Maxcut.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "a64add2d-a9e8-4a20-b1f0-848edf533b2e",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import networkx as nx\n",
    "import timeit\n",
    "\n",
    "from qiskit import Aer\n",
    "from qiskit.circuit.library import TwoLocal\n",
    "from qiskit_optimization.applications import Maxcut\n",
    "from qiskit.algorithms import VQE, NumPyMinimumEigensolver\n",
    "from qiskit.algorithms.optimizers import SPSA\n",
    "from qiskit.utils import algorithm_globals, QuantumInstance\n",
    "from qiskit_optimization.algorithms import MinimumEigenOptimizer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "42732830-264b-463f-bb9d-e62ef571740f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generating a graph of 6 nodes\n",
    "\n",
    "n = 6  # Number of nodes in graph\n",
    "G = nx.Graph()\n",
    "G.add_nodes_from(np.arange(0, n, 1))\n",
    "elist = [(0, 1, 1.0), (0, 2, 1.0), (0, 3, 1.0), (1, 2, 1.0), (1, 3, 1.0), (2, 4, 1.0), (3, 5, 1.0), (4, 5, 1.0)]\n",
    "# tuple is (i,j,weight) where (i,j) is the edge\n",
    "G.add_weighted_edges_from(elist)\n",
    "\n",
    "colors = [\"y\" for node in G.nodes()]\n",
    "pos = nx.spring_layout(G)\n",
    "\n",
    "\n",
    "def draw_graph(G, colors, pos):\n",
    "    default_axes = plt.axes(frameon=True)\n",
    "    nx.draw_networkx(G, node_color=colors, node_size=600, alpha=0.6, ax=default_axes, pos=pos)\n",
    "    edge_labels = nx.get_edge_attributes(G, \"weight\")\n",
    "    nx.draw_networkx_edge_labels(G, pos=pos, edge_labels=edge_labels)\n",
    "\n",
    "\n",
    "draw_graph(G, colors, pos)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "fe075fd6-4df4-4dff-900c-db3b3947a404",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0. 1. 1. 1. 0. 0.]\n",
      " [1. 0. 1. 1. 0. 0.]\n",
      " [1. 1. 0. 0. 1. 0.]\n",
      " [1. 1. 0. 0. 0. 1.]\n",
      " [0. 0. 1. 0. 0. 1.]\n",
      " [0. 0. 0. 1. 1. 0.]]\n"
     ]
    }
   ],
   "source": [
    "# Computing the weight matrix from the random graph\n",
    "w = np.zeros([n, n])\n",
    "for i in range(n):\n",
    "    for j in range(n):\n",
    "        temp = G.get_edge_data(i, j, default=0)\n",
    "        if temp != 0:\n",
    "            w[i, j] = temp[\"weight\"]\n",
    "print(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "094eb194-24c7-4e28-b235-8e4ba1af81c9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "case = [0, 0, 0, 0, 0, 0] cost = 0.0\n",
      "case = [1, 0, 0, 0, 0, 0] cost = 3.0\n",
      "case = [0, 1, 0, 0, 0, 0] cost = 3.0\n",
      "case = [1, 1, 0, 0, 0, 0] cost = 4.0\n",
      "case = [0, 0, 1, 0, 0, 0] cost = 3.0\n",
      "case = [1, 0, 1, 0, 0, 0] cost = 4.0\n",
      "case = [0, 1, 1, 0, 0, 0] cost = 4.0\n",
      "case = [1, 1, 1, 0, 0, 0] cost = 3.0\n",
      "case = [0, 0, 0, 1, 0, 0] cost = 3.0\n",
      "case = [1, 0, 0, 1, 0, 0] cost = 4.0\n",
      "case = [0, 1, 0, 1, 0, 0] cost = 4.0\n",
      "case = [1, 1, 0, 1, 0, 0] cost = 3.0\n",
      "case = [0, 0, 1, 1, 0, 0] cost = 6.0\n",
      "case = [1, 0, 1, 1, 0, 0] cost = 5.0\n",
      "case = [0, 1, 1, 1, 0, 0] cost = 5.0\n",
      "case = [1, 1, 1, 1, 0, 0] cost = 2.0\n",
      "case = [0, 0, 0, 0, 1, 0] cost = 2.0\n",
      "case = [1, 0, 0, 0, 1, 0] cost = 5.0\n",
      "case = [0, 1, 0, 0, 1, 0] cost = 5.0\n",
      "case = [1, 1, 0, 0, 1, 0] cost = 6.0\n",
      "case = [0, 0, 1, 0, 1, 0] cost = 3.0\n",
      "case = [1, 0, 1, 0, 1, 0] cost = 4.0\n",
      "case = [0, 1, 1, 0, 1, 0] cost = 4.0\n",
      "case = [1, 1, 1, 0, 1, 0] cost = 3.0\n",
      "case = [0, 0, 0, 1, 1, 0] cost = 5.0\n",
      "case = [1, 0, 0, 1, 1, 0] cost = 6.0\n",
      "case = [0, 1, 0, 1, 1, 0] cost = 6.0\n",
      "case = [1, 1, 0, 1, 1, 0] cost = 5.0\n",
      "case = [0, 0, 1, 1, 1, 0] cost = 6.0\n",
      "case = [1, 0, 1, 1, 1, 0] cost = 5.0\n",
      "case = [0, 1, 1, 1, 1, 0] cost = 5.0\n",
      "case = [1, 1, 1, 1, 1, 0] cost = 2.0\n",
      "case = [0, 0, 0, 0, 0, 1] cost = 2.0\n",
      "case = [1, 0, 0, 0, 0, 1] cost = 5.0\n",
      "case = [0, 1, 0, 0, 0, 1] cost = 5.0\n",
      "case = [1, 1, 0, 0, 0, 1] cost = 6.0\n",
      "case = [0, 0, 1, 0, 0, 1] cost = 5.0\n",
      "case = [1, 0, 1, 0, 0, 1] cost = 6.0\n",
      "case = [0, 1, 1, 0, 0, 1] cost = 6.0\n",
      "case = [1, 1, 1, 0, 0, 1] cost = 5.0\n",
      "case = [0, 0, 0, 1, 0, 1] cost = 3.0\n",
      "case = [1, 0, 0, 1, 0, 1] cost = 4.0\n",
      "case = [0, 1, 0, 1, 0, 1] cost = 4.0\n",
      "case = [1, 1, 0, 1, 0, 1] cost = 3.0\n",
      "case = [0, 0, 1, 1, 0, 1] cost = 6.0\n",
      "case = [1, 0, 1, 1, 0, 1] cost = 5.0\n",
      "case = [0, 1, 1, 1, 0, 1] cost = 5.0\n",
      "case = [1, 1, 1, 1, 0, 1] cost = 2.0\n",
      "case = [0, 0, 0, 0, 1, 1] cost = 2.0\n",
      "case = [1, 0, 0, 0, 1, 1] cost = 5.0\n",
      "case = [0, 1, 0, 0, 1, 1] cost = 5.0\n",
      "case = [1, 1, 0, 0, 1, 1] cost = 6.0\n",
      "case = [0, 0, 1, 0, 1, 1] cost = 3.0\n",
      "case = [1, 0, 1, 0, 1, 1] cost = 4.0\n",
      "case = [0, 1, 1, 0, 1, 1] cost = 4.0\n",
      "case = [1, 1, 1, 0, 1, 1] cost = 3.0\n",
      "case = [0, 0, 0, 1, 1, 1] cost = 3.0\n",
      "case = [1, 0, 0, 1, 1, 1] cost = 4.0\n",
      "case = [0, 1, 0, 1, 1, 1] cost = 4.0\n",
      "case = [1, 1, 0, 1, 1, 1] cost = 3.0\n",
      "case = [0, 0, 1, 1, 1, 1] cost = 4.0\n",
      "case = [1, 0, 1, 1, 1, 1] cost = 3.0\n",
      "case = [0, 1, 1, 1, 1, 1] cost = 3.0\n",
      "case = [1, 1, 1, 1, 1, 1] cost = 0.0\n",
      "\n",
      "Best solution = [0, 0, 1, 1, 0, 0] with cost = 6.0\n",
      "\n",
      "Time taken for brute force: 0.0017513551283627748\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def brute():\n",
    "    max_cost_brute = 0\n",
    "    for b in range(2**n):\n",
    "        x = [int(t) for t in reversed(list(bin(b)[2:].zfill(n)))] # create reverse of binary combinations from 0 to 2**n to create every possible set\n",
    "        cost = 0\n",
    "        for i in range(n):\n",
    "            for j in range(n):\n",
    "                cost = cost + w[i, j] * x[i] * (1 - x[j])\n",
    "        if cost > max_cost_brute:\n",
    "            max_cost_brute = cost\n",
    "            xmax_brute = x\n",
    "    \n",
    "max_cost_brute = 0\n",
    "for b in range(2**n):\n",
    "    x = [int(t) for t in reversed(list(bin(b)[2:].zfill(n)))] # create reverse of binary combinations from 0 to 2**n to create every possible set\n",
    "    cost = 0\n",
    "    for i in range(n):\n",
    "        for j in range(n):\n",
    "            cost = cost + w[i, j] * x[i] * (1 - x[j])\n",
    "    if cost > max_cost_brute:\n",
    "        max_cost_brute = cost\n",
    "        xmax_brute = x\n",
    "    print(\"case = \" + str(x) + \" cost = \" + str(cost))\n",
    "\n",
    "colors = [\"m\" if xmax_brute[i] == 0 else \"c\" for i in range(n)]\n",
    "draw_graph(G, colors, pos)\n",
    "print(\"\\nBest solution = \" + str(xmax_brute) + \" with cost = \" + str(max_cost_brute))\n",
    "\n",
    "time = timeit.timeit(brute, number = 1)\n",
    "print(f\"\\nTime taken for brute force: {time}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "abf6d83a-d99d-4208-ba70-02ed732d193c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\\ This file has been generated by DOcplex\n",
      "\\ ENCODING=ISO-8859-1\n",
      "\\Problem name: Max-cut\n",
      "\n",
      "Maximize\n",
      " obj: 3 x_0 + 3 x_1 + 3 x_2 + 3 x_3 + 2 x_4 + 2 x_5 + [ - 4 x_0*x_1 - 4 x_0*x_2\n",
      "      - 4 x_0*x_3 - 4 x_1*x_2 - 4 x_1*x_3 - 4 x_2*x_4 - 4 x_3*x_5 - 4 x_4*x_5\n",
      "      ]/2\n",
      "Subject To\n",
      "\n",
      "Bounds\n",
      " 0 <= x_0 <= 1\n",
      " 0 <= x_1 <= 1\n",
      " 0 <= x_2 <= 1\n",
      " 0 <= x_3 <= 1\n",
      " 0 <= x_4 <= 1\n",
      " 0 <= x_5 <= 1\n",
      "\n",
      "Binaries\n",
      " x_0 x_1 x_2 x_3 x_4 x_5\n",
      "End\n",
      "\n"
     ]
    }
   ],
   "source": [
    "max_cut = Maxcut(w)\n",
    "qp = max_cut.to_quadratic_program()\n",
    "print(qp.export_as_lp_string())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "218fd958-2679-493a-9582-dc6f0c319fac",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Offset: -4.0\n",
      "Ising Hamiltonian:\n",
      "0.5 * IIIIZZ\n",
      "+ 0.5 * IIIZIZ\n",
      "+ 0.5 * IIIZZI\n",
      "+ 0.5 * IIZIIZ\n",
      "+ 0.5 * IIZIZI\n",
      "+ 0.5 * IZIZII\n",
      "+ 0.5 * ZIZIII\n",
      "+ 0.5 * ZZIIII\n"
     ]
    }
   ],
   "source": [
    "qubitOp, offset = qp.to_ising()\n",
    "print(\"Offset:\", offset)\n",
    "print(\"Ising Hamiltonian:\")\n",
    "print(str(qubitOp))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "d1f6ce1c-e8d3-4adc-8fee-0717bca01bf4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "optimal function value: 6.0\n",
      "optimal value: [0. 0. 1. 1. 0. 1.]\n",
      "status: SUCCESS\n",
      "\n",
      "Time taken for exact classical eigensolver force: 0.016265451908111572\n"
     ]
    }
   ],
   "source": [
    "# solving Quadratic Program using exact classical eigensolver\n",
    "\n",
    "exact = MinimumEigenOptimizer(NumPyMinimumEigensolver())\n",
    "\n",
    "def classical_eigen(): \n",
    "    result = exact.solve(qp)\n",
    "    \n",
    "result = exact.solve(qp)\n",
    "print(result)\n",
    "    \n",
    "time = timeit.timeit(classical_eigen, number = 1)\n",
    "print(f\"\\nTime taken for exact classical eigensolver force: {time}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "3585e02f-76fb-460e-bb90-3fb8d2246aa4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "energy: -2.0\n",
      "max-cut objective: -6.0\n",
      "solution: [0 0 1 1 0 1]\n",
      "solution objective: 6.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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NOXPm9Lqj1+HDh8nPzycxMZFnn32WhQsXEhoa6oKqBejuT6+pqaGlpQW9Xu82iw+0Wi0PPPAA0P07s3//fiZPnkxiYiKlpaVERUUB8Ne//pWUlBTGjx/vynIFROgOO0VRKC8vp7CwkKKiIhITE5kzZw6TJk3qc6VYcXExa9eu5a233uKaa65xcsVCbyRJYunSpTgcjj4D12q10tTU5LKDKtPT00lPTwe6+2/9/Py4//77mTVrFuvWrWPdunWnbCdps9lob28Xp1s4mViRNkw6OjrYsWMHBQUFdHV1MWvWLGbNmjWgtfTCyGOz2fj73//OO++8w3//+18MBoOrS+pZXafT6bj88svJyso6ZbWi3W7nf//3fwkKCiIvL4+JEyeKbochIpYBO4ksyxw8eJDCwkK++eYbMjIyyMnJYfTo0W7zcVQYPmazmbFjx3LllVfy1FNPubqcAXE4HOzevZsvv/yS9vZ2cnNzycnJcYs/GiOZCN1hVl9f37N9YkBAADk5OUydOhWj0ejq0gQnOXHiBA8++CC1tbW8/PLLp+2HMRKUlpaSn5/PgQMHmDFjBuedd96IO+3ZXYjQHQY2m43du3dTUFBAZWUl06dPZ9asWSPyzSYM3g+3U9y2bRv3338/48aN44UXXjjt8ZGmqamJTZs2sXXrVlJTU8nLyyM9PV18WhsEEbpD5OSg2NatW9m1axdJSUnk5OQwadKkPtfFC57HZrNxww03cM8992AymXjooYe49dZb+fWvfw2M7MD9IavVyvbt29mwYQNqtZrc3FymTZsmtgodABG656i9vb1nUMxisZCTk8PMmTPFqK8Xe/PNN/n5z39OSkoKr7zyCtnZ3e8vT9xWU1EUDh48SH5+PmVlZcydO5d58+YRGBjo6tLclgjdsyDLMgcOHKCgoICDBw8yceJEZs+eTVpamviYJQDwwAMPsH79enbv3g10/85IktTz+9HR0dGzkjAxMdGVpQ6ZmpoaNmzYQFFRERkZGeTl5XnM9zaUROgOQl1dXc+gWFBQUM+gmDPPzRJGjmeeeYYZM2Ywc+bMU1q569ev51//+heVlZU9x673dsrHSNXZ2cnWrVvZsGEDoaGh5OXlMXnyZI9r5Z8ttw1ds8PBrvZ29ra383VHByarFYeiYFSrGeXjw0RfX6b4+5M0zIFntVp7BsWqq6t7BsViY2OH9b7CyOdwOHj11VeZNGkSU6ZMAeC5557jP//5D0uWLCElJYXJkyczceJE3n77bWbOnOniioeWLMt89dVX5Ofn09TUxHnnncfs2bO9fuZOf6HrktGfDoeD90wm1jU0YJZlNICfWk2AWt19SoKi8E1HB0WtrbxUU8NYo5GboqKYNIQn2CqKQllZWc+gWEpKCueddx4TJ04Ug2LCgKnVai655BKOHj0KwJo1a9i1axd33303U6dOxd/fH4ALLrjAI4/RUalUTJkyhSlTpnD8+HE2bNjAww8/zLRp08jNzXXZ6jx35vSW7p62Nv5cUUGjzUakTof+DB9HFEWh0W6n3eHg4pAQfhYTg+85jAy3tbX1DIrZbDZycnKYMWOGGBQThsQvf/lLMjIyuPbaawkICAC6t+PcuXMnX3zxhVcMPjU3N7N582a2bNlCYmIiCxYsYMyYMV41FuI23Quf1tfzXGUlQRoNgYNsTToUhSqLhQSDgcdSUggZxLQVWZb55ptvKCgo4Ntvv2XSpEnk5OSIQTFhSB06dIhf/OIX5Ofno9FoqK+v58EHH6Szs5Onn36ayMjInkNGvYHNZmPnzp18+eWXKIpCXl4e06dP73WDJ0/jFqG7vqGBp06cIHoArdv+VFutxOh0/Dk1Ff8zBLfJZKKwsJBt27YRHBxMTk4O2dnZYlBMGDY/+clPiI+PZ+bMmTzzzDNcdNFF/PznP2fUqFFeFbg/pCgKhw4dIj8/n9LSUubMmcP8+fMJCgoa+nvJCp2HOzEfN9N5oBNbkw0JCU2YBt/xvvgk+2BIMQz7v4PLQ/eE2czyw4cJ1WoxDMHoZoXFwvnBwdwVH3/aYxaLpWdQrKamhhkzZjBr1ixiYmLO+b6CcCYdHR0888wzNDQ0MG/evJ5Nw4VuJpOJDRs2sGPHDsaPH8+CBQtISko65+s6Oh00rm+k7v067I12FFlBpVchabvDVbEqKLburNPF6ohYGkHQ/CBUuuGZbeHS0JUVhXuOHuWY2UzkEH2skBWFCouFx1JSyPL3R1EUjh07RkFBAbt37yY1NZWcnBwyMjLEoJgguKHOzk4KCwvZsGEDgYGB5OXlkZmZeVYr+dr3tVP+53Js9Ta0IVrUfn1fQ1EUHG0O7E12DIkG4u+Lxzhq6GdauDR097S18eCxY8TrdEPapG+02QgBFldVsa2wEIfD0TMoNhwfWwThXHjiSrWhIMsye/fuJT8/n/r6+p4pZz/c97cviqJgetdEzSs1aAI1aIIG18CyNdiQu2Rifx1L6AVDe0CAS6eMfVhfj+EHq3T6su/ll2k9cQLpu19MfUAA2XfccdrzFEWhsamJmpoaiqxWRtntXH/99YwaNcor+8sE9yfLMu+88w4XX3yxmCXzIyqViszMTDIzMykvLyc/P5/f/va3ZGdnk5ubS3R0dJ+vNb3THbi6WB0q7eD/oGlDtchmmRNPnwAY8uDty7CGbpfDQXFbGzED7FYYdcklRH03wfy0a3V1UVNTQ63JhEGvJyoqCr+AAGJjYkgTcwEFN6ZSqQgJCWHlypXcd999osurDwkJCSxbtozW1lY2b97M008/TXx8PLm5uYwfP/6URlXb7jZqXj37wD1JZVChi9RR+bdKjKlGfFKHf5B9WD/vVFgsqADVWbZAHQ4HtbW17N27l7179wIwMSODyZMnExUVRYBWy7729iGsWBCGx4UXXkhISAhvvfVWrydAC98LCAhg4cKFPPbYY2RnZ/Phhx/y+9//ns2bN2OxWLC326l4qgJNsOacAvcklUGFyqCi4qkKZNvwn5I8rH9yKywWHIN4/rH16yn94gvU/v7ox4+n02AgMCCAuLg4QkJCTus+8FOrOdLVNbRFC8IwkCSJm2++mSeeeIItW7Ywd+5cV5fk9rRaLbNmzWLmzJkcOXKE/Px8Pv74Y86TziPGFINf6tCtUNWGaek61kXzlmZCcof3SK1hDV2zLCMP8K960gUXYAgLY//+/bQdPUrz558z8847CfjuNNPeaCSJTnn4/zIJwlDQ6/WsWLGCJ598ktjYWFJTU11d0oggSVLPoZt1NXXsWryLb5q/IcAaQGxsLAH+AfCjD9Pbq7azp3YPpg4TE8InsHj04jPeRxOooW5NHcHnBQ/r+NCwdi+oOO1n0aeAuDhQq+myWJh3zTXEjhtH+/Hj/b5GAUb+VtGCN4mIiOCmm25i1apVNDc3u7qcEcen1oeY4BiyZ2UTGBDIoUOH2LNnDyaTCUX+voEXoAtgXvw8MiMzB3xtdaAaS7kFS7llOErvMayhG6zRoB7EXwydVovBx4f2jg6gO1T7Y5ZlwsQu9sIIk5GRwbx583jhhRew2+2uLmdE6SzpBKV7o6GY2Biys7OJT4inpqaGnUU7KS8vx2azMS5sHGPDxmLUDnwO7snWrbnMPFzlA8McugkDPFHU3tVF45EjyDYbgf7+lG3bRktZGcGjRvX7unaHg3EDmM8nCO7m4osvJiAggHfffdfVpYwonfs7Ufl8H1uSJBEaGsrEiROZMGECZrOZ4qJijhw5QmdH5+BvoILOQ2fxukEY1j7dKJ0Oo1qNWZb7Xf4rOxyU5edzsL4es8WCXadj2nXXYTzDVnhmRWGyCF1hBJIkiWXLlvH444+zdetWZs+e7eqSRgRbkw1J1/unZ19fX9LT07El26iurmbvvr182/ItUUl9jwv9mEqnwtZgG6pyezWsoauSJC4LDeUtk4k4vb7P5+n8/Mhcvhzo3pmoqKiIoJSUfq9tVxS0ksRML9gqT/BMBoOBFStW8NRTTxEbG0tycrKrSxrxZFmmpaWF9vZ2rFYrzS3NhNndax/jYV+XuCAkBAmwDXCWgVarRa/X036G+be1VivnBwefcacxQXBnUVFR3Hjjjbzwwgu0tra6uhy3pw3W9mxcc5KiKDQ1NnHo0CF2bN9BdXU1wUHB3S3ftPRBnV4sW2W0ocM7TjTsoRup03FtRATVVuuAXxMUFERLS0ufj3c4HBhUKm4QK9EED3Byf2cxsHZmxglG5E4ZRVFoaW7hyJEj7Ni+g/LycgL8A8jOziZjQgbNrc34+PoQFBSEoijYZBuyMoCGnwzG9OE9asgpzcSlEREUtLZSZbEMaKexwMBAampqiIuLO+0xu6JQZ7Px28REgsXMBcFDXHrppZSXl/P+++9zzTXXuLoct6QoCk0+TVTXVFNbWYtWpyUiIoLMrEz0P+i+rK6uZmvlVso15T0zEvaa9jI/cT65ibn9Xh/AkDSwCQBnyymhq1OpeCQpiXtKSqi1Ws8YvIGBgRw+fPi0TZ+tskyV1cpPIyOZLfpyBQ/yw4G1bdu2edwBlmdLURQqKyspLi6mqKgIDRpm+85mQvQEfINPH0Rva22jrKyMG2bdMOjDChytDvTxevQJfY8/DQWndYhG6HQ8lZrK748do8xsJlqnQ9vHjAatVoveYKC9vb3nYL8Gm41OWebn0dFcGR4udhQTPI7RaOT222/nqaeeIiYmhsTERFeX5DImk4mioiKKioqwWq1kZ2ezfPly4uLiqHuvjupXquFHG7bZbDYOHjxIWlraWZ0OY2+2E/3z6OE/VcLZB1NaZJl3TSbeNZkACNdqez2+p6SkBK1ej29kJB2yTLxez33x8aR5+dHOguf76quveO+993jooYd6Gh0jVXl5OW1tbYwfPx6g3yOLmpqaelq0TU1NTJkyhalTp5KSknLKa+xtdg794hAAmgBNz3W/3v81/gH+Z3USha3ehjZMS9rf04bkNAm3OoJdr1Lx06goFgQH83ljI582NFBn654X51AUJLpXoln9/alqauIig4El4eFM9ffvs2UsCJ4kMzOTsrIyVq1axV133TUiNz9vbm7mgQce4N///jc5OTkkJibyxBNPnPY8RVHYsWMHW7dupaqqismTJ7N48WLS09P7/L41/hoS7k2g9OFS1EY1kkai7HgZSJzVpwPZIiN3ycTfFz9sx/f8kMvmW8Xo9SyLjubGyEgqrVbKzGYabDbsioKvWk2oLLP6T3/iz5dcclZHeAjCSLZo0SKee+451q5dy9KlS11dTr96a73W1tZSUlJCeXk5XV1dZGRksGTJErKzT2382Ww2VCoVF1xwAePGjRvwXsP+U/yJvCGSmtdq6DB2YKozkZmZOeiuAdkiY622EndX3LAc29Mbl/8J1ahUJBoMzA0K4orwcJZGRPCT0FCmh4cTGxhIWVmZq0sUBKdTqVT87Gc/Y+/evezYscPV5fTKZrOxZcuWXoPu0KFDTJgwgbq6Onx8fLjqqqt4//336fhuX5WTdDod06ZNY+LEiYPe3D3y+kiMlxmp3FPJ6LjRg5qPC2BrtGEz2Yi9M5bQi5xzagS4Qej2Z/To0Rw6dMjVZQiCSxiNRlasWMF7771HRUWFq8s5xerVq0lJSWHBggWcHPeRZbln2pXFYunecPy7ecdLlixh//79Q7qzmtVq5e36t4n8bSR+AX6Yy804Os+8g7e9zY65zIwmUMOoZ0YRdrFzV6y59XKu0aNHs2nTJi6++GJXlyIILhEbG8u1117L888/z0MPPYSf3/cbdzs6HbQVt9G+v53ObzqxNdhQZAWNvwbjGCO+Gb74Z/ujCx+aU7h/aPr06XzwwQd8+umnvPPOO2RnZ6MoSk8/7Jw5c1i9ejWVlZVERUWRlZWFyWTixIkTxMbG9jugNhCKovDGG2+QmJjI3Jvm4rjGQdMXTdS9X4el0gIOkAwSKp0KRVFQrAqyRUZSSWgjtMTdEUdwXjAqvfPbnW4dumlpabz88svY7XZxrpTgtbKzsykvL+fFF1/k17/+NY4WB6b3TDT+uxHFqiBpJFR+KlTG7gCRbTIt21po2tiEJEkEzAwg8oZIfJKH7vyvsWPHIkkSHR0d3HvvvQA9Yy+KohAVFUVqaipbtmwhPj6eyMhI0tPT2bt3L9OnTz/naVmbNm2iurqaBx54AEmS0PhpCF8cTuiiULoOddF1rIvOA53dG+RIEtpQLcbxRnxSfPAZ5YOkct2UU7dOMqPRSHh4OGVlZWKXfcGrXX755Tz7t2dZ9/g6Ur9KxdHpQBep6320XQdq43cBKCu0FbfRuq2VyBsjCV8SPiTnip0MzenTp6PX6/nvf//L3Llze7oTNBoNy5YtY/Xq1TzxxBOMHTuW5uZmFi1adM73Likp4bPPPuM3v/nNaf24Ko0K3/G++I73hUvP+VbDwq37dEH06woCdIfc5X6XY/unjaaOJgzxhgFNb5JUErooHdpILTWv1FD2aBkO82BOLuyfj48P8+bN4+233wa6w1aj0aAoCllZWTz88MPIsszGjRv55S9/SVQ/x28NRGtrK6tWreKmm24i7Axbv7qrERG6hw8fdnUZguBSpndMtKxpIXlqMqWVpafNAjgTlU6FPlFPW3Eb5Y+VI9sHfrZgY2MjX3zxBWvXrsVsPv1UhWXLlrFv3z4Ajhw5wscff8yzzz5LS0sLUVFR/O1vf+Ptt98+57EZWZZ58cUXycnJISMj45yu5UpuH7qjRo2itLRU7L4keK2Obzqofa0WXZwOvyA/UlNTOfDNAey2wb0nJElCF6+jdUcr9R/V9/vc1tZWNm3axJNPPskf/vAHTCYTEyZMOGVjmZO++eYbtm3bhsFgYO3atYwdO5bbb7+dwCHeH+XDDz9Eq9Vy6aVu2m8wQG7dpwvd/bpRUVEcP36cUWc4vkcQPI3D7KD8yXJU/qqevtjwiHDa2tv49tC3jB8/flCDUpIkoYvRUfNKDQFTAzAkfr+jVmdnJ1999RVFRUUcP36ciRMnctFFF/W7aOHAgQM8//zz/O1vf+P6668nJGR4ji/fvXs3u3bt4uGHHx6RK/R+yO1DF77v1xWhK3ibli0t2Ey203a+Sk5OZv/+/ZSVlQ16rwGVTgUSmN4zEXlHJPv27aOoqIhDhw4xduxY5syZw+23345uANuwjhs3js8//3xQ9x+smpoa3nzzTe644w58PeB4rhERuunp6Xz55Zdccsklri5FEJxGURTq1tShDjx9GbwkSYwdO5avvvoKPz8/jIFGPj7yMUebjmLUGjk/6XwmRkzs/bqyQpumjfLXy9lcspn4cfFMnTqVZcuWndXuXMPJYrGwcuVKrrjiCo/ZdW1EhG5aWhovvviimK8reBVrlRXLCQu6uN5bnFqtlnFjx/H1119TYixBq9PywIwHqG6v5o1v3iDSN5JI3+7TVU6etGCqM9HQ0ICv0ZdwYzh3LbqLmJ/EOPPbGjBFUXjttddISUnxqIM7R0TniMFgIDo6mmPHjrm6FEFwGnOZGST67bP18/cjLjGOwpJC5sbNRafWkRiYyJiQMeyt3UtraytHjx5lx44dHDt+DF9fX7Kyspg4aSIhESEoZX1v7epqGzZswGQyce2117q6lCE1IkIXxHxdwft0lXYN6HnqADU+Bh/qy+pRFIX29naUdoXig8UcOXwEnU7HpEmTyMzMJDY2tmcGgtpXTceBwU09c5YjR47w73//m+XLlw96Ixt3N2JCNz09XYSu4FUcrQ4kzZlnJlgcFiJCIrBarRQUFHDwwEEMagMhkSFMyZ5CQkJCr321kkZC7hj4fF1naWlp4aWXXmLZsmWEhjpv9y9nGTGhO2rUKMrKyrB9t+G5IHg8Fd07+p+BXq3HbDcTGBhIdHQ0U6dOJTg8GH+fAZw64WYJ4HA4WLVqFXPmzOk5bcLTuNmPvG8Gg4GYmBjRryt4DV2UDtl25pZoqE8oCgonGk50L42VoKajhnBjeL+vk83ysOxAdi4++OADDAaDR89UGjGhC6KLQfAuPsk+SOozdy/o1DpGB4+m0FSI3qinvLWcbxu+ZVLEpH5f5+hw4DvJfea9FhcXs2fPHm655RaPPnh2RIWuGEwTvIkh2QAKKI4z9zHMj5yPWqvmzzv/zJqDa1g4amHPdLG+SEgYR7vHQa/V1dW8/fbbLF++3CMWQPRnRE16HTVqFOXl5dhsNo8b0RSEH9MEaAicHUjr9lZ0Uf13A1g7rSxNX0pycvKAru3odKAOUOOb4fqAM5vNPP/881x55ZXEx8e7upxhN6Jaunq9ntjYWEpKSlxdiiA4RdiiMGSrjCL339ptbWklICBgwNe11dsIvzIclca1EaAoCq+++irp6enMmjXLpbU4y4gKXRBdDIJ3MY4zEjQvCGu1tc/nKIpCa9vAQ9fWZEMfpSd0oeunY61fv57GxkauueYaV5fiNCMydMX+uoK3kCSJmOUxqP3U2Jt738qxs6MTnU43oC432Swjt8nE3xuP2nD6ng7OdPjwYdavX89tt93mVcv7R1zopqSkUFFRgdXa919+QfAk2iAtyf8vGdkqY2s6fZ56S2vLgFq5slnGWmMl9s7Y7uNsXKi5uZmXXnqJW265Zdi2g3RXIy509Xo9cXFxol9X8CrGNCOpT6ai0qiwnLCc0sfb2tLa74bhiqJgNVmxNdpIuD+B0Atd261gt9tZtWoV8+fPZ+zYsS6txRVGXOiC6NcVvJMxzUj6ynSCzgvCWmnFUmVBsSl9tnQVWcFWb8NaYcWQaCD9H+kE5wW7oPJTrV27Fl9f33M+vmekGpEdKaNHj+aTTz5xdRmC4HSaAA3x98QTtiiMhs8aMP3HhL5Nj1QnYZEsIHXP65U0EijgN8mPsCvC8Mv0c/lMBYCioiL279/PQw895NELIPozIkM3JSWFEydOYLFYej2zSRA8mSRJGNONGNONVGZV0r6pnfhZ8dgabeDo3nXMkGBAn6BHG+Q+89mrqqp45513uOuuuzAa3WNRhiuMyNDV6XQkJCRQUlLCuHHjXF2OILhMyYkSEnMSCVng3oNRXV1dPP/88yxdupS4uDhXl+NSrv+8cZbEPgyCACUlJW5/dqCiKLzyyiuMGzeOGTNmuLoclxuxoSvm6wrerrOzk/r6erdfOvvFF1/Q0tLC0qVLXV2KWxixoZuSkkJlZSVms9nVpQiCS5SWlpKUlIRa7dpFDv359ttv+fLLL71uAUR/RmzoarVaEhMTxXxdwWsdPXrUrbsWmpqa+Oc//8mtt95KcLDrp6q5ixEbuiD6dQXvdvToUVJTU11dRq/sdjsvvPACCxYsYMyYMa4ux62M6NAViyQEb2W32ykvL3fb0F2zZg2BgYFccMEFri7F7Yzo0E1OTqa6ulr06wpep7y8nIiICAwGg6tLOc327ds5cOAAN998s9cugOjPiA5drVZLUlISR48edXUpguBU7tqfe+LECdasWcOKFSt6PYFYGOGhC6JfV/BO7tif29nZycqVK7nmmmuIiYlxdTlua8TP4cjJyUFRBnBOtSB4CEVRKCkp4dprr3V1KT0URWH16tVMmDCBqVOnuroctzbiW7pBQUFetx+n4N1MJhN6vd6tpmHt2bOHjo4OlixZ4upS3N6Ib+mKjnrB27hjf+748eMZO3asWAAxAB7/E5JlGZVqxDfoBaGHO/bn6nT9n1YsfM9j00iWZTZs2MCNN97o6lIEYUi5uqUrxlDOjUeEbl1d3Wn/TaVSMWHCBNavXy+mlAkeo7W1lfb2dqfPDpBlmY6ODkB06Z0rjwjdq666ioMHDwLw1VdfsXLlSm644QauvPJKfH19qa+vd3GFgjA0SkpKSElJcWrw7d+/n6VLl3Lddddxxx13YDKZkGXZaff3NB4RuikpKSxatIj58+ezbNky8vPzmT59OitXruTYsWNiD0/BYzi7a0FRFG6//XYuvPBC/v73v1NbW8uKFSvYuHGj02rwNB4xkHbxxRfz4YcfUlhYSHh4+GmPi8E0wVMcPXrUqdOyqqqq8PHxITc3l4SEBN59913+7//+j0ceeYTOzk4WLlzotFo8hUckUV5eHldeeWVP4DocDhwOR0+HvwhcwRNYLBaqqqpISkpy2j1jY2PJzc3lo48+wmQyAfA///M/3HXXXdxzzz0cOHDAabV4Co9Io+DgYC699NKeATWVSoUkSWKUVfAox48fJy4uDq3WuYdNzp07l+3bt7NmzRpOnDiB1Wpl8eLFXHTRRb0OYgv984juBejuezp48CDh4eFIktTrQIOiKGLkVRixrFYrmZmZTr/vrFmzUKvV/OlPf6KiooLo6GgSEhJ47733WLFihdPrGemk/lqD2dnZSnFxsRPLOXu1tbXY7XZiY2Opr69n+/btFBcX43A4yMzMJCMjg7S0NFeXKQhnzWazoVKpnHY8z48bKY2Njbz77rtUV1dz7NgxFi9ezBVXXOGUWkYaSZJ2KYqS3etjnhK6J23dupXVq1djt9tJS0sjOjqaTZs2ceLECV5++WWSk5NdXaIguK2nn36a9PR0Lr30UqB7fEStVvf870l2u10s+e1Hf6HrUT+1jRs38vjjj3PVVVdx4YUXEhwcjCRJ3Hrrrdx0002sXbuWe++919VlCoJbeuONN3jkkUdITk5m165d/P73vz8tcHft2kVKSopbbbYz0njEQNpJmzdvZurUqfzsZz8jPj4ePz8/fH196ejowN/f36mjvoIwkiiKgslk4p///CeffPIJhYWFXHXVVbS2tvYE7rFjx9iyZQt6vd7F1Y5sHhW6EyZMYOPGjVRUVFBYWMhzzz3H9ddfz6RJkzCbzaL/SRhRnDn7RpIk7r77bi644AISExN55513iIiIYMGCBRw5cgTo/iS5dOlSjEaj0+ryRB7VvbBo0SI6Ozu58sor0Wq1ZGdnk5uby2OPPUZiYqKryxOEQXHFDJzAwECgexrmX//6V1599VWWLFnCsWPHeOSRR4iNjR22e3sLjxtIg+9/Me12O5IkoVarkWW5z6lkguBu7HY769evJzQ0lKCgIAIDA4mMjBz2+/YW6nl5eYSFhfHuu+8O+/09hdcMpJ10cmHED0dXxao0YaRoaWnh3nvvpba2lqqqKgIDAwkODiYtLY2lS5eSlZU1rPc2Go09++Pu3bsXRVF46623hu2e3sZjk0i0aIWR6vPPP+fYsWN88sknFBcXs2bNGpYvX05LSwsPPvggJSUlw3Lf/fv38+STT57Slzxp0iTWrVvntLnB3sBjQ1eWZbEMWBiROjo6CAkJwWQyYbFYCAkJYcGCBfzjH/8gLy+PP//5z0N+z/r6el599VVuvfXW02Yn+Pr6Dvn9vJlHdi9A98ciX19f0tPTXV2KIAzK4sWLOXToEE8++WTPbAKtVovNZmPPnj1DvlWpzWZj5cqVXHLJJW53DJAn8tjQbWho4ODBgyJ0hREnMDCQe+65h9WrV/P888/jcDiIi4ujrq6OyMhIrr766iG7l6IovPnmm0RHRzN//vwhu67QN48N3fT0dLZs2eLqMgThrISHh3P//fcD3adFVFRUMGrUKOLi4ob0Plu2bKGsrIzf/OY3YhzESTw2dOPi4mhtbaW1tZWAgABXlyMIg6IoCoqioFKpSE1NJTU1FYvFgs1mG7KtHY8fP84nn3zCfffdJ1aZOZHHDqSpVCrS0tI4dOiQq0sRhAFTFKVnA/6T0xwdDgcA+fn5bN++fUju097ezgsvvMANN9zglPm/wvc8NnShu4vh8OHDri5DEAbs5GKeH84rPzkLp6ura0h2yZNlmZdeeolp06YxefLkc76eMDgeHbqjR48WLV1hxCgpKWH+/PnceeedvP/++1RVVQH0LPI5fPjwkCzD/eSTT1AUhcsuu+ycryUMnsf26UJ3v25bWxvNzc0EBQW5uhxB6Ne6detoaWkhISGBV155hT/84Q9otVqysrLQ6XR8+eWXPPjgg+d0j71797J9+3YefvhhsUrTRTz6py5JkuhiEEYMWZa5+uqrufvuu/n000/Jz8/nL3/5C7NmzeLjjz/mwgsvPKfrm0wmXn/9dW677Tb8/f2HqGphsDy6pQvf9+tOmzbN1aUIQr/uvvtubDZbz6YzoaGhzJ07l7lz57JmzRrmzp171te2Wq2sXLmShQsXitNTXMyjW7og+nWFkUWr1fY6X/auu+4665auoii88cYbxMfHn1NwC0PD40M3NjaWjo4OmpqaXF2KIAyYzWbrmSoG3dsrnu0eCJs3b6ayspLrr79eLIBwAx4fuqJfVxiJHn30Uerr68/5OqWlpXz66acsX768Z7tGwbU8PnRBdDEII0trayvt7e1ERESc03Xa2tpYtWoVP/3pTwkPDx+i6oRzJUJXENxMSUkJKSkp59QVIMsyL774IjNnzmTixIlDWJ1wrrwidKOjozGbzTQ2Nrq6FEE4o6NHjzJq1KhzusZHH32ESqVi4cKFQ1SVMFS8InRFv64wkpxr6H711VcUFRXxs5/9TCyAcENe8y8iuhiEkcBqtVJVVUVSUtJZvb62tpY333yT2267DT8/v6EtThgSInQFwY0cP36cuLi4s9q+0WKxsHLlSi677LKzDm1h+HlN6EZFRWG1WmloaHB1KYLQp7PtWlAUhddff52kpCRmz549DJUJQ8VrQleSJNHaFdze2Ybuxo0bqamp4brrrhMLINyc14QuiP11BfcmyzKlpaWkpKQM6nUlJSX861//Yvny5UN2qoQwfLwqdE+2dMXR7II7qqqqIiAgYFA7gLW2trJq1SpuvvlmwsLChrE6Yah4VehGRkZit9tFv67glgbbteBwOFi1ahWzZ89mwoQJw1iZMJS8KnRFv67gzgYbuh9++CF6vZ5LL710GKsShppXhS6Ifl3BfQ0mdHfv3s3u3bu55ZZbxMDZCON1oSv6dQV31NjYiN1uH9DGNNXV1bz11lssX778rLd7FFzH60I3IiICWZaHZNs8QRgqJ1u5Z2q1ms1mXnjhBa644goSEhKcVJ0wlLwudE/uwyD6dQV3UlJScsauBUVReO211xg1ahQ5OTlOqkwYal4XutDdxSD6dQV3MpD+3Pz8fOrr67n66qudVJUwHLw2dEW/ruAuOjs7qaurIz4+vs/nHDlyhM8//5zbbrtNLIAY4bwydE8OVtTV1bm4EkHoPlInKSkJtVrd6+MtLS289NJLLFu2jNDQUCdXJww1rwxdMV9XcCclJSWkpqb2+tjJBRDz5s1j3LhxTq5MGA5eGbogtnoU3Ed//blr167FaDRy8cUXO7kqYbhoXF2Aq6Snp/PRRx+hKIqYXC4MuxqLhf0dHXzd0cHRri66ZBmtJBGj1bLTYmFBTMxpv4vFxcXs27ePhx56SPyOehCvDd2wsDDUajUmk4nIyEhXlyN4qG86OnjXZKK4rQ0F0EkSvioVaknCCmxrbqZ0zBgerKggtraWqyMiOC84GFNNDW+//TZ33nknRqPR1d+GMIS8NnR/2K8rQlcYap0OB6/U1PBJfT0+KhWxOh2qXlqrTe3txOv1xOl0tDkcPFVRwTqTCen997lm6dJ+ZzQII5PX9umC6NcVhkeDzcbdR4/yaUMDcXo9EX0ELnRvzRgYGIgkSQRoNMTr9Ww6fJitU6bgK3YO80heHbonN78R83WFodJqt/NgaSlVVivxej3qfvpiFbpDNyAgoOe/VVVWou/qYlR8PA+VlnKwo8MJVQvO5LXdCwBB+iDCasM49LdDaKu1ODocSCoJXZQO3wxffNJ8MI42ikEMYUAUReG5ykoqLRbi9PozPt/c1YVKpUL/3XNbWlo4ceIEmZmZ6LVaFLud/1dWxqr0dPw0Xv1W9She+S9pqbRQ90EdTeubyDieQc2RGsITwpE0EoqiYD5hpmVrCwC6aB3hV4UTnBuMSuvVHwyEM9jW0sLm5mYSBhC4AC0/aOVarFYOfvstY8aM6QnhII2GCouFf1ZX82vRt+sxvCp0ZbtMw6cNVP+zGhTQRerwU/nR2NhIdFD090/87rQURVFwtDk48cwJGtY1EH9vPD5JPq4pXnBrsqLwYnU1IRpNn/23P9ba0kJgYCCyonDwwAFiY2IICgo65TmxOh2fNzWxNCKCmAGGueDevCZ0HWYH5Y+V07qjFV20DpW+u9UaFBjEsWPHujvYfvRekSQJTYAGtb8aS5WFI786QuJDiQTODHT+NyC4ta87Oqi1Wok3GPp9nmy3c/TTT2kuKaGyrIzolBRMGRloo6OJ66U1q5IkJODzxkaWRUeffkFhxPGKz8uyTe4O3J2t6BP1PYELoDfoUavUdHZ29vl6SZLQhevQBGkoe7SM1qJWZ5QtjCCbmpvRDKCFq8gy+oAAxv70p0Rccw0h06dT+vHHJEZG/vhvfo8wrZZ/NzaKAV8P4RWha1pjonVHK/oEfa+DYoFBgbS0tJzxOmqjGk2IhrI/lmGtsw5HqcIItb+jA/8BDHapdToSc3OxqFT4GAw0ShLRycmYa2r6fI1BpaLD4aDRbh/KkgUX8fjQ7SrtwvSGCV2Mrs9ZCEGBQTS3NA/oemo/Nchw4m8nvKrlIcsyXV1dWCyWXh93OBwUFxfz5ptvsmXLFidX51pWWabSYsFXNfC3U1NTE01NTcRHRmJva8MYEdHv8yWgwmw+x0oFd+Dxfbo1r9YgaSVUur7fEIFBgZSWlvbar9sbbZSWtl1tdB7oxHe8559R1dXVxU9+8hN27NjBkiVLeO2113A4HKdsRbh7927uv/9+goOD0Wg0NDc3s3DhQo/a20JRFBwOBzab7ZSvRouFrs5OWsxmZFk+/cvhOO2/HSstJTIigobNm4mcPBnjAM5G65RlJ3yXwnDz6NC11lppK2pDF6vr93l6vR61Rk1HZwdmlZn/2/V/jA8bz5Vjruz1+ZLUHeL16+q9InR1Oh1/+ctfKCkp4ZVXXgE4JUjb2tpYt24d559/Pg899BCfffYZf/zjH4ctdGVZxmq1YrPZsNvtTv3/KpUKrVZ7ypdsMFA9dizm7x7v70uj0aBSqcjOzqZm/XpktZrUSy4Z0Pft8R9LvYRHh27r9lZQQFKd+U0fGNjdr7u+YT2x/rFnfL42XEvL1hYcXQ7UPr1vPu0p1Go1WVlZVFVV9dq90NjYSElJCffddx8AqampaDQa2tvb8fPzO+W5NTU1FBcXn9ZaHMyXoijodDo0Gg06nQ6tVjuo/+/n53dWr9Vqtah66UKwyzJ7v/6aSJ2u3xVoJymKwpGPPsLe0cGEG29E1cfm5T82kD5jwf159L9i+752VMaBtQ+CgoLYdmwbhgAD4cZwmrqa+n2+pO5+c1kqLBjTXbMLlKIo2O32IW/NhYaGsnDhQgw/mv5kMBiw2Wyn1aFSqWhtbe05DtxgMBAQEIDJZDotdBVFQZZlDAYD/v7+p7UaB/LV1wkLrqJRqUg2GKiz2QgYQDAe/fRTOuvqyLj5ZlQDOHpHURRkGPCiC8G9eXTodn7b2T3wNQAGPwNbq7by20m/ZVftroHdwAHmMjP6VP05tdzO9stut6NWq8+6xafT6TAajaf995NheNrPqI/QNRgMqNVqzN8N9BgMBpqbm08LXIDo6GgWLVo0sJ/vCJLp78/7dXVnDF1zUxPVRUWoNBq2P/lkz39PW7iQiEmTen1NhywTpdWKlq6H8Oh/RUebA23EwA7x21q9ldF+o6ksqaSyuZJmazPfOL7pfWDkuy9Di4GPnvqI6g+qz6rFdvLLz8/vrF/rzEEqHx8f5O8Gc374MdtoNJKcnExBQQEZGRnYbDZqa2uJOMOIvCfJDQ7mvbq6M/ZhG4KDmfvoo4O6dpPNxorYM3d5CSODR4fuQGYiAFS3V1PSVMKtc26lpakFX7svDquDqKiofgdFbCds5K7IJeJy7wgXm81Ge3s7bW1tKIrS078aFhbG4sWL+f3vf09kZCSFhYUsWbLE1eU6VaLBwHijkdKuLsJ1/Q/cDoZFltGoVMz70fJgYeTy6NDVBGuQLTJqY/9dDMdbjtNsaea5Pc8BYHVYkRWZ98reY0XWij5f59A40AZ5x3HYS5YsYfv27XR1dTFt2jR+97vfYTab0ev1XHfddcyZM4elS5fy2muvkZCQwCOPPOLqkp1ueUwMdxw9ik2W0Q5izm5fFEWhxmrlFzExA+orFkYGqb8J/tnZ2UpxcbETyxlaZX8qo3V7K7qI/lseVocVq+P7FWZbT2yl2dzMpaMuxU93er/kSZZKC2nPpuGTIjbBEbq9UVPD67W1JOp7X/04GNVWKykGA0+lpqIZghAXnEeSpF2KomT39phH/0v6TfJDMZ951ZhOrcNP59fzpVPr0Kq0/QaubJORVBL6ODGiLHzvmogI5gQGUm6xIJ/DisVaq5UgjYbfJiaKwPUwHv2ZJWB6AJXqShS7gqQZeKsjNzH3jM+xmWyEXBTS70o3wftoVCoeSEhAV1FBfnMz4VotvoOY4mZXFKqtVuJ0Ov6QkkLYEPYPC+7BoxNDG6wlaF4Q1tqh3ZxGkRVwQOhPQof0uoJn0KpU3JeQwIMJCXTKMhUWC50OR7+vsX23f0O11crS8HCeTUsjQgSuR/Loli5A5I2RtGxpQTbLqAxD8zfGWmUl+Pxg0Zcr9EmSJOYHBzPZz48vm5r4oL6eSosFhe6WjkqSUOhu2aoAtSRxcUgIl4SGkuQjfq88mceHrj5KT/SKaCqfqUSfqB/QkuD+2JpsaAI1RP9cbCgtnFmQVsuSiAguDwuj3GKh3GymtKuLDllGK0kk6PUk+fiQZDBgdLOVdsLw8PjQBQi9KJSuI100ftaIPl7fs4R3sOzNdhSbQtIfk9D4e8WPThgiGpWKFB8fUnx8mB8c7OpyBBfy6D7dkyRJIu6XcYRdHoalwoK9bXCbQSuygqXSAgqk/ikVY5pr9loQBGHk85rmmqSSiFkeg1+mHyeeOYGl3IImVIPat++PdIqsYKu3IXfJBM0JIub2GLTB3rEYQhCE4eE1oQvdLd7AGYH4vuhLU34Tde/XdbdgZZA0Us8R7LKlew4uCvhn+xO+OBzfib4esxm3IAiu41Whe5ImQEP4FeGELQqj61gXljILnYc7cbQ5kDQSumgdPqN88EnxQRsqWraCIAwdrwzdkyS1hHGUEeMoI8F5YnBDEITh5xUDaYIgCO5ChK4gCIITidAVBEFwIhG6giAITiRCVxAEwYn63cRckqQ6oMx55QiCIHiEREVRwnt7oN/QFQRBEIaW6F4QBEFwIhG6giAITiRCVxAEwYlE6AqCIDiRCF1BEAQn+v+r2J57X7ZKtQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Making the Hamiltonian in its full form and getting the lowest eigenvalue and eigenvector\n",
    "ee = NumPyMinimumEigensolver()\n",
    "result = ee.compute_minimum_eigenvalue(qubitOp)\n",
    "\n",
    "x = max_cut.sample_most_likely(result.eigenstate)\n",
    "print(\"energy:\", result.eigenvalue.real)\n",
    "print(\"max-cut objective:\", result.eigenvalue.real + offset)\n",
    "print(\"solution:\", x)\n",
    "print(\"solution objective:\", qp.objective.evaluate(x))\n",
    "\n",
    "colors = [\"m\" if x[i] == 0 else \"c\" for i in range(n)]\n",
    "draw_graph(G, colors, pos)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "f3015545-68cb-4ff7-b69c-9c48f3e9041a",
   "metadata": {},
   "outputs": [],
   "source": [
    "algorithm_globals.random_seed = 99\n",
    "seed = 1010\n",
    "backend = Aer.get_backend(\"aer_simulator_statevector\")\n",
    "quantum_instance = QuantumInstance(backend, seed_simulator=seed, seed_transpiler=seed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "7602221e-ae1d-4ba0-b84f-ff9190ad4d3a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "energy: -1.995958462482359\n",
      "time: 4.2608020305633545\n",
      "max-cut objective: -5.995958462482359\n",
      "solution: [0. 1. 0. 1. 1. 0.]\n",
      "solution objective: 6.0\n",
      "\n",
      "Time taken for VQE: 5.3587478790432215\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# construct VQE\n",
    "spsa = SPSA(maxiter=300)\n",
    "ry = TwoLocal(qubitOp.num_qubits, \"ry\", \"cz\", reps=5, entanglement=\"linear\")\n",
    "vqe = VQE(ry, optimizer=spsa, quantum_instance=quantum_instance)\n",
    "\n",
    "# run VQE\n",
    "# def vqe_solve():\n",
    "#     result = vqe.compute_minimum_eigenvalue(qubitOp)\n",
    "# time = timeit.timeit(vqe_solve, number = 1)\n",
    "result = vqe.compute_minimum_eigenvalue(qubitOp)\n",
    "\n",
    "# print results\n",
    "x = max_cut.sample_most_likely(result.eigenstate)\n",
    "print(\"energy:\", result.eigenvalue.real)\n",
    "print(\"time:\", result.optimizer_time)\n",
    "print(\"max-cut objective:\", result.eigenvalue.real + offset)\n",
    "print(\"solution:\", x)\n",
    "print(\"solution objective:\", qp.objective.evaluate(x))\n",
    "# print(f\"\\nTime taken for VQE: {time}\")\n",
    "\n",
    "# plot results\n",
    "colors = [\"m\" if x[i] == 0 else \"c\" for i in range(n)]\n",
    "draw_graph(G, colors, pos)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "f33a3954-1d35-4f5a-9c33-1b0e32a253cc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "optimal function value: 6.0\n",
      "optimal value: [1. 1. 0. 0. 1. 0.]\n",
      "status: SUCCESS\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# create minimum eigen optimizer based on VQE\n",
    "vqe_optimizer = MinimumEigenOptimizer(vqe)\n",
    "\n",
    "# solve quadratic program\n",
    "result = vqe_optimizer.solve(qp)\n",
    "print(result)\n",
    "\n",
    "colors = [\"m\" if result.x[i] == 0 else \"c\" for i in range(n)]\n",
    "draw_graph(G, colors, pos)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f5540640-52b0-4009-ab53-3061f7a9356f",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Qiskit v0.35.0 (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": "3.8.13"
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {},
    "version_major": 2,
    "version_minor": 0
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}