z6tUURE6ocmhYmI6RUUwz8+hc+2uR9mT5dxCGYvhb1HLrwt8S3x8fHMnj2b+Ph4o0sREQ9SoBURUysohuc/h4PHPNtuUSm89AXs+dmz7YqxGjduzMiRI2ncuLHRpYiIBynQiohplVfAq6udE8DqQ2kFvLYaDp+sn/bF+44dO8a//vUvjh3z8CsgMYUmTZqQlJREmzZtiIuLw+LiYPlbb72Vdu3a1VN1ciE0hlZETOuzbXDgF9fOuX8IRDWAk6fgmRXnP764DN79BiZdAVZ1AZheTk4Os2bNomvXrkRHRxtdjtSz2NhYbr75Zvr06UO3bt1ITEys9vjJkyfZvHkzGzduZOHChWzYsKHWtu68805eeOEFsrKyGDRoEJmZmfVdvrggIH49Hz16lGnTptGuXTtsNhuJiYlMnjyZwsJCxo8fj8Vi4fnnnze6TBFxQdYx+OxH18+LagCNw52f62rfUfhyp+vXEhFj9OjRg3//+98cOHCAOXPmcPXVV58VZgGioqIYMGAAU6ZM4bvvvmPDhg3ccsstWM949VoZZgESEhK4+uqrvfE0xAV+30Obnp7O0KFDyc3NJSIigo4dO3Lo0CGeffZZ9uzZU/W2U9euXY0tVOrFlj2reeDlQUwY9jSjBz5Q4zFXTLXQq8MwZt32sZer854TRfDtHsg94dxQICIM0hKhYwvz9jp+lO6ZCWB1tfwH6N0ObCHeu6aIuKZBgwbMmjWLe++996xQmpeXx+bNmzl06BAOh4OoqCjS0tJo1apV1THdu3dnwYIF/OlPf+LWW28lMzOzWpgFmDVrFnPnzvXac5K68etAe/ToUUaMGEFubi5Tpkxh5syZREZGAjBnzhymT59OcHAwFouFtLQ0g6sV8byCYnh/g3ON1TPD33c/QZMIGJoGPdsYU5+7jpyEnTnevWZpOWzcC/1SvHtdEambjh078p///IeUlP/+kB4+fJh58+bx9ttvs3PnThyOs18Fx8TEMHLkSO688066desGQL9+/fjhhx/44IMP+MMf/lB17KxZs3jkkUfq/8mIy0zaN1M3kyZNIisri7vvvpu5c+dWhVmAadOm0aVLF8rLy0lKSiIqKsrASkU8L+8U/P1TSD9Qe0/m8UJ45xv33ro30rrdxlx37S6o4e+hmEhERAR9+/YlIiLC6FLEg7p27cpXX31VFWaLi4t54IEHSExMZMaMGezYsaPGMAvOzq/58+fTvXt3Lr/8cvbs2QM4e3sVZs3DbwPt9u3bWbhwITExMTz55JM1HlP5SqxLly5V91UG4J49exIWFubyDEgRX2B3wLzVcDS/bscv3eIMvmaxLduY6+bm1byNrphHUlIS8+bNIykpyehSxEPatWvHp59+StOmTQHYvHkzXbt25a9//StlZWUutbVq1SrS0tJYs2ZNtfs//vhjhVkf57eB9t1338VutzN27FgaNmxY4zENGjhnhZweaDMzM/nggw+IjY2lR48eXqlV6l9xWRF5hUdr/PBHOw65vi7rZz+ao/exuMy5o5dRsrTak6lVVFRQUFBARUWF0aWIBwQFBfH222/TrFkzANauXcuAAQPYudP9WZzjxo3jsssuq3bf4MGDufjiiy+oVqlffjuGduXKlQAMGjSo1mOysrKA6oG2f//+5OQ4B+c9+uijrFu3rh6rFG9589OZvPnpTKPL8Jq1u1w/J/u4czZ/62aer8eTsg0OlAePQZeWxtYg7tuxYwfXX38977//PqmpqUaXIxfo/vvvp1evXgDs3LmT4cOHk5/v/iveMyeAbdy4ke7du2Oz2Xj99dfp168fdrv9gusWz/PbQLt//36AarMXT1deXl4VVk8PtGfOihT/MKzXBPqnja7xsemvXeHlauqXwwE73Jwwtf2Q7wfa40UGX19DDkR8QlxcHP/7v/8LOHvex40bR16e+7us1LSawRNPPEF6ejopKSn07t2b2267jXnz5l1w7eJ5fhtoCwudf3VOnTpV4+MLFy7k6NGjREZG0rp163qtpXv37uTm5tbrNfxNaHADXr3bczN/4mOSuTRlsMfaq0lySjKl5TV/v3lTUEgDrpnl3tfuhZf/yYSPfLsnO6nHjXS/vuYlcyo3TTiXKNt/Pz96Te3H1bbxwocfLeWhG+6oY7XiDePGjavzsZXvwC1btozNmzfX+bwFCxa4WJXvuebWe4loGEVObg4JCQln3fY15+sJvf3227HZnD/Qzz33HN9++63b16opzFaOmb3ttttYu3YtAPfcc885A21ycrI6xi5AbGwsGzdudOtcvw20sbGxHD9+nO+//57evXtXeywnJ4epU6cCkJaWVu8Tv3Jzc8nONmgWi0nZQsKNLsFlOYcOUVxmcPchYLG4/8v0xLHDPv+9Gtn651ofq9w0oS6s1rofe7rC/Dyf/xoFmqKiuv/cFRcXV3125Tx/+D+3/zpu2F5RQXZ29lm3zSQ4OJg77nC+sCwvL7+gdWHPFWYB1q1bx7p16+jbty9paWn069evKuCeqfIFk3if3wbawYMHs337dmbPns0VV1xRtZTHhg0buPnmmzl61DkZyBsbKsTGxtb7NfxNaLAL2zj5iLgWLXyihxbg2MF0ohO7unxe2fE9xMfHe74gD4oIrX3m2sk6fPmjbM4wa7fDyeLaj6utLav9lM9/jQJNeHjdX5lU9ujZbDaXzvOH/3NrUFDV5/j4+LNu+xq73V5rQOzfvz8tWrQAYMmSJW4H8vOF2Uovvvgiffv2BeCmm26qNdDGxcWph/YCXEhe8ttAO23aNN555x0OHjxIamoq7du3p7i4mMzMTIYOHUpSUhKffPJJtfGz9cXd7vNAVlEKq541ugrX7N61m6BQo6twWr8H3nXx3bfG4fDNin8S5OO/i/NPwSOLan6spiECZ3r0GudzPVkMj/7H9evPnDqeni+Nd/1EqTc7duyo87FlZWWMHz+eyMhIQkLqvu3brFmz3CnNpzzxwr84WVBIXGwcWVlZZ932NYWFhbWuUtS9e/eqf3/44YdutV/XMAvw0Ucf1XjtM+3evVtrHBvEx/90uS8hIYE1a9YwbNgwbDYb+/btIzo6mldeeYWlS5eya5dzGrg3Aq2It13SCiJtrp1zWQo+H2YBIhtAIwM78BOjjbu2XLiQkBCio6NdCrPieyrXkQf3Oo1cCbMA+fn5VS+c0tLS9P3jg0zw58t9HTp04OOPPyY/P5/8/HzWr1/PhAkTKCwsZN++fVitVjp16mR0mSIeFxoMfxrg/FwXaYkwqEP91uRJyc2NuW6UDZprU0FTO3DgAHfeeScHDphoJxE5S/v27QEoKSlxqYceXA+zldLT0wEICwur98nk4jq/HXJwLtu2bcPhcJCSklLjGKr3338fgIyMjGq3k5KSzvlWg/ieLm0H8tnT594t4HyPm1WrGLhnMLy+pvbdrSwW6NMOru3uHFdqFn2SYeM+71/3N+3M9XWSs+Xn57Nq1Sruuusuo0uRC/Dzzz9z8OBBioqKXFoX9o477nArzIJzYuChQ4c4deqUdhH1QQEZaLdu3QrUPtxg9OjRNd6+5ZZb/GLpFgkciU1hxkjIOARf74btOc51aq0W+G1HZzBsYsLhXq2bQYsmcOi4965ptTi/XiJivCuucG/98G3btlFQUEDDhg1dCrMADzzwAA888IBb15X6p0BbA4cZ9v8UqSOrFTolOD9mLoK8U87xtcO6Gl2Z+ywWGNIZ5n/lvWv2auveMl8i4jvWrl3L0KFDGTRoEH/5y1+MLkc8SIFWREwpLdE5+W3z/vq/VpNwGHVp/V9HROrf2rVra112S8wrIAPtypUrjS5BRDzguu6w5/C515M9U+X6snVZsxbAAtz4G7BpUrNfaN68OdOnT6d5c4NmFopIvQjIQCsi/qGhDSYMguc/h+Kyup1Tl7VqT3d9T7g4zvXaxDfFxMS4tFWuiJiD5uuKiKklRMNdgyEizLPtWoDRPaGvJoL5lby8PFasWEFeXp7RpYiIBynQiojpJUbDlCGQ4qFdpptEwJ9/qzDrj7Kysrjvvvt8cmcsEXGfhhyIiF+Ibgh/vhy+yYSP06Go1PU2rBbo3Q5GXKIxsyIiZqJAKyJ+w/LrWrHdW0P6AVi7Cw78cv7zGjVwnvebdsZuqysiIu5RoBURvxMaDD3bOD/yT8HBY86P44VQVgFBVmgY5hx/mxgNTSOdvbMiImJOCrQi4tciG0DHeOeHiM1mo0OHDthsNqNLEREPUqAVEZGA0bZtWxYtWmR0GSLiYVrlQERERERMTYFWREQCRkZGBmlpaWRkZBhdioh4kAKtiIgEDIfDQVlZGQ6Hw+hSRMSDFGhFRERExNQ0KUx8kjUEBk0yugrXWLUQv4iIx4SHh1NQUOCx9p5+5d+cLCwiKiKcqXfceNZtTwgPD/dIO+I6BVrxSRYLBIUaXYWIiBjFYrEQERHhsfZCw2yEllUQGmYjIiLirNtibgq0IiISMNq2bcuSJUtITEw0uhQR8SAFWhERCRg2m43k5GSjyxARD9OkMBERCRjZ2dnMmDGD7Oxso0sREQ9SoBURkYBx4sQJPvjgA06cOGF0KSLiQQq0IiIiImJqCrQiIiIiYmoKtCIiIiJiagq0IiISMGJiYrj99tuJiYkxuhQR8SAFWhERCRgWi4XQ0FAsFovRpYiIBynQiohIwDhy5AgvvPACR44cMboUEfEgBVoRERERMTUFWhERERExNQVaERERETE1BVoREQkYjRo1YsSIETRq1MjoUkTEg4KNLkBERMRbEhISmDNnjtFliIiHqYdWREQCRklJCfv376ekpMToUkTEgxRoRUQkYGRmZjJkyBAyMzONLkVEPEhDDkRERER8kMPhoKioyOgy6iw8PNywTUsUaEVERER8UFFREQ0bNjS6jDorKCggIiLCkGtryIGIiIiImJoCrYiIiIiYmoYciIhIwEhNTWX79u1GlyEiHqYeWhERERExNQVakQDhcDg/Kv8tEoj27t3LjTfeyN69e40uRUQ8SEMORPxUeQX8mA0//QwHj0H2cSgtdz52shj+dzEkNoXEaOicCM2jDC1XxCuKiorYsmWLqZZCEpHzU6AV8TN5RbB2F3yzBwqKaz/uWKHzY8sB+DgdUmKhXwp0TgCDlhEUERFxiwKtiJ9wOODbPbB4E5SUu37+rlznR0os3NgLos2z9KGIiAQ4jaEV8QOFJfDKKli43r0we7pduTB7KWzUEEMRETEJ9dCKmFz+KXjxC8jJ81ybJeXw9tdQUAID23uuXRGjxcfHM3v2bOLj440uRUQ8SD20IiZ2qhReWuXZMHu6xZvgm8z6aVvECI0bN2bkyJE0btzY6FJETMdqtfrsi0H10IqY2KKNcOh4/V7j/Q3Qqim0aFK/1xHxhmPHjrF8+XKGDh1KdHS00eWI1LuwsDC6detGt27d6N69O/Hx8YSFhVFaWkpubi6bNm1i06ZNbNiw4Zyrf1itVt58800GDhzIwIEDycz0rd4OBVoRk/oxCza4OM71/iEQ1QBOnoJnVtTtnAo7vPMt3HclBOk9HTG5nJwcZs2aRdeuXRVoxa+1bt2aO+64g/HjxxMTE1PrcTfddBMAeXl5vPnmm7z00ktn7aZXGWbHjh0LwCeffEKHDh0oLS2tvyfgooD483T06FGmTZtGu3btsNlsJCYmMnnyZAoLCxk/fjwWi4Xnn3/e6DJF6qy8Av7vO9fPi2oAjcOdn12RdQzW7HT9eiIi4l0NGzbkxRdfJDMzk+nTp58zzJ6uUaNG3HPPPWRkZPD2229XveA7M8yWlpZy7733+lSYhQDooU1PT2fo0KHk5uYSERFBx44dOXToEM8++yx79uzh2LFjAHTt2tXYQkVckH4A8k5595prdkH/i8EaEC+DRUTMZ8CAASxYsICkpKSq+0pKSli0aBGrV69m06ZN7Ny5k+LiYsLCwmjXrh3dunXjsssuY8yYMYSHhwMwduxYfvvb3zJx4kRGjx5dLcxef/31fPTRR0Y8vXPy60B79OhRRowYQW5uLlOmTGHmzJlERkYCMGfOHKZPn05wcDAWi4W0tDSDqxWpu7W7vH/NXwpgew6k+uZ8ABGRgHbTTTfxxhtvEBzsjHaFhYU8+eSTvPrqqxw5cuSs48vLy9myZQtbtmxh/vz53Hvvvdx666088sgjREdHExsby+LFi6uO9+UwC34+5GDSpElkZWVx9913M3fu3KowCzBt2jS6dOlCeXk5SUlJREVp308xh6P5sO+oMdfe8JMx1xXxlIiICPr27UtERITRpYh4zJgxY3jrrbeqwuzq1avp3Lkzjz/+eI1htiZ5eXn8/e9/JzU1lSVLllR7rLy83KfDLPhxoN2+fTsLFy4kJiaGJ598ssZjunXrBkCXLl2q7nv//fe57rrraNWqFeHh4bRv356HH36YgoICr9Qtcj77fzHu2gePGXdtEU9ISkpi3rx51d6SFTGztLQ03nrrLay/jgd78cUXufzyy9m7173dcX7++Wfy8/Or3RccHHzWfb7GbwPtu+++i91uZ+zYsTRsWPMeng0aOGfGnB5o586dS1BQEE888QTLly/nz3/+My+99BJDhgzBbrd7pXaRczloYKD9pcC5K5mIWVVUVFBQUEBFRYXRpYhcsODgYBYsWEBoaCgAr732GnfddRcOh8Ot9s6cAHb6z8n8+fN9+p0Nvw20K1euBGDQoEG1HpOVlQVUD7QfffQR7733HmPHjmXAgAFMnjyZ559/nnXr1rF27dr6LVqkDnLraRMFs1xf5ELs2LGDHj16sGPHDqNLEblg06dP55JLLgFg69at3H333W63VdNqBtdeey1ffvkl4FwGrLZ3vH2B304K279/PwCtWrWq8fHy8nLWrVsHVA+0zZo1O+vY7t27A5Cdne1WLd27dyc3N9etc0XONHDiB8S07lXjY5XrzNYmyvbfz49ec+7r1LZW7Q2/v5ncnavqWK1I/Rs3blydj83JyQFg2bJlbN68uc7nLViwwMWqfM81t95LRMMocnJzSEhIOOu2vzPj8z/XO8M2m437778fcGaacePGub2UVk1htnLM7I8//sjWrVsJDw9nwoQJPPbYY/zyS81vFSYnJ1cNfXBHbGwsGzdudOtcvw20hYWFAJw6VfPaRgsXLuTo0aNERkbSunXrc7a1apXzj3eHDh3cqiU3N9ftMCxyppKS2t/zr1xn9nys1rodV5MjR37W97P4lHPtbnSm4uLiqs+unOcP3/P2X98+tldUkJ2dfdZtf+dvz/+GG26oWiv23Xff5fvvv3ernXOFWYCffvqJl156iSlTphAWFsZtt93G008/XWNblS8YjeC3gTY2Npbjx4/z/fff07t372qP5eTkMHXqVMA5mNpisdTaTnZ2No888ghDhgxxe63a2NhYt84TqUmQpfaxfyfPszZtlM0ZZu12OFl87mNra6tJVAQVPrqXtwSmyrUz68Jms1V9duU8X92/3hXWoKCqz/Hx8Wfd9ndmfP52u73WkHj77bdX/fuFF15wq/3zhdlKlYG28rq1Bdq4uLgL7qF1l98G2sGDB7N9+3Zmz57NFVdcQUpKCgAbNmzg5ptv5uhR57pH5wqpBQUFjBo1itDQUObPn+92Le52n4vU5MPvYdX2mh8733a2j17j7Jk9WQyP/se966/7YhERYe6dK1IfXBkPu23bNubPn89VV11Fampqnc+bNWuWO6X5lCde+BcnCwqJi40jKyvrrNv+zozPv7CwsMaJ7WFhYfTs2RNwfv+vX7/e5bbrGmYB9uzZw1dffUX//v1JTk6mefPmHD58+Kzjdu/ebdjEMb+dFDZt2jSaNm3KwYMHSU1NpXPnziQnJ9OzZ0/atGnD5ZdfDlQfP3u6U6dOMWLECPbu3cunn35KXFycN8sXqVWCgdvPN22IwqyYWkpKCuvWravq5BAxo86dOxMSEgLAt99+6/L5roTZSqdfp3LZU1/it4E2ISGBNWvWMGzYMGw2G/v27SM6OppXXnmFpUuXsmuXc6ulmgJtWVkZ119/PRs3bmT58uV07NjR2+WL1KpVU+Ou3dLAa4t4QkhICNHR0VVhQMSMKlc2ANi0aZNL57oTZs+8zqWXXurSNb3Bb4ccgHMS18cff3zW/QUFBezbtw+r1UqnTp2qPVa5du0XX3zBsmXLqrr0RXxFTCS0bgZ767b5i0f1OPf8SRGfd+DAAZ566ikefPBBWrZsaXQ5Im6pnAwGcPDgwTqf526YPfM6TZo0caFa7/DrQFubbdu24XA4SElJOWtSwF133cX//d//8eCDDxIeHl6ti71t27Y1Lusl4m39kr0faJs2hPYtvHtNEU/Lz89n1apV3HXXXUaXIuK2f/3rX6xfvx6bzebS6gbt27dn1KhRgGthFiAjI4OrrrqK4uJi9u3b507Z9SogA+3WrVuBmocbLF++HICnnnqKp556qtpjr7/+ukvrHYrUly4t4aN0OFH3VYcuWP+LwVr7giAiIuIlWVlZbk1ky8jIYOjQoXz44YeMGzeuzmEWIC8vryoj+SIF2jP44qsOkTMFB8GYnvDqau9cr2VT6Kc5NCIiprd27VqSkpLIz883uhSP8ttJYedyrkArYhYd46FnG9fOOXnK2at7vvVqTxdkhZt6Oz+LiIj5+VuYhQDtoV25cqXRJYh4xLXd4dAJyDpWt+PPt05tTcb0hNhGrp8n4ouaN2/O9OnTad68udGliIgHqc9FxMRsITBxELSopwmn13WHXm3rp20RI8TExDBu3DhiYmKMLkVEPEiBVsTkGtrg7sGQ6sGdG20h8Me+cNnFnmtTxBfk5eWxYsUK8vLyjC5FRDxIgVbED4SHwp8GOMe6Ngi9sLbax8GDw+HSJI+UJuJTsrKyuO+++3x2q1MRcU9AjqEV8UcWi3OSWIc4WLcbvsmEvDpO/rLgXGO2X7JzsplFy3OJiIiJKNCK+JnIBjAkDa7oBBnZ8NMR56SxrONwqtR5jNXi3CghMRoSm0LnBOcOZCIiImakQCvip4Ks0DnR+VHJ7gCHQ0twiYiIf1GgFQkgVgvO8QUiAcpms9GhQwdsNpvRpYiIBynQiohIwGjbti2LFi0yugwR8TC98SgiIiIipqZAKyIiASMjI4O0tDQyMjKMLkVEPEiBVkREAobD4aCsrAyHw2F0KSLiQRpDKyIiIuKDwsPDKSgo8EhbT7/yb04WFhEVEc7UO26s9b4LER4efsFtuEuBVkRERMQHWSwWIiIiPNJWaJiN0LIKQsNsVW3WdJ9ZaciBiIiIiJiaemhFRCRgtG3bliVLlpCYmHj+g0XENBRoRUQkYNhsNpKTk40uQ0Q8TEMOREQkYGRnZzNjxgyys7ONLkVEPEiBVkREAsaJEyf44IMPOHHihNGliIgHKdCKiIiIiKkp0IqIiIiIqSnQioiIiIipaZUDERExtfbt29f52EaNGjFz5kz69OlDXFxcPVYlIt6kQCsiIgEjLi6ORx991OgyRMTDNORARERERExNgVZERERETE2BVkRERERMTYFWRERERExNgVZERERETE2BVkRERERMTYFWRERERExNgVZERERETE2BVkRERERMTYFWRERERExNgVZERERETE2B1ge89dZbdOvWjSZNmtCgQQM6dOjAM888g8PhMLo0ERGRWi1btoyuXbsSFhZGUlISzzzzjNEledVXX33FqFGjaNWqFRaLhVmzZhldklc9/fTT9O7dmyZNmtC4cWP69evHihUrDKkl2JCrSjUXXXQRjzzyCBdffDFhYWGsWbOGO++8k6CgICZPnmx0eSIiImfZuHEjo0aN4oEHHuDdd99l/fr1TJw4kfDwcCZOnGh0eV5RUFBAx44duemmm7j33nuNLsfrVq5cyW233UaPHj0IDw9n3rx5DB8+nC+//JK+fft6tRYFWh9w5ZVXVrvdpk0bFi9ezOrVqxVoRUTEJz3zzDP06NGDJ598EoAOHTqwbds2nnrqqYAJtFdddRVXXXUVANOnTze4Gu9bvnx5tdtz5sxhxYoVLFq0yOuBVkMOfIzD4eC7775j3bp1DBo0yOhyREREarRu3TqGDBlS7b4hQ4awf/9+srKyDKpKjGS32zl58iQRERFev7Z6aH1EXl4e8fHxlJaWYrfbmTlzJpMmTTK6LBERMZlfjp/klxMnz7q/vKKi6vOuvVln3T5d25YtCAo6d59XTk4OsbGx1e6rvJ2Tk0NCQoLbz+FClJWXs/dg7ln3u/L8m0U3okmjyPovtp5k5RyhqLik2n01Pd/avgZhIcG0Sqj+f1sXTzzxBCdOnGDChAnulu42BVofERkZSXp6OkVFRXz99dc89NBDtGjRgvHjxxtdmoiImEhQkJV3Pvyc4pLSGh8vOlXM/PeW1Xq7W+cUUlobE0Y9ITgoiO/St/Pjrr01Pn6+5x8RbuO+20bXe531qaDoFAver3ly1pnPt6b7rh86wOVA++KLL/LEE0+wZMkSQ17MaMiBj7BarbRr1460tDQmTpzItGnTePjhh40uS0RETKZxVENGXeHe+MUmjSIZ8ds+dTo2Li6O3NzqPaGHDx+ueswoFouFa668jIYRDdw6/7oh/d0+11e0b9uSnl3au3Vux+QkunVOcemcuXPnMnXqVJYsWcLgwYPduu6FUqD1UXa7neLiYqPLEBERE+rasR2dL27j0jkWYMywgdjCQut0fN++ffnkk0+q3bdixQpatWpl2HCDShHhNq4fOsDl87qnXUzH5CTPF2SAYZf3pmnjKJfOaRjegGuHXIbFYqnzOf/zP//DY489xrJlywwLs6BA6xNmzpzJ559/zk8//cTOnTt57bXXmD17NrfccovRpYmIiAlZLBauvrIfkQ3D63xO/15daJ1Y957V++67j++++46HH36YHTt28MYbb/Dcc8/x4IMPulOyx7Vv25JeXTvU+fjoRpGMuLy3S9coKCggPT2d9PR0SktLyc3NJT09nczMTFfL9biw0BDGDB/kUji9dmh/GobXvXf63nvv5emnn+att97i4osvJjc3l9zcXPLy8twp+YJYHFq933D33XcfH330EdnZ2dhsNtq0acNtt93GxIkTCQoKMro8ERExqZ0/HeT1/1t+3uNim0Vz9x+vITjYtb85S5cu5f/9v//Hjh07iI2NZfLkydx///3ulutxJaVlPLvgA345fvYkudNZgDvGjiTJxXGjq1evrnFFogEDBrB69WqX2qovn3y1gVXfbD7vcT3S2nPd0P4utV1bWL7llltYsGCBS21dKAVaERERP7b407V8uzmj1seDgqzc/cdriLuoqRer8p4D2Yd56V9Lzrn75oBeXRg6sJcXq/Ke8ooKXnxrMYcO/1LrMdGNI5k87jrC6jjcxBdpyIHJHMz5+aylOERERGpz1cBexDRpVOvjv7ush9+GWYCW8c0Z9JuutT4ed1FTrujX3XsFeVlwUBA3DL+c4Fre8bVYLIwZNsjUYRYUaE2lvKKCt//zGbNfeocD2YeNLkdEREwg9NexlNYa3h5unRjHZT06G1CVd/22bzfim8ecdX9QkJUbhg9yeaiF2TSPacKQAT1rfGxAry4uD7XwRQq0Z6ioqOCtt97id7/7Hc2aNSMsLIyWLVsyZMgQ5s2bR8WvixAbYdPWneTlFxIaGuLXr6ZFRMSzWra4iEG9L6l2X1hoCKOHDcRq9f8oEBRkZUwNwfXK/j2JbRZtUFXe1ad7J9q2alHtvriLmjK4XzeDKvIs//8udsHJkye54oor+OMf/8hnn31GaGgoXbp0wW638+mnn3L77beTn59vSG3lFRWs/No5qHtgr66EhGhPDBERqbvL+1xKQmyzqtsjBvch2sS7YbnqzF7K1olx9AuA3ulKVouF0Vf9d1k251CEQbUORTAbBdrTjB8/nlWrVpGQkMDKlSvJzs7mu+++Iysri5ycHB5//HFCQkIMqa2ydzayYbjbiyWLiEjgOr2XsmNyEt06ubZ4vj/o060T7VrFO5e0GjawxmEY/uz0TTeu7N/Dr3qntcrBrzZt2kT37t0JDg5m8+bNdOrUyWNtP/fGIvILTl1ACw7yC0/hcDiwhYUSalCoFhER8ystKyc4OCjgwlwlu91Ohd1OSHBgvtPpcDgoLSsnNCTYpTVqvSGyYQPuueVat84NzP/NGixevBiAYcOGeTTMAuQXnOJkQaFH2iouKa11f24REZE60WI5nArwL0JJqX9lCQXaX2VkONfo693btV1C6iKy4YXsCa3eWREREfF/F5KXFGh/dfKkcxeRRo1qX6vPXe52nwOsT9/Ofz5ZQ2TDcKZNuFGTwURERETOoHT0q6ioKIB62X/Y/TG0zt5ZgLKycp5+daFnCxMRERHxERpD6wGpqaksWrSIb775xuNte2IMrcbOioiIiNRMgfZX11xzDX/5y19YtmwZGRkZdOzY0WNtuzcmRGNnRUREJHBcyBhaLdt1mhtuuIH33nuPli1b8uabbzJgwICqxw4fPsz8+fOZNGkSERER9V6Lxs6KiIiI1I0C7WlOnjzJqFGjWL16NQDx8fG0aNGCnJwcsrOzcTgcHD9+nMaNG9drHeUVFcx9dSEnThYw4rd96Nvds8uIiYiIiPgT7RR2mqioKD7//HP++c9/MnDgQIqKitiyZQtWq5Urr7ySf/7zn0RG1v82gZu27uLEyQLtCiYiIiJSB+qh9UGbt+1m+ervGNCri3pnRURERM5DgdZHlZWXY8FCcHCQ0aWIiIiI+DQFWhERERExNY2hFRERERFTU6AVEREREVNToBURERERU1OgFRERERFTU6AVEREREVNToBURERERU1OgFRERERFTU6AVEREREVNToBURERERU1OgFRERERFTU6AVEREREVNToBURERERU1OgFRERERFTU6AVEREREVNToBURERERU1OgFRERERFTU6AVEREREVNToBURERERU1OgFRERERFTU6AVEREREVNToBURERERU1OgFRERERFTU6AVEREREVNToBURERERU1OgFRERERFTU6AVEREREVNToBURERERU1OgFRERERFTU6AVEREREVNToBURERERU1OgFRERERFTU6AVEREREVNToBURERERU1OgFRERERFTU6AVEREREVNToBURERERU1OgFRERERFTU6AVEREREVNToBURERERU/v/fZQcFh+tZccAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 872.774x367.889 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit\n",
    "from numpy import pi\n",
    "\n",
    "qreg_q = QuantumRegister(3, 'q')\n",
    "creg_c = ClassicalRegister(3, 'c')\n",
    "circuit = QuantumCircuit(qreg_q, creg_c)\n",
    "\n",
    "circuit.ry(1.91063324, qreg_q[0])\n",
    "circuit.ch(qreg_q[0], qreg_q[1])\n",
    "circuit.cx(qreg_q[1], qreg_q[2])\n",
    "circuit.cx(qreg_q[0], qreg_q[1])\n",
    "circuit.x(qreg_q[0])\n",
    "circuit.barrier(qreg_q[0], qreg_q[1], qreg_q[2])\n",
    "circuit.measure(qreg_q[0], creg_c[0])\n",
    "circuit.measure(qreg_q[1], creg_c[1])\n",
    "circuit.measure(qreg_q[2], creg_c[2])\n",
    "\n",
    "display(circuit.draw(\"mpl\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1fc88d3",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### 3. Initialize the Qiskit Runtime Sampler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "2756a944",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from qiskit_ibm_runtime import Sampler\n",
    "\n",
    "sampler = Sampler(backend=backend)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "617bbd25",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### 4. Invoke the Sampler and get results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "b474b4ea",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ">>> Job ID: cjs5i78vndeds0nkr0d0\n",
      ">>> Job Status: JobStatus.RUNNING\n"
     ]
    }
   ],
   "source": [
    "job = sampler.run(circuit)\n",
    "print(f\">>> Job ID: {job.job_id()}\")\n",
    "print(f\">>> Job Status: {job.status()}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "19a1b861",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ">>> SamplerResult(quasi_dists=[{4: 0.3275, 2: 0.339, 1: 0.3335}], metadata=[{'shots': 4000}])\n",
      "  > Quasi-probability distribution: {4: 0.3275, 2: 0.339, 1: 0.3335}\n",
      "  > Metadata: {'shots': 4000}\n"
     ]
    }
   ],
   "source": [
    "result = job.result()\n",
    "print(f\">>> {result}\")\n",
    "print(f\"  > Quasi-probability distribution: {result.quasi_dists[0]}\")\n",
    "print(f\"  > Metadata: {result.metadata[0]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "9e30b5e6-5f92-4895-8ecd-8c6fbefb553f",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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YqOjoaEt7qVKl1LFjR8XGxurgwYOW9vLly6tVq1aKiYnRsWPHLO32Pvacd596Cs4h+1hwnWPPefdJuvl187h9HHnsBQQE5LsOp7sJJDQ0VJGRkYqJiVHNmjVzLK9cubJSUlIKFAIlKSUlRYcPH9abb76pTZs2af78+Ro4cGCe/a9du6Zu3bopKipKU6ZM0bhx4265jdxGAKtWrarExETLxZj2/quRC3udx9xRjAA6wz49O4sRQGcxeyQjgM6yTyM+ZgTQGcwd5dgRwNTU1HzfBOJ0I4DZI395Bbzk5GSVLl26wOstWbKkQkJC9P3336tp06YaPny4unTpovLly+fom5aWpp49eyoqKkpjx47NV/iTJE9PT3l6euZo9/DwsFxHmM3NzU1ubm45+uZ1nSHXH94Z8vqc/vn529JuNBpzHeLPqz2vY8xex96dsE8oWo76vXcnHHvOtk9wHs7ye8/pjorsa/9yu84vPj5eKSkpuV4fmF/u7u7q0KGDUlNTtW/fvhzLr127pocffliRkZF65ZVXNHXqVJu3BQAA4IycLgC2a9dO0o3r5v5pw4YNVn1sdf78eUk5/4K6du2aevbsqcjISL300kuaPn16obYDAADgjJwuAHbq1EmBgYFatGiR1cWQSUlJmjp1qooVK6ZBgwZZ2uPi4nT06NEcXxnnNron3QiR3333nfz8/NSyZUtLe/bXvpGRkRo9erTeffdd++4YAACAk3C6C8vc3d01b948hYWFqW3btlaPgjt9+rRmzJihGjVqWPqPHTtWERERWrBggYYMGWJpb9asmerVq6cGDRqoSpUqSk1N1aFDh7Rjxw55eHho/vz58vb2tvR/5plnFBkZqYoVK6pUqVKaNGlSjtqGDBlitW0AAIA7kdMFQOnG7e87d+7UxIkTtWTJEmVkZKh+/fqaPn26+vXrl691TJ06VVFRUdq2bZsSEhJkNBpVrVo1DR8+XKNGjdL9999v1f/UqVOSblxnmNtULpLUvn17AiAAALjjOd00MHcTngXsWnjuqXPgnHAenBPOg/PCOfAsYAAAABQZAiAAAICLIQACAAC4GAIgAACAiyEAAgAAuBgCIAAAgIshAAIAALgYAiAAAICLIQACAAC4GAIgAACAiyEAAgAAuBgCIAAAgIshAAIAALgYAiAAAICLIQACAAC4GAIgAACAiyEAAgAAuBgCIAAAgIshAAIAALgYAiAAAICLIQACAAC4GAIgAACAiyEAAgAAuBgCIAAAgIshAAIAALgYAiAAAICLIQACAAC4GAIgAACAiyEAAgAAuBgCIAAAgIshAAIAALgYAiAAAICLIQACAAC4GAIgAACAiyEAAgAAuBgCIAAAgIshAAIAALgYAiAAAICLIQACAAC4GAIgAACAiyEAAgAAuBgCIAAAgIshAAIAALgYAiAAAICLIQACAAC4GAIgAACAiyEAAgAAuBgCIAAAgIshAAIAALgYAiAAAICLsTkA1qlTRx988IEuXbpkz3oAAADgYDYHwDNnzuill15SlSpVNGDAAG3ZssWedQEAAMBBbA6A8fHxmj17turVq6clS5aoS5cuqlmzpt5++23Fx8fbs0YAAADYkc0BsGTJkhoxYoT27t2rn3/+Wc8++6yuXLmicePGqVq1anr00Ue1bt06mc1me9YLAACAQrLLTSD169fXJ598ovPnz+vLL79UmzZttGLFCnXv3l3Vq1fX5MmTde7cOXtsCgAAAIVk17uAPT09FRYWpq5du6pixYoym806e/asJk+erMDAQI0cOVJ//fWXPTcJAACAArJbANy4caP69u2rKlWq6NVXX5XBYNAbb7yh33//XUuXLlXjxo312WefaeTIkfbaJAAAAGzgXpg3nzt3TvPnz9eCBQt0+vRpSVJoaKhGjBihHj16yM3NTZIUGBioPn36qEePHlqxYkXhqwYAAIDNbA6A3bt314YNG5SVlSV/f3+9+uqrGj58uGrUqJHne1q1aqW1a9faukkAAADYgc0BcO3aterYsaNGjBihRx55RO7ut15Vjx49FBAQYOsmAQAAYAc2B8Djx4+rZs2aBXpPvXr1VK9ePVs3CQAAADuw+SaQqVOnauXKlTfts3r1ag0bNszWTQAAAMABbA6ACxcu1MGDB2/a5+eff1ZERIStmwAAAIAD2HUewH9KS0vL17WBAAAAuH0Klc4MBkOu7WazWbGxsVq3bh03fQAAADiZAo0AGo1Gubm5Web3mzRpkuX13/9zd3fXPffco/3796t///4OKRwAAAC2KdAIYNu2bS2jftu3b1e1atVynffPzc1NZcqUUceOHRUeHm6XQgEAAGAfBQqAW7dutfy/0WjU0KFDNWHCBHvXBAAAAAey+SYQk8nk0PC3d+9ede3aVX5+fvL29laLFi20dOnSfL3XbDZr3bp1+te//qUGDRrI19dXJUqUUMOGDTV16lSlpaXlaz3/+te/ZDAYZDAYFB8fX5jdAQAAcBpOeYtuVFSUwsLC5OXlpf79+6tUqVJavny5+vXrp9jYWI0ZM+am709PT1fXrl3l6emp9u3bKywsTGlpadqwYYPGjx+v77//Xlu3blWJEiXyXEdkZKQ+++wzeXt7KzU11d67CAAAUGTyHQCHDRsmg8GgqVOnyt/fP98TPBsMBv33v//Nd0GZmZkKDw+X0WjU9u3b1ahRI0nShAkTFBISonHjxqlPnz6qXr16nutwc3PTf/7zHz377LMqXbq0pT0jI0O9e/fWqlWrNGvWLL388su5vj8pKUnDhg1Tnz59lJCQoG3btuW7fgAAAGeX7wC4cOFCGQwGvfrqq/L399fChQvz9b6CBsAtW7boxIkTGjp0qCX8SZKvr6/GjRunIUOGKCIi4qZfP3t4eGj8+PG5to8dO1arVq3Stm3b8gyA//73v3Xt2jXNmjVLffv2zXftAAAAd4J8B8A//vhDklS5cmWr1/aWfaNJaGhojmVhYWGSVKgROQ8PD0nKc4LqVatWKSIiQosWLVKFChUKtO709HSlp6dbXicnJ0u6MfKYkZEh6f+n0snKypLJZLL0zW7PzMyU2Wy2tLu5ucloNObZDueS1+eU/flnyz7+MjMz89Xu4eEhk8mkrKwsS5vBYJC7u3ue7XkdY/Y69px3nzwE5+Co33vOe+w57z45+LkPKABHHnsFke8A+M+vXG/2FWxhxMTESJJq1aqVY1nFihVVsmRJSx9bzJ8/X1LuAfPSpUsKDw9Xr169NGDAgAKve9q0aZo8eXKO9o0bN1quN6xWrZqCg4N16NAhnTlzxtKndu3aCgoK0p49e5SQkGBpb9SokapXr67t27fr6tWrlvaWLVsWOKDC8fL6nDZu3Gj1C7tDhw4qXry41q5da/X+rl276tq1a4qKirK0ubu7q1u3bkpMTFR0dLSlvVSpUurYsaNiY2OtHstYvnx5tWrVSjExMTp27Jil3d7HnvPuU0/BOWQfC65z7DnvPkmO+TcbBefIY68gD98wmP/+p4gTCA0NVWRkpGJiYlSzZs0cyytXrqyUlBQlJSUVeN3r1q1T9+7dVbt2bR04cECenp5Wy/v166fIyEgdPnxYFStWlCS1b99e27ZtU1xcnKUtL7mNAFatWlWJiYny8fGRZP+/GsM/LPCPAQ4ydxQjgM6wT8/OYgTQWcweyQigs+zTiI8ZAXQGc0c5dgQwNTVVvr6+SkpKsuSOvOR7BPDvKbOgqlWrZvN77WXv3r3q16+ffH19tWzZshzhb8mSJVq6dKm++OKLWwa9vHh6euZYr3TjxMz+6jnb35+o8nd5fTXNM5XvDHl9Tv/8/G1pNxqNuQ7x59We1zFmr2PvTtgnFC1H/d67E449Z9snOA9n+b2X71RRo0aNPJ/9ezMGgyHHXyo34+vrK0l5jvAlJydb3dmbH/v27VNoaKiMRqM2bNigunXrWi2/fPmyRo4cqW7duunJJ58s0LoBAADuNPkOgIMGDbIpABZU9rV/MTExatKkidWy+Ph4paSkKCQkJN/r27dvn7p06SKTyaSNGzeqWbNmOfqcOXNGly5d0po1a/Lcx0qVKkmSDhw4YHV3MgAAwJ2mQNPA3A7t2rXTtGnTtHHjRvXv399q2YYNGyx98iM7/GVlZWnDhg1q3rx5rv3Kli2rp556Ktdla9asUXx8vAYOHKjixYurbNmyBdgbAAAA5+N0F5Z16tRJgYGBWrRokV544QXLaFtSUpKmTp2qYsWKadCgQZb+cXFxSkpKUqVKlSxfH0vSTz/9pC5duigzM1Pr169Xy5Yt89xm1apVNW/evFyXtW/fXvHx8XrvvfdsvjYQAADAmThdAHR3d9e8efMUFhamtm3bWj0K7vTp05oxY4Zq1Khh6T927FhFRERowYIFGjJkiKQb1/R16dJFf/75px588EFFRkYqMjLSajt+fn4aNWrU7dsxAAAAJ+F0j4KTbsx/tHPnTk2cOFFLlixRRkaG6tevr+nTp6tfv363fH9ycrKuXLkiSVq/fr3Wr1+fo0/16tUJgAAAwCXlex5Ao9Eog8GgI0eO6L777sv3beUGg8FqXhtXkpycnO/5eGzFPIDOY+6ooq4AEueEM+GccB6cF87B0edEQXKH0z0KDgAAAI7ldI+CAwAAgGMxPTgAAICLKXQA/O6779SzZ09Vq1ZNvr6+qlatmnr16qXvv//eDuUBAADA3myeBiYzM1MDBw7U8uXLZTab5e7urrJlyyo+Pl4rV67UqlWr1Lt3by1atIjn2AIAADgRm0cAp02bpm+++UYPPPCAduzYobS0NMXFxSktLU3bt29XmzZttHz5cr399tv2rBcAAACFZHMAXLBggYKCgrRp0ya1bt3aMi2M0WhUmzZttGnTJt13332aP3++3YoFAABA4dkcAOPi4tSjR488v9718PBQjx49FBcXZ3NxAAAAsD+bA2DVqlWVkpJy0z6pqamqVq2arZsAAACAA9gcAJ9++mktXbo0zxG+c+fOacmSJXr66adtLg4AAAD2l+/bc8+cOWP1um/fvtq1a5eCg4M1atQotWnTRv7+/rpw4YJ27Nihjz76SG3atNFjjz1m96IBAABgu3wHwBo1ashgMORoN5vNGj9+fK7tK1eu1OrVq5WZmVm4KgEAAGA3+Q6AgwYNyjUAAgAA4M6S7wC4cOFCB5YBAACA24VnAQMAALgYAiAAAICLKdRDeq9evaqZM2dq06ZNOn/+vNLT03P0MRgMOnHiRGE2AwAAADuyOQAmJCSoVatWOnHihHx8fJScnCxfX19dv35d165dkyQFBATIw8PDbsUCAACg8Gz+CnjSpEk6ceKEvvjiC125ckWS9OKLLyo1NVW7d+9WSEiIatSood9++81uxQIAAKDwbA6Aa9euVadOnfTEE0/kmB6mWbNmWrdunU6dOqXJkycXukgAAADYj80BMC4uTsHBwZbXbm5ulq9+Jal06dJ66KGHtHTp0sJVCAAAALuyOQD6+voqIyPD8rp06dI6e/asVR8fHx9duHDB9uoAAABgdzYHwMDAQJ06dcryOjg4WJGRkbp06ZIk6dq1a1q1apWqVatW6CIBAABgPzYHwNDQUG3evFl//fWXJGnEiBG6ePGiGjZsqMcee0z16tXTiRMnNGTIEHvVCgAAADuwOQA+88wzmjt3riUAPvroo3r33XeVmpqq5cuXKz4+XqNHj9bLL79st2IBAABQeDbPA1ipUiX169fPqm3MmDEaNWqUEhMTVaFChRx3BwMAAKDoFepJILlxc3OTv7+/vVcLAAAAOyl0AIyLi9PixYt14MABJSUlydfXV8HBwerfv78qVapkjxoBAABgR4UKgLNmzdLLL7+s9PR0mc1mS/tXX32l8ePHa8aMGXr22WcLXSQAAADsx+YAuHjxYj3//PMqV66cxo8frwceeED+/v66cOGCtm/fro8++siyvG/fvvasGQAAAIVgcwB85513VK5cOR08eFABAQGW9tq1a6tt27YaMmSIgoODNX36dAIgAACAE7F5GpgjR46ob9++VuHv76pUqaLHHntMR44csbk4AAAA2J/NAdDPz0/e3t437VOyZEn5+fnZugkAAAA4gM0B8OGHH9aqVauUmZmZ6/KMjAytWrVKPXv2tLk4AAAA2J/NAfCdd96Rt7e3QkND9eOPP1oti46OVmhoqEqVKqW333670EUCAADAfvJ9E0hgYGCOtuvXr2v//v1q3bq13N3dVa5cOSUmJlpGBStVqqTGjRvrxIkT9qsYAAAAhZLvAGgymXI82s3Dw0PVqlWzavvnTSEmk6kQ5QEAAMDe8h0AT5065cAyAAAAcLvYfA0gAAAA7kyFfhawJGVmZurYsWNKTk6Wj4+PateuLXd3u6waAAAAdlaoEcDLly8rPDxcvr6+atCggdq0aaMGDRrIz89Pw4cP16VLl+xVJwAAAOzE5mG6y5cvq0WLFvr9999VpkwZPfDAA6pUqZLi4+O1b98+zZs3T9u2bVN0dLTKlCljz5oBAABQCDaPAL711lv6/fff9fLLL+v06dNav369FixYoHXr1un06dN69dVXFRMToylTptizXgAAABSSzQFwxYoVat++vaZPn57jkXAlSpTQtGnT1L59e3333XeFLhIAAAD2Y3MAPH/+vFq2bHnTPi1bttT58+dt3QQAAAAcwOYA6Ovrq9OnT9+0z+nTp+Xr62vrJgAAAOAANgfAdu3aadmyZdq0aVOuyzdv3qxly5apffv2tm4CAAAADmDzXcATJ07UmjVrFBYWpq5du6pdu3by9/fXhQsXtHXrVq1bt04lSpTQhAkT7FkvAAAACsnmAFi3bl1t2LBBQ4YM0Zo1a7RmzRoZDAaZzWZJ0r333quFCxeqbt26disWAAAAhVeox3W0adNGMTEx2rVrlw4cOGB5EkhwcLBat24tg8FgrzoBAABgJzYHwGHDhql+/fp68cUX1aZNG7Vp08aedQEAAMBBbL4JZNGiRbp48aI9awEAAMBtYHMAvPfeexUXF2fPWgAAAHAb2BwAhw0bpjVr1ujcuXP2rAcAAAAOZvM1gL1791ZUVJRatWqlV155Rc2aNZO/v3+uN35Uq1atUEUCAADAfmwOgIGBgZZpX1544YU8+xkMBmVmZtq6GQAAANiZzQFw0KBBTPMCAABwB7I5AC5cuNCOZQAAAOB2sfkmEAAAANyZCvUkEElKT0/X2rVrdeDAASUlJcnX11fBwcHq2rWrPD097VEjAAAA7KhQAXDlypUaPny4EhISLM8Alm7c+FGhQgV9/vnn6tGjR6GLBAAAgP3YHAA3b96s3r17y83NTcOGDdMDDzwgf39/XbhwQdu3b9dXX32lRx99VBs2bFDHjh3tWTMAAAAKweYAOHHiRBUvXlw//PCD6tWrZ7Vs0KBBeuGFF9S6dWtNnDiRAAgAAOBEbL4J5MCBA+rXr1+O8JetQYMG6tu3r/bv329zcQAAALA/mwNgiRIlVL58+Zv2qVChgkqUKGHrJgAAAOAANgfAzp07a9OmTTfts2nTJnXp0sXWTQAAAMABbA6AM2bM0MWLFzVo0CDFxsZaLYuNjdWTTz6pxMREzZgxo9BFAgAAwH5sDoBPPvmkSpcura+//lr33nuvatasqdatW6tmzZq69957tWjRIvn5+emJJ55Qx44dLf916tQpX+vfu3evunbtKj8/P3l7e6tFixZaunRpvus7ceKEJk2apIcffliVK1eWwWBQjRo1bvk+k8mk+fPnq02bNvLz81OJEiV03333aejQobp69Wq+tw8AAOCsbL4LeOvWrZb/z8zM1MmTJ3Xy5EmrPj///HOO9+Xn+cFRUVEKCwuTl5eX+vfvr1KlSmn58uXq16+fYmNjNWbMmFuuY8eOHZo8ebLc3Nx0//33Kz4+/pbvSU9PV58+fbR69Wo1aNBAQ4YMkaenp86cOaO1a9fqrbfeUqlSpW65HgAAAGdmcwA0mUz2rMMiMzNT4eHhMhqN2r59uxo1aiRJmjBhgkJCQjRu3Dj16dNH1atXv+l62rZtq+joaDVs2FDFixeXl5fXLbf92muvafXq1Xr77bf16quvWi1z1P4CAADcbk73LOAtW7boxIkTGjhwoCX8SZKvr6/GjRun69evKyIi4pbrCQwMVIsWLVS8ePF8bffcuXOaOXOmHnjggRzhT5KMRqOMRqf7cQEAABRYoZ8FnO3MmTM6deqU2rZtW6j1ZH+1HBoammNZWFiYJGnbtm2F2kZuvvnmG2VmZuqxxx7T1atXtXLlSp05c0b+/v4KCwtT5cqV7b5NAACAomC3ALhgwQK9+eabysrKKtR6YmJiJEm1atXKsaxixYoqWbKkpY89/fTTT5KkP//8U7Vr11ZcXJxlWbFixfT222/rxRdfvOk60tPTlZ6ebnmdnJwsScrIyFBGRoakGyOJbm5uysrKsvpaObs9MzPT6rnKbm5uMhqNebbDueT1OWV//tnc3d0t/fPT7uHhIZPJZHV+GQwGubu759me1zFmr2PPeffJQ3AOjvq957zHnvPukxN+4eeyHHnsFYTdAqC9JCUlSbrxlW9ufHx8LH3s6eLFi5KkyZMnq0uXLtq0aZOqVq2q7du3a/jw4Ro9erSCgoL00EMP5bmOadOmafLkyTnaN27caJkQu1q1agoODtahQ4d05swZS5/atWsrKChIe/bsUUJCgqW9UaNGql69urZv3251F3LLli1VoUKFQu837Cuvz2njxo1Wv7A7dOig4sWLa+3atVbv79q1q65du6aoqChLm7u7u7p166bExERFR0db2kuVKqWOHTsqNjZWBw8etLSXL19erVq1UkxMjI4dO2Zpt/ex57z71FNwDtnHgusce867T9LNr5vH7ePIYy8gICDfdRjMf/9TpBAmT55slxHA0NBQRUZGKiYmRjVr1syxvHLlykpJSSlwCPTy8lLFihV16tSpm263UqVK+v33362eYLJu3Tp17dpVnTp1uunk17mNAFatWlWJiYny8fGRZP+/GsM/LNCPAQ40dxQjgM6wT8/OYgTQWcweyQigs+zTiI8ZAXQGc0c5dgQwNTVVvr6+SkpKsuSOvDjdCGD2yF9eAS85OVmlS5d22HY7d+6c4/F1YWFh8vT01L59+266Dk9PT3l6euZo9/DwkIeH9T9Kbm5ucnNzy9E3++TObzucS16f0z8/f1va87oRKa/2vI4xex17d8I+oWg56vfenXDsOds+wXk4y+89ux0Vvr6+qlatWqHXk33tX27X+cXHxyslJSXX6wMLq3bt2pIkPz+/HMuMRqNKlSqla9eu2X27AAAAt5vdAuCoUaP0xx9/FHo97dq1k3Tjurl/2rBhg1Ufe+rYsaMk6fDhwzmWJSQkKDExMV9PEgEAAHB2Tjcu3KlTJwUGBmrRokVWF0MmJSVp6tSpKlasmAYNGmRpj4uL09GjRwt9Y0i7du10//33a/PmzYqMjLS0m81mjRs3TpLUt2/fQm0DAADAGeT7wrLt27dLkkJCQuTl5WV5nR8FmRvQ3d1d8+bNU1hYmNq2bWv1KLjTp09rxowZViNxY8eOVUREhBYsWKAhQ4ZY2hMTE/XSSy9ZXmdkZCgxMdGqz4wZM1SuXDlJN75LX7BggTp27KiuXbvq0UcfVZUqVbRz507t2bNHjRs31muvvZbv/QAAAHBW+Q6A7du3l8Fg0JEjR3TfffdZXudHQe8M7tChg3bu3KmJEydqyZIlysjIUP369TV9+nT169cvX+tISUnJ8cSQ1NRUq7ZJkyZZAqAkNW/eXHv27NHEiRO1efNmJScnq1q1aho7dqzGjRsnb2/vAu0HAACAM8p3AJwwYYIMBoMlMGW/dpSQkBCtW7fulv0WLlyohQsX5mivUaOGbJnhpm7duvrmm28K/D4AAIA7Rb4D4KRJk276GgAAAHcGp7sJBAAAAI5lcwC8evWqTp48mWP28iVLlujxxx/XU089pf379xe6QAAAANiXzY+XeOWVV/TVV1/pwoULlhnJP/30Uz333HOWa+8WL16sn376SUFBQfapFgAAAIVm8wjgtm3bcjw27e2331blypW1fft2LV26VGazWe+++65dCgUAAIB92DwCGBcXpwcffNDy+siRI4qNjdU777yjNm3aSJK++eabAs0XCAAAAMezeQQwPT1dxYoVs7zetm2bDAaDQkNDLW2BgYE6d+5c4SoEAACAXdkcAKtUqaJDhw5ZXq9evVplypRRgwYNLG2XLl1SyZIlC1chAAAA7Mrmr4AfeughzZo1Sy+99JK8vLy0fv16q2f0StLx48dVrVq1QhcJAAAA+7E5AI4dO1arVq3S+++/L0mqVKmS3nzzTcvyixcvateuXXruuecKXyUAAADsxuYAWLFiRf3222/avHmzJKlt27by8fGxLE9MTNS7776rsLCwwlcJAAAAu7E5AEpS8eLF1b1791yX1alTR3Xq1CnM6gEAAOAAPAoOAADAxRRqBDArK0tLly7Vpk2bdP78eaWnp+foYzAYLF8TAwAAoOjZHABTU1MVGhqqH3/8UWazWQaDwfIIOEmW1waDwS6FAgAAwD5s/gr4P//5j6KjozV58mQlJibKbDZr0qRJiouL05IlSxQYGKjHHnss11FBAAAAFB2bA+C3336rFi1a6PXXX1eZMmUs7f7+/nrssccUFRWlTZs28SxgAAAAJ2NzADxz5oxatGjx/ysyGq1G+6pUqaJu3bopIiKicBUCAADArmwOgN7e3jIa///tvr6+iouLs+pTsWJFnTlzxvbqAAAAYHc2B8Dq1atbhbt69eppy5YtllFAs9mszZs3q1KlSoWvEgAAAHZjcwDs1KmToqKilJmZKUkaPHiwzpw5o5YtW+rll19WmzZtdPDgQfXu3dtuxQIAAKDwbJ4GJjw8XGXLllVCQoIqVaqkYcOG6cCBA5o9e7YOHjwoSerdu7cmTZpkp1IBAABgDzYHwFq1aunVV1+1avvkk080YcIEnTx5UtWrV1fFihULXSAAAADsq1BPAslN+fLlVb58eXuvFgAAAHbCs4ABAABcjM0jgIGBgfnqZzAYdOLECVs3AwAAADuzOQCaTKZcn/OblJSkP//8U5JUqVIlFStWzObiAAAAYH82B8BTp07ddNno0aN14cIFRUZG2roJAAAAOIBDrgGsUaOGlixZoitXrmj8+PGO2AQAAABs5LCbQDw8PNSlSxctXbrUUZsAAACADRx6F/Bff/2ly5cvO3ITAAAAKCCHBcAdO3bof//7n2rXru2oTQAAAMAGNt8E0rFjx1zbMzMzde7cOctNIhMmTLB1EwAAAHAAmwPg1q1bc203GAwqXbq0QkNDNXr0aHXp0sXWTQAAAMABCjUPIAAAAO48hX4W8MWLF3Xu3DmZTCZVrlxZFStWtEddAAAAcBCbbgJJT0/XO++8o1q1aqlSpUpq2rSpQkJCVLlyZZUrV04vvvjiTSeKBgAAQNEpcACMjY1Vs2bNNHbsWJ04cUKVKlVSSEiIQkJCVKlSJV2+fFkfffSRmjZtqk2bNlneFxcXx5yAAAAATqBAATAjI0Ndu3bVr7/+qgEDBujIkSM6e/asoqOjFR0drbNnz+rIkSN6/PHHdfnyZfXq1UunTp3SiRMn1KZNGx09etRR+wEAAIB8KtA1gHPmzNFvv/2miRMnauLEibn2qV27tr788kvdd999mjhxoh5//HGdOnVKiYmJatKkiV2KBgAAgO0KNAK4dOlS1axZM19z+73++uuqVauWoqOjlZaWpg0bNqhbt242FwoAAAD7KFAAPHz4sEJDQ2UwGG7Z12AwWPru3r1b7du3t7VGAAAA2FGBAmBKSop8fX3z3d/Hx0fu7u6qWbNmgQsDAACAYxQoAFaoUEG///57vvufOHFCFSpUKHBRAAAAcJwCBcCWLVtq3bp1io+Pv2Xf+Ph4rVmzRm3atLG5OAAAANhfgQLgM888o5SUFD3yyCNKTEzMs9+lS5f0yCOP6K+//tKIESMKXSQAAADsp0DTwHTo0EHh4eGaO3eu7r//fo0YMUIdO3ZU1apVJd2YJHrz5s2aO3euEhMTNXz4cG7+AAAAcDIFfhbw7Nmz5ePjow8++EDTpk3TtGnTrJabzWYZjUa99NJLOZYBAACg6BU4ALq5uendd9/V8OHDtXDhQkVHR1uuCaxYsaJatWqlwYMHq1atWnYvFgAAAIVX4ACYrVatWpoyZYo9awEAAMBtUKCbQAAAAHDnIwACAAC4GAIgAACAiyEAAgAAuBgCIAAAgIshAAIAALgYAiAAAICLIQACAAC4GAIgAACAiyEAAgAAuBgCIAAAgIshAAIAALgYAiAAAICLIQACAAC4GAIgAACAiyEAAgAAuBgCIAAAgIshAAIAALgYpw2Ae/fuVdeuXeXn5ydvb2+1aNFCS5cuLdA60tPT9eabb6pWrVry8vJSQECAhg8frosXL+ba/9q1a3r//ffVuHFjlS5dWn5+fmrYsKGmTJmipKQke+wWAABAkXMv6gJyExUVpbCwMHl5eal///4qVaqUli9frn79+ik2NlZjxoy55TpMJpN69uypDRs2qEWLFurdu7diYmI0b948bd68WT/++KPKly9v6Z+RkaEOHTpo9+7datSokYYMGWKp5fXXX9f//vc/7dmzRyVKlHDUbgMAANwWThcAMzMzFR4eLqPRqO3bt6tRo0aSpAkTJigkJETjxo1Tnz59VL169ZuuJyIiQhs2bNCAAQP09ddfy2AwSJI+++wz/etf/9Lrr7+uOXPmWPp/99132r17tx555BF9++23Vuvq1auXVqxYoW+++UaDBg2y7w4DAADcZk73FfCWLVt04sQJDRw40BL+JMnX11fjxo3T9evXFRERccv1zJ07V5I0bdo0S/iTpBEjRigwMFBff/21rl27Zmk/efKkJOmhhx7Ksa5u3bpJkhISEmzaJwAAAGfidAFw69atkqTQ0NAcy8LCwiRJ27Ztu+k60tLStHv3btWuXTvHSKHBYFCXLl2Umpqqffv2Wdrr1asnSVq3bl2O9a1Zs0YGg0EdOnQo0L4AAAA4I6f7CjgmJkaSVKtWrRzLKlasqJIlS1r65OXEiRMymUy5ruPv646JidEDDzwg6cYoX69evfTdd98pODhY7du3l3TjGsA//vhDn3/+uRo3bnzT7aanpys9Pd3yOjk5WdKN6wszMjIkSUajUW5ubsrKypLJZLL0zW7PzMyU2Wy2tLu5ucloNObZDueS1+eU/flnc3d3t/TPT7uHh4dMJpOysrIsbQaDQe7u7nm253WM2evYc9598hCcg6N+7znvsee8++SE4z0uy5HHXkE4XQDMvtvW19c31+U+Pj63vCM3P+v4ez/pxg96+fLlGjdunN555x0dPHjQsmzw4MHq0qXLLWufNm2aJk+enKN948aNlptHqlWrpuDgYB06dEhnzpyx9Kldu7aCgoK0Z88eq6+aGzVqpOrVq2v79u26evWqpb1ly5aqUKHCLWvC7ZXX57Rx40arX9gdOnRQ8eLFtXbtWqv3d+3aVdeuXVNUVJSlzd3dXd26dVNiYqKio6Mt7aVKlVLHjh0VGxtrdbyWL19erVq1UkxMjI4dO2Zpt/ex57z71FNwDtnHgusce867T9LNr5vH7ePIYy8gICDfdRjMf/9TxAmEhoYqMjJSMTExqlmzZo7llStXVkpKyk1D4A8//KDWrVvr8ccf11dffZVj+dy5czV8+HC9//77evHFFyVJf/31lwYMGKDdu3fro48+UufOnSVJmzZt0r///W+ZzWbt3r1bNWrUyHO7uY0AVq1aVYmJiZbQae+/GsM/zLMc3GZzRzEC6Az79OwsRgCdxeyRjAA6yz6N+JgRQGcwd5RjRwBTU1Pl6+urpKQkS+7Ii9ONAGaP2uUV8JKTk1W6dOlCr+Pv/SRp6tSpWrlypVasWKGHH37Y0t6vXz95eXmpV69emjJliuXmktx4enrK09MzR7uHh4c8PKz/UXJzc5Obm1uOvtknd37b4Vzy+pz++fnb0m40GnMd4s+rPa9jzF7H3p2wTyhajvq9dycce862T3AezvJ7z+mOir9fn/dP8fHxSklJyfPavmyBgYEyGo15XiuY23WG2Td/5HajR3bbgQMH8rEHAAAAzs3pAmC7du0k3bhu7p82bNhg1ScvxYsXV0hIiI4dO6bTp09bLTObzYqMjJS3t7eaNm1qab9+/bqk3Kd6yW7LbXQPAADgTuN0AbBTp04KDAzUokWLrC6GTEpK0tSpU1WsWDGryZjj4uJ09OjRHF/3Dh8+XJI0duxYq+st5syZo5MnT+rxxx9X8eLFLe2tW7eWJE2ePNnqO/WsrCxNnDhRUu6jgwAAAHcap7uwzN3dXfPmzVNYWJjatm1r9Si406dPa8aMGVY3YowdO1YRERFasGCB5fFt0o07d5csWaL//e9/+uOPP9SuXTv9/vvv+vbbb3XPPffoP//5j9V2x40bpxUrVuiLL77QTz/9pI4dO0qSNm/erMOHD6tWrVr5egQdAACAs3O6EUDpxkjbzp071bp1ay1ZskSffvqp/P39tXjx4nyHMKPRqBUrVmjSpElKSEjQBx98oF27dumpp55SdHS01XOApRu3Vf/000967rnnlJ6erjlz5ujzzz9XVlaWXn75Ze3evfuWN58AAADcCZxuGpi7SXJycr5vx7YV08A4j7mjiroCSJwTzoRzwnlwXjgHR58TBckdTjkCCAAAAMchAAIAALgYAiAAAICLIQACAAC4GAIgAACAiyEAAgAAuBgCIAAAgIshAAIAALgYAiAAAICLIQACAAC4GAIgAACAiyEAAgAAuBgCIAAAgIshAAIAALgYAiAAAICLIQACAAC4GAIgAACAiyEAAgAAuBgCIAAAgIshAAIAALgYAiAAAICLIQACAAC4GAIgAACAiyEAAgAAuBgCIAAAgIshAAIAALgYAiAAAICLIQACAAC4GAIgAACAiyEAAgAAuBgCIAAAgIshAAIAALgYAiAAAICLIQACAAC4GAIgAACAiyEAAgAAuBgCIAAAgIshAAIAALgYAiAAAICLIQACAAC4GAIgAACAiyEAAgAAuBgCIAAAgIshAAIAALgYAiAAAICLIQACAAC4GAIgAACAiyEAAgAAuBgCIAAAgIshAAIAALgYAiAAAICLIQACAAC4GAIgAACAiyEAAgAAuBgCIAAAgIshAAIAALgYAiAAAICLIQACAAC4GAIgAACAiyEAAgAAuBgCIAAAgIshAAIAALgYAiAAAICLIQACAAC4GAIgAACAiyEAAgAAuBgCIAAAgIshAAIAALgYpw2Ae/fuVdeuXeXn5ydvb2+1aNFCS5cuLdA60tPT9eabb6pWrVry8vJSQECAhg8frosXL+b5nq+//lohISHy9vZW6dKl1b17d+3fv7+wuwMAAOA0nDIARkVFqXXr1tq5c6f69u2rZ555RvHx8erXr5/ee++9fK3DZDKpZ8+emjhxosqVK6dRo0apZcuWmjdvnlq2bKmEhIQc75kyZYqeeOIJXbx4Uc8884wee+wxbd++Xa1atdKuXbvsvZsAAABFwr2oC/inzMxMhYeHy2g0avv27WrUqJEkacKECQoJCdG4cePUp08fVa9e/abriYiI0IYNGzRgwAB9/fXXMhgMkqTPPvtM//rXv/T6669rzpw5lv4xMTGaNGmS7rvvPu3Zs0e+vr6SpGeffVYtWrRQeHi4fv31VxmNTpmZAQAA8s3p0syWLVt04sQJDRw40BL+JMnX11fjxo3T9evXFRERccv1zJ07V5I0bdo0S/iTpBEjRigwMFBff/21rl27ZmlfsGCBMjMzNX78eEv4k6RGjRppwIABOnLkiHbu3GmHPQQAAChaTjcCuHXrVklSaGhojmVhYWGSpG3btt10HWlpadq9e7dq166dY6TQYDCoS5cumjNnjvbt26cHHnggX9tduHChtm3bprZt2+a53fT0dKWnp1teJyUlSZIuX76sjIwMSZLRaJSbm5uysrJkMpksfbPbMzMzZTabLe1ubm4yGo15tl9Pu+mPArdRcrLy/JyyP/9s7u43Tr3MzMx8tXt4eMhkMikrK8vSZjAY5O7unmd7XseYvY49Z92n62kegnO4dMkxv/ec9dhz5n26nuZ04z0uKTlZDj32UlNTJcnqGMuL0wXAmJgYSVKtWrVyLKtYsaJKlixp6ZOXEydOyGQy5bqOv687JibGEgBjYmJUsmRJVaxY8ab9b2batGmaPHlyjvZ77rnnpu/D3eGLsUVdAeBcOCcAa7frnLh69arVt5m5cboAmD1qllfhPj4+lj6FWcff+2X/f4UKFfLdPzdjx47V6NGjLa9NJpMuX76ssmXLWn0NDWvJycmqWrWqYmNjLT9rwJVxTgDWOCfyx2w26+rVqwoICLhlX6cLgHcyT09PeXp6WrX5+fkVTTF3IB8fH05s4G84JwBrnBO3dquRv2xOd1FAduF5jbYlJyffcufys46/98v+/4L0BwAAuFM5XQC82fV28fHxSklJyfPavmyBgYEyGo15XrOX23WGtWrVUkpKiuLj4/PVHwAA4E7ldAGwXbt2kqSNGzfmWLZhwwarPnkpXry4QkJCdOzYMZ0+fdpqmdlsVmRkpLy9vdW0aVO7bhe28fT01MSJE3N8fQ64Ks4JwBrnhP0ZzPm5V/g2yszMVO3atXXu3Dn9+OOPlrkAk5KSFBISolOnTunYsWOqUaOGJCkuLk5JSUmqVKmS1Ve0CxYs0LBhw/KcCHr48OFWE0EfP35cdevWVWBgoNVE0AcPHlSLFi0UGBjIRNAAAOCu4HQBULrxKLiwsDB5eXmpf//+KlWqlJYvX67Tp09rxowZGjNmjKXvkCFDFBERoQULFmjIkCGWdpPJpK5du2rDhg1q0aKF2rVrp99//13ffvutatSood27d6t8+fJW250yZYpef/11Va9eXb1799bVq1e1ePFiXb9+XZs3b1br1q1v148AAADAYZxyOKtDhw7auXOnWrdurSVLlujTTz+Vv7+/Fi9ebBX+bsZoNGrFihWaNGmSEhIS9MEHH2jXrl166qmnFB0dnSP8SdL48eP11VdfqXz58vr000+1dOlSPfDAA/rhhx8IfwAA4K7hlCOAAAAAcBynHAEEAACA4xAAAQAAXAwBEAAAwMUQAAEAAFwMARAAAMDFEAABwInkNTEDEzYAsCcCIAA4EYPBoJiYGCUlJens2bO6dOmSpR2ANf4wsp17URcA15aVlSWj0cg/bnB56enpWrZsmWbPnq0DBw7IaDSqVq1aqlmzppo0aaJWrVqpcePGKlWqVFGXCtx2Fy9eVEJCgsqWLaurV6+qfPny8vPz49+OQmAiaBSJ2NhYVa1a1fLaZDLJbDbLzc2tCKsCis6YMWP00UcfqXr16qpVq5Y8PDz0559/6pdfflFycrKqVq2q7t27a9iwYWrSpElRlwvcFnFxcRo/frwiIyN17tw5lSpVSvfcc4/uv/9+NW/eXG3atFH9+vXl6elZ1KXecQiAuO1OnTqlwMBAhYaGasCAAerevbvKli1rWZ6VlSWDwSCj0Siz2SyDwaDr16+rWLFiRVg14Dh//PGH6tSpox49emjWrFkqX768rl69qj///FNxcXHavn27vvvuO+3du1eVK1fW5MmTNWjQIMv5AdyN4uPj9cgjj2j37t168MEHVbJkSRmNRp0+fVqHDh3StWvXVKdOHfXt21fh4eGqVKlSUZd8ZzEDt9nUqVPNBoPB8l+5cuXMgwcPNq9Zs8ackZFh1Tc9Pd1sNpvNn332mblTp07mY8eOFUXJgENNmTLFXKZMGfPmzZvNZrPZnJmZabU8IyPDfPLkSfOHH35oLl++vNlgMJjXr19fFKUCt82ECRPMvr6+5g8//NDSduXKFXNsbKx5+/bt5tdff91cp04ds9FoNLds2dK8c+dOs9lsNptMpqIq+Y7CCCBuux49emjbtm364IMPtGPHDi1btkzXrl2TJN17773q1auX+vbtq2bNmlne07t3b3333Xe6evWqvL29i6p0wCFGjhypRYsW6ZdfflGVKlVuOrIXGRmpwYMHy8fHRz///DNffeGuVbduXQUGBmr+/PkqX758jvMiPT1dx44dU0REhD744APVrl1b27ZtU4UKFYqw6jsHdwHjtkpISNDFixfl4+Ojp556SgsXLtSlS5f01VdfqWPHjjpx4oTee+89NW/eXCEhIfrkk0+0bNkyRUdHq3v37oQ/3JWaNGmipKQkrVy50vKPXFZWVq53OHbp0kVDhgzRuXPndPjw4SKoFnC8CxcuyGw2Kz09XeXLl5eU8054T09PNWjQQNOnT9dHH32kY8eO6f333y+Kcu9IBEDcVmlpafL09FSjRo0kSdevX5eXl5cGDhyoTZs26dy5c3r33XdVr1497du3T//+9781aNAgxcfH65lnnina4gEHCQkJUUBAgN544w2tWbNGkuTm5iaDwSCz2aysrCxJN26WkqTy5csrMzNTaWlpRVYz4Chms1nly5dX3bp1tXv3bu3Zs8fSnn0u/J27u7uef/551atXT3v37lVKSsrtLvmORADEbVWxYkVNnjxZ48ePl8lkUrFixSwntclkUqVKlTRmzBgdOnRIR48e1bPPPqv09HSVLl1aXbt2LeryAbszm82qV6+e5s2bpxIlSujhhx/Wgw8+qGXLlunKlSsyGAyWu+ONRqNSU1P1448/ytvbWy1btizi6gH7y74JMDQ0VFevXtVLL72k3377zepcMJlMVqPk2XfKX7x4USVLlizK8u8YBEDcVh4eHurQoYOaN28uo/HG4Zd9Umff9ZuZmamsrCzdd999Gjx4sIoXL64+ffoUceWAY2R/rdW5c2d9+OGHql+/vjZu3Kh+/fqpQ4cOeu655/Ttt9/q6NGj+u677/TUU09p+fLlCg8PL+LKAccKDw/XtGnTtGvXLtWvX19DhgzRxo0blZaWJqPRaDVt2N69e/Xzzz/zR1EBcBMIbqusrCy5ubnJbDbLZDLdct6/559/XrNmzdLevXuZ+wwu4/vvv9e8efO0YcMGy1de2V8He3h4aOTIkXr11Vfl7+9fxJUCjpF9Leyff/6p+fPna/r06UpISJCbm5uaNGmi1q1bq0OHDvL19dXevXs1c+ZMXb16VVu2bFH9+vWLuvw7AgEQTis5OVkjRoxQVFSU4uPji7ocwKFy+6MoPj5eUVFR2rVrlzw8PBQQEKCgoCD16NGjCCsFHO+fd/ympaUpIiJCX3zxhaKjo3P0r1OnjsaOHavHH3/8dpZ5RyMA4ra5ePGifvnlFx0/flwpKSkKCQlRUFCQypYtK3f3G08lzB4hzJaenq6LFy9aPTUEuFuYTCbLpRC38s9z42ZTxQB3szNnzmjTpk369ddfVbFiRVWoUEFt2rRRzZo1i7q0OwoBELfFunXr9J///CfHX25lypRR586d1a9fP/Xo0cMSBAFXk1cY/PvzsjMzMzlHcNdbv369fv31Vx08eFD+/v5q2rSpatasqapVq6ps2bLy8PAo6hLvCgRAOFxsbKzat2+v1NRUDRkyRB06dNDJkyd14MAB/fzzzzp06JDS09NVt25djR07Vn369FGxYsUKNDoC3EkuXLigd955R6GhoWrevLn8/Pwsy7J/JTO6B1fz559/atq0aXr33Xfl5uZmNeVLmTJl1Lp1az3yyCN6+OGHVaZMGcsyRsNtw5+ScLg5c+boypUrmjdvnh599FGrZWfPntUPP/yglStXatGiRXriiSd09uxZvfLKK4Q/3LVmz56tDz74QN99953q1Kmj9u3bq127dmrQoIHVkz1MJpPMZrPc3Ny0detWpaWl6cEHHyzCygHHmTt3rmbOnKlevXrphRdeUEBAgA4cOKBjx45p7969io6O1qpVqxQcHKw33nhDvXr1ksQfS7ZiBBAO16JFCxUvXlzLli1TuXLllJmZaTWfU7aoqCiNGTNGhw8f1uzZszVs2LAiqhhwrODgYB0+fFiNGzfW/v37lZGRoerVq1vubGzdurWCgoIs/f/66y8NGDBAq1evVmpqqry8vIqwesAxatSooXr16ikiIkJly5a1Wnb+/HkdOHBAK1eu1Pz585WVlaXPP/9cTz/9dBFVe+djiAUOlZKSolKlSik+Pl4lSpSQJKv5m7LvfJSkDh066L///a9KlCihFStWWJYDd5PY2Fj9+eefql+/vrZv365t27bp9ddfl6+vrxYtWqQRI0aoX79+ev7557Vs2TIlJyfrt99+0549e9StWzfCH+5KR48e1aVLl9SwYUNL+DOZTJZ/HwICAtStWzd98sknWrFihe655x69+uqrud4RjPwhAMKhSpYsqSZNmujYsWNavHixJOX4ajf7tclkUnBwsNq2baujR4/q9OnTDO3jrhMXF6fk5GTVq1dPHh4eatasmSZNmqSNGzdq7dq1Cg8PV1JSkmbNmqUhQ4aoR48eGjt2rC5cuKDhw4cXdfmAQ5jNZvn5+enEiROSpMzMTEn//++D2WyW2WxWsWLF1LVrV73//vu6cuWKduzYUWQ13+m4BhAO9/zzz2vt2rV6+umndfDgQQ0ZMkR16tSRl5eXJeBl392YnJysYsWKKS0tTdWrVy/iygH7K1OmjNq3b6/Q0FBJsoyGV6hQQQ8++KA6deqk8+fPa8eOHVq1apU2bdqkK1euyM/PT927dy/K0gGHuf/++1W5cmWtXbtW69at00MPPZSjj8FgsNwc+MADD6hGjRrau3dvEVR7d2AEEA5XuXJlvfnmm6pRo4ZmzpypESNGaMaMGdq6datOnz6ttLQ0y9QWq1at0tatW3M9+YG7Qc2aNTV//nyFhYXlutzDw0PVq1fXwIEDtWTJEk2dOlWSNGDAgNtZJnDbZF/q8/HHH8vHx0fdunXTiy++qD179igtLU3S/9/okZGRIUk6duyY0tPTFRAQUDRF3wW4CQQO889b8y9fvqxp06Zp6dKlio2NVfny5VWvXj0FBASoRIkSunbtmpYuXap77rlH33//vWrXrl2E1QP2l9t0FVlZWTIYDHne9f7KK69oxowZ2rdvnxo3bnw7ygSKRFZWlr766iuNHTtW8fHxqlOnjkJDQ9WqVSvVqVNHQUFBMhqNOnfunF5++WUtW7ZMu3fv5rywEQEQDpX9D97Zs2cVEBAgo9GoX3/9VatXr9bWrVt15MgRxcbGSpJKly6tRo0a6eOPP1bdunWLuHLAMbLPifj4eFWoUMEq+P190mfpxjRJ3bp10/nz55WQkFBUJQO3VUJCgmbOnKmlS5fq+PHjKlGihCpXrqySJUuqTJkyOnr0qBISEjR06FDNnj27qMu9YxEA4RCZmZnatWuX5s+fr+PHj8tgMKhEiRJq1qyZ+vbtq+DgYJnNZsXGxuratWs6efKkgoKCVLVqVbm7uzOxJ+46/zwnjEajihcvroYNG6p3795q1apVjvckJibqyy+/VEBAgPr161cEVQO3z9+fh33t2jXFxMRo79692rVrl3bv3q2jR4+qfPnyqlq1qp5++mk98cQT8vb2Luqy71gEQDjEjBkz9NZbb+nq1auqWbOm3NzcdOzYMcvyOnXq6Nlnn1WfPn1UoUKFIqwUuD1udU4EBQUpPDxcAwYMUMWKFS3t169fl7u7OxOjwyWZTCalpaWpWLFiSkpKUnx8PN8Q2QkBEHb3xx9/qH79+mrcuLEiIiJUrFgx+fv7Kz4+XqtWrdKyZcu0detWSTfm/ps+fbqaNm1atEUDDlSQc6Jjx4565513uK4Jd71r167pzJkzqlatmooXL261zGQyyWAwWL4J+ue3QjwqtPAIgLC7CRMmaM6cOVq0aJE6deokKefJ+8svv2jGjBlaunSpqlevrq+//lpNmjQpqpIBhyrMOcHlELhbvf3221q+fLkeffRRtWjRQrVr15a/v7/VU6L++WzshIQElS5d2jJzBGxHAITd9e7dWwcPHlRUVJSqVatmmePv79d3ZPvoo4/04osvavDgwVqwYEERVg04DucEkFOVKlV0/vx5ubm5ydfXV61atVJoaKiaN2+uwMDAHI+DS01N1aRJk3Tp0iXNmzePEcBC4qcHuwsODtYff/yhlJQUSbL8pfb35/9m/93x73//W48++qi2bNmikydPFk3BgINxTgDWjh8/rqSkJLVs2VIffvih2rRpo927d+uFF17QY489pjFjxuirr77Sb7/9pj///FOS9Ouvv2ru3Lm6fPky4c8O+AnC7jp06CBJevzxx7VlyxZdv349135ZWVmSpNq1aysxMdHyjyNwt+GcAKwdP35caWlpCg0N1ciRI/XRRx/pyy+/1MSJE1W9enUtX75cQ4cO1cCBAzV58mRt2LBBy5cvV3JyssLDw4u6/LsCXwHD7rKysvTqq6/q/fffV1BQkEaOHKk+ffrI398/R98rV65o1KhRWrdunS5evFgE1QKOxzkBWPvmm2/Ut29fLV68WH379rW0Z2Rk6PTp0/r555+1Y8cOy3yxHh4eMpvN8vT01OXLl4uw8rsHARAOM2fOHL377rs6efKkAgIC9Mgjj+ihhx5S1apV5ebmJj8/P33yySf68MMP9eyzz+q9994r6pIBh+KcAG4wm806evSovLy8dM899+R6s1NqaqqOHz+uY8eOacGCBYqMjNRzzz2njz/+uIiqvrsQAOEwZrNZv//+u+bOnavFixfr7Nmzkm489N7Dw0NxcXEymUwaMGCApk+fripVqhRxxYBjcU4At5ZbGHzhhRc0c+ZM/fTTTwoODi6iyu4uBEDcFqmpqdqzZ49Wrlyp8+fP6+LFi/Lx8VHfvn3Vu3dveXl5FXWJwG3FOQHcXPZcf6dOnVLPnj115coVnTlzpqjLumsQAHHbZWRkyMPDo6jLAJwG5wSQt127dik8PFyDBg3Sa6+9VtTl3DUIgAAAwGmZzWadPXtWZcqU4dm/dkQABAAAcDHMAwgAAOBiCIAAAAAuhgAIAADgYgiAAAAALoYACAAA4GIIgAAAAC6GAAgAAOBiCIAAAAAu5v8ALOVGV0xmTSQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.visualization import plot_histogram\n",
    "plot_histogram(job.result().quasi_dists[0].binary_probabilities())"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.8"
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {},
    "version_major": 2,
    "version_minor": 0
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}