qiskit-maxcut.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from functools import reduce\n",
    "import networkx as nx\n",
    "from networkx import Graph\n",
    "\n",
    "g = Graph()\n",
    "g.add_nodes_from([0, 1, 2, 3])\n",
    "g.add_edges_from([(0, 1), (1, 2), (2, 3), (3, 0)])\n",
    "nx.draw(g, with_labels=True, alpha=0.8, node_size=500)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "outputs": [],
   "source": [
    "from qiskit import QuantumCircuit, QuantumRegister, transpile\n",
    "from qiskit import Aer"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "outputs": [],
   "source": [
    "from qiskit.circuit import Parameter\n",
    "\n",
    "def mixer(g: Graph, beta: Parameter):\n",
    "    qubits = QuantumRegister(g.number_of_nodes())\n",
    "\n",
    "    qc_mix = QuantumCircuit(qubits)\n",
    "    for q in qubits:\n",
    "        qc_mix.rx(2 * beta, q)\n",
    "\n",
    "    u = qc_mix.to_gate()\n",
    "    u.name = \"$H_M$\"\n",
    "    return u"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "outputs": [],
   "source": [
    "def problem(g: Graph, gamma: Parameter):\n",
    "    qc_problem = QuantumCircuit(g.number_of_nodes())\n",
    "    for i, j in g.edges():  # pairs of nodes\n",
    "        qc_problem.rzz(2 * gamma, i, j)\n",
    "\n",
    "    u = qc_problem.to_gate()\n",
    "    u.name = \"$H_P$\"\n",
    "    return u"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "outputs": [],
   "source": [
    "def maxcut_obj(x: str, g: Graph):\n",
    "    return reduce(lambda obj, e : obj - (1 if x[e[0]] != x[e[1]] else 0), g.edges(), 0)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "outputs": [],
   "source": [
    "def compute_expectation(counts, g: Graph):\n",
    "    avg, sum_count = reduce(lambda t, c: (t[0] + (maxcut_obj(c[0], g) * c[1]), t[1] + c[1]), counts.items(), (0, 0))\n",
    "    return avg/sum_count"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "outputs": [],
   "source": [
    "def create_qaoa_circ(g: Graph, theta: list[Parameter]):\n",
    "    mid = len(theta) // 2\n",
    "    betas = theta[:mid]\n",
    "    gammas = theta[mid:]\n",
    "    qubits = QuantumRegister(g.number_of_nodes())\n",
    "    qc = QuantumCircuit(qubits)\n",
    "\n",
    "    # initial_state\n",
    "    qc.h(qubits)\n",
    "\n",
    "    for i in range(mid):\n",
    "        qc.append(problem(g, gammas[i]), qubits)\n",
    "        qc.append(mixer(g, betas[i]), qubits)\n",
    "\n",
    "    qc.measure_all()\n",
    "\n",
    "    return qc"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 831.22x451.5 with 1 Axes>",
      "image/png": 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\n"
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "betas = [Parameter(\"$\\\\beta_0$\"), Parameter(\"$\\\\beta_1$\")]\n",
    "gammas = [Parameter(\"$\\\\gamma_0$\"), Parameter(\"$\\\\gamma_1$\")]\n",
    "theta = betas + gammas\n",
    "\n",
    "c = create_qaoa_circ(g, [Parameter(\"$\\\\beta$\"), Parameter(\"$\\\\gamma$\")])\n",
    "c.draw('mpl')"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "outputs": [],
   "source": [
    "def get_expectation(g: Graph, nparams: int, shots=512):\n",
    "    backend = Aer.get_backend('aer_simulator')\n",
    "    mid = nparams // 2\n",
    "    betas = [ Parameter(f\"$\\\\beta_{i}$\") for i in range(mid) ]\n",
    "    gammas = [ Parameter(f\"$\\\\gamma_{i}$\") for i in range(mid)]\n",
    "    theta = betas + gammas\n",
    "    qc = create_qaoa_circ(g, theta)\n",
    "\n",
    "    def execute_circ(params: list[float]):\n",
    "        binding = {theta[i]:params[i] for i in range(len(params))}\n",
    "        qc.bind_parameters(binding)\n",
    "        counts = backend.run(transpile(qc, backend), shots=512).result().get_counts()\n",
    "        return compute_expectation(counts, g)\n",
    "\n",
    "    return execute_circ"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "outputs": [
    {
     "data": {
      "text/plain": "     fun: -3.951171875\n   maxcv: 0.0\n message: 'Optimization terminated successfully.'\n    nfev: 50\n  status: 1\n success: True\n       x: array([2.06605623, 2.09611733, 1.0305495 , 1.05048815])"
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.optimize import minimize\n",
    "\n",
    "init_params = [1.0, 1.0, 1.0, 1.0]\n",
    "expectation = get_expectation(g, len(init_params))\n",
    "res = minimize(expectation, init_params, method='COBYLA')\n",
    "res"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 700x500 with 1 Axes>",
      "image/png": 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xAImIiIgoV0wAiYiIiFSGCSARERGRyjABJCIiIlIZJoBEREREKsMEkIiIiEhlmAASERERqQwTQCIiIiKVYQJIREREpDJMAImIiIhUhgkgERERkcowASQiIiJSGSaARERERCrDBJCIiIhIZZgAEhEREakME0AiIiIilWECSERERKQy9pYOgMgcRiywdATAj2MtHQEREVH+8AwgERERkcowASQiIiJSGSaARERERCrDBJCIiIhIZZgAEhEREakME0AiIiIilbHaBPDw4cPo0qULSpcujVKlSqFp06ZYt27dM6/v/v37qFSpEhRFQefOnXOsoyhKrj/Dhg175m0TERERWROrHAdw586dCAkJgbOzMwYOHAhXV1esX78eAwYMQHR0NCZMmFDgdY4ePRpJSUlPrefj45NjshcQEFDgbRIRERFZI6tLADMyMjBixAhoNBrs2bPHkHhNnToVgYGBmDRpEvr27QsfH598r3P9+vX4+eefsWjRIowePTrPur6+vpg+fboJLSAiIiKyblZ3CXjHjh24fPkyXn75ZaOzbu7u7pg0aRLS09MRGhqa7/XFx8fjrbfewuDBg9G1a9dCiJiIiIioeLG6M4C7du0CAHTq1CnbspCQEADA7t27872+N998E3Z2dvjmm2/ydQk4MTERS5cuRUJCAjw9PdGiRQvUrVs339sjIiIisnZWlwBGRUUBAPz8/LIt8/b2houLi6HO06xevRr//e9/sWHDBnh4eOQrATx58iRGjRplVNa5c2eEhoaiXLly+douERERkTWzugRQn6S5u7vnuNzNzS1fidytW7fw7rvvYtCgQejZs2e+tj1hwgT06dMHNWvWhKOjI86cOYNPP/0UW7ZsQbdu3RAZGQk7O7tc35+Wloa0tDTD6+TkZACAVquFVqsFAGg0GtjZ2SEzMxM6nc5QV1+ekZEBETGU29nZQaPR5FquX6+evX3WR5qRkZGvcgcHB+h0OmRmZhrKFEWBvb19ruW5xW7ZNjnAGvBzYpvYJmtrkwJL02q1/JzYpiJpU0FYXQJoLm+88QYcHBywcOHCfL9n3rx5Rq+bNWuGjRs3ol27dti9ezf++OMPvPTSS7m+f/bs2ZgxY0a28m3btqFkyZIAgKpVq6JBgwY4deoUbty4YahTq1Yt+Pv749ChQ4iPjzeUBwQEwMfHB3v27MGDBw+MYitXrhy2bdtmtIMFBwejRIkS2Lx5s1EMXbp0wcOHD7Fz505Dmb29Pbp27YqEhARERkYayl1dXdGuXTtER0fjxIkThnIvLy80b94cUVFRuHDhgqHcOtqUvyS/sPFzYpvYJutqkzV8Ody8eTM/J7apSNpUsWJF5Jcij6e4VqBfv3747bffcOTIETRq1CjbcldXV3h4eBg1+kmhoaEYNmwYfv31V/Tt29dQfu3aNVSrVg0hISHYunVrvmNas2YNXn31VYwfPx7z58/PtV5OZwCrVKmChIQEuLm5AVDft5GiatPbiy1/kP9xLM8Ask1sk7W1aeQ3lj8D+N07PAPINhVNm1JTU+Hu7o6kpCRD3pEbqzsDqL/3LyoqKlsCGBcXh5SUFAQGBua5juPHjwPISiZzEh4eDkVRUL9+faNsOzdly5YFAKSmpuZZz8nJCU5OTtnKHRwc4OBgnKDY2dnleDlZv9Pkt/zJ9T5LuUajyfHUcW7lucVuTW2yFH5ObBPbZH1tsrTH4+LnxDYVdpvyy+oSwDZt2mD27NnYtm0bBg4caLQsPDzcUCcvzZo1Q0pKSrbylJQUhIWFoXLlyggJCUHVqlXzFdPBgwcBZI0RSERERFTcWd0l4IyMDNSqVQs3b97EgQMHDGMBJiUlITAwENeuXcOFCxcMyVhsbCySkpJQoUKFXB8c0cvrEvDp06fh7++fLVvfv38/OnbsCK1Wi3PnzuG5557Ld1uSk5PzfSqWTDNigaUjyLoETETWhccGUpOC5B1WdwbQ3t4ey5YtQ0hICFq3bm00Fdz169cxb948ozNxEydORGhoKFasWGHSfL3z58/Hpk2b0LJlS1SpUgUODg44e/Ystm3bBkVRsHjx4gIlf0RERETWyuoSQCDrqZq9e/di2rRpCAsLg1arRd26dTFnzhwMGDCgULbZs2dPJCYm4uTJk9i+fTvS09Ph7e2NgQMHYuzYsU+975CIiIiouLC6S8C2hJeAiw4v8xBRTnhsIDUpSN5hdXMBExEREVHhYgJIREREpDJMAImIiIhUhgkgERERkcowASQiIiJSGSaARERERCrDBJCIiIhIZZgAEhEREakME0AiIiIilWECSERERKQyTACJiIiIVIYJIBEREZHKMAEkIiIiUhkmgEREREQqwwSQiIiISGWYABIRERGpDBNAIiIiIpVhAkhERESkMkwAiYiIiFSGCSARERGRyjABJCIiIlIZJoBEREREKsMEkIiIiEhlmAASERERqQwTQCIiIiKVYQJIREREpDJMAImIiIhUhgkgERERkcowASQiIiJSGSaARERERCrDBJCIiIhIZZgAEhEREamMfWGs9Nq1a9i+fTucnZ3Ru3dvuLi4FMZmiIiIiOgZmHQGcNasWahWrRru379vKNu1axdeeOEFvPnmmxg2bBgaNmyIe/fumRwoEREREZmHSQnghg0b4OvrCw8PD0PZRx99BJ1OhxkzZuCtt97CpUuXsGDBAlPjJCIiIiIzMSkBvHbtGurUqWN4fevWLRw+fBjvvPMOJk+ejEWLFqF9+/b4/fffTQ6UiIiIiMzDpAQwOTkZpUuXNrzes2cPFEVB9+7dDWUNGzbEjRs3TNkMEREREZmRSQlg+fLlcf36dcPr7du3w8nJCUFBQYayR48eQVEUUzZDRERERGZk0lPATZo0wR9//IGNGzfC2dkZYWFhCA4OhpOTk6HO1atXUbFiRZMDJSIiIiLzMOkM4KRJk5CRkYGePXsiJCQEjx49wqRJkwzL09LSsGfPHqMzgkRERERkWSadAWzYsCEOHDiA//znPwCA/v37IzAw0LD8+PHjCA4Oxssvv2xalERERERkNiYPBF2/fn3Ur18/x2VNmzblE8BEREREVsZsM4GkpKTg4sWLSE1NRatWrcy1WiIiIiIyM5PnAr527Rp69uwJDw8PNGnSBMHBwYZl+/btQ506dbBr1y5TN0NEREREZmJSAnjjxg00bdoUmzdvRs+ePdGsWTOIiGF5UFAQEhIS8Msvv5gcKBERERGZh0kJ4LRp03D//n3s3r0bv/32Gzp27Gi03N7eHq1atcK+fftMCpKIiIiIzMekBDA8PBy9e/dG8+bNc63j4+ODmzdvmrIZIiIiIjIjkxLAe/fuwdfXN886IoK0tDRTNkNEREREZmTyVHBRUVF51jl9+jSqVq1qymaIiIiIyIxMSgA7duyIjRs34tSpUzku/+eff7Bjxw506dLFlM0QERERkRmZlABOnjwZJUqUQOvWrfH555/j0qVLAIAtW7ZgypQp6Ny5M8qWLYsPPvjALMESERERkelMGgja19cX4eHhGDhwIKZMmQJFUSAi6NatG0QEVatWxW+//YYKFSqYK14iIiIiMpHJM4EEBQUhKioKf/31Fw4ePIh79+7Bzc0NQUFB6NmzJxwdHc0RJxERERGZiVmmgrO3t0fv3r3Ru3dvc6yOiIiIiAqRyVPBEREREVHxUqAzgKtWrQIA9O7dG66urobX+TFkyJCCRUZEREREhaJACeCwYcOgKAqaNm0KV1dXw+u8iAgURWECSERERGQlCpQALl++HIqiGJ7qXbFiRaEERURERESFp8BnAB83dOhQc8ZCREREREXApIdA9uzZgxs3buRZJzo6Gnv27DFlM0RERERkRiYlgMHBwVi5cmWedVatWoXg4GBTNkNEREREZmRSAigiT62j0+me+qAIERERERWdQh8HMCoqCu7u7oW9GSIiIiLKpwLPBPLaa68Zvd6wYQOuXbuWrV5mZqbh/r8XX3zxmQMkIiIiIvMqcAL4+D1/iqLgxIkTOHHiRI51FUVBkyZN8PXXXz9rfERERERkZgVOAK9evQog6/6/6tWrY+zYsXjvvfey1bOzs4OHhwdKlSplepREREREZDYFTgB9fHwM/1+xYgUCAgKMyoiIiIjIuhU4AXwcB4ImIiIiKn4KlADqB3QODAyEs7NzgQZ4bt26dcEiIyIiIqJCUaAEsG3btlAUBefOnUPNmjUNr/MjMzPzmQIkIiIiIvMqUAI4depUKIqCsmXLGr0mIiIiouKjQAng9OnT83xNRERERNav0GcCISIiIiLrwgSQiIiISGUKdAm4Xbt2z7QRRVEQERHxTO8lIiIiIvMqUAK4a9euZ9oIHxQhIiIish4FSgB1Ol1hxUFERERERYT3ABIRERGpDBNAIiIiIpXhVHBEREREKsOp4IiIiIhUhlPBEREREamM1U4Fd/jwYUybNg379++HVqtF3bp1MX78ePTv3z9f79+yZQtCQ0Nx4sQJxMXFIT09HVWrVkWLFi3w0UcfoWbNmjm+Lzw8HLNmzcKxY8egKAoaNWqEyZMno3379uZsHhEREZHFFCgBLCo7d+5ESEgInJ2dMXDgQLi6umL9+vUYMGAAoqOjMWHChKeuY/PmzThw4ACCgoLw4osvwsHBAefOnUNoaCjWrFmDzZs3ZxvYevXq1Rg8eDC8vLwwbNgwAEBYWBg6duyIdevWoW/fvoXRXCIiIqIipYiImLqStLQ0bN68GcePH0dSUhLc3d3RoEEDdOnSBU5OTgVaV0ZGBvz9/RETE4MDBw4gICAAAJCUlITAwEBcu3YNFy9ehI+PT57refToEZydnbOVR0REoEOHDmjcuDEOHz5sKL9//z6qV68Oe3t7HD9+HJUrVwYAxMTEoEGDBgCAK1euwNXVNd9tSU5Ohru7O5KSkuDm5pbv91HBjVhg6QiAH8daOgIiehKPDaQmBck7TB4G5s8//4SPjw/69u2Lzz77DN9++y0+++wz9O3bF76+vvjrr78KtL4dO3bg8uXLePnllw3JHwC4u7tj0qRJSE9PR2ho6FPXk1PyBwDt27eHh4cHLl26ZFT+66+/IjExEWPGjDEkfwBQuXJljB49GgkJCfj9998L1BYiIiIia2RSAhgREYE+ffogMTERr732GlauXIktW7Zg5cqVGD58OO7fv4+XXnoJO3bsyPc69dPNderUKduykJAQAMDu3bufOebIyEjcv38fL7zwQpFul4iIiMhamHQP4LRp01CiRAns378/W0I1ZMgQvPvuu2jRogWmTZuW7X673ERFRQEA/Pz8si3z9vaGi4uLoU5+bNu2Dfv370daWhqioqKwceNGlC1bFl9//XW+t6sve9p209LSkJaWZnidnJwMANBqtdBqtQAAjUYDOzs7ZGZmGk2tpy/PyMjA41fl7ezsoNFoci3Xr1fP3j7rI83IyMhXuYODA3Q6ndEwPYqiwN7ePtfy3GK3bJscYA34ObFNbJO1tcnyI1VotVp+TmxTkbSpIExKAI8fP46XX345W/KnV69ePfTv3x9r167N9zqTkpIAZF3yzYmbm5uhTn5s27YN8+fPN7yuUaMG1q5di0aNGuV7u/rr6E/b7uzZszFjxowcYyhZsiQAoGrVqmjQoAFOnTqFGzduGOrUqlUL/v7+OHToEOLj4w3lAQEB8PHxwZ49e/DgwQNDebNmzVCuXDls27bNaAcLDg5GiRIlsHnzZqMYunTpgocPH2Lnzp2GMnt7e3Tt2hUJCQmIjIw0lLu6uqJdu3aIjo7GiRMnDOVeXl5o3rw5oqKicOHCBUO5dbSpZ7Z+twR+TmwT22RdbbKGL4ebN2/m58Q2FUmbKlasiPwy6SEQLy8vjBgxArNmzcq1zsSJE7Fs2TKjDs5Lp06dsH37dkRFRaFGjRrZlleqVAkpKSkFSgIBICUlBf/73/8wc+ZM/P3331i+fDlefvllw/KaNWsiKioKWq3WkLnrabVaODo6ol69ejh58mSu28jpDGCVKlWQkJBgSCLV9m2kqNr09mLLH+R/HMszgGwT22RtbRr5jeXPAH73Ds8Ask1F06bU1NR8PwRi0hnADh064O+//84zAfz777/RsWPHfK9TfwYutwQvOTkZHh4eBQsUgIuLCwIDA7FhwwY0btwYI0eORMeOHeHl5ZVtu2XKlMm2zcfr5MbJySnHp54dHBzg4GCcoNjZ2cHOzi5b3SeTz6eVP7neZynXaDQ5njrOrTy32K2pTZbCz4ltYpusr02W9nhc/JzYpsJuU36Z9BDIvHnzcOfOHQwZMgTR0dFGy6KjozF48GAkJCRg3rx5+V5nXvfbxcXFISUlJcf79PLL3t4ewcHBSE1NxZEjR/K13bzuDyQiIiIqbgqUALZr187oZ/DgwfDw8MCaNWvw3HPPoUaNGmjRogVq1KiB5557Dj///DNKly6NwYMH53sbbdq0AZB139yTwsPDjeo8q1u3bgEwzsyLYrtERERE1qBA9wAW9AkTw0YUxei6dl4yMjJQq1Yt3Lx5M9eBoC9cuABfX18AQGxsLJKSklChQgWjS7RHjhxB48aNs60/PDwc3bt3R6lSpRATE4NSpUoByBoIulq1anBwcOBA0MUQB3slopzw2EBqUpC8o0D3AD5+s2Fhsbe3x7JlyxASEoLWrVsbTQV3/fp1zJs3z5D8AVkPmYSGhmLFihWG6dsAoEmTJnjhhRdQr149VK5cGampqTh16hT++ecfODg4YPny5YbkDwA8PDywaNEiDB48GA0bNsSAAQMAZE0Fd/fuXYSFhRUo+SMiIiKyVlY5F3BwcDD27t2LadOmISwsDFqtFnXr1sWcOXMMidnTzJo1Czt37sTu3bsRHx8PjUaDqlWrYuTIkRg7dixq166d7T2vvvoqypYti1mzZmHFihVQFAWNGjXC5MmT0aFDB3M3k4iIiMgizDIXMOWMl4CLDi/zEFFOeGwgNSm0S8C5iYmJwc6dO3Hr1i2jcfD0FEXBlClTzLEpIiIiIjKRyQngBx98gG+++cboIQ8RgaIoRv9nAkhERERkHUwaB/DHH3/E/PnzERwcjN9++w0igqFDh+KXX37Bm2++CXt7e/Tr1w87duwwV7xEREREZCKTzgAuXboUvr6+2LJli2GIGF9fXwwYMAADBgxA//790bFjR/Tr188swRIRERGR6Uw6A3j+/Hl07tzZaHzAx+e9a9OmDbp27VqgmUCIiIiIqHCZlAACQOnSpQ3/L1WqFO7evWu0vFatWjh79qypmyEiIiIiMzEpAaxUqRJiYmIMr5977jkcPHjQqM6ZM2eMBlwmIiIiIssyKQFs0aIFDhw4YHjds2dPHD9+HKNGjcKmTZswceJEbNmyBa1btzY5UCIiIiIyD5MeAhk8eDBu3bqF69evw8fHBx988AE2btyIH3/8EcuWLYOIwNfXF3PnzjVXvERERERkIpMSwLZt26Jt27aG1y4uLjhw4AD++OMPXL58GT4+PujevTsvARMRERFZEbPPBezg4IC+ffuae7VEREREZCZmSwDv3r2LkydPIikpCe7u7qhfvz7KlCljrtUTERERkZmYnABeu3YN7733HjZt2gQRMZQrioJu3bphwYIF8PX1NXUzRERERGQmJiWAly9fRosWLXDnzh34+fmhRYsWKF++PG7fvo39+/fjzz//xIEDB7B//35Ur17dXDETERERkQlMSgA/+ugjxMfHY8mSJRgxYgQURTEsExEsXboUb7/9Nj766CP8+uuvJgdLRERERKYzKQGMiIhAjx49MHLkyGzLFEXBqFGjsHnzZvz999+mbIaIiIiIzMikgaAzMzPx/PPP51nnhRdeQGZmpimbISIiIiIzMikBbNiw4VPn+T179iwaN25symaIiIiIyIxMSgA///xzbNmyBcuWLctx+dKlSxEeHo7PPvvMlM0QERERkRkV6B7AmTNnZisLDg7GqFGjMH/+fKOngPft24eLFy8iJCQEERERaN68udmCJiIiIqJnp8jjg/c9hUbzbCcMFUVR5X2AycnJcHd3R1JSEtzc3Cwdjk0bscDSEQA/jrV0BET0JB4bSE0KkncU6Azgzp07TQqMiIiIiCyvQAlgmzZtCisOIiIiIioiJj0EQkRERETFj8lzAQPAvn37sHLlSpw4cQLJyclwc3NDgwYNMGTIELRs2dIcmyAiIiIiMzE5ARw3bhwWLlwI/bMkiqJARHD06FH89NNPeO+99/DVV1+ZHCgRERERmYdJl4BDQ0PxzTffwM/PD2vWrMGtW7eQkZGB2NhY/Pzzz6hZsya++eYbrFq1ylzxEhEREZGJTEoAv//+e1SuXBkHDx7EoEGD4O3tDUVRUL58eQwcOBAHDhxApUqV8N1335krXiIiIiIykUkJ4NmzZ9GnTx+4u7vnuNzd3R19+vR56nRxRERERFR0Cv0pYEVRCnsTRERERFQAJiWAzz//PNavX4+UlJQclz948ADr16/H888/b8pmiIiIiMiMTEoAR40ahZiYGDRr1gzr169HQkICACAhIQG//fYbmjdvjpiYGLz11ltmCZaIiIiITGfSMDDDhw/H8ePHsWjRIvTv3x9A1nzBOp0OACAiGDNmDIYOHWp6pERERERkFiaPA7hw4UL069cvx4Gghw4dilatWpkjTiIiIiIyE5MSwD179sDNzQ2tWrViokdERERUTJh0D2BwcDCWLl1qrliIiIiIqAiYlACWK1cOzs7O5oqFiIiIiIqASQlgx44dsWvXLsM8wERERERk/UxKAL/44gvcvXsXI0eOxL1798wVExEREREVIpMeAnn11VdRunRpLF++HKtXr0a1atVQvnz5bLN/KIqCiIgIkwIlIiIiIvMwKQHctWuX4f9paWk4f/48zp8/n60ep4MjIiIish4mJYD6AZ+JiIiIqPh4pnsAIyMj0a5dO7i6usLd3R0dO3bEoUOHzB0bERERERWCAp8BPH36NNq3b49Hjx4ZyiIiIrB//34cOnQIzz//vFkDJCIiIiLzKvAZwC+++AKPHj3CJ598gri4OMTFxWHKlCl4+PAh5syZUxgxEhEREZEZFfgM4D///IOWLVvi008/NZTNmDEDu3btwu7du80aHBERERGZX4HPAN6+fRtNmzbNVh4UFITbt2+bJSgiIiIiKjwFTgC1Wi1cXFyylZcqVQpardYsQRERERFR4TFpJhAiIiIiKn6eaRzA1atX48CBA0Zlly5dAgB06dIlW31FUbBp06Zn2RQRERERmdkzJYCXLl0yJHxP2rp1a7YyzgRCREREZD0KnABevXq1MOIgIiIioiJS4ATQx8enMOIgIiIioiLCh0CIiIiIVIYJIBEREZHKMAEkIiIiUhkmgEREREQqwwSQiIiISGWYABIRERGpDBNAIiIiIpVhAkhERESkMkwAiYiIiFSGCSARERGRyjABJCIiIlIZJoBEREREKsMEkIiIiEhlmAASERERqQwTQCIiIiKVYQJIREREpDJMAImIiIhUhgkgERERkcowASQiIiJSGSaARERERCrDBJCIiIhIZZgAEhEREakME0AiIiIilWECSERERKQyTACJiIiIVIYJIBEREZHKMAEkIiIiUhkmgEREREQqY7UJ4OHDh9GlSxeULl0apUqVQtOmTbFu3bp8v//y5cuYPn06evTogUqVKkFRFPj6+ub5HkVRcv0ZNmyYaQ0iIiIishL2lg4gJzt37kRISAicnZ0xcOBAuLq6Yv369RgwYACio6MxYcKEp67jn3/+wYwZM2BnZ4fatWsjLi4uX9v28fHJMdkLCAgoYCuIiIiIrJPVJYAZGRkYMWIENBoN9uzZY0i8pk6disDAQEyaNAl9+/aFj49Pnutp3bo1IiMjUb9+fZQoUQLOzs752r6vry+mT59uYiuIiIiIrJfVXQLesWMHLl++jJdfftnorJu7uzsmTZqE9PR0hIaGPnU91atXR9OmTVGiRIlCjJaIiIio+LG6M4C7du0CAHTq1CnbspCQEADA7t27C237iYmJWLp0KRISEuDp6YkWLVqgbt26hbY9IiIioqJmdQlgVFQUAMDPzy/bMm9vb7i4uBjqFIaTJ09i1KhRRmWdO3dGaGgoypUrl+d709LSkJaWZnidnJwMANBqtdBqtQAAjUYDOzs7ZGZmQqfTGerqyzMyMiAihnI7OztoNJpcy/Xr1bO3z/pIMzIy8lXu4OAAnU6HzMxMQ5miKLC3t8+1PLfYLdsmB1gDfk5sE9tkbW1SYGlarZafE9tUJG0qCKtLAJOSkgBkXfLNiZubm6GOuU2YMAF9+vRBzZo14ejoiDNnzuDTTz/Fli1b0K1bN0RGRsLOzi7X98+ePRszZszIVr5t2zaULFkSAFC1alU0aNAAp06dwo0bNwx1atWqBX9/fxw6dAjx8fGG8oCAAPj4+GDPnj148OCBobxZs2YoV64ctm3bZrSDBQcHo0SJEti8ebNRDF26dMHDhw+xc+dOQ5m9vT26du2KhIQEREZGGspdXV3Rrl07REdH48SJE4ZyLy8vNG/eHFFRUbhw4YKh3Dra1DNbv1sCPye2iW2yrjZZw5fDzZs383Nim4qkTRUrVkR+KfJ4imsFOnXqhO3btyMqKgo1atTItrxSpUpISUkpcBLo7OwMb29vXLt2rUDv0+l0aNeuHXbv3o3169fjpZdeyrVuTmcAq1SpgoSEBLi5uQFQ37eRomrT24stf5D/cSzPALJNbJO1tWnkN5Y/A/jdOzwDyDYVTZtSU1Ph7u6OpKQkQ96RG6s7A6g/85dbgpecnAwPD48ii0ej0WDEiBHYvXs39u3bl2cC6OTkBCcnp2zlDg4OcHAwTlDs7OxyPJuo32nyW/7kep+lXKPR5HjqOLfy3GK3pjZZCj8ntoltsr42WdrjcfFzYpsKu035ZXVPAevv/cvpPr+4uDikpKTkeH9gYSpbtiwAIDU1tUi3S0RERFQYrC4BbNOmDYCs++aeFB4eblSnqBw8eBAAnjqTCBEREVFxYHUJYPv27VG9enX8/PPPRjdDJiUlYdasWXB0dMSQIUMM5bGxsTh//rzJD4acPn0627V9ANi/fz/mzJkDBwcH9OvXz6RtEBEREVkDq7sH0N7eHsuWLUNISAhat25tNBXc9evXMW/ePKMzcRMnTkRoaChWrFhhNIVbQkIC3n//fcNrrVaLhIQEozrz5s0zXN6dP38+Nm3ahJYtW6JKlSpwcHDA2bNnsW3bNiiKgsWLF+O5554r7OYTERERFTqrSwCBrMeq9+7di2nTpiEsLAxarRZ169bFnDlzMGDAgHytIyUlJduMIampqUZl06dPNySAPXv2RGJiIk6ePInt27cjPT0d3t7eGDhwIMaOHYvAwEDzNZCIiIjIgqxuGBhbkpycnO/Hsck0IxZYOoKsYWCIyLrw2EBqUpC8w+ruASQiIiKiwsUEkIiIiEhlmAASERERqQwTQCIiIiKVYQJIREREpDJMAImIiIhUhgkgERERkcowASQiIiJSGSaARERERCrDBJCIiIhIZZgAEhEREakME0AiIiIilWECSERERKQyTACJiIiIVIYJIBEREZHKMAEkIiIiUhkmgEREREQqwwSQiIiISGWYABIRERGpDBNAIiIiIpVhAkhERESkMkwAiYiIiFSGCSARERGRyjABJCIiIlIZJoBEREREKsMEkIiIiEhlmAASERERqQwTQCIiIiKVYQJIREREpDJMAImIiIhUhgkgERERkcowASQiIiJSGSaARERERCrDBJCIiIhIZZgAEhEREakME0AiIiIilWECSERERKQyTACJiIiIVIYJIBEREZHKMAEkIiIiUhkmgEREREQqwwSQiIiISGWYABIRERGpDBNAIiIiIpVhAkhERESkMkwAiYiIiFSGCSARERGRyjABJCIiIlIZJoBEREREKsMEkIiIiEhlmAASERERqQwTQCIiIiKVYQJIREREpDJMAImIiIhUhgkgERERkcowASQiIiJSGSaARERERCrDBJCIiIhIZZgAEhEREakME0AiIiIilWECSERERKQyTACJiIiIVIYJIBEREZHKMAEkIiIiUhkmgEREREQqwwSQiIiISGWYABIRERGpDBNAIiIiIpVhAkhERESkMkwAiYhs0OLFi+Hr6wtnZ2cEBQXh0KFDedb/9ddf4e/vD2dnZ9StWxebN282Wi4imDp1KipUqIASJUqgQ4cOiIqKMqpz7NgxdOzYEaVLl0aZMmUwcuRIpKSkmL1tRGQ6JoDFXFEf5Hft2gVFUXL8OXz4cKG0kYgKJiwsDOPHj8e0adNw7Ngx1K9fHyEhIbhz506O9ffv349Bgwbh9ddfx/Hjx9GrVy/06tULZ86cMdT58ssvsXDhQixZsgQHDx5EqVKlEBISgkePHgEAbt26hQ4dOqBGjRo4ePAgtm7dirNnz2LYsGFF0WQiKiAmgMWYJQ7yzZs3R2xsrNHPG2+8gWrVqqFx48ZF0m7KmSXO+Pj6+mb7IvDFF1+YvW1UMF999RVGjBiB4cOHo06dOliyZAlKliyJ5cuX51j/m2++QefOnfHBBx+gdu3a+PTTT9GwYUMsWrQIQNa+sGDBAkyePBk9e/ZEvXr1sGrVKty6dQsbNmwAAGzcuBEODg5YvHgxatWqhSZNmmDJkiVYv349Ll26VFRNpxxY4tgAAJs2bUJQUBBKlCgBDw8P9OrVy5zNIhMxASzGLHGQd3R0hLe3t+GnTJky+OOPPzB8+HAoilJUTacnWOLLgN7MmTONvhCMGTOmUNtKeUtPT8fRo0fRoUMHQ5lGo0GHDh0QGRmZ43siIyON6gNASEiIof7Vq1cRFxdnVMfd3R1BQUGGOmlpaXB0dIRG8++flRIlSgAA9u7da57GUYFZ6tiwfv16DB48GMOHD8fJkyexb98+vPzyy4XeXso/JoDFlKUO8k/6888/cffuXQwfPtzUJpEJLPFlQM/V1dXoS0GpUqUKu7mUh4SEBGRmZqJ8+fJG5eXLl0dcXFyO74mLi8uzvv7fvOq0a9cOcXFxmDt3LtLT03H//n18/PHHAIDY2FjTG0bPxBLHhoyMDLz33nuYO3cu3nzzTdSsWRN16tRB//79i6rZlA9MAIspSx3kn/TTTz8hJCQElStXfqZ2kOks/WXgiy++QJkyZdCgQQPMnTsXGRkZ5mqaRRT0chllef755xEaGor58+ejZMmS8Pb2RrVq1VC+fHmjs4JUdCx1bDh27Bhu3rwJjUaDBg0aoEKFCnjxxReNziIWR7Z2bOBvJT2zmJgYhIeH4/XXX7d0KKpmyS8D7777LtauXYudO3di1KhRmDVrFj788EOT22QpBb1cZo3Kli0LOzs73L5926j89u3b8Pb2zvE93t7eedbX//u0db788suIi4vDzZs3cffuXUyfPh3x8fGoXr26ye2igrPUseHKlSsAgOnTp2Py5MnYuHEjPDw80LZtW9y7d8/0hlmALRwbnsQEsJiy5EFeb8WKFShTpgx69OjxzO2g4m38+PFo27Yt6tWrhzfffBPz58/Ht99+i7S0NEuH9kwKernMGjk6OqJRo0aIiIgwlOl0OkRERKBZs2Y5vqdZs2ZG9QFg+/bthvrVqlWDt7e3UZ3k5GQcPHgwx3WWL18eLi4uCAsLg7OzMzp27GiOplExodPpAACffPIJ+vTpg0aNGmHFihVQFAW//vqrhaN7NrZwbHgSE8BiytIHeRHBihUrMGTIEDg4OJirWfQMrOHLgF5QUBAyMjJw7dq1gjbD4p7lcpm1Gj9+PH788UeEhobi3LlzeOutt5Cammq4V3fIkCGYOHGiof57772HrVu3Yv78+Th//jymT5+OI0eOYPTo0QAARVEwduxYfPbZZ/jzzz9x+vRpDBkyBBUrVjR6snPRokU4duwYLl68iMWLF2P06NGYPXs2SpcuXZTNp//PUseGChUqAADq1KljWO7k5ITq1avjxo0bJrTIMmzp2PA4JoDFmKUO8gCwY8cOXL16FW+88UaRtZdyZukvA487ceIENBoNypUrZ0qTLOJZLpdZqwEDBmDevHmYOnUqAgICcOLECWzdutXQths3bhg9mNG8eXP8/PPPWLp0KerXr4/ffvsNGzZswAsvvGCo8+GHH2LMmDEYOXIkmjRpgpSUFGzduhXOzs6GOocOHULHjh1Rt25dLF26FD/88APefffdoms4GbHUsaFRo0ZwcnLChQsXDHW0Wi2uXbsGHx8fs7WvqNjSseFx9pYOgJ7dgAEDEB8fj6lTpyIuLg4BAQHZDvKP33ytP8hPnjwZkyZNgp+fX44H+dTUVIwcORKJiYlo2bJltoM8kPXwR/PmzeHv7180jaU8jR8/HkOHDkXjxo0RGBiIBQsWZPsyUKlSJcyePRtA1peBNm3aYP78+ejatSvWrl2LI0eOYOnSpQCMvwz4+fmhWrVqmDJlitGXgcjISBw8eBDBwcFwdXVFZGQkxo0bh1dffRUeHh4W6Qf61+jRow1f7p60a9eubGX9+vVDv379cl2foiiYOXMmZs6cmWudVatWFThOKlyWODa4ubnhzTffxLRp01ClShX4+Phg7ty5AJDnPkZFiwlgMWeJgzwA/PzzzwWKkwqXJb4MODk5Ye3atZg+fTrS0tJQrVo1jBs3DuPHjy/axpvJs1wuI7J2ljpRMHfuXNjb22Pw4MF4+PAhgoKCsGPHjmL55dBWjw2KiIilg8jJ4cOHMW3aNOzfvx9arRZ169bF+PHjCzSOUFpaGubMmYP//Oc/iI6OhqenJ7p164bPPvss10tUa9aswTfffIOzZ8/C0dERLVq0wMyZM9GwYcMCtyE5ORnu7u5ISkqCm5tbgd9P+TdigaUjAH4ca+kIyFRBQUEIDAzEt99+CyDrclnVqlUxevRow5h2VLzw2EDmUFyODQXJO6zyDODOnTsREhICZ2dnDBw4EK6urli/fj0GDBiA6OhoTJgw4anr0Ol06NmzJ8LDw9G0aVP06dMHUVFRWLZsGSIiInDgwAF4eXkZvefzzz/H5MmT4ePjgzfffBMPHjzA2rVr0bx5c0RERKBFixaF1WQisgJPu1xWnDDxITIfWzo26FldApiRkYERI0ZAo9Fgz549CAgIAABMnToVgYGBmDRpEvr27fvUG0lDQ0MRHh6OQYMGYc2aNYZpypYsWYK33noLkydPxg8//GCoHxUVhenTp6NmzZo4dOgQ3N3dAQBvv/02mjZtihEjRuDMmTNWN6ApD/JE5vO0y2VEpE62eGywugRwx44duHz5MoYPH25I/oCskcYnTZqEYcOGITQ0FFOnTs1zPT/++CMAYPbs2UZz1I4aNQpz587FmjVrsGDBAsNclStWrEBGRgY++eQTQ/IHAAEBARg0aBBWrlyJvXv3onXr1mZsLZF58QuB6fK6r5aouOKxwXS2dmywrtNZ+PfBhU6dOmVbFhISAgDYvXt3nut49OgRDh48iFq1amU7U6goCjp27IjU1FQcOXLErNslIiIiKg6s7gxgVFQUAMDPzy/bMm9vb7i4uBjq5Oby5cvQ6XQ5ruPxdUdFRaFVq1aG/7u4uOT4RM/j9fOSlpZmNANCUlISAODevXvQarUAsgaPtLOzQ2ZmpmG09MfLMzIy8PhzOXZ2dtBoNLmWpz/KM6Qicf9+plnbpO8rPXv7rN30yTlmHy9Pf2T5waiTk2HWNj3OwcEBOp0OmZmZhjJFUWBvb29Ubg39cPdu/tqa3zY9Xp7bPmbJfc9a22RN+4IlP6f0Rwos7e5drcX3vfRHlj/fk5SU1e7i+PtUXI4RqampAID8PN9rdQmgPml6/DLs49zc3Ax1TFnH4/X0/8/tyeCc6udk9uzZmDFjRrbyatWq5fm+4m7VxKfXUQP2Qxb2A+lxX8jCfsjCfig6Dx48yDUH0rO6BLA4mzhxotEYaDqdDvfu3UOZMmWM7kO0JsnJyahSpQqio6NVPVQN+4F9oMd+yMJ+yMJ+YB/oFYd+EBE8ePAAFStWfGpdq0sA9RlrbmfbkpOTnzqQZH7W8Xg9/f8LUj8nTk5OcHJyMiorLnNgurm5We0OXZTYD+wDPfZDFvZDFvYD+0DP2vvhabmKnuVvCnhCXvfbxcXFISUlJdd7+/SqV68OjUaT6z17Od1n6Ofnh5SUlBzn9cvrvkQiIiKi4sbqEsA2bdoAALZt25ZtWXh4uFGd3JQoUQKBgYG4cOECrl+/brRMRLB9+3aUKlUKjRs3Nut2iYiIiIoDq0sA27dvj+rVq+Pnn3/GiRMnDOVJSUmYNWsWHB0dMWTIEEN5bGwszp8/n+3y7ciRIwFk3Zf3+NMwP/zwA65cuYJXXnnFMAYgAAwfPhz29vb4/PPPjdZ14sQJ/PLLL6hduzZatmxp7uZanJOTE6ZNm5bt0rXasB/YB3rshyzshyzsB/aBnq31g1XOBZzbVHDXr1/HvHnzjKaC0w8MvWLFCgwbNsxQrtPp0KVLF8NUcG3atMGlS5fw3//+F76+vjh48GCeU8H16dPHMBVceno6p4IjIiIim2F1ZwABIDg4GHv37kWLFi0QFhaG77//HuXLl8fatWvzNQ8wkDUezh9//IHp06cjPj4eX3/9Nfbt24fXX38dkZGR2ZI/APjkk0+wevVqeHl54fvvv8e6devQqlUr7N+/n8kfERER2QyrPANIRERERIXHKs8AEhEREVHhYQJIREREpDJMAImIiIhUhgkgERERkcowASQiIiJSGSaARGTk8YEBRAQcKICIyPYwASQioyRPURSkp6cb/q8oCgAgMzPTIrERWQOdTpfj/9WG/WA7OA4gEQHImm7xv//9L/bt24fMzEzodDrUqVMHXbt2xQsvvGCoJyKGpNCWqaWdlH/Jyclwc3MzvNafIddo1HUuhf1gG5gAqphWq4WdnV2Bf2lt7Q8j+yFrzuupU6di48aNAICyZcsiISHBsLxBgwYYMWIE+vfvD09PT0uFWeiSk5Nhb2+PkiVLFuh9trQv0L9EBCdPnsSaNWtw9epVaLVauLq6okmTJujVqxd8fHyM6trqPsB+yM4W2skEUMWmTp0KHx8ftG7dGpUrV0aJEiWe+h5b2OmfxH4AXnzxRfzzzz+YOXMmWrVqhQoVKiAhIQEbN27EH3/8gaNHjwIAmjVrhk8++QRdunSxcMSF47333oObmxuCg4Ph7++PcuXKwd7ePs/36HQ6mzzz8fDhQzg7Oxd4P7el342lS5di+vTpiIuLg4eHBzQaDe7evWtY3q5dO7z55pvo1q0bnJ2dLRhp4WI/ZDl//jwqV64MFxcXQ5k+hcprn7fa3wkhVbp27ZooiiKKooiPj4+MGDFC/vzzT4mJiZH09HSjupmZmYb3LFy4UPbu3WuJkAsF+yGrPRqNRqZNm5ZrncjISBk4cKA4ODiIr6+vhIeHi4iITqcroigL3+P7QpkyZaRbt26ycOFCOXDggCQkJBjV1bc7KipKPvroI9mwYYMlQi40N2/elKFDh8p///tfuX79uqSlpT31PVqttggiKzrXr1+X0qVLS0BAgERGRsq5c+fk3r17EhkZKR9++KHUqlXLsL8MHDhQLl68aOmQCwX7IUt0dLQ0bNhQ3nvvPVm3bp1cvHhRMjIyjOrojwv6fx8+fFjkcRYEE0CV+u6770RRFGnXrp0EBgaKo6OjKIoidevWlUmTJsmePXskPj7ekPSIiCxatEgURZFffvnFgpGbF/tBZPny5eLk5CRhYWEiIobENzMzM9sBbv369eLg4CANGjSQO3fuFHmshemHH34QRVHkpZdekn79+kn58uVFURSpWrWqDB48WFatWiWnT5+W5ORkw3u+//57URRFQkNDLRi5+X3yySeiKIrY2dmJv7+/TJgwQSIiIuT27du5/tELDw+XWbNmyc2bNy0RstlNnTpVypUrJ1u3bs21zqZNm6Rt27aiKIq0bdtWLl++XIQRFg32Q5Zp06aJoiji5OQkpUqVkpYtW8qUKVNk8+bNEhMTY1RX/zvxn//8Rzp27CinTp2yRMhPxQRQpcaNGyeKosiBAwfk1q1bsnz5chk2bJj4+fkZdvK2bdvKvHnz5PTp0xIXFyf9+vUTRVEkJSXF0uGbDftBJCIiQhRFkWXLluVaJyMjw3BQ++qrr0RRFNmyZUtRhVgkPvzwQ1EURfbv3y8pKSmyZcsWmTFjhrRt21ZcXV3F3t5eXnjhBXn33Xdl48aNcvr0aenTp49N7Qt6bdq0kRIlSsiAAQPk+eefF0VRxMHBQZo3by5ffPGFHD58WBITEw3J4KNHj6Rnz55SokQJqz/rkV9du3aV2rVrS3R0tIiIoa1PfjHSarWGhHn8+PEWibUwsR+ydO3aVUqVKiVffvmlvPHGG1K1alVRFEW8vLyke/fuMm/ePNm7d6/R1YJ+/fqJRqOR1NRUC0aeOyaAKpScnCy9evUSRVHk0aNHhvJHjx7JkSNHZMGCBdK7d2/x9vYWRVHE09NT2rdvL46OjtK1a1cLRm5e7IcssbGxUrVqVfH29pYNGzbk+gdcf4lv9+7d4ujoKHPnzi3KMAtVamqqvPbaa+Lk5CSJiYmGcq1WK5cuXZL169fLuHHjpEGDBuLo6CglS5aUhg0biqIo0q1bNwtGbn63bt2SevXqSb169URE5MSJE7J48WLp37+/VK5cWRRFETc3N+nevbssWbJEoqOjZceOHeLt7S0hISEWjt58PvzwQ7Gzs8t2dudx+isDOp1O2rVrJ7Vq1bKZM6B67AeR27dvS2BgoFSpUkVERO7duydHjhyR7777Tnr06CFlypQRRVGkWrVq8sorr8jq1aslNDRUvLy85MUXX7Rw9LljAqhCmZmZsnr1ahk6dKjhMt7jlzhFRO7fvy8REREyffp0ad++vbi4uIiiKLJ582ZLhFwo2A//WrZsmSiKItWrV5dvv/1Wbt++nWvd0NBQsbOzs6kzgDqdTv766y+ZMGGCxMfHG8oel5qaKidPnpTly5fL66+/brhEbGv7wtGjR8XJyUl69eplVJ6cnCx79uyRzz//XDp27CgeHh6iKIpUqlRJAgMDRVEU+euvvywUtflt2rRJFEWRjh07ytGjR7Nd+hbJ2kf0x4zx48eLm5ubnDlzpqhDLVTsB5HLly9LQECA9OnTx6g8IyNDYmNjZffu3fLZZ59Jy5YtpUSJEuLo6Gj4smTNvxNMAMnIkwmQiMipU6fkhRdeEHd396IPyELU2A9r166V2rVri6Io4ufnJ5MmTZL9+/dLTEyM3Lp1S9LS0uTo0aNSv359wzdhNcjpQZeLFy9Ko0aNbHJfSE1NlenTp8uSJUtEq9WKTqfL1gdxcXHy559/yscffyyNGzcWRVHEw8PDQhEXjrS0NHn11VdFURRp2bKl/Pbbb7le6k9MTJRhw4aJl5dXEUdZ+NgPWX3w888/y4YNG3J92OnRo0dy5coVCQ8Pl7ffflscHR2t/neCCaBK5fQt7kn6hwEiIiKkZMmS8vrrrxd2WEXuySd986pjq/2g/+Oenp4uERER8tprrxnObimKIrVq1ZLWrVuLv7+/KIoi5cuXl59++snCUZtffn4n9Af/bdu2iZOTk83tC0+T0xej5cuXi6IoMmrUKAtEVPhmzJghZcuWFUVRpGHDhjJnzhw5cuSIXL16VaKjo+Xhw4fyxRdfiIuLi7zzzjuWDrfQsB/y7/fffxdHR0cZMWKEpUPJU94DXJHNsrOze2odBwcHAMA///yDhw8fYtSoUYUdVpESEUMbH/fkuG623g/68akcHBzQrl07tGvXDseOHcP27dtx5MgR3Lx5E3Fxcbh//z6GDRuGt956C40bN7Zw1OaXn98J/ZiAp0+fRkZGhs3tC0DW70VmZmaO4x/qfy/ksbHPLl26BAB44403ii7IIqA/Drz33nuoWbMm1q5dix07duDjjz+GnZ0d/Pz84OjoiJs3b+Lu3bvo3LkzJkyYYOmwzU6r1cLBwQFjxoxBjRo1sG7dOtX1g+RjrL/H7d27F1qtFiNHjizMsEzGgaDpqfbs2YOtW7di1qxZlg7F7KKiolCuXDk8ePAAJUqUQJkyZXKta8v9oPdk8pueno7bt2+jdOnScHBwgJOTk3UOaFrEjh8/jn379mH06NGWDqXI5DTgdWxsLAYNGoQbN27gypUrFoqsaGi1Whw4cAA7duzA6dOncffuXcTGxqJ06dIYMGAAXnvtNbi7u1s6zEKXnp6Offv2YdeuXTh79qxq+yE39+/fx4QJE3DkyBGcOnXK0uHkiQmgCmVmZkKj0aj2D3laWhp+/fVXfPfddzh+/Dg0Gg38/PxQo0YNNGrUCC1atEBAQIDRXJe2SH+mx87OLtu+oNPpoChKtnKx1hHtTZBXP6jRnTt3EB8fjzJlyiAlJQVly5ZF6dKlc6yr/11ydnZG3759izbQIiI5zHObmpqKlJQUlC9fHmlpaXBycrJghIUjMzMTUVFRuH//PkQEOp0O1atXR8WKFQ11Hjx4gJSUFFSoUMFm+6GgMjMzcfz4cYgImjRpYulw8sQEUEWio6NRpUoVw2udTgcReeqlr4yMjKdOh1WcTJgwAd988w18fHzg5+cHBwcHJCYm4syZM0hKSkKVKlXQrVs3vPbaa2jUqJHhffokwRZcvnwZzz33nOG1TqeDTqezqc85P9gP/4qNjcUnn3yC7du34+bNm3B1dUW1atXg7++Ppk2bomXLlqhbt67N/pHXf7nJax948ouR/j229sXowoULmDhxIjZv3oz09HQ4OTnBw8MDPj4+aNq0KTp16oSWLVvC1dUVgO1Oh2jrmACqxLVr11C9enV06tQJgwYNQrdu3Ywud2ZmZkJRFGg0GsPBLD09HY6OjhaM2vyuXr2KOnXqoHv37li8eDG8vLzw4MEDJCYmIjY2Fnv27MHvv/+Ow4cPo1KlSpgxYwaGDBliUwf4y5cvw8/PD/7+/njttdfw6quvwtvb27A8MzMTQNY9cfp26894lClTxmaSI/bDv+Li4tC7d28cPHgQnTt3houLCzQaDa5fv45Tp07h4cOHqFOnDvr3748RI0agQoUKAHI+O1ZcJScnIzExEVWrVjWUPb4PqMWtW7fQuXNnnD17FoMHD0bZsmVhb2+Ps2fP4p9//kFycjJKly6N3r17Y+TIkQgKCrJ0yIXi/v37OHXqFJo2bWqzX3r4FLBKzJo1y/BUp6IoUrZsWRk6dKhs2rQp22Pt+nk/lyxZIu3bt5cLFy5YIuRC8fnnn4unp6dERESISPYnP7VarVy5ckUWLFggXl5eoihKnlMgFUdz5swx2hf00zetXr0621PRj+8LgYGBcuzYMUuEXCjYD/+aOnWquLu7y4IFCwxl9+/fl+joaNmzZ49MnjxZ6tSpIxqNRpo1a2aYB9uW5oIeP368KIoirVq1kuXLl2ebvUGr1WZ7Cjo2NlZu375tU/0wefJk8fDwMJoZKC0tTdLT0+XGjRvyww8/SIsWLUSj0UidOnVk48aNImJb+4KIyPvvv2944vnTTz/Nc1xDfdsvXrwoJ06cyNfoEtaACaBKdOvWTVxdXWXZsmUydOhQKVmypOGPXo0aNeT999+XQ4cOGb3npZdesrlprt5++20pXbq0YVqjvA5a27ZtkwoVKkitWrWMZgop7vr06SMlSpSQn3/+WaZOnSp16tQx7AsODg4ycOBAQ4KsZ4v7AvvhX3Xq1JFu3boZBkR/8vfi0aNHcvLkSUOS5O/vn+dg4cVR3bp1s30h6N27t2zatMmonr5vkpOT5ZVXXpGQkJBcx4YrjurXry+dO3c2fL45HSPj4+Pl22+/FU9PT3F1dZX//e9/RR1moQsICBCNRiOenp6G/SE4OFh++OGHHGdFSUlJkUGDBknTpk2ZAJL1uHPnjgQGBkqlSpUMZQ8fPpQ1a9ZI+/btjQ54TZo0kYULF8q6deukQoUK0r17dwtGbn4//fSTKIoiixcvNhzYHp/n9kkTJ04UFxcXmznjEx8fL82bNxdvb29DWVpammzZskVef/11qVChgmFf8PLyko8//lhWr15tc/sC++FfcXFxUrt2benYseNT62q1Wlm4cKEoiiIfffRREURXNC5fvixeXl7Spk0b2bNnj7z11luGuV71g1y//fbbRseB48ePi4eHh7Rp08ZygZtZQkKCNG7cWJo2bfrUulqtVtauXWuTY0BevXpVKlasKE2bNpUTJ07Ip59+Kq1btxZnZ2dRFEVcXV2lf//+8vvvv8vdu3dFROTQoUPi6ekpwcHBFo4+/5gAqsCNGzekVatWhvlr9Zez9G7duiXz5s0z+gas39Gf/PZb3J0+fVoqVaoknp6e2abo0el0RhOdi4h89dVX4uzsLPv37y/yWAtDXFycdO7cWTp27CharTbbN9X4+HhZtWqV9OjRQ0qVKmX05cCW9gX2Qxb9FF59+/YVNzc3OXjwoKE8r4Gx69atK+3atZMHDx4UVaiFatu2baIoikyYMMFQlpiYKGFhYdKvXz9xd3c3fP7PPfecfPHFF/LRRx+JoiiGS6DFnf5L8IgRIwxTmOm/HOd1hrNFixbSpEkTQyJkC3bs2CEajUbeffddQ9mDBw8kPDxcxo0bJ/Xq1TPsD5UqVZKxY8fKqFGjit3+wARQBdLT02XHjh2yf/9+o0m7MzIyst3TcuHCBXnnnXdEURTx9PS0RLiFRn+A27Jli2GexpCQEFm3bp3cu3cvW/2UlBTp37+/lClTpqhDLVRRUVFy5syZbPvCk2dBb9y4ITNnzpSSJUta/ZRGz4L98K+lS5ca7n978l6nzMxMo35JSkqSLl26yAsvvGCJUAvF/v37pUqVKrJ06VIRkWwJz/Xr1+Xbb7+Vtm3bGn0ZsMX9YfPmzaIoitSsWVPCw8ONlmVkZBjtC4mJidKrVy+pWbOmJUItNCdOnBA/Pz9ZuHChiGS/Vzw2NlZ++eUXGTp0qFSrVq3Y7g9MAFUkp2mcRMTwDU+/kx86dEhKliwpI0eOLMrwioxWq5XffvvN6Ftc/fr15Z133pH169fLuXPn5L///a8MGDBA7Ozs5OOPP7Z0yEVGnwTp94XIyEib3hdyo8Z++OKLL0Sj0YiiKDJ06FAJDw+Xhw8fGpbr/+j//fffUqlSJauf5qog0tPT5ezZsxIXF2coy+0s6MWLFw1z49rqlGdr1qwxTAcZHBwsYWFhRve96veFTZs2ScWKFW1qX9BLTk7OdmIgp7+hN2/elNGjR4uiKPL2228XVXhmwQRQBfQHsadd1tHT78xHjhwp7NAs7vfff5euXbuKvb29IRnU/xF0dHSUcePGGf1RUBv92WA17At5seV+0P8xv3//vsyfP1/KlSsniqKIvb29BAUFyfjx4+Wvv/6SPXv2yPz586VatWpStmxZOXXqlIUjLzpPHjtnzJhhs/uDSNZDP2vWrJFGjRoZjovly5eX/v37y48//iirVq2SDz/8UMqUKSMVK1bM8wlZW/Tk/jB16tRiuT9wHEAykpycjFGjRmHnzp2Ii4uzdDiFQv7/qPaPj+0VFxeHnTt3Yt++fXBwcEDFihXh7++P7t27WzBSy0pNTcU777yDzZs3486dO5YOx2JsvR/kiTEuHz16hNDQUKxatQqRkZHZ6tepUwcTJ07EK6+8UpRhFir9QMZ5Dfau76eLFy+ie/fuyMjIwOXLl4s40qIlIvjrr7+wdOlSbNu2DRkZGUbLmzVrhsmTJ+PFF1+0UISWd+XKFfTq1QsPHjzA1atXLR1OgTABtHF37tzB6dOncfHiRaSkpCAwMBD+/v5GA9k+edBLS0vDnTt3jGYNKe4KMlL9k/3x5B/I4upZR+tPTk62qWnx2A/5d+PGDfz99984c+YMvL29Ua5cObRs2RI1atSwdGgWc+HCBfTq1Qvdu3fHl19+aelwCoXkMMB3UlISdu3ahStXrqBixYpwcXFBkyZNUK5cOQtGanlXr17FqFGj0KZNG3zyySeWDqdAmADasC1btuCzzz7L9i3e09MTHTp0wIABA9C9e3ebmtEgP3JLAB6fI9nWpr97Un6SoIyMDCiKYtOzIKi9H7Zu3YozZ87gxIkTKF++PBo3bowaNWqgSpUqKFOmDBwcHCwdYqF7vA/KlSuHJk2aoEaNGvDx8UGZMmWMZoJ5nK0dI3I7+/n4LFFq8KxTfhbHqUKZANqo6OhotG3bFqmpqRg2bBiCg4Nx5coVHD9+HCdPnsSpU6eQlpaG559/HhMnTkTfvn3h6Ohoc3M63r59G19++SU6deqEoKAgo0nt9bu+LZzdywv7IAv74V+JiYmYPXs25s6dCzs7O8OUZ0DWF8QWLVqgd+/e6NGjBzw9PQ3LbOVsOJD/PujVq5fRvlIc/9Dn5cljfk5n/54sFxFkZmbaVAKc3354UrGeMrWI7jWkIvbJJ5+Ih4eHrF+/Ptuy6OhoCQsLk1deecVwg++cOXMsEGXh09+cW61aNenatavMnTtXDh06lG1mD/1QFyIiO3fulC1btlgi3ELBPsjCfvjXl19+KSVLlpTevXvLzp075cKFC7J27VqZMWOGdOvWzTANYsOGDeX333+3dLiFgn2Q5bvvvpP+/fvLxo0bs43rmJmZmevoEbZGjf3ABNBGBQUFSdu2bSU+Pl5ExGiYl8ft2LFDGjRoIE5OTvLTTz8VdZiFLiAgQBwdHaVp06bi6OgoiqKIr6+vvPLKK7Js2TI5d+6cUf3U1FTp0aOHaDQaoyEwijP2QRb2w798fHyka9eukpCQkG3ZzZs3ZePGjTJy5EjD0/E//vijBaIsXOyDLL6+vobB/4OCgmTKlCkSGRmZbTxM/diIqamp8vXXX8uOHTssEW6hUWM/MAG0QQ8ePJAOHTqIv7+/YULzx7+96Ef/1zt27Jh4eHhIjx49DMttwY0bN8TX11caNWok6enpEhkZKVOmTJH69euLoihiZ2cn9erVk9GjR8u6deskKSlJDh06JN7e3jYz3Rf7IAv74V/nzp0TFxcXmTRpkqEspzMcaWlpsmnTJqlevbp4enrazGw4IuwDvTNnzoiiKNK4cWPp2LGj4YqQi4uLhISEyDfffJPti9E///wjiqJIixYtLBS1+am1H5gA2ij9NEU5ndV7PMHTH/B69uwpNWvWlGvXrhVZjIXt4MGD4unpKUOHDhURMcx8cvv2bdmyZYu8+eab4uPjI4qiSMmSJaV169aGuZGfnCauuGIfZGE//Ot///ufVK5cWQYMGCAiWWc0nvyC+PgxYsOGDTZ3mwj7IMsvv/wiiqLIV199JSJZM0HNmTNHAgICDElQhQoVZNCgQbJq1Sq5d++ezJ8/v9hNefY0au0HJoA2KiYmxjC375gxY+To0aPZLmPpT2UnJSVJv379pGrVqpYItdBERUXJSy+9JGvWrMlxeXp6uly7dk3+85//SP/+/cXT07NYTueTF/ZBFvaDsaCgIHF1dZXNmzdnW6ZPfPQJ0d27d6VatWrSt2/fIo2xsLEPRH744QdRFCXHPjh06JCMGzdOqlSpYkiCatasKd7e3uLu7l70wRYitfYDE0Ab9vvvvxvmKWzcuLF8+umnsnPnTrl27ZpRMrh69Wrx8vKSUaNGWTDawpGYmJjjPT6P0x/klyxZUiyn83ka9kEW9sO/ic3BgwelUqVKoiiKjB07Vg4ePJjtC6L+4Zj9+/dLxYoV5d133y3yeAsD+yCLTqeTyMhIGTdunFy6dMmo/HEPHz6UjRs3ytChQ8Xd3V0URZHRo0cXdbiFRs39wATQxjy50969e1fef/99qVq1qiiKIuXKlZN27drJq6++KiNHjpTBgweLk5OT+Pv7y/nz5y0UtfnldB+j/rJfbj744ANRFEWOHj1amKEVGfZBFvZDdhkZGbJy5UqpUKGCKIoizz//vIwbN05+/fVXOXv2rKFvYmJiZNCgQWJvb29zfcE+yPLgwQNJS0vLcdmTvzv6KRGPHz9eBJEVLTX2A8cBtEHy/8fqiomJQcWKFaHRaHDmzBls3LgRu3btwrlz5xAdHQ0A8PDwQEBAABYuXIjnn3/ewpGbl74f4uLiUK5cOaPxnB4f9BkAYmJi0LVrV9y6dQvx8fGWCtns2AdZ2A85i4+Px6JFi7Bu3TpcvHgRJUuWRKVKleDi4gJPT0+cP38e8fHxGD58OL777jtLh1so2Ad50//uXL58GQMGDEBSUhKioqIsHVaRs8V+sJ1RHAkZGRnYt28fli9fjosXL0JRFJQsWRJNmjRB//798fHHH+Ojjz5CdHQ0Hj58iCtXrsDf3x9VqlSBvb29zQzy+mQ/aDQalChRAvXr10efPn3QvHnzbAO5Ojs7Y9iwYahYsaKFojYv9kEW9kPO5P/Ph+3l5YWPP/4Yffr0weHDh7Fv3z4cPHgQx48fh5eXF6pUqYJPPvkEr776qqVDNjv2Qf7o/yacO3cOx44dwwcffGDhiCzDJvvBQmceqRDMnTtX3NzcRFEU8fPzE39/f8NNq/pLHIsXL5bbt29bOtRC9bR+qF27tnz11VcSGxtr9L60tDSbGeyTfZCF/ZB/mZmZkpqaKlqtVhISEuTMmTOWDqnIqbEP8jvsV1xcnKxcuVLu3r1byBFZhhr7gQmgjbhy5YqUKlVKWrVqJVeuXJGYmBjRarUSHR0t3333nQQHBxv+6LVr104OHz5s6ZALRUH6oX379jZ5Tw/7IAv74V//93//J+fPn5f/+7//y7YsMzPT6I/fk38IbSURZh9kyasfnianyQSKK/YDE0CbMWXKFClXrpz8/fffhrInD2KnTp2SIUOGiLOzs9SqVUuOHDlS1GEWOlP6wVYGwGYfZGE//Gv27NnSuHFjmTVrluzYsUNu3ryZ7Y/Yk2Pf3blzxzBUlC1gH2TJTz88if2Qxdb6gQmgjXjppZekevXqcv36dRH5d4w/nU6XbadesGCBKIoiw4YNK/I4Cxv7gX2gx374l364E3t7eylTpox0795dvv32Wzl06FCOQ+OkpKTI+++/L8OHD7eZs1/sgyym9IOtnPkSYT+IMAG0GZ9++qkoiiJnz57Ntc7j32z79OkjVatWlcuXLxdFeEWG/cA+0GM/ZLlw4YK4uLhI8+bNZdGiRdKzZ08pV66cKIoiPj4+MnToUPnPf/4jZ86ckfv374uIyIEDB8Td3V169uxp0djNhX2Qhf2Qhf2QhU8B24jg4GAAwCuvvIL58+ejZcuWcHR0zFYvMzMTdnZ2qFWrFrZs2YKUlJSiDrVQsR/YB3rshywXL17Eo0eP0KlTJ7zzzjvo1q0bLly4gMjISOzYsQPr16/HmjVrUKdOHbRr1w6dO3dGREQEkpOTMWLECEuHbxbsgyzshyzsh//P0hkomUdGRoZMmDDB8GTjokWLJC4uLse69+7dkyFDhoiXl1cRR1n42A/sAz32Q5Zff/1VFEWRsLAwo/L09HSJioqS3377Td577z2pX7++ODo6SqlSpaRkyZI2NQ0e+yAL+yEL+yELE0Abs2TJEnnuuedEURSpVKmSjB49WjZt2iSnTp2Ss2fPys2bN+Xjjz8WZ2dnGT9+vKXDLTTsB/aBntr7QafTyf/+9z+5cuWK4fWTUlJS5NixY/LLL79Ip06dDHOI2wr2QRb2Qxb2QxYmgDZGp9PJxYsX5YMPPjCavLp8+fJSuXJlsbOzE0VR5OWXX5bo6GhLh1to2A/sAz32Q+5y+sM3ZswYURRFjh07ZoGIih77IAv7IYua+oFTwdmw1NRUHDp0CH/++Sdu3bqFO3fuwM3NDf3790efPn3g7Oxs6RCLBPuBfaDHfsiZTqeDRqPBtWvX0LNnT9y/fx83btywdFhFin2Qhf2QRQ39wIdAbFipUqUQHByM4OBgaLVaODg4WDoki2A/sA/02A8508+NfPPmTWi1Wrz99tsWjqjosQ+ysB+yqKEfeAaQiIgAZM2PGxMTA09PT5QqVcrS4VgE+yAL+yGLLfcDE0AiIiIildFYOgAiIiIiKlpMAImIiIhUhgkgERERkcowASQiIiJSGSaARERERCrDBJCIiIhIZZgAEhEREakME0AiIiIilWECSERERKQy/w8Sys+EJLMwqwAAAABJRU5ErkJggg==\n"
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.visualization import plot_histogram\n",
    "\n",
    "backend = Aer.get_backend('aer_simulator')\n",
    "\n",
    "binding = {theta[i]:res.x[i] for i in range(4)}\n",
    "qc_res = create_qaoa_circ(g, theta).bind_parameters(binding)\n",
    "\n",
    "counts = backend.run(transpile(qc_res, backend), shots=512).result().get_counts()\n",
    "\n",
    "plot_histogram(counts)"
   ],
   "metadata": {
    "collapsed": false
   }
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}