VQE_with_Qiskit_runtime.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "b8caec8e",
   "metadata": {
    "tags": []
   },
   "source": [
    "# ***Quantum Experience Demo: Solving an Optimization Problem by using Qiskit Runtime***\n",
    "**Qiskit Runtime is used to solve an illustrative combinatorial optimization problem on quantum computers, examining an example from Max-Cut solved with the hybrid quantum variational algorithm VQE.**\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2d7b621-2497-4e43-aa64-5b37d6d0eb5b",
   "metadata": {},
   "source": [
    "### Authors:\n",
    "_Dr. Stefan Kister_<br>\n",
    "IBM Quantum Technical Ambassador, IBM DACH - Düsseldorf<br> \n",
    "<br>\n",
    "_Dr. Thorsten Muehge_<br>\n",
    "IBM Quantum Technical Ambassador, IBM DACH - Frankfurt<br> \n",
    "<br>\n",
    "Last update on 2.August, 2023\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2645deb2-8964-4de1-974a-6d55bf8be0f9",
   "metadata": {},
   "source": [
    "# 1. Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a10d433d",
   "metadata": {},
   "source": [
    "# **<center>Optimization – general aspects and challenges</center>**\n",
    "![Optimization Classical View](./images/optimization_classic_quantum.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1df8e5a5",
   "metadata": {},
   "source": [
    "# 2. Using qiskit to solve an optimization problem"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7786abf",
   "metadata": {},
   "source": [
    "## Qiskit Architecture\n",
    "![Qiskit Optimization Module](./images/qiskit-architecture-overview.svg)\n",
    "\n",
    "## Qiskit Optimization Module\n",
    "![Qiskit Optimization Module](./images/qiskit_optimization_module.png)\n",
    "https://qiskit.org/documentation/optimization/\n",
    "\n",
    "## Variational Quantum Algorithm\n",
    "![Variational Quantum Algorithm](./images/vqa_intro.png)\n",
    "\n",
    "## Transform QUBO Problem to Quantum\n",
    "![Variational Quantum Algorithm](./images/qubo_to_quantum.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "fa341284",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/xp/_lkpwwss4kz10m14lgzy2p5m0000gp/T/ipykernel_3973/532143317.py:11: DeprecationWarning: ``qiskit.algorithms`` has been migrated to an independent package: https://github.com/qiskit-community/qiskit-algorithms. The ``qiskit.algorithms`` import path is deprecated as of qiskit-terra 0.25.0 and will be removed no earlier than 3 months after the release date. Please run ``pip install qiskit_algorithms`` and use ``import qiskit_algorithms`` instead.\n",
      "  from qiskit.algorithms import VQE, NumPyMinimumEigensolver\n"
     ]
    }
   ],
   "source": [
    "# useful additional packages\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.axes as axes\n",
    "import numpy as np\n",
    "import networkx as nx\n",
    "\n",
    "from qiskit import Aer\n",
    "from qiskit.tools.visualization import plot_histogram\n",
    "from qiskit.circuit.library import TwoLocal\n",
    "from qiskit_optimization.applications import Maxcut, Tsp\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\n",
    "from qiskit_optimization.problems import QuadraticProgram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "72cef810-ac7e-4709-a06c-2acd006defc9",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "def23db6",
   "metadata": {},
   "source": [
    "## 2.1. Example for an Optimization Problem: "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8dd2ab25",
   "metadata": {},
   "source": [
    "### Weighted Max Cut Problem:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "63180128",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generating a graph of 3 nodes \n",
    "\n",
    "n=3 # Number of nodes in graph\n",
    "G=nx.Graph()\n",
    "G.add_nodes_from(np.arange(0,n,1))\n",
    "elist=[(0,1,1),(0,2,2.0),(1,2,3.0)]\n",
    "# tuple is (i,j,weight) where (i,j) is the edge\n",
    "G.add_weighted_edges_from(elist)\n",
    "\n",
    "colors = ['r' for node in G.nodes()]\n",
    "pos = nx.spring_layout(G)\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=.8, 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",
    "draw_graph(G, colors, pos)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7c68690",
   "metadata": {},
   "source": [
    "Nodes and edges.\n",
    "\n",
    "Here we have $n = 3$ red nodes edges.\n",
    "\n",
    "Each edge carries a weight.\n",
    "\n",
    "The weights of the edges are 2.0, 3.0 and 1.0 respectively."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4092f4b9",
   "metadata": {},
   "source": [
    "### Make an example cut:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8acdb876",
   "metadata": {},
   "source": [
    "#### Separate node 0 from node 1 and node 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "eef19843",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Cost = 1 + 2 =  3\n"
     ]
    },
    {
     "data": {
      "image/png": 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hJCkJ6NGDKwco6F1tImLXrl3/8nexsbF4880367iq4KdSqWAwGGAwGHw+bOLxeP4QILzdZvzP8zOqCirVOanV1/Mz6uWk1sOHpUnj9bGC4EoMBimQHDnCMFAj998P3HEH8MEH0mlShw9LN3jgv8tD1GoYBAGa0lIgL09qCQFSJ6FNG2mv6J49qz1WRETkLzQaDUwmE0w+3u++fMvx6m4zXvlRflJrVV2QaykPUHUxP6NiaeyRI+UX8+n3rlrKO9tHjgDdu8tXRyWBFQYAqUswaJC0feT330u7Ov38M3DggLSGUxAQIghQuVzSrM277pI2EercWVrbGcjtLSKiOlRfJ7XWdDJo+Umtfw4q3gybaDQahIaGYvKpU7g3Px/5TifUarX0UKmgKv/z5bfVld6u6n0+kZfnm+fxgcALA+XUauloyPLjIQVBGoMpLcWKV19FsduNGcuWVe/UKSIiqhP1cVKrN5M/b1y2DPr8fISGhkIQBIiCAEEQILjdEERR+vPlhygI+PMUUEEQ4HG7ob7hhtoVLYrScIWfCJ47pVotHW4EoKx5c2SdOcMgQESkANU6qXX3buDECZiaNr3mh4qQhk7Kw0Fubi7ycnNhMpth92KlyDX50T3KfyrxIZPJhJKSErnLICIif1ONjYZUkIZOPKKIrKwsOOx2REdHo1HjxjjsxRyIqz+5qkaH8dUVhgEiIlKOm26S/iuKXoWCouJiZGVlQa1S4bqWLWHywRbh8Hik67dpU/vn8hGGASIiUo62baX2/DWWFwqiiJwLF5CXn48wsxnNYmKg1WiwKS8PRYKAi243AOCr4mLkXP5z3wYNYPZmknpZmbQCzo/27wjKMGA2m1FSUlKxFzsREREA6QZsMgF2+xXDQJnTiXPnzqGsrAxNmzZFgwYNUH4nWZeXh/MuV8XH7iwqws6iIgDAI+Hh3oWBkhJpeXurVrX9anwmKMOAyWSq2Mu8LmauEhFRgAoLAx56CNi48S/zB0SgYp8ErVaLVnFxMBgMf/j0D32xiqCsTNrvxo+WugflCRnlG3FwqICIiP6ib1/p4LtKkwA9goCsc+eQlZWF8PBwtG7V6i9BwCeKiwGjEejTx/fPXQsMA0REpCx33gm0by/tYCuKcJSW4tTJkygqLkbz5s0R06xZ3ZwmKYpAYaG0P07btr5//lpgGCAiImVRqwGrFWJICGyZmTh96hQ0Wi1at26NiLo8mTcvTxqmmDKl7q5RQ0EZBso3niguLpa5EiIi8kd5HTrg08aN4crLQ8PISLRs2RL68vML6kJZmXRg3tix0hb5fiYowwA7A0REdCW7d+9Gv379kGo2Q9uhA6I9Hqi9OK2xxtxu4OJFoFMnYNy4urtOLQRlGCg/rpVhgIiIyrndbrz55puYMGEC2rRpg1VbtiBi40agRQsgO1vaDMj3F5We+6abgGXLpP0F/FBQLi3U6XTQ6/UMA0REBADIysqC1WrF4cOH8fzzz2PgwIHSJMGoKGDNGmD4cOD0aaBhQ8BXS9JLSqRJiu3aAe+8AzRv7pvnrQNB2RkA/rvxEBERKdv27dvx7LPPIi8vDytXrsTgwYP/uFqgfXtgwwagSxfp5p2TI52EW1OCIHUDioqARx8FMjKAuLhafx11KSg7A4A0b4ATCImIlMvhcGDevHn44IMP0L17d1it1iufbBgXB6SlSV2C+fOBrCxph8LISMDbiYVOJ1BQIP23aVPAYgF695ZWL/i5oA0DRqORnQEiIoU6fvw4LBYLsrOzkZSUhB49elx7e3qtFhgxArj/fqlTsGmT9ApfEKRNigwGKSCUP48g/HeVgMsl7SjYvDnQr5/0iImp+y/UR4I2DPCwIiIi5RFFEZs3b8bChQvRsmVLrFu3Dq2qewZAXBzwyivA888D27YBu3cDP/4IZGZKmwaJovRxarUUDtq2lVYK/P3vQPfufjtJ8GqCNgxwzgARkbLYbDZMmzYNX3zxBfr06YNJkyZBr9fX/AlNJqnN37u39HZeHvD771I3AJBu+nFxQF1uVFRPgjYMmEwmXLhwQe4yiIioHvz0009ISEiAw+HA/Pnz0aVLF99fJCpKegQh/5/VUEMcJiAiCn6CIGD58uUYPXo0mjdvjg0bNtRNEAhyQd0ZYBggIgpeOTk5SEhIwP79+zFy5EiMHDmybg4YUgCGASIiCji7du1CSkoKDAYDUlNT0alTJ7lLCmhBGwY4gZCIKPg4nU688cYb2LhxI7p06YKkpCRERETIXVbAC9owYDKZ4HQ64XQ6azeblIiI/MKZM2dgsVhw+vRpvPTSS+jdu/e19w4grwTt4Er5yYV2u13mSoiIqDZEUcTWrVsxYMAAOJ1OrF69Gn369GEQ8KGg7gwA0smFkZGR8hZDREQ1UlJSglmzZuHTTz/Fk08+iRdffBGhvjpIiCooIgwQEVHgOXToECwWCwoKCjBr1ix0795d7pKCVtAOE5QfRsHDioiIAosgCFi7di2GDRuGyMhIpKenMwjUMXYGiIjIb+Tl5SE5ORnfffcdBg8ejHHjxkGrDdpbld8I2u8wwwARUWD5/vvvkZSUBABYvHgx7rzzTpkrUo6gHSYICQmBWq1mGCAi8nNutxuLFi3ChAkT0KZNG2zYsIFBoJ4FbWdApVJx4yEiIj937tw5WK1WHDlyBBMnTsTAgQO5pbAMgjYMANJQAScQEhH5p+3bt2PmzJmIjIzEqlWr8D//8z9yl6RYQR8G2BkgIvIvDocDc+fOxdatW/HQQw/BarVWzPMieQR1GDAajQwDRER+5Pjx47BYLMjOzkZSUhJ69OjBnQT9QFCHAc4ZICLyD6IoYvPmzVi4cCHi4uKwfv16xMXFyV0WXRbUYcBkMqGwsFDuMoiIFM1ms2Hq1Kn48ssv0bdvX/zzn//kAXJ+JujDQFZWltxlEBEp1r59+5CQkIDS0lIsWLAA9913n9wlURWCev0GJxASEclDEAQsW7YMY8aMQWxsLDZs2MAg4MeCvjPAMEBEVL9ycnKQkJCA/fv347nnnsOIESO4d4CfC+owwAmERET168svv8TUqVNhMBjw9ttv47bbbpO7JPJCUIcBk8kEu90OQRCYSomI6pDT6cTChQuxadMmdO3aFUlJSQgPD5e7LPJS0IcBALDb7RVHGhMRkW+dPn0aVqsVp0+fxksvvYTevXtz74AAE9Qvl3lyIRFR3RFFEVu3bsXAgQPhdDqxevVq9OnTh0EgACmiM8AwQETkW8XFxZg1axa2b9+OJ598Ei+++CJCQ0PlLotqKKjDQPnQAA8rIiLynV9//RUWiwWFhYWYNWsWunfvLndJVEscJiAiIq8IgoC1a9di+PDhiIqKQkZGBoNAkAjqzgDDABGRb+Tl5SEpKQnff/89hgwZgrFjx0KrDepbiKIE9b+k0WgEwDBARFQb33//PZKSkgAAS5Yswd/+9jeZKyJfC+phArVazWOMiYhqyOVyYdGiRZgwYQJuuukmbNiwgUEgSAV1ZwCQhgo4gZCIqHrOnTsHq9WKI0eO4J///CcGDBjAzduCmCLCADsDRETe2759O2bOnInIyEi88847aN++vdwlUR1jGCAiIgCAw+HA3LlzsXXrVjz88MOwWCwVE7EpuDEMEBERjh07BqvViuzsbCQnJ+Pxxx/nToIKwjBARKRgoihi8+bNWLhwIeLi4pCWloaWLVvKXRbVM0WEgby8PLnLICLyO4WFhZg2bRq+/PJL9OvXDxMnToRer5e7LJKBIsIAOwNERH+0b98+JCQkoKysDAsWLMB9990nd0kko6BfJ8IwQET0Xx6PB8uWLcOYMWMQGxuLjIwMBgEK/s6A2WxmGCAiAnDhwgUkJCTg559/xnPPPYcRI0Zw7wACoIAwUL7pkCiKnBlLRIr15ZdfYurUqQgNDcXbb7+N2267Te6SyI8oIgwIgoCysjIYDAa5yyEiqldOpxMLFy7Epk2b0LVrVyQlJSE8PFzussjPKCIMANJhRQwDRKQkp06dgtVqxZkzZ/Dyyy/jmWeeYYeUqhT0g0U8xpiIlEYURXzwwQcYNGgQ3G431qxZg969ezMI0BUFfWfAbDYDAA8rIiJFKC4uxqxZs7B9+3Y89dRT+Ne//oXQ0FC5yyI/F/RhgJ0BIlKKgwcPwmq1orCwELNmzUL37t3lLokCBMMAEVGAEwQB69atw9KlS9GuXTukpqYiJiZG7rIogAR9GDAajQAYBogoOOXm5iIpKQl79uzBkCFDMGbMGGi1Qf+rnXws6P+P0ev10Ov1DANEFHS+++47JCcnQ6VSYfHixfjb3/4md0kUoIJ+NQHw342HiIiCgcvlwqJFi/D888+jbdu2yMjIYBCgWgn6zgDA8wmIKHicO3cOFosFR48exaRJk9C/f39uKUy1xjBARBQgPv30U8ycORNRUVF455130L59e7lLoiDBMEBE5OccDgfmzp2LrVu34uGHH4bFYqlYKUXkCwwDRER+7NixY7BYLMjJyUFKSgoee+wx7iRIPqeIgSZOICSiQCOKIjZu3IghQ4YgJCQE69evx+OPP84gQHVCMZ0Bu90udxlERF4pLCzE1KlTsWvXLvTr1w8TJ06EXq+XuywKYooJAxwmIKJAsG/fPiQkJKCsrAwLFizAfffdJ3dJpACKGCYwm80MA0Tk1zweD95++22MGTMGsbGxyMjIYBCgeqOYzgDnDBCRv7pw4QISEhLw888/Y9SoURg+fDj3DqB6pZgw4HQ64XK5oNPp5C6HiKjCF198gWnTpiE0NBTLli3DrbfeKndJpECKCQMAYLfbERERIXM1RESA0+nE66+/js2bN+Mf//gHEhMTER4eLndZpFCKCgMlJSUMA0Qku1OnTsFiseDs2bN45ZVX8PTTT3PJIMlKEWHAbDYDAOcNEJGsRFHEBx98gLlz5yImJgZr167FDTfcIHdZRMoIA5U7A0REciguLsasWbOwfft29OzZE//6179gMBjkLosIAMMAEVGdO3jwIKxWK2w2G1599VU8+OCDcpdE9AcMA0REdUQQBKxbtw5Lly5F+/btkZqaipiYGLnLIvoLRYQBg8EAtVrNMEBE9SY3NxdJSUnYs2cPhg4ditGjR0OrVcSvXApAivg/U6VSceMhIqo33333HZKTk6FSqbBkyRJ07txZ7pKIrkoxW1zxfAIiqmsulwtvvPEGnn/+ebRt2xYZGRkMAhQQFNEZABgGiKhuZWZmwmq14tixY5g0aRL69+/PLYUpYDAMEBHV0r///W/MmjULUVFRWLVqFdq3by93SUTVwjBARFRDdrsdc+fOxYcffohHHnkEr7zySsXqJaJAoqgwYLPZ5C6DiILEsWPHYLFYkJOTg5SUFDz22GPcUpgClmIGtEwmE+x2u9xlEFGAE0URGzZswJAhQ2AwGJCWlobHH3+cQYACmqI6AxwmIKLaKCgowLRp07Br1y48++yzeP7556HX6+Uui6jWFBMGzGYzwwAR1diPP/6IxMRElJWV4fXXX8e9994rd0lEPqOoYQJuOkRE1eXxeJCamooxY8agRYsWyMjIYBCgoKOYzkD5nAFBELj2l4i8kp2djYSEBBw4cABjxozBsGHD+PuDgpKiwgAAOBwOLv0homv6/PPPMX36dBiNRixfvhwdO3aUuySiOqO4MFBSUsIwQERXVFZWhoULF2Lz5s3o1q0bEhISEB4eLndZRHVKMWHAbDYDAIqLixEdHS1zNUTkj06ePAmr1YqzZ8/CYrGgV69eXDJIiqCYwa/KnQEiospEUcT777+PQYMGQRAErF27Fk8//TSDACmGYjoDDANEVJXi4mLMnDkTO3bsQK9evTB58mQYDAa5yyKqVwwDRKRYv/zyC+Lj42Gz2TB79mw88MADcpdEJAsOExCR4giCgNWrV2PEiBFo1KgR0tPTGQRI0RTTGVCr1QgNDeXGQ0QKl5ubi8TERPzwww8YOnQoRo8eDa1WMb8KiaqkqJ8Ank9ApGzffvstkpOToVarsWTJEnTu3Fnukoj8AsMAEQU9l8uFJUuWYP369bj77ruRkpKCqKgoucsi8hsMA0QU1H7//XfEx8fj2LFjeOGFF/Dss89yS2GiP1FUGODJhUTK8sknn+DVV19Fw4YNsWrVKrRv317ukoj8kqLCgNFo5ARCIgWw2+2YM2cOPvroIzz66KN45ZVXYDQa5S6LyG8pKgyYTCbk5+fLXQYR1aGjR4/CYrHg4sWLmDp1Kh577DG5SyLye4oLA3a7Xe4yiKgOiKKIDRs2YNGiRWjdujXS0tJw3XXXyV0WUUBQVBjgnAGi4FRQUIBp06Zh165d6N+/PyZMmAC9Xi93WUQBQ1FhwGQycc4AUZD58ccfkZCQAJfLhddffx333nuv3CURBRxFra8pX1ooiqLcpRBRLXk8HqSmpmLMmDFo2bIlMjIyGASIakhxnQGPxwOn04mQkBC5yyGiGsrOzkZ8fDx++eUXjB07FkOHDuXeAUS1oLgwAEiHFTEMEAWmnTt3Yvr06TCZTFi+fDk6duwod0lEAU9RYcBsNgOQzi/nVqREgaWsrAyvv/463n33XXTr1g0JCQkIDw+XuyyioKCoMNCyZUtMmTKFv0CIAszJkydhtVpx9uxZWCwW9OrVCyqVSu6yiIKGosJAVFQUevXqxeNKiQKEKIp4//33MW/ePDRv3hzr1q3D9ddfL3dZREFHUXdFlUoFnU4ndxlE5IWioiLMnDkTn332GXr16oXJkyfDYDDIXRZRUFJUGCCiwHDgwAEkJCTAZrNh9uzZeOCBB+QuiSioMQwQkd8QBAFr1qzBW2+9hQ4dOiA1NRUxMTFyl0UU9BgGiMgvXLp0CUlJSfjhhx8wbNgwjBo1ivN7iOqJon7SRFGEKIpX3Jxkz549iIqKwg033FDPlREp27fffovk5GRoNBosWbIEnTt3lrskIkVR1JZdGo0GTzzxBHJycqp8/8qVKzFp0iS43e56roxImcrPE5g4cSLat2+PjIwMBgEiGSgqDERFRWHv3r0YMGAATpw48Zf3T5o0Cfv27UNhYaEM1REpy++//47hw4dj48aNmDx5Ml5//XU0aNBA7rKIFElRYcDpdGLjxo0wGo3o168f9uzZU/E+j8eDG264AW63GwUFBfIVSaQA27Ztw4ABA1BcXIx33nkH/fv359kCRDJS1E+f0WiE3W7HBx98gA4dOmDYsGHYtGkTAGkIYceOHYiMjIQgCDJXShSc7HY7UlJSkJSUhK5duyItLQ3t2rWTuywixVPUBEKj0Yj8/HwAwOrVqxEfH4+XX34ZW7duRVxcHFatWoX+/fsjNjZW5kqJgs/Ro0dhsVhw8eJFTJs2DY8++qjcJRHRZYrqDDRu3BgOhwOANCwwc+ZMzJ8/HwUFBfjss8/wzDPPYNKkSQgNDZW5UqLgIYoiMjIyMHToUBiNRqSlpTEIEPkZlSiK4rU+yGazISIiAoWFhQF9yM+XX36JmJgY3HjjjQCkDU7KxykdDgdDAJGP5efnY+rUqfj666/Rv39/TJgwAXq9Xu6yiBTD2/u3ooYJunTp8oe31Wo1BEGASqWqCAKiKPI0NCIf2Lt3LxISEuB2u7Fw4ULcc889cpdERFegqGECt9uNS5cuVQwVAFIgqHzzZxAgqh2Px4O33noLY8eORVxcHDIyMhgEiPycosJARkYGbr/9dnz00UcAwFUDRD52/vx5jBo1Cu+88w7Gjh2LpUuXonHjxnKXRUTXoKhhgtatW6N79+5o1qwZAGlIQBCEiqGB8gcRVd/OnTsxffp0mEwmrFixArfccovcJRGRlxQ1gZCIfK+srAwLFizAli1b0K1bNyQkJPD3BJGf4ATCq3A6nThz5gwyMzNx4cIF2Gw2aLVatG/fHnfeeafc5REFDFEUsXv3bnz44YewWq3o2bMnu2tEAUhxnYGCggKkpqZi48aNyMnJgcfjgdlshtlsBgDceeedmD17NiIjI+UtlCiAXLhwAU2aNJG7DCL6E3YGqlBWVoZXX30VixcvRmJiIu655x40adIEGo0GBQUF+Prrr7F8+XLMmjULc+bMkbtcIlldunQJxcXFiIuLu+rHiaLIIEAU4BQVBi5evIj169fjk08+wX333feX93fq1AktWrTAuHHjGAZI0dLS0jBo0CAMHToU8+bNQ1RU1BU/lsMCRIFPUUsLDQYD8vPzK3YgrEpZWRlPTyNFe/fddzF79mz07dsXaWlp2LJlC1wul9xlEVEdUtRdLyIiAh06dMDUqVNx6tQpXLhwAXl5ecjOzsbBgwfx9ttvY8qUKRg7dqzcpRLJony5bY8ePZCRkYHnn38eFosFP/zwg9ylEVEdUtwEwu+//x5PP/00IiIi0K5dO6jVatjtdhQVFaGgoAD33HMPZsyYcdW2KFEwKykpQVlZWcXPQKdOnRAWFoZ169bhuuuuk7k6IqoOb+/figsDAFBYWIh169Zh7969KC4uRlhYGFq1aoXOnTvj4Ycflrs8Ir/gcrmg0+mQmZmJG2+8EePHj0dycjLCwsLkLo2IvMQwQES15na7odVqsW7dOgwdOhTp6el45pln8O233+LixYvo1auX3CUS0VV4e/9W1JwBIqoerVZacDRo0CAMHjwYr7zyCoYMGYIuXbrg4sWLMldHRL6iqKWFRFS18gZhVcsEBUGAWq2GxWLBmjVrIAgCduzYgfvvv7++yySiOsLOAJHCHTlyBG+++eYV9wtQq9XYsWMH2rZti8ceewwnTpxgECAKMooNA06nU+4SiGQliiLS09MxdOhQ7NmzByUlJVf8WLPZjLfeegsffvghdDpdPVZJRPVBkWEgLS0NDz74oNxlEMkmPz8fL7zwAhYsWIA+ffpg1apVMJlMV/z4u+66C6NHj67HComoPilyzoDRaITdbq8YCyVSkr179yIhIQFutxtvvPEG/v73v8tdEhHJTJF3QpPJBFEUUVpaKncpRPXG4/Fg6dKlGDt2LFq1aoWMjAwGASICoNDOQPlxxcXFxTAajTJXQ1T3zp8/j/j4eBw8eBBjx47F0KFD2RUjogqKDAPlY6NXmzBFFCx27tyJ6dOnw2w2Y8WKFbjlllvkLomI/AzDAFGQKisrw/z58/Hee+/h/vvvR0JCArcSJqIqMQwQBaGTJ0/ilVdeQWZmJqxWK3r27HnFfQSIiBQ5aMgwQMFKFEW89957GDhwIABg/fr16NWrF4MAEV2VojsDxcXFMldC5Ds2mw0zZ87Ef/7zHzz99NOYPHkyQkJC5C6LiAKAIsOARqOBwWBgZ4CCxoEDB2C1WlFSUoI5c+agW7ducpdERAFEkcMEgNQdYBigQCcIAlatWoWRI0ciOjoa6enpDAJEVG2K7AwADAMU+C5evIikpCTs3bsXw4YNw+jRo6HRaOQui4gCkGLDgNlsZhiggPX1118jJSUFWq0WS5cuxR133CF3SUQUwBQbBkwmEycQUsBxOp1YvHgx0tPTcc899yA5ORkNGjSQuywiCnCKDgPsDFAgOXv2LKxWK06cOIHJkyfj2Wef5ZJBIvIJxU4gNBqNDAMUMLZt24aBAwfCbrdj9erV6N+/P4MAEfmMYjsDnDNAgcBut2P27NnYtm0bHnvsMbz88ss8XIuIfE6xYYDDBOTvDh8+DKvVitzcXEybNg2PPvqo3CURUZBS7DABwwD5K1EUkZ6ejmHDhsFsNmP9+vUMAkRUpxTfGRBFkWOv5Dfy8/ORkpKCb775BgMGDMCECROg0+nkLouIgpyiw4Db7YbL5YJer5e7HCL88MMPSExMhMfjwRtvvIG///3vcpdERAqh2GECs9kMgIcVkfw8Hg+WLl2KcePGoXXr1sjIyGAQIKJ6pejOACAdYxwVFSVzNaRUWVlZSEhIwMGDBzFu3DgMGTIEarViMzoRyYRhgJMISSb/+c9/MH36dISFhWHFihW45ZZb5C6JiBSKYYBhgOpZaWkpFixYgPfeew8PPPAA4uPjERYWJndZRKRgDAMMA1SPfvvtN1gsFmRmZsJqtaJnz55czUJEslPs4CQnEFJ9EkUR7733HgYNGgSVSoX169ejV69eDAJE5BcU2xnQ6XTQarXsDFCds9lsmDFjBnbu3Imnn34akydPRkhIiNxlERFVUGwYUKlU3IWQ6tzPP/+M+Ph4lJSUYM6cOejWrZvcJRER/YVihwkAbklMdUcQBKxatQrPPfccmjRpgvT0dAYBIvJbiu0MADy5kOrGxYsXkZiYiB9//BHDhw/HqFGjoNFo5C6LiOiKFB0GTCYTJxCST3399ddISUmBTqfDW2+9hf/93/+VuyQiomtSfBhgZ4B8wel0YvHixUhPT8e9996L5ORkREZGyl0WEZFXFB8GcnNz5S6DAtzZs2dhsVhw8uRJ/Otf/0K/fv24ZJCIAgonELIzQLXw8ccfY8CAAXA4HHjnnXfw7LPPMggQUcBRfGeAYYBqwm63Y/bs2di2bRsef/xxvPTSSzAajXKXRURUIwwDDANUTYcPH4bVakVubi6mT5+ORx55RO6SiIhqhcMEDAPkJUEQkJaWhmHDhsFsNiMtLY1BgIiCguI7A6WlpfB4PFwHTleVl5eHqVOn4ptvvsHAgQMxfvx46HQ6ucsiIvIJRYeB8sOKSkpKEB4eLnM15K/27NmDxMRECIKARYsW4e6775a7JCIin1L8MAHAY4ypam63G0uXLsX48eNx/fXXIyMjg0GAiIKSojsDDAN0JVlZWUhISMDBgwcxbtw4DBkyBGq1orMzEQUxhgEwDNAfffbZZ5gxYwbCwsKwYsUK3HLLLXKXRERUpxgGwDBAktLSUixYsADvvfceHnjgAcTHxyMsLEzusoiI6pyiw0D5BEIeVkS//fYbLBYLzp07h/j4eDz11FPcSZCIFEPRg6AGgwEqlYqdAQUTRRFbtmzBoEGDoFKpsG7dOvTs2ZNBgIgURdGdAbVaDaPRyDCgUDabDTNmzMDOnTvxzDPP4IUXXkBISIjcZRER1TtFhwGAuxAq1c8//4z4+HiUlJRgzpw56Natm9wlERHJRtHDBIA0b4BhQDkEQcDKlSvx3HPPoUmTJsjIyGAQICLFY2fAZOIEQoXIyclBUlISfvzxR4wYMQLPPfcct6EmIgLDAIcJFOKrr75CSkoK9Ho9UlNTcfvtt8tdEhGR32AYYBgIak6nE2+++SYyMjJw7733Ijk5GZGRkXKXRUTkVxgGTCbk5OTIXQbVgbNnz8JiseDkyZN48cUX0bdvXy4ZJCKqAsMAOwNB6eOPP8bs2bPRuHFjrF69GjfddJPcJRER+S2GAYaBoGK32zF79mxs27YNPXr0wJQpU2A0GuUui4jIrzEMMAwEjUOHDsFqtSIvLw/Tp0/HI488IndJREQBQfH7DJSHAVEU5S6FakgQBKSlpWH48OEIDw9Heno6gwARUTUovjNgNpshiiIcDgfbyQEoLy8PKSkp+PbbbzFw4ECMHz8eOp1O7rKIiAKK4sNA5WOMGQYCy549e5CYmAhBELBo0SLcfffdcpdERBSQOExQKQxQYHC73ViyZAnGjx+P66+/HhkZGQwCRES1wM4Aw0BAycrKQnx8PH799VeMHz8egwcPhlqt+ExLRFQrDAMMAwHjs88+w4wZMxAeHo6VK1fi5ptvlrskIqKgoPgwYDabAYCHFfmx0tJSzJ8/H//3f/+HBx98EFarFWFhYXKXRUQUNBQfBsonDbIz4J9OnDgBq9WKc+fOISEhAU8++SS3FCYi8jHFD7ZqtVqEhIQwDPgZURTx7rvvVswJWLduHZ566ikGASKiOqD4zgDAXQj9jc1mw4wZM7Bz50707t0bkyZNQkhIiNxlEREFLYYBSPMGGAb8w/79+xEfHw+Hw4G5c+fiH//4h9wlEREFPcUPEwBSZ4ATCOUlCAJWrFiBUaNGoVmzZkhPT2cQICKqJ+wMgMMEcsvJyUFiYiL27duHkSNHYuTIkdBoNHKXRUSkGAwDYBiQ01dffYWUlBSEhIQgNTUVt99+u9wlEREpDsMApDBw/vx5uctQFKfTiUWLFmHDhg247777kJSUhMjISLnLIiJSJIYBsDNQ386cOQOLxYJTp07hxRdfRN++fblkkIhIRgwD4ATC+iKKIj7++GO89tpraNy4MVavXo2bbrpJ7rKIiBSPYQBSGLDb7XKXEdRKSkowe/ZsfPLJJ+jRowemTJnCI6OJiPwEwwA4TFDXDh06BKvViry8PMyYMQMPP/yw3CUREVEl3GcA0qZDLpcLTqdT7lKCiiAIWL9+PYYPH47w8HCkp6czCBAR+SF2BvDHY4z1er3M1QSHvLw8pKSk4Ntvv8WgQYMwbtw46HQ6ucsiIqIqMAzgj2GgQYMGMlcT+Pbs2YPExESIoohFixbh7rvvlrskIiK6CoYB/DEMUM253W6kpqZizZo1uOOOOzB9+nQ0bNhQ7rKIiOgaGAbAMOALWVlZiI+Px6FDhzBhwgQMGjQIajWnpBARBQKGAUgTCAFwr4Ea2rFjB2bMmIGIiAisWLECN998s9wlERFRNTAMgJ2BmiotLcW8efPw/vvvo3v37rBarRXBioiIAgfDAAC9Xg+NRsMwUA0nTpyAxWJBVlYWEhMT8cQTT3BLYSKiAMUwAEClUnHjIS+JoogtW7ZgwYIFaNmyJdavX49WrVrJXRYREdUCw8BlZrOZYeAabDYbpk+fjs8//xx9+vTBpEmTuC8DEVEQYBi4jIcVXd3+/fsRHx8Ph8OBefPmoWvXrnKXREREPsK1X5dxmKBqgiBg+fLlGDVqFGJiYpCRkcEgQEQUZNgZuIxh4K9ycnKQkJCA/fv3Y8SIERg5ciQ0Go3cZRERkY8xDFxmMpmQn58vdxl+Y9euXZg6dSpCQkKQmpqKTp06yV0SERHVEQ4TXMYJhBKn04l58+Zh8uTJ6NixIzIyMhgEiIiCHDsDlxmNRsVPIDxz5gwsFgtOnTqFKVOmoE+fPtw7gIhIARgGLjOZTLDb7XKXIQtRFPHRRx9hzpw5iI6Oxpo1a9CmTRu5yyIionrCMHCZUicQlpSU4NVXX8W///1vPPHEE5gyZQpCQ0PlLouIiOoRw8BlZrMZDocDgiAo5rS9Q4cOwWq1Ii8vDzNnzsRDDz0kd0lERCQDZdz1vKCkw4oEQcC6deswbNgwhIeHIz09nUGAiEjB2Bm4rHIYCAsLk7maupOXl4fk5GR89913GDx4MMaOHQudTid3WUREJCOGgcuU0BnYvXs3EhMTAQBvvvkm7rrrLpkrIiIif8AwcFkwhwG324233noLa9euRefOnTFt2jQ0bNhQ7rKIiMhPMAxcZjabASDo9hrIysqC1WrF4cOH8fzzz2PgwIGKmSBJRETeYRi4LBg7A9u3b8fMmTMRERGBlStXokOHDnKXREREfohh4LLytfXBEAYcDgfmz5+P999/H927d4fVaq3ofBAREf0Zw8BlarUaRqMx4MPA8ePHYbFYkJ2djaSkJPTo0YNbChMR0VUxDFQSyIcViaKIzZs3Y+HChWjZsiXWrVuHVq1ayV0WEREFAIaBSkwmU0BOILTZbJg2bRq++OIL9OnTB5MmTYJer5e7LCIiChAMA5UE4vkEP/30ExISEuBwODBv3jx07dpV7pKIiCjAcI1ZJYEUBgRBwPLlyzF69GjExMQgIyODQYCIiGqEnYFKAiUM5OTkICEhAfv378fIkSMxYsQIaDQaucsiIqIAxTBQidlsxqVLl+Qu46p27dqFlJQUGAwGpKamolOnTnKXREREAY5hoBKj0ei3EwidTifeeOMNbNy4Effddx+Sk5MREREhd1lERBQEGAYq8ddhgjNnzsBiseDUqVN46aWX0Lt3b+4dQEREPsMwUInJZILdbpe7jAqiKOLDDz/EnDlz0KRJE6xZswZt2rSRuywiIgoyDAOVlG86JIqi7K+8S0pKMGvWLHz66ad44oknMGXKlIotk4mIiHyJYaASk8kEQRBQWloq64330KFDsFgsyM/Px8yZM/HQQw/JVgsREQU/7jNQidwnFwqCgLVr12LYsGGIjIxERkYGgwAREdU5dgYqqRwGGjVqVK/XzsvLQ3JyMr777jsMHjwYY8eOhU6nq9caiIhImRgGKpGrM7B7924kJiYCABYvXow777yzXq9PRETKxmGCSsxmMwDU214DbrcbixYtwvjx49GmTRts2LCBQYCIiOodOwOV1Gdn4Ny5c7BarThy5AgmTpyIgQMHQq1mNiMiovrHMFCJ0WgEUPdhYPv27Zg5cyYiIiKwcuVKdOjQoU6vR0REdDWKDwN2jwdH7XYctttxxG7H2b598ZpGgy2HDyNSq0UboxHtjEa0N5kQrdfX6loOhwNz587F1q1b0b17d1it1oqhCSIiIrkoNgwcKinBppwcbLl0CYVuN5yCAJVKhcJ27fCLToff8vIgqlSAKEKtUiFUrcZd4eHo36QJ7m/QAPpqtvSPHz8Oi8WC7OxsJCUloUePHrJvbERERAQoMAwcs9sx7fRpfGOzweHxwKBWI1yjQYhWC5VKhdKSEoSp1YiOjAQgbQnsFkU4BAGfFRRgZ0EB4gwGTG7RAr0aNbrmDV0URWzevBkLFy5Ey5YtsX79esTFxdX9F0pEROQlxYQBlyBgVXY2Fv7+O/LdbkRotYjS6/9yM1er1RAEoeJtlUoFnUoFnVqNcABlgoDTpaX45/Hj+DQ3FymtWiEmJKTKa9psNkydOhVffvkl+vTpg0mTJkFfy6EGIiIiX1NEGChwuTD22DF8WVgInUqF5lWEgHJqtRqeSmHgz0LUajTT61Hi8WBrbi5+LC7GkhtvxJ1/Ok74p59+Qnx8PEpLSzF//nx06dLFp18TERGRrwT9WrY8lwtDjhzB5wUFaKDVorFOd9XWvlqj+UNn4EpMGg2a6fXIcjox/OhR7CooACBtKbxs2TKMHj0asbGx2LBhA4MAERH5taDuDNg9How+dgy7bTZE63ReTfrTqNVwuVxePb9GpUKMTofzTifGHz+O16OjsWnmTOzfvx8jR47EyJEjuXcAERH5vaAOA29kZuLrwkI08jIIAH+dM3AtKpUKTfV6nCkpQe+dO3HHhQtITU1Fp06dalo2ERFRvQraMPCDzYYV588jVKWCoRqvzq81Z+DPRFFETk4OHAUFUDVrhv997TV0atu2JiUTERHJIih72E5BQPypUyjxeNBAW728o9ZoIHg83l3H6cTp06dRkJ+PZtHRaBoZiQ0FBfjBZqtJ2URERLIIyjCwMz8fv5aUXHOyYFU0Xg4TFBQW4uSpUxBEEXGtWqFBgwaI1Ghg93iwJju7pqUTERHVu6AcJsjIyYEAaRlgdQguF2wffADHrl04AiDkuusQ/cwzMFU6O0AQBJw/fx42mw2RkZFo0rQp1JcDh0qlglmjwfb8fJwrK0PzK+w/QERE5E+CrjNwwm7H14WFCKvBLP7zy5ah+D//geaWW9C4f3+o1GqcnTcP9qNHAQCO0lKcPHkSxcXFaN68OZo1a1YRBMqFazQocrvx3sWLPvl6iIiI6lrQhYE9RUUo8XgQptFU6/Mcv/0G2+7daNCrF3QPPYTwLl1wncUCXaNGyNm4Ebm5uTh9+jS0Wi1at26N8PDwKp9HrVJBBeCbwkIffDVERER1L+jCwBG7HSqg2nMFin74AVCpENm1KwDAIwhQ63QIv/deFB46hAvHj6NhVBRaxsVBp9Nd9bkMajUOlpTAVY1VCURERHIJujDwY1ERNDU4DbD09GnomzWD1mQCAAgeD0pKSpCr10MQBDQWBERHR8ObZzao1Sj2ePCbw1HtOoiIiOpb0IWBM6Wl0NcgDLgLC6GNjIT68vBCbm4uzp49C0PDhggJCYG2tNTr5wpRq+EURfxeVlbtOoiIiOpbUIUBQRThEsW/TOrz6nOdTqi0Wmgubzpks9kQHR2N5nFxUKlUEJ1Or59LfbmWMg4TEBFRAAjKpYU1odbrIbrdUKlUaN+uHZxOJwwGA8oyMwEAqmocPSxe/m915y0QERHJIag6A2qVCiFqNQRRvPYH/4k2IgLuyycPqtVqGAwGANLwAQBoIyO9fi7hci3V2QaZiIhILkF3t7oxNBRlNQgDIS1bwnn+PDx/mvTn+O03AIChZUuvn6tMEBCiVqPV5UBBRETkz4IuDNxqNteoMxB+xx2AKKLg888r/k5wuVD41VcIbd0auoYNvX6uUkFApEaDOIYBIiIKAEE3Z6Cd0QhAmsBXnYmEoTfcgLA77kDOpk3w2GzQRUej8Ouv4bx4ES1HjKhWDaWiiJvN5hpNZCQiIqpvQRcG7o6IQJhWC5vHg8hqnlgYM2YMLr77Lgq/+QaekhKEtGiBFpMnw1iNI4k9ogiIIrpWY44BERGRnIIuDMSEhOChqChszslBhEZTrRn9ap0OTZ59Fk2efbbG1y9wu9FAp8NTjRrV+DmIiIjqU9DNGQCAftHR0KvVcNTzOn9RFOEQBPRs1AhR19iymIiIyF8EZRi4Kzwcd4aHI8/trtFkwpq65HYjQqvFkKZN6+2aREREtRWUYUCtUmFmq1aI0ulwye2ul2uWCgJcoohJsbFoc3kSIxERUSAIyjAAADcajZgcGwuPKKLY46nTa3lEEZdcLtwZHo6RzZrV6bWIiIh8LWjDAAAMbdoUPRs1QqHbDXsdBQKPKOK804lWoaGYf/310HHXQSIiCjBBt5qgMq1ajXnXXw+XKGLrpUtwiyLCq7nc8GqcgoAclwtxBgNW3XQTWoWG+uy5iYiI6kvQv4w1aDR488YbMahpU5SJIrKcTrhrOalQFEXku93IcbnQwWRCWvv2aGcy+ahiIiKi+hX0YQAA9Go1XmvdGqlt2uC6kBBkO53IdbmkDYKqQRRFFHk8OHf5OOOJsbHYevPNuJ4dASIiCmBBPUxQmUqlwiMNG6JzeDjeyMzElosXke1yQQ3ApFbDoFZDp1L9ZZMijyiiVBBgFwSUCQJCNRr8IzISL7Rogc7h4fJ8MURERD6kEsVrvzy22WyIiIhAYWEhwoPkBpjncuGDS5ewIScHvzkcKBUEeEQRKpUKIoDySCACMKjViNRq8WTDhugTHY32HBIgIqIA4O39WzGdgT+L0ukwrFkzDGvWDLkuFw6XlOCw3Y6LLhecggCtSgWzRoM2RiPaGo2IMxh48BAREQUlxYaByhrqdLgnMhL38HAhIiJSIEVMICQiIqIrYxggIiJSOIYBIiIihWMYICIiUjiGASIiIoVjGCAiIlI4hgEiIiKFYxggIiJSOIYBIiIihWMYICIiUjiGASIiIoVjGCAiIlI4rw4qKj/l2Gaz1WkxRERE5Dvl9+3y+/iVeBUGioqKAAAtWrSoZVlERERU34qKihAREXHF96vEa8UFAIIgICsrC2FhYVCpVD4tkIiIiOqGKIooKipCTEwM1OorzwzwKgwQERFR8OIEQiIiIoVjGCAiIlI4hgEiIiKFYxggIiJSOIYBIiIihWMYICIiUjiGASIiIoX7f4gsHIFc9bL+AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xbest_brute = [1,0,0]\n",
    "colors = ['r' if xbest_brute[i] == 0 else 'c' for i in range(n)]\n",
    "draw_graph(G, colors, pos)\n",
    "\n",
    "print('\\nCost = 1 + 2 = ', 1+2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a06bac0",
   "metadata": {},
   "source": [
    "red is mapped to 0\n",
    "\n",
    "blue is mapped to 1\n",
    "\n",
    "here we have [1, 0, 0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87d3caee",
   "metadata": {},
   "source": [
    "### The goal is to find the ultimate cut that gives the highest cost (maximization problem)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "74fd06b9",
   "metadata": {},
   "source": [
    "## Weighted Max-Cut Examples:\n",
    "\n",
    "1) Optimize layout of electronic circuits\n",
    "\n",
    "2) Design verification\n",
    "\n",
    "3) Production scheduling optimization\n",
    "\n",
    "4) Yield Optimization\n",
    "\n",
    "5) Supply chain optimizing\n",
    "\n",
    "6) Supply chain disruption recovery\n",
    "\n",
    "and more"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "de9a23e2",
   "metadata": {},
   "source": [
    "## 2.2. Calculating the Max-Cut problem using the Brute force approach"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef11bac4",
   "metadata": {},
   "source": [
    "Try all possible $2^n$ combinations. \n",
    "\n",
    "For $n = 3$ -> 8 combinations (as in the present example)\n",
    "\n",
    "For $n = 10$ -> 1024 combinations\n",
    "\n",
    "For $n = 50$ -> 1 125 899 906 842 624\n",
    "\n",
    "For $n = 127$ -> 170 141 183 460 469 231 731 687 303 715 884 105 728\n",
    "\n",
    "For $n = 275 $ -> 60 708 402,882 054,033 466 233 184 588 234 965 832 575 213 720 379 360 039 119 137 804 340 758 912 662 765 568 \n",
    "\n",
    "($\\approx$ 6.1 x $10^{82}$) More combinations than there are Atoms in the observable Universe. \n",
    "\n",
    "This is a hard problem.\n",
    "\n",
    "***Classically the solution of the Max-Cut problem requires resources that scale exponetially with the number of nodes.***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ae36e2da",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0. 1. 2.]\n",
      " [1. 0. 3.]\n",
      " [2. 3. 0.]]\n"
     ]
    }
   ],
   "source": [
    "# Computing the weight matrix from the above 3-node example\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": 5,
   "id": "fe603740",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "case = [0, 0, 0] cost = 0.0\n",
      "case = [1, 0, 0] cost = 3.0\n",
      "case = [0, 1, 0] cost = 4.0\n",
      "case = [1, 1, 0] cost = 5.0\n",
      "case = [0, 0, 1] cost = 5.0\n",
      "case = [1, 0, 1] cost = 4.0\n",
      "case = [0, 1, 1] cost = 3.0\n",
      "case = [1, 1, 1] cost = 0.0\n",
      "\n",
      "Best solution = [1, 1, 0] cost = 5.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "best_cost_brute = 0\n",
    "for b in range(2**n):\n",
    "    x = [int(t) for t in reversed(list(bin(b)[2:].zfill(n)))]\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 best_cost_brute < cost:\n",
    "        best_cost_brute = cost\n",
    "        xbest_brute = x \n",
    "    print('case = ' + str(x)+ ' cost = ' + str(cost))\n",
    "\n",
    "colors = ['r' if xbest_brute[i] == 0 else 'c' for i in range(n)]\n",
    "draw_graph(G, colors, pos)\n",
    "print('\\nBest solution = ' + str(xbest_brute) + ' cost = ' + str(best_cost_brute))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "033a8b27",
   "metadata": {},
   "source": [
    "## 2.3. Mapping the Classical Max-Cut Problem to a Quantum Problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "b66625d7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "maximize -2*x_0*x_1 - 4*x_0*x_2 - 6*x_1*x_2 + 3*x_0 + 4*x_1 + 5*x_2 (3 variables, 0 constraints, 'Max-cut')\n"
     ]
    }
   ],
   "source": [
    "max_cut = Maxcut(w)\n",
    "qp = max_cut.to_quadratic_program()\n",
    "print(qp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "4e1e994c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Offset: -3.0\n",
      "Ising Hamiltonian:\n",
      "SparsePauliOp(['IZZ', 'ZIZ', 'ZZI'],\n",
      "              coeffs=[0.5+0.j, 1. +0.j, 1.5+0.j])\n"
     ]
    }
   ],
   "source": [
    "IsingOperator, offset = qp.to_ising()\n",
    "print('Offset:', offset)\n",
    "print('Ising Hamiltonian:')\n",
    "print(str(IsingOperator))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "e1449247",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "energy: -2.0\n",
      "max-cut objective: 5.0\n",
      "solution: [1. 1. 0.]\n",
      "solution objective: 5.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Making the Hamiltonian in its full form and getting the lowest eigenvalue and eigenvector classically\n",
    "from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver\n",
    "ee = NumPyMinimumEigensolver()\n",
    "result = ee.compute_minimum_eigenvalue(IsingOperator)\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 = ['r' if x[i] == 0 else 'c' for i in range(n)]\n",
    "draw_graph(G, colors, pos)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3d99032",
   "metadata": {},
   "source": [
    "## 3. Running it on quantum computer"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ba6de99",
   "metadata": {},
   "source": [
    "## 3.1 Using Variational Quantum Eigensolver (VQE)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a42ad80",
   "metadata": {},
   "source": [
    "![Variational Quantum Algorithm](./images/vqe_method.png)\n",
    "\n",
    "Source: Ioannis Kolotouros, Petros Wallder, \"An evolving objective function for improved variational quantum optimisation\", e-print arXiv 2105.11766"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "718e17d8",
   "metadata": {},
   "source": [
    "## 3.1. Defining classic optimizer and preparing VQE trial state (Ansatz)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12a837dd",
   "metadata": {},
   "source": [
    "### Set up the Qiskit runtime service using the Estimator and Sampler primitives"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "bce63206-5284-488d-b7e6-5bd30e1c8357",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<IBMBackend('ibm_brisbane')>,\n",
       " <IBMBackend('ibm_kyoto')>,\n",
       " <IBMBackend('ibm_osaka')>,\n",
       " <IBMBackend('ibmq_qasm_simulator')>,\n",
       " <IBMBackend('simulator_extended_stabilizer')>,\n",
       " <IBMBackend('simulator_mps')>,\n",
       " <IBMBackend('simulator_statevector')>,\n",
       " <IBMBackend('simulator_stabilizer')>]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.primitives import Sampler, Estimator\n",
    "\n",
    "from qiskit_ibm_provider import IBMProvider\n",
    "provider = IBMProvider()\n",
    "provider.backends()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "067e7bbb-3828-4d9b-8be8-c99123673104",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "backend = provider.get_backend('ibmq_qasm_simulator')\n",
    "sampler = Sampler(options = {\"backend\": 'ibmq_qasm_simulator'})\n",
    "estimator = Estimator(options = {\"backend\": 'ibmq_qasm_simulator'})"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6df00e35",
   "metadata": {},
   "source": [
    "## 3.2. Using VQE with Qiskit runtime on a quantum device"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8fed4ee6",
   "metadata": {},
   "source": [
    "## Qiskit Runtime \n",
    "![Qiskit Runtime](./images/runtime-architecture.png)\n",
    "https://qiskit.org/documentation/partners/qiskit_ibm_runtime/getting_started.html\n",
    "\n",
    "### Primitives - Sampler and Estimator\n",
    "| Primitive      | Description | Example output   |\n",
    "| :---        |    :---   |          :--- |\n",
    "| Sampler      | Allows a user to input a circuit and then generate quasiprobabilities. This generation enables users to more efficiently evaluate the possibility of multiple relevant data points in the context of destructive interference.       | ![Sampler](./images/sampler.png) |\n",
    "| Estimator   | Allows a user to specify a list of circuits and observables and selectively group between the lists to efficiently evaluate expectation values and variances for a parameter input. It is designed to enable users to efficiently calculate and interpret expectation values of quantum operators that are required for many algorithms.        |  ![Sampler](./images/estimator.png)   |\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d2eb3e6",
   "metadata": {},
   "source": [
    "### 3.2.1. Defining VQE and running it on an IBM Quantum Simulator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "110ac6ad-e7a8-4638-82b3-0e24de7bc68b",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/stefan.kister/opt/virtual/qiskit/lib/python3.9/site-packages/qiskit/visualization/circuit/matplotlib.py:266: FutureWarning: The default matplotlib drawer scheme will be changed to \"iqp\" in a following release. To silence this warning, specify the current default explicitly as style=\"clifford\", or the new default as style=\"iqp\".\n",
      "  self._style, def_font_ratio = load_style(self._style)\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1040x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.circuit.library import TwoLocal\n",
    "\n",
    "num_qubits = IsingOperator.num_qubits\n",
    "\n",
    "ansatz = TwoLocal(num_qubits, \"rx\", \"cz\", reps=2, entanglement=\"linear\", insert_barriers = True)\n",
    "\n",
    "ansatz.decompose().draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "dc5c395e-4b04-469f-a7d2-f903002b7522",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "calculated cost: 3.5785667188811536\n",
      "calculated cost: 4.104821864548146\n",
      "calculated cost: 4.2097905853806745\n",
      "calculated cost: 4.2955762633816015\n",
      "calculated cost: 4.296268138779466\n",
      "calculated cost: 4.27967676182824\n",
      "calculated cost: 4.434539213589724\n",
      "calculated cost: 4.50111962031504\n",
      "calculated cost: 4.587694034033736\n",
      "calculated cost: 4.5895307471793645\n",
      "calculated cost: 4.592211578952465\n",
      "calculated cost: 4.6160180782381826\n",
      "calculated cost: 4.712363403197369\n",
      "calculated cost: 4.7463848546683725\n",
      "calculated cost: 4.758670470382682\n",
      "calculated cost: 4.77721803371815\n",
      "calculated cost: 4.781307759076644\n",
      "calculated cost: 4.788899924286964\n",
      "calculated cost: 4.79337953494549\n",
      "calculated cost: 4.793435036997254\n",
      "calculated cost: 4.810281772811182\n",
      "calculated cost: 4.813337947119592\n",
      "calculated cost: 4.825673748486577\n",
      "calculated cost: 4.833691520823015\n",
      "calculated cost: 4.835124594526725\n",
      "calculated cost: 4.872544006457827\n",
      "calculated cost: 4.877315711655578\n",
      "calculated cost: 4.877738401632164\n",
      "calculated cost: 4.891546054179571\n",
      "calculated cost: 4.896336872220137\n",
      "calculated cost: 4.896373030764702\n",
      "calculated cost: 4.9056319577165715\n",
      "calculated cost: 4.922962089065576\n",
      "calculated cost: 4.9263362437257125\n",
      "calculated cost: 4.935005883445491\n",
      "calculated cost: 4.947667663533352\n",
      "calculated cost: 4.9491278008316435\n",
      "calculated cost: 4.963704869009111\n",
      "calculated cost: 4.964221752058982\n",
      "calculated cost: 4.964501259440308\n",
      "calculated cost: 4.9687141467778275\n",
      "calculated cost: 4.969735325658217\n",
      "calculated cost: 4.974533122176962\n",
      "calculated cost: 4.9746889662315485\n",
      "calculated cost: 4.974775444160581\n",
      "calculated cost: 4.975284727166747\n",
      "calculated cost: 4.980906370448126\n",
      "calculated cost: 4.980601136717056\n",
      "calculated cost: 4.982687022996428\n",
      "calculated cost: 4.9827803015207905\n",
      "calculated cost: 4.981899604106154\n",
      "calculated cost: 4.981905815722657\n",
      "calculated cost: 4.981673190256598\n",
      "calculated cost: 4.982189269122007\n",
      "calculated cost: 4.985779780784514\n",
      "calculated cost: 4.985747450213156\n",
      "calculated cost: 4.985780889917885\n",
      "calculated cost: 4.986052831619222\n",
      "calculated cost: 4.985795609804882\n",
      "calculated cost: 4.98638138471353\n",
      "calculated cost: 4.98591708862005\n",
      "calculated cost: 4.986676167632986\n",
      "calculated cost: 4.9868779129770004\n",
      "calculated cost: 4.9872737086662475\n",
      "calculated cost: 4.988557731200115\n",
      "calculated cost: 4.989212187642492\n",
      "calculated cost: 4.988756191639343\n",
      "calculated cost: 4.988757549433122\n",
      "calculated cost: 4.989543035586261\n",
      "calculated cost: 4.990203632155307\n",
      "calculated cost: 4.990708976690138\n",
      "calculated cost: 4.991345611804784\n",
      "calculated cost: 4.991670591076071\n",
      "calculated cost: 4.9919401222824344\n",
      "calculated cost: 4.99193300372016\n"
     ]
    }
   ],
   "source": [
    "from qiskit.algorithms.optimizers import SPSA\n",
    "from qiskit.primitives import Sampler, Estimator\n",
    "\n",
    "\n",
    "estimator = Estimator()\n",
    "\n",
    "\n",
    "history = {\"nfevs\": [], \"points\": [], \"fvals\": [], \"updates\": [], \"accepted\": []}\n",
    "num_iter = 75\n",
    "\n",
    "job_list = []\n",
    "\n",
    "estimator = Estimator()\n",
    "def evaluate_expectation(x):\n",
    "    x = list(x)\n",
    "    result = estimator.run(circuits=ansatz, backend_options=\"statevector\", observables=IsingOperator, parameter_values=[x]).result()\n",
    "    results = result.values[0] \n",
    "    job_list.append(result)\n",
    "    return np.real(results)\n",
    "\n",
    "def callback(nfev, point, fval, update, accepted):\n",
    "    print('calculated cost: {}'.format(-fval-offset))\n",
    "    history[\"nfevs\"].append(nfev)\n",
    "    history[\"points\"].append(point)\n",
    "    history[\"fvals\"].append(-fval-offset)\n",
    "    history[\"updates\"].append(update)\n",
    "    history[\"accepted\"].append(accepted)    \n",
    "\n",
    "np.random.seed(42)\n",
    "initial_point = np.random.random(ansatz.num_parameters)\n",
    "optimizer = SPSA(num_iter, callback=callback)\n",
    "result = optimizer.minimize(fun=evaluate_expectation, x0=initial_point)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "621c95db",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "optimized circuit parameters:\n",
      "[ 1.18732215  0.59127337 -0.11410829  0.4227846  -0.24446975 -0.73730266\n",
      "  1.51022413  2.66283344  0.7637898 ]\n",
      "\n",
      "Objective Value = 4.9651589295616825\n"
     ]
    }
   ],
   "source": [
    "print('optimized circuit parameters:\\n{}'.format(result.x))\n",
    "print()\n",
    "print('Objective Value =', history['fvals'][num_iter - 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "858011be",
   "metadata": {},
   "source": [
    "### Use the Sampler primitive to get bitstrings from the approx ground state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "dedd5014-e891-4dc4-83aa-a7bacb0d8383",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/stefan.kister/opt/virtual/qiskit/lib/python3.9/site-packages/qiskit/visualization/circuit/matplotlib.py:266: FutureWarning: The default matplotlib drawer scheme will be changed to \"iqp\" in a following release. To silence this warning, specify the current default explicitly as style=\"clifford\", or the new default as style=\"iqp\".\n",
      "  self._style, def_font_ratio = load_style(self._style)\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 1416.5x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ansatz.measure_all()\n",
    "ansatz.decompose().draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "1a8b5fda",
   "metadata": {},
   "outputs": [],
   "source": [
    "sampler = Sampler()\n",
    "\n",
    "strings = sampler.run(circuits=ansatz, parameter_values=[result.x], shots=8000, backend_options=\"statevector\").result()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "42bc948b-5f9b-4211-a920-449f00e3a92c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'001': 0.000625, '010': 0.002, '011': 0.968125, '101': 0.02925}\n"
     ]
    }
   ],
   "source": [
    "bitstrings = strings.quasi_dists[0].binary_probabilities()\n",
    "print(bitstrings)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "7c60dc13-a308-4919-ad8b-6683d991be18",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best Solution:\n",
      "('011', 0.968125)\n"
     ]
    }
   ],
   "source": [
    "# Extract best solution\n",
    "from operator import itemgetter\n",
    "bitstring_list = [(k, v) for k, v in bitstrings.items()]\n",
    "best_solution = sorted(bitstring_list, key=itemgetter(1), reverse = True)[0]\n",
    "best_solution_string = best_solution[0]\n",
    "\n",
    "# Convert bitstring\n",
    "bitstring = []\n",
    "for k in range(num_qubits):\n",
    "    bitstring.append(best_solution_string[k])\n",
    "\n",
    "bitstr = [int(x) for x in bitstring]\n",
    "\n",
    "print('Best Solution:')\n",
    "print(best_solution)\n",
    "#print(bitstring)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "cd8060ed",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Optimization Summary - Results:\n",
      "Objective Value = 4.9651589295616825\n",
      "Best Solution [0, 1, 1]\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0.98, 'Optimization Summary - Graphics')"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1400x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "print()\n",
    "print('Optimization Summary - Results:')\n",
    "print('Objective Value =', history['fvals'][num_iter - 1])\n",
    "print('Best Solution', bitstr)\n",
    "print()\n",
    "\n",
    "qbest = bitstr\n",
    "colors = ['r' if qbest[i] == 0 else 'c' for i in range(n)]\n",
    "draw_graph(G, colors, pos)\n",
    "    \n",
    "fig, axs = plt.subplots(1,2, figsize=(14, 5))\n",
    "axs[0].plot(history['fvals'])\n",
    "axs[1].bar(list(bitstrings.keys()), list(bitstrings.values()))\n",
    "axs[0].set_xlabel(\"# of Iteration\")\n",
    "axs[0].set_ylabel(\"Cost\")\n",
    "axs[0].set_title(\"Convergence of Cost Calculation\")\n",
    "axs[1].set_xlabel(\"Solution Values\")\n",
    "axs[1].set_ylabel(\"Probability\")\n",
    "axs[1].set_title(\"Probability Distribution of Solutions\")\n",
    "\n",
    "fig.suptitle('Optimization Summary - Graphics')\n"
   ]
  },
  {
   "cell_type": "raw",
   "id": "178f2308-bc36-4e8c-abce-741fa73216a2",
   "metadata": {},
   "source": [
    "\n",
    "| |The end| |\n",
    "| :---  | :--- | :--- |\n",
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    "**References:**\n",
    "\n",
    "Qiskit Runtime overview:\n",
    "\n",
    "https://qiskit.org/documentation/partners/qiskit_ibm_runtime/\n",
    "\n",
    "Variational Quantum Algorithms with Qiskit Runtime: Combinatorial Optimization \n",
    "\n",
    "https://github.com/jenglick/scipy22-qiskit-runtime-tutorial/blob/main/docs/tutorials/Part3_VQA_Optimization_EXERCISE-Solution.ipynb\n",
    "\n",
    "Optimization Tutorials:\n",
    "\n",
    "https://qiskit.org/documentation/optimization/tutorials/index.html\n",
    "\n"
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