{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "9c2adb1c-235f-4552-bb7a-70773aedf685",
   "metadata": {},
   "source": [
    "# 06 - Max-Cut and Traveling Salesman Problem\n",
    "### Modified for use with Quantum Rings toolkit for Qiskit 2.x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "271d3551-4f7b-45bb-96d5-9cdd8da4b94a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# This code is from the tutorial at:\n",
    "# https://qiskit-community.github.io/qiskit-optimization/tutorials/06_examples_max_cut_and_tsp.html\n",
    "\n",
    "# Modified for use with Quantum Rings toolkit for Qiskit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3122191f-f0d2-40c9-b27e-fca18f872e58",
   "metadata": {},
   "outputs": [],
   "source": [
    "#\n",
    "# Setup your account\n",
    "# You can also save your account locally using the class method QrRuntimeService.save_account(...) and\n",
    "# invoke the QrRuntimeService class constructor without any arguments.\n",
    "#\n",
    "\n",
    "import os\n",
    "my_token = os.environ[\"QR_TOKEN\"]\n",
    "my_name = os.environ[\"QR_ACCOUNT\"]\n",
    "\n",
    "#\n",
    "# Set the backend of your choice, depending upon the task and your hardware configuration.\n",
    "# See SDK documentation for additional help.\n",
    "#\n",
    "\n",
    "my_backend = \"scarlet_quantum_rings\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b6104ae0-94f5-44e4-832a-45f2a204de0b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import from Quantum Rings Toolkit\n",
    "from quantumrings.toolkit.qiskit import QrRuntimeService\n",
    "\n",
    "# Acquire Quantum Rings backend\n",
    "qr_services = QrRuntimeService(name = my_name, token = my_token)\n",
    "qr_backend = qr_services.backend(name = my_backend, precision = \"single\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2ad20ca7-aa64-4b09-9605-fe6605924391",
   "metadata": {},
   "outputs": [],
   "source": [
    "# useful additional packages\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import networkx as nx\n",
    "\n",
    "#from qiskit.circuit.library import TwoLocal\n",
    "from qiskit.circuit.library import n_local as TwoLocal\n",
    "from qiskit_optimization.applications import Maxcut, Tsp\n",
    "from qiskit_algorithms import SamplingVQE, NumPyMinimumEigensolver\n",
    "from qiskit_algorithms.optimizers import SPSA\n",
    "from qiskit_algorithms.utils import algorithm_globals\n",
    "\n",
    "# Switch to Quantum Rings's Sampler\n",
    "#from qiskit.primitives import Sampler\n",
    "from quantumrings.toolkit.qiskit import QrSamplerV2 as Sampler\n",
    "\n",
    "\n",
    "from qiskit_optimization.algorithms import MinimumEigenOptimizer\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "422f007f-5d7f-40e9-9658-a7747a2e113e",
   "metadata": {},
   "source": [
    "# Max-Cut problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ff384808-e876-4f3f-b528-6e480fa42322",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generating a graph of 4 nodes\n",
    "\n",
    "n = 4  # 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), (2, 3, 1.0)]\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",
    "\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=0.8, 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",
    "\n",
    "draw_graph(G, colors, pos)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a4af4e0f-0d34-41e9-af9f-af26abc26b0f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0. 1. 1. 1.]\n",
      " [1. 0. 1. 0.]\n",
      " [1. 1. 0. 1.]\n",
      " [1. 0. 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": "markdown",
   "id": "1793bf50-1d60-4be7-bdea-c1175b0205cd",
   "metadata": {},
   "source": [
    "# Brute force approach"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d5eb8c2c-217f-4e0e-b328-2b07de592178",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "case = [0, 0, 0, 0] cost = 0.0\n",
      "case = [1, 0, 0, 0] cost = 3.0\n",
      "case = [0, 1, 0, 0] cost = 2.0\n",
      "case = [1, 1, 0, 0] cost = 3.0\n",
      "case = [0, 0, 1, 0] cost = 3.0\n",
      "case = [1, 0, 1, 0] cost = 4.0\n",
      "case = [0, 1, 1, 0] cost = 3.0\n",
      "case = [1, 1, 1, 0] cost = 2.0\n",
      "case = [0, 0, 0, 1] cost = 2.0\n",
      "case = [1, 0, 0, 1] cost = 3.0\n",
      "case = [0, 1, 0, 1] cost = 4.0\n",
      "case = [1, 1, 0, 1] cost = 3.0\n",
      "case = [0, 0, 1, 1] cost = 3.0\n",
      "case = [1, 0, 1, 1] cost = 2.0\n",
      "case = [0, 1, 1, 1] cost = 3.0\n",
      "case = [1, 1, 1, 1] cost = 0.0\n",
      "\n",
      "Best solution = [1, 0, 1, 0] cost = 4.0\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": "76d000d7-204b-4b5c-b5d8-e90c45bc80f3",
   "metadata": {},
   "source": [
    "# Mapping to the Ising problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "8869d923-87b2-4b90-93e3-e7bb3af46ef8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Problem name: Max-cut\n",
      "\n",
      "Maximize\n",
      "  -2*x_0*x_1 - 2*x_0*x_2 - 2*x_0*x_3 - 2*x_1*x_2 - 2*x_2*x_3 + 3*x_0 + 2*x_1\n",
      "  + 3*x_2 + 2*x_3\n",
      "\n",
      "Subject to\n",
      "  No constraints\n",
      "\n",
      "  Binary variables (4)\n",
      "    x_0 x_1 x_2 x_3\n",
      "\n"
     ]
    }
   ],
   "source": [
    "max_cut = Maxcut(w)\n",
    "qp = max_cut.to_quadratic_program()\n",
    "print(qp.prettyprint())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "3aa7a557-d233-4e69-aea1-430a8cfb04cf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Offset: -2.5\n",
      "Ising Hamiltonian:\n",
      "SparsePauliOp(['IIZZ', 'IZIZ', 'ZIIZ', 'IZZI', 'ZZII'],\n",
      "              coeffs=[0.5+0.j, 0.5+0.j, 0.5+0.j, 0.5+0.j, 0.5+0.j])\n"
     ]
    }
   ],
   "source": [
    "qubitOp, offset = qp.to_ising()\n",
    "print(\"Offset:\", offset)\n",
    "print(\"Ising Hamiltonian:\")\n",
    "print(str(qubitOp))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "d00ae02d-cbf9-4388-9dc0-a2b6cf8e7b30",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "objective function value: 4.0\n",
      "variable values: x_0=1.0, x_1=0.0, x_2=1.0, x_3=0.0\n",
      "status: SUCCESS\n"
     ]
    }
   ],
   "source": [
    "# solving Quadratic Program using exact classical eigensolver\n",
    "exact = MinimumEigenOptimizer(NumPyMinimumEigensolver())\n",
    "result = exact.solve(qp)\n",
    "print(result.prettyprint())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "901a4813-d5d3-4923-8273-4aa88ca55e66",
   "metadata": {},
   "source": [
    "# Checking that the full Hamiltonian gives the right cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "aead4c26-09c6-4ed5-906a-3c5706e817da",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "energy: -1.5\n",
      "max-cut objective: -4.0\n",
      "solution: [1. 0. 1. 0.]\n",
      "solution objective: 4.0\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\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 = [\"r\" if x[i] == 0 else \"c\" for i in range(n)]\n",
    "draw_graph(G, colors, pos)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7058ab98-ead0-41cd-a078-cde054abc845",
   "metadata": {},
   "source": [
    "# Running it on quantum computer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "22d4ae96-6b35-437d-87ce-b7d36605a36a",
   "metadata": {},
   "outputs": [],
   "source": [
    "algorithm_globals.random_seed = 123\n",
    "seed = 10598"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "17357062-0425-48a4-827d-605ab46ee15b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "energy: -1.5\n",
      "time: 94.41707682609558\n",
      "max-cut objective: -4.0\n",
      "solution: [0 1 0 1]\n",
      "solution objective: 4.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# construct SamplingVQE\n",
    "optimizer = SPSA(maxiter=300)\n",
    "ry = TwoLocal(qubitOp.num_qubits, \"ry\", \"cz\", reps=5, entanglement=\"linear\")\n",
    "vqe = SamplingVQE(sampler=Sampler(backend = qr_backend), ansatz=ry, optimizer=optimizer)\n",
    "\n",
    "# run SamplingVQE\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",
    "\n",
    "# plot results\n",
    "colors = [\"r\" if x[i] == 0 else \"c\" for i in range(n)]\n",
    "draw_graph(G, colors, pos)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "e0501475-4b6a-4bfe-81d7-f8b132bb8c30",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "objective function value: 4.0\n",
      "variable values: x_0=1.0, x_1=0.0, x_2=1.0, x_3=0.0\n",
      "status: SUCCESS\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# create minimum eigen optimizer based on SamplingVQE\n",
    "vqe_optimizer = MinimumEigenOptimizer(vqe)\n",
    "\n",
    "# solve quadratic program\n",
    "result = vqe_optimizer.solve(qp)\n",
    "print(result.prettyprint())\n",
    "\n",
    "colors = [\"r\" if result.x[i] == 0 else \"c\" for i in range(n)]\n",
    "draw_graph(G, colors, pos)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9384ad2c-6c93-4ef2-bb71-3165f0a29173",
   "metadata": {},
   "source": [
    "# Traveling Salesman Problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "0a7a6831-88f9-496d-bb35-3b2bb08804e2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "distance\n",
      " [[ 0. 48. 91.]\n",
      " [48.  0. 63.]\n",
      " [91. 63.  0.]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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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 = 3\n",
    "num_qubits = n**2\n",
    "tsp = Tsp.create_random_instance(n, seed=123)\n",
    "adj_matrix = nx.to_numpy_array(tsp.graph)\n",
    "print(\"distance\\n\", adj_matrix)\n",
    "\n",
    "colors = [\"r\" for node in tsp.graph.nodes]\n",
    "pos = [tsp.graph.nodes[node][\"pos\"] for node in tsp.graph.nodes]\n",
    "draw_graph(tsp.graph, colors, pos)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11143657-7d03-45b1-ae63-6eea9d44d6e9",
   "metadata": {},
   "source": [
    "# Brute force approach"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "9db117eb-9244-4982-b62a-6dbfd9d090a8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "order = (0, 1, 2) Distance = 202.0\n",
      "Best order from brute force = (0, 1, 2) with total distance = 202.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from itertools import permutations\n",
    "\n",
    "\n",
    "def brute_force_tsp(w, N):\n",
    "    a = list(permutations(range(1, N)))\n",
    "    last_best_distance = 1e10\n",
    "    for i in a:\n",
    "        distance = 0\n",
    "        pre_j = 0\n",
    "        for j in i:\n",
    "            distance = distance + w[j, pre_j]\n",
    "            pre_j = j\n",
    "        distance = distance + w[pre_j, 0]\n",
    "        order = (0,) + i\n",
    "        if distance < last_best_distance:\n",
    "            best_order = order\n",
    "            last_best_distance = distance\n",
    "            print(\"order = \" + str(order) + \" Distance = \" + str(distance))\n",
    "    return last_best_distance, best_order\n",
    "\n",
    "\n",
    "best_distance, best_order = brute_force_tsp(adj_matrix, n)\n",
    "print(\n",
    "    \"Best order from brute force = \"\n",
    "    + str(best_order)\n",
    "    + \" with total distance = \"\n",
    "    + str(best_distance)\n",
    ")\n",
    "\n",
    "\n",
    "def draw_tsp_solution(G, order, colors, pos):\n",
    "    G2 = nx.DiGraph()\n",
    "    G2.add_nodes_from(G)\n",
    "    n = len(order)\n",
    "    for i in range(n):\n",
    "        j = (i + 1) % n\n",
    "        G2.add_edge(order[i], order[j], weight=G[order[i]][order[j]][\"weight\"])\n",
    "    default_axes = plt.axes(frameon=True)\n",
    "    nx.draw_networkx(\n",
    "        G2, node_color=colors, edge_color=\"b\", node_size=600, alpha=0.8, ax=default_axes, pos=pos\n",
    "    )\n",
    "    edge_labels = nx.get_edge_attributes(G2, \"weight\")\n",
    "    nx.draw_networkx_edge_labels(G2, pos, font_color=\"b\", edge_labels=edge_labels)\n",
    "\n",
    "\n",
    "draw_tsp_solution(tsp.graph, best_order, colors, pos)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d616ab9-64cf-4be9-b093-9589ab113f22",
   "metadata": {},
   "source": [
    "# Mapping to the Ising problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "4b14c63f-dd00-497e-8554-2841e4b7bc32",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Problem name: TSP\n",
      "\n",
      "Minimize\n",
      "  48*x_0_0*x_1_1 + 48*x_0_0*x_1_2 + 91*x_0_0*x_2_1 + 91*x_0_0*x_2_2\n",
      "  + 48*x_0_1*x_1_0 + 48*x_0_1*x_1_2 + 91*x_0_1*x_2_0 + 91*x_0_1*x_2_2\n",
      "  + 48*x_0_2*x_1_0 + 48*x_0_2*x_1_1 + 91*x_0_2*x_2_0 + 91*x_0_2*x_2_1\n",
      "  + 63*x_1_0*x_2_1 + 63*x_1_0*x_2_2 + 63*x_1_1*x_2_0 + 63*x_1_1*x_2_2\n",
      "  + 63*x_1_2*x_2_0 + 63*x_1_2*x_2_1\n",
      "\n",
      "Subject to\n",
      "  Linear constraints (6)\n",
      "    x_0_0 + x_0_1 + x_0_2 == 1  'c0'\n",
      "    x_1_0 + x_1_1 + x_1_2 == 1  'c1'\n",
      "    x_2_0 + x_2_1 + x_2_2 == 1  'c2'\n",
      "    x_0_0 + x_1_0 + x_2_0 == 1  'c3'\n",
      "    x_0_1 + x_1_1 + x_2_1 == 1  'c4'\n",
      "    x_0_2 + x_1_2 + x_2_2 == 1  'c5'\n",
      "\n",
      "  Binary variables (9)\n",
      "    x_0_0 x_0_1 x_0_2 x_1_0 x_1_1 x_1_2 x_2_0 x_2_1 x_2_2\n",
      "\n"
     ]
    }
   ],
   "source": [
    "qp = tsp.to_quadratic_program()\n",
    "print(qp.prettyprint())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "c2baead7-e00f-4ae8-bbee-38e2e66f1a53",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Offset: 7581.0\n",
      "Ising Hamiltonian:\n",
      "SparsePauliOp(['IIIIIIIIZ', 'IIIIIIIZI', 'IIIIIIZII', 'IIIIIZIII', 'IIIIZIIII', 'IIIZIIIII', 'IIZIIIIII', 'IZIIIIIII', 'ZIIIIIIII', 'IIIIIIIZZ', 'IIIIIIZIZ', 'IIIIIZIIZ', 'IIIIZIIIZ', 'IIIZIIIIZ', 'IIZIIIIIZ', 'IZIIIIIIZ', 'ZIIIIIIIZ', 'IIIIIIZZI', 'IIIIIZIZI', 'IIIIZIIZI', 'IIIZIIIZI', 'IIZIIIIZI', 'IZIIIIIZI', 'ZIIIIIIZI', 'IIIIIZZII', 'IIIIZIZII', 'IIIZIIZII', 'IIZIIIZII', 'IZIIIIZII', 'ZIIIIIZII', 'IIIIZZIII', 'IIIZIZIII', 'IIZIIZIII', 'IZIIIZIII', 'ZIIIIZIII', 'IIIZZIIII', 'IIZIZIIII', 'IZIIZIIII', 'ZIIIZIIII', 'IIZZIIIII', 'IZIZIIIII', 'ZIIZIIIII', 'IZZIIIIII', 'ZIZIIIIII', 'ZZIIIIIII'],\n",
      "              coeffs=[-1282.5 +0.j, -1282.5 +0.j, -1282.5 +0.j, -1268.5 +0.j, -1268.5 +0.j,\n",
      " -1268.5 +0.j, -1290.  +0.j, -1290.  +0.j, -1290.  +0.j,   606.5 +0.j,\n",
      "   606.5 +0.j,   606.5 +0.j,    12.  +0.j,    12.  +0.j,   606.5 +0.j,\n",
      "    22.75+0.j,    22.75+0.j,   606.5 +0.j,    12.  +0.j,   606.5 +0.j,\n",
      "    12.  +0.j,    22.75+0.j,   606.5 +0.j,    22.75+0.j,    12.  +0.j,\n",
      "    12.  +0.j,   606.5 +0.j,    22.75+0.j,    22.75+0.j,   606.5 +0.j,\n",
      "   606.5 +0.j,   606.5 +0.j,   606.5 +0.j,    15.75+0.j,    15.75+0.j,\n",
      "   606.5 +0.j,    15.75+0.j,   606.5 +0.j,    15.75+0.j,    15.75+0.j,\n",
      "    15.75+0.j,   606.5 +0.j,   606.5 +0.j,   606.5 +0.j,   606.5 +0.j])\n"
     ]
    }
   ],
   "source": [
    "from qiskit_optimization.converters import QuadraticProgramToQubo\n",
    "\n",
    "qp2qubo = QuadraticProgramToQubo()\n",
    "qubo = qp2qubo.convert(qp)\n",
    "qubitOp, offset = qubo.to_ising()\n",
    "print(\"Offset:\", offset)\n",
    "print(\"Ising Hamiltonian:\")\n",
    "print(str(qubitOp))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "ab21af8d-a365-46d7-a19f-7c82a0864741",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "objective function value: 202.0\n",
      "variable values: x_0_0=1.0, x_0_1=0.0, x_0_2=0.0, x_1_0=0.0, x_1_1=1.0, x_1_2=0.0, x_2_0=0.0, x_2_1=0.0, x_2_2=1.0\n",
      "status: SUCCESS\n"
     ]
    }
   ],
   "source": [
    "result = exact.solve(qubo)\n",
    "print(result.prettyprint())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "c8aa754a-07a2-4fbb-95d4-c53942ddcd56",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "energy: -7379.0\n",
      "tsp objective: 202.0\n",
      "feasible: True\n",
      "solution: [0, 1, 2]\n",
      "solution objective: 202.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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XXZVgoDZWWil2CJxD4GZFDgomTUp6VQCAmkhlMGCUF+YnqHIfAucQfPllHBu8/nrSqwIA5CrVwQA7A/mx6aZRbbDuupFYeOutVGoAQClJdTDg6YVctPKjTZvoR3D88dI990j9+kkTJiS9KgBANlIdDHiM8bhxSa+kvI4N+vSJhEL3cfCxwb/+lfSqAADLk9pgwI2HjKOC/Ntkkzg22Ggj6eSTY8fAgRcAoDjVT3PvfbfbJYmwMFq1iumHDgaGDZOOOYZdGAAoVvXT3EDH5YXMKCjsscGhh0bp4cSJMdvg5ZeTXhUAYEmpDQaM8sK64eMC7w706CGddlrsGMyenfSqAAAZqQ8GyBmoGy1bStdeK51+uvTww1LfvlHNAQBIXuqDAWe900q3btSrJx10UEw9rKyMY4MXXkh6VQCA1AcDlBfWvW7d4thgiy2kM8+UrrlGmjUr6VUBQHqlOhigvDA5zZtLV10lnX229PjjMRqZ/wcASEaqgwFPL3RVAUmEyR0b9OwZHQunT5d695aefTbpVQFA+qQ6GMiUF3JHmqyuXaUHHpC23VY691zpiiukmTOTXhUApEeqgwGjoqA4NGsmDRwonXee9OST0db4q6+SXhUApAPBAMFAUR0b7LefdN990YfgkEOkp59OelUAUP5SHww4iZDywuLSpUsEBDvtJF14oXTppdKMGUmvCgDKV+qDgU6d4i6U8sLiOza45BLpoosiqfCww6RRo5JeFQCUp9QHA5nyQmYUFKdf/zp2CcxzDp54Qpo/P+lVAUB5SX0wsMoqlBcWu86dIyDYffc4MvBuwbRpSa8KAMpH6oMBygtLQ5Mm0gUXSJddJv3zn7FL8L//Jb0qACgPqQ8GMnkDBAOlYY89opVx48bS4YdLjz3GsQEA1BbBAOWFJZnncffdkU/gBkXuTfDjj0mvCgBKF8HAgouLEwgpLywd3hk45xzpyiulV1+NngSffpr0qgCgNBEMLNgZcHnh+PFJrwS52mWXODZYccXoWvjwwxwbAECuCAYWBAPGUUHp/v8NHSrtv3+MQz7rLGnq1KRXBQClg2BgQXlh/foEA6WsUSPpjDMiGHjzzZiA+PHHSa8KAEoDwYCkBg0oLywXbmE8fLjUqpV05JHxa44NAGDZCAYWoKKgfHTsKA0ZIh14oDRokDRggFRVlfSqAKB4EQwsQK+B8tKwoXTqqREMvPeedPDB0gcfJL0qAChOBAMLUF5YnrbbLo4K2reXjj462hrzfwwAiyMYWOSYYNYsacKEpFeCfOvQQbrzzuhFcNNNsWMwZUrSqwKA4kEwsADlheWfJHriiREMfPRRHBv85z9JrwoAigPBwCJJZ5QXlr+ttopjA1ePHHts9Cfg2ABA2hEMLHLn6ICAYKD8OX/g9tulI46QbrstdgwmT056VQCQHIKBRVBemK7R1f37SzffHKOQe/WS3n476VUBQDIIBhax1lo0qEmbLbaIYwP/3x93XCQacmwAIG3qzZ+//MtfVVWVKioqVFlZqZYtW9bNyoA65ADAjYruukvq0UMaOFBq2zbpVQFA7WR7/WZnAPAPQv3oQ+Acgi+/jGqDN95IelUAUDcIBoBFbLppHBt07SqdcIJ0663S3LlJrwoACotgAFhCmzbRj8A5BPfcI/XrRzMqAOWNYABYyrGBSw+dUDhmTFQbvPZa0qsCgMIgGMiCUyzZKk6nTTaJY4MNN5ROOil2DObMSXpVAJBfBAPV+PTTyCw//HBp3XWl9daTDj00LgqUnaVPq1bSDTdIJ58sDRsmHXOMNG5c0qsCgPwhGFiEL/TXXCPtv7/0+99Lzz8fDWl23jkuCKefLl1/vTRtWtIrRRLHBg4IXXro/AFXG7z8ctKrAoD8IBhYxIsvSoMHRzDgXYD334/3R4yQLrhAevJJ6f77uQikWffu8b3h44PTTpMGDZJmz056VQBQOwQDi3jgAWnHHaXLLosz4pVWii3hhg2l++6LZjRrrCG98krSK0WS3LfDO0QDBkgPPyz17SuNHZv0qgCg5ggGFuGL/5JHAH6/WTOpXr1438OMPv88keWhiPj7wRUGnno4ZUocG7zwQtKrAoCaIRhYxO67S998E7kBHlrz0ksx5va996R99oks8q23lnbbLemVolh06xZJhZtvLp15ZuSczJqV9KoAIDfMJliEz34ffFC6+uo4GvBYW8+9P/98aa+9IsGwslJq2lRq0iTp1aKY+Kfo0Ucjh2DttaUrr4wpmACQpGyv3wQD1XAFgZMH27WLOz+/BbItSz37bOm77yKI3HXXpFcEIM2qCAYKY/ToCBa23FJaccWkV4Ni9OOP0uWXS88+G5UpTjRs3DjpVQFIoyqmFtbMqFHSX/8ad3aWCZUyb5017q1g5xQA1XGQ6GDgvPOiHLVPH+mrr5JeFQAsHcHAEtxU5o47FiaBOWv8rbekDz+M93/xi2hA4+RCYGn8fbPfftK998b30iGHSE8/nfSqAKB6BANL8IW+eXNplVUWfsw9BpwQZt7u3XjjyCkAlmeddaJRlftXXHihdOml0owZSa8KABZHMLAEz7H/7LP4daazXNu20kcfLX4mzOAiZMt9Ki65JIKBv/9dOuywOI4CgGJBMLCETTeVfvghjgFcXmgffBA9Btx/wPkCLiFzn3ogl2MD96rwLoH5++eJJxbmogBAkhok+uxFyFMK3VPA3eX23TcqB0aOjPNef2zqVKlnT2mPPZJeKUpR585x7OTmRD4ycCKqSxG9ewAASSEYWIJ3Ay66KHYCPKDIPQbch36DDWKHwI2I2rRJepUoZW5Y5SODX/4yclE+/jjeOr8AAJJAn4FlcBmhEwY9s8D8L5WZUQDkg0sOvTPgtz6GcgUC32MA8oU+A3ngoUSZQMB4kUa+eQrmPfdIe+8tXXFF9CZwgioA1CWCgWo40/uqq6RXX433PZMAKBTvPp17bgQD/p5zTwK3NQaAukIwUI1PPolgwDkCS+4I+KiA4ACF4DkGnoDoDobuWvjII1QbAKgbBAPV2HbbKPtyKdiSL8YODNyYyHihRr550uHQoZE74OmZzidwBQsAFBIJhFkaNy6SvDyzwB3kNtuMEbUorBdeiPJD/8h5p8oTNAEgFyQQ5ikAOOMMadVV47HddlLv3jGa1r0IvKXrEkSgEHbaSRo+XGrVSjryyPg1u1EACoE+A0tRVSWdeKL0+edS//5xdNCpk9SggTRhgjRkSGzjenfAQQJQqIoWf68NHhzdL995J/pgpHSDDkCBEAwshVsOu/ugM7z33PPn5WA+JnAXwueeIxhA4RthnXZaNCm6+GLp4IOjSdFGGyW9MgDlgmOCpXBXuLXW+nkgkOFBRa4qoCYcdcVBp4+m2reXjjoq2hpT2QIgHwgGlmKTTaT//lf68MOFH/MUw/Hjo598374x3dAlYEBd8WjtO++M3JWbboodgylTkl4VgFLHMcEyar7/+U9p663jjsx942fNinyB0aNjZ4CtWiTBeSsnnRQTNj3jwAHpQw/FzIOloZU2gGWhtHAZPJTowQelN96IHYGZM6UOHeLsdrfdCASQPAenHqjlBNdM/4vqeCy3A9iJE6UuXepyhQCSlO31m2AgC34h9d3Ysu68gGLlpkVuYvTtt1LTprHL5dyDZQUPAMoDfQbyqHlzAgGULg9BqqyUzjpLuvXWaJzlaphJk5JeGYBiQc4AUMb+9a/oTfD00wtLYO+9VzrwwOio2bZt0isEUAzYGQDKmHNcXIHgyYiLfsyls841MCfGAkg3goEsOPHKHQmBUuM7/5VWks45J0pj/b18443RXrtr16gy+OtfoyrBpbQA0olgIAtuS+wyQqBUuI22G2JVVEgvvRQzNDbcMCZxDhgQjYs6d45yQ/+5Tz+NioTrrkt65QCSQDCQBd9FubcAUArchMjttF95Jd73EcHLL0sDB8YugQcfnXnmwnyBww6LqYhue/zUU3TVBNKIYCALHkb09ddMjENp8MXe5bCeYfDYY5Eb4H4Ejz8uffCBdMIJ0i67xJ/NTN10N0OXz952m7TiiokuH0ACqCbIMhiYNk36/nupTZukVwMs32WXReKgOxX6qGDMmOgv4EDAcw3M+QMOAB5+OIIBN9hab72kVw4gCQQDWVh99Xjr3QGCAZSK446T9t03jrh80Xf74kxLYgcCK6wgjRol9esXQcMBByS9YgBJIRjIMmfA/KK68cZJrwbIXseO8Vi0G6GPARwI+IjA+QLdusVoZADpRc5AFtx90NnX3hkASpXHHTuHwEcF7kh43nmRT3D77XGUACC92BnIIW/gm2+SXgVQc55FsOOOUUnwpz/F0CLnCbjkMJtph25O9N57UW3gdsZu0w2gPLAzkEMwQHkhyiH/xRM4e/WK98eOjfyBpclU0DzxhNS7t7TlltLpp0ePgn/8o27WDKDwCAZyeBGlvBDlwl0I77orhhcNGfLzlsT+PndOgXcT3n5b6t9/YR+C556Lo4ZTTmG3DCgXBANZ6tQptkddXgiUg759Y1hR9+5So0bxsTfeiLc+GnAFgvMM9t9f2nzzaFm8xx5S69bSEUdE74KRIxP9KwDIE4KBHMsLuRNCOXEvAm/9my/2ffrEnX/GMcdIzZpJF1yweA8CBxGuSGjXru7XDCD/CAZqUF4IlKOddooEw402ivfdrfDNN+OIYIMNFi9PdMDgADmzowCgtFFNkKWmTeMuiPJClKsddpC22SaOB8xTDseNk7beevERyK++Kg0bJvXsKa27bmLLBZBH7AzUYEYBUK4ygUAmGHD5oIcbZbz4ojRoUHwsM8mTpFqg9LEzkGMwQMIU0mLttaMZ0bnnxthjj0L2sKMZM6SHHoo/4wRDVxwAKG38GOeA8kKkiY/Fnn5a+uKLGG7kEcjbbhuTDR0oEAgA5YOdgRx3Bjwa1vPiXV4FpKHa4PXXIyBw3kyHDgt/LxMIuB/BzJmMPgZKGXF9jsGAkTeAtFlrrcUDgSXbFXvn4KKLYtQ3gNJDMJBj4yEjGACCAwH3Gzj0UOmFF2IK4mefJb0qALkiGMiBt0nbtiUYAJa0557S/fdHNYIDgj//mdwaoJQQDNQwiRDA4tZcU7r3XmnvvaXLL5fOP59jA6BUEAzU4KiAYAConpsTuRTxiiukV16JSYeffpr0qgAsD8FADXYG3JKYLVBg6XbdVXrggZhr4KFGjzzCzwxQzAgGalheWFmZ9EqA4g+c775b2ndf6eqrpbPPjp8dAMWHYCBHlBcC2fMgozPPlK65JsYj+9jg44+TXhWAJREM5IjyQqBmExE93MjtjY88UnrwQY4NgGJCMJAjn4F6SAvBAJD7GPAhQ6QDDpCuv1464wypqirpVQEwgoEaoLwQqJmGDaXTTotg4J134tjgww+TXhUAgoEa5g24ogBAzWy/vTR8eDTx6ts3Kg88+AhAMggGahgMfPNN0qsASn8I0l13xe7AjTfGjgFVOkAyCAZqGAz4rJMXLqB23L74pJMiGPjvf6VevaT33kt6VUD6EAzUMGfAyBsA8mObbaLCoGNH6Zhjoj8BxwZA3SEYqAHKC4H8a99euuMOqU8f6dZbpZNPliZPTnpVQDoQDNSwvLBNG4IBIN88Dvm446TBg6VPPpEOPlh6992kVwWUP4KBGqK8ECicLbeMaoM11pD69YtEQ44NgMIhGKghyguBwmrXTrrtNumoo6Q775ROOEH67rukVwWUJ4KBWgQD7AwAhVW/fiQUOofg88+j2uDNN5NeFVB+CAZqWV5IO1Wg8DbbLKoNunSRjj9euv12ae7cpFcFlA+CgRqivBCoW07avflmqX9/aejQeDtxYtKrAsoDwUANUV4IJHNs4KmH3hnwz56PDV57LelVAaWPYKCGVlwx7lRIIgTqXo8eUW3QrVt0MPSOAccGQM0RDNQCMwqA5LRuHW2MHQzcd18kGo4fn/SqgNJEMFALlBcCyR8bHHaY9Ic/SOPGxbHBK68kvSqg9BAM1AKNh4Di0L17HBtssol06qnSDTdIs2cnvSqgdBAM1DKJ0JMLKS8EkldRIV1/fYxCfugh6eijpbFjk14VUBoIBvJQXkjeAFAc6tWLeQYuPfSQo969pRdfTHpVQPEjGKgFyguB4rTBBtKwYdGs6PTTpeuuk2bNSnpVQPEiGKiF5s0jo5kkQqD4tGghXX21dOaZ0p/+JPXtyy4esDQEA7XEjAKguI8NDjggjg2mTo1jg+eeS3pVQPEhGKglggGg+K2/fhwbbLWVdPbZ0lVXcWwALIpgoJYoLwRKp2voFVdI554rPfGE1KcPR3xABsFAHnYGpkyJLUgAxX9ssP/+0j33SDNmSIccIj3zTNKrApJHMFBLVBQApadrV+mBB6Ttt5fOP18aODCCAyCtCAbysDNgZCkDpaVZM+nSS6ULL5T+9jfp8MOlL75IelVAMggG8lC+1KoVZ49AqR4b7LNPDDqaN0869FDpySeTXhVQ9wgG8oAkQqC0rb12BAS77CJdfHE8pk9PelVA3SEYyFPeAMEAUNqaNpUuuki65JLoReBdgs8/T3pVQN0gGMgDdgaA8rHXXpFc2KBBBASPPy7Nn5/0qoDCIhjIUxLh999LP/yQ9EoA5MOaa0r33huBgSsNLrhAmjYt6VUBhUMwkMeKAnYHgPLRuLF03nnS5ZdLL78cPQlGjkx6VUBhEAzkAb0GgPK1225xbNCkSXQtfPRRjg1QfggG8qBlS6migmAAKOe8IHct/M1vYq6BWxpzLIhyQjCQJyQRAuWtUSPprLNiLPJrr8UExBEjkl4VkB8EA3nMG6DxEFD+fvUrafjw2A088kjpj3/k2AClj2Agj8EALYmBdFh1VekPf5B69pSuvVY680ypqirpVQE1RzCQx2Bg8mTpxx+TXgmAujo2GDBAuu466e23o9rgww+TXhVQMwQDeUJ5IZBOO+wQxwZt2kh9+0rDhnFsgNJDMJAnBANAeq2yShwbHHywdMMN0mmnSZWVSa8KyB7BQB7LC/0gGADSye2LTz5ZuvFG6YMPIjB4//2kVwVkh2AgjygvBLDNNtKDD0odOkhHHx39CTweGShmBAN5RHkhAGvfXrrzTunww6Wbb5ZOOSXmlwDFimAgz8EAOwMAbIUVpOOPlwYPjuZEPjZ4992kVwVUj2AgjygvBLCk//u/qDbwMWK/ftKQIRwboPgQDBSgooDmQwAW1a6ddNttUXp4++3SCSfEjQNQLAgG8siRv3FUAGBJ9etLxx4r3XKL9Nln0kEHSW++mfSqgEAwUIDyQpIIASzN5ptHtUGXLpFTcMcdHBsgeQQDecaMAgDLs9JKUWWQySHo31+aODHpVSHNCAbyjPJCANkeG2RyCPya4WqDf/876VUhrQgG8ozGQwBy0aNHVBusv7504omRUzB3btKrQtoQDORZp07Sd99J06YlvRIApaJ162hj7GDg3nsj0XDChKRXhTQhGMgzygsB1PTYwB0L77pLGjtW6tVLevXVpFeFtCAYyDPKCwHUxsYbR7VB9+7Rxvj3v5fmzEl6VSh3BAN55tLCFi1IIgRQcxUV0qBB0qmnRj6BBx59+23Sq0I5IxjIs3r1mFEAID+vJb17R+nhpElRbfDii0mvCuWKYKAACAYA5MuGG0rDhkmbbiqdfrp0/fXS7NlJrwrlhmCgACgvBJDv48drr5XOOEN69NHoTzBmTNKrQjkhGCjQzoC39SgvBJDPY4MDD5SGDpUqK+PY4Pnnk14VykWDpBdQjjp1nKeOM7/Sd49+qWbtZ0rz50tNmkhrrCGtuWbUEAFADbg5kY8NBg6UzjpL+t3vItGwUaOkV4ZSVm/+fF+plq2qqkoVFRWqrKxUS+9X4efcaegvf5Fefllz331f40dWql3LmWq4woIJJA4A/NPqNOGNNpK23Vbad1+pffukVw6gBPmV+7HHIofA9xhXXbWwtBnI9fpNMFBbI0ZI990nPf64NGVKfKxJE81t1ET1mzZWvcwugMeSzZwpzZgRD/+zt2ol7b231KdPZAkBQI5GjpTOPjuOJs87T9ptt6RXhGJCMFBos2bF7FGPHvMBXrNmcde/wgrZfb6bj/vznFjgxgQeW3bccXGcAAA58MvIFVdIzzwj7bdfVB00bpz0qlAMCAYK6X//i5+2t96KrX/PI3V2T034n3/y5Ngt+MUvpOuuk7p1y/eKAZQ5v5Q88YR09dVxXOBjAx8fIN2qsrx+k8mWqw8+iDTeN96IIKBt25oHAubPzXydd9+VDjlEevvtfK4YQAr4peQ3v5Huvz82Hv1S8tRTSa8KpYJgINf8gCOOiClEq6yS3304f62OHaPn6FFHRdABADlae+1IY9p5Z+mii6RLLpGmT096VSh2BAPZqqqS+vWLTh8OBLLNDciFkw39tcePjxmmPj4AgBw1bSpdfHE8/vGPmIY4alTSq0IxIxjIltt/ffqptPLKhe0T4K/t5/jii8gIWn5KBwBUy8VKPjbwEcKhh0ZOAS8pqA7BQDZefll64IHI+m/YsPDP16BB9B995JEI6wGghtZaS7r3XmmPPaRLL5UuvJDuqPg5goHlcRjtDH9n+9dlJYWfy+WL3pFwjwIAqCFXLJ9/fnQtfOmlSC50fwIgg2Bged55R3r//WgQlEPVwLR583THxIk6cfRo7TRypH45YoT+mmlKlK02beJo4rXXcl83ACxh991jk9PBgXuduYMhxwYwgoHl+eMfo3OgmwrlYMqcObpr0iR9MWuW1qlp1YF/Yr078NBDNft8AFiCexDcc4+0zz6RlnTuudKPPya9KiSNYGBZHAQ8/XSk5ubYS6Btgwb6+zrr6MkuXXRyTecP+DlXXDHyBqZOrdnXAIAluFeaWxhfeWVsPPbuLX3ySdKrQpIIBpbXafCHH3LeFbBG9etrJScC1paf20XCPi4AgDzaZZeYgOjcaLdQefhhjg3SimBgeU2GvDuQZJNvh/CzZ8daACDPOnWShgyRfvtb6ZprYiwyG5HpQzCwvJ0B1/0Xsq/A8mSOJ0j9BVDAew6PW3HhlEeu+Njgo4+SXhXqEsHAsjg8LoayPq+BUB1Age2wQxwbuJCpb19p+HCODdKCYGBZ5sxRUfDugI8KFuEfUG8W3HKLNGhQYisDUGY8IuWuu6SDDorXlgEDohs7yhvBwPL2zmozkTCfmjT5KQDwycWtt0p77SXttlt0E3PSDwDkixutnnKKdMMN0nvvSb16MTut3BEMLEu7dsURDNSvr0lqqy5dpM03l845JyYoe2n+ofXHASDftt1WevBBqUOHGKbqaYjFcHKK/MtD7VsZW2+9eOvh4IWYUpgN/+TNn68VNlxfTZ6JrsjeIfCpgX/tnkSvvhrdxFZbLR7ODs78uqKiOOIZAKXJc9PuuEO6/Xbpppukt9+OscitWye9MuQTwcCydOsWXQBd59+8ec6f/vDkyZo6b54mLsg9eOWHHzRhwa8PbN1azbMJMHzFb9xYrbfupvcOiR9K/0BWVsaF/rvvpO23j2Ek33wTmcCTJi38dC+7uiDBDycJESgAWB63TDnhBKlHjziaPPhg6fLL432Uh3rz5y8/V7SqqkoVFRWqrKxUy7oc1pM035Vvs4309dcRHufo1599pm+XSPzLeGLttdXROQnLM2FCHFf4XGBBEyOf3Z15ZoxMsLvvjp7jGZ5INmZMLHvJh79chhsrVhck+NG2bbIVlQCKk19DPPTIuQT9+sWuJK8VxSvb6zc7A8vi73Cn1LpnpwODHL/j/1rbw3zHaT4HOPDA/x8IWPfuMWDkxhtjdMK66/68aeE668RjSe6hVF2g4I7H48YtPA90nFJdkOCP+fyQH34gndxd/bbbouLAbz3L7bLLYqcRpYudgeUZOzaKb32V9OTCuuR6Hucr+ErdufNSTxF8kpEPjju+/XbxIMFHD37rACITKDguWXXVnwcJfrvKKovFLQDK2Jtvxi6Bjxs9HnmzzZJeEWp6/SYYyMbJJ8ctuAtw6+qW2FdeByIeLXbnnUqaUx28c7BkkJAJFDKnIf7n8T9TdXkK/ng2JyMASofzlhwQOLHw6KOj6oCdw+JBMJBPvtrtvbc0cWLskdeF8eNjJ+KJJyI7sIg5bvFylwwSMu/7aMJ89+B/vuryFLzTkK8dDgB1/xowdGjct/ziF5Fc6LwjJI9gIN/c2ee002K8l8cKF5IzAF0u4FyFww5Tqb9IuLphySAhEyj4r7roWeTS8hRqMDgSQB17913p3HPjdNN5BFtumfSKUEUwUICr2vHHS3/+c4S8hbqN9W20dyD22CNGiZXxfpu/877/vvogYfTomB6d4eSk6oIEv3V8BqA4TJ4sXXSR9PrrMRb52GOTa9MCEQwUhG9jfSj2/PNxdcr37aqzAX0b7XJG77ml+N/a35XOn6wumdGPKVMW/ln3W6guSKDpEpDcvZO7Fbp1+sYbx7GBd/5Q9wgGCsW3qyeeKP3975ENt9JKtb/aZG6R3dxop52iXift/87L4SGOmeBgySMIJzRl0HQJSI57EfjYwBuel14qbb110itKnyqCgQJyDZ57c958c9y+1ubYIHMs4KuWO3i4zReZdLXewHGAUF2eAk2XgLrl9CcfG7htulOgjjuO8uO6RDBQF/773wh7//OfyJjxBd0H2Mu7ivif3Le2fvgwbcMNpSuuoLdnHVha0yUHDjRdAgrDP1fDh0uDB0sbbBAvd3VVmJV2VQQDdViA//LL8Z3+4ovSjz/Gx32Rb9x44VXDPw2+EjloMOcbbLddzAbdcccYP4hE0XQJqJv7J79MXnxxvASisAgGkvDFF5FCO2JEHJZ99tnCi7+DA/cL8N3/+utLW2whrb120itGlmi6BOSHT1adP+B7Jw88cgoW90KFQzBQDPxP66uI3/q7nWy1srSspkt+eMfBaLoEBL8kuqmr56t07SpddVUEy8g/ggGgCJRL0yXvfPgIxQM0nXgJ5MPHH0vnnBNJhh6N7GIq5BfBAFDkSqHpkk+5fMLlCXUe0eGTrj/9SVpvvfj9zz+XPv00AhlPz6QBFHLl73N3K3T7lgMOkE45heO0fGKEMVDkfGzgi7wfbsySTdOlr76KEq26aLrkEy4nQ7pxjNtqeDvX6S6ZnQGP0b7lltj5cG8H74KccUacAZNEiWy5CMvHBA4yBw2S3n8/3vf3L+oOP7JAEfIF3BdyP1x5mm3TJY+UzVfTJV/QfcF3OZjnZZ15ZgQCmbn13t7dZJPomr3GGtKjj0qHHx6lY7vu+vOv5wDHz+d1PvlkBA/Oo/VgG9rVppu/L3r2lLp3l84+W+rdOyYhVvd9hMIgGABKkLfjfZfuR7ZNl1zgsmjTJX8Nb80urWfCP/8Zs7l8sXfhi3cAunRZeBTg7V3vaKy5Zrz/u9/FroCPDap7EfcL/kcfReMZBxXOQ7j66mhVe8gh5Ncidp8eeCC+J1yC6LHIAwZElTYKi2AAKDNONvSLqh/Larrko4ZlBQIDB0rDhkULWec2+HMz/eV9l+8GnD4m8K6Ady/8Of6aO+9c/df05/iuz4GAX/AdRNx0k3TUUdKvfkU2ORZ+//p7b7PNpGuuid4EPjbw9xkKh2AASBHfYXXuHI9l5Qo8+GBc3H3RduuMzI5DZka9gwMnOTqHwccF3nFwAqHv5KrbrbCRI6XnnpMef3zhboI7cHt3wDkJnnAHmHeJ9t03gkwHkN458vfZnnsmvbLyRTAAYDHeLfDYWQcM3tb/y1+kDz+MrnF9+8bOgncIXGFw7bXSb34TVQW+sLvNrJtxVseJj61bR45Ahhs5bbSR9Mkni+cVAOZjKU8/dMDo0kMHm85doSdH/hEMAPhZMLDppvHI8BnuU09Jxx8fteCHHhrHAb5789m/X7T9MVcevPNOfK4TBDMXdr91Tbm3elu1Wvh1vdvgz89UHxAMoLpjg0sukX75ywgKHJj62GBZu1vIHeNWACxVZh7DqFFR2eD8Ac9f8AXcL8pOKsy0knUegn+d6VzioMIX9sz7TmhceeWF75s7N7oyInNssKQvv1y8MRPS69e/jl0Cc+DpCpfld8lBttgZALBUmQTDlVaKrVm/tfPOi7Pc00+PnQLnEHj3wJnfmZyB116LwMFljP46zldwEyPnJGSywz3w0wFDpnxy0YRGByLuXe92zn7e6nop+C2NjtLDuwEOCHw85fkGPjbw92HSHTrLAR0IAdTIs89GouG770orrhg9Bpzo5V+bL9Z77RX95x1I+E7Of+aRR+KIwTkIzhjfZpvIGl/0+CATDDhnobqZD25fm+HPW1ovBb9ccexQnv72t8hRcf6Kjw3WWSfpFRUn2hEDSIwv5N496NYttnTNRwv9+0eHOScROunQxwDudbC0Y4KlcXfG6nop+DF58sI/512D6oIEP5zMSKBQ2lzR4p0Bfx95l2q//fg/XRLBAICi4xJET6t7443oK+A+9PnuL5BpulTdzIdFmy55a3lpg6FcQrm0HgwoLj5Guv76aGfsZlcOQjO7UxDBAAAsacaMhU2XFg0S/NZljplXQ+c0LBkoZN53EiSBQvH5xz9i4JHzS3xs4L4XEMEAAOR6hzl27M+DBD/88UxlhSsmVl21+jwFJ0wyZyE5/j/zsYGPoE49NVpkp/3YoIpgAADywxUQ335bfTKjdxr8++ZAwMce1eUpOFBgNG/dBHW//30cR7nS5YILFp+n4UBhySmhy+QSGH+SO2ONGBF1tj6LcpThSWAuccgMCnHyS5FtGxEMAEAd8I6BjxiWlqfgi5P5GtGhQ/V5Ct5pYBhPfr3wQpQf+pLlY4P11ovOmu6E6amZHr61TBMmSH/+cwzocKaih3M4APB/eOaCn/m1L6MumXH3LY9c3GefheM9E0YwAAAJ87XCjZmqCxL8dvr0hX/WJXLVJTP6QR19zfh4xzMNPEnTvSxcjujgzCWu1123lE+aMkUaNEh6+OGoYfV2j697vtgv7a7fuwdOSHGZi//THQi4jOakkxL/zyMYAIAi5ldel0FWFyT4RtR9GDKW1nTJD+9UY+lc0nrWWdEq28c0/rf09d2Bwc96E/zzn3Gu8NlncRF3281ck0AcGDigcHCwwQbRDGHzzZUUggEAKFF+VfZNaXXJjDRdyo0DLvcfcPts7wr45t6zMPr0iZLEn8ybF20Nb7st/pC3aTIDM2rKX2fixAgqzjgjzigS+M8gGACAMkXTpez5xnzw4IVtsD0Lw8cz/vu/9JK0Xtd50kUXSUOHxlGAo6t8/cP48vrdd7Fb4PIGP+r4Hz3b6zezCQCgxPg13d0d/ci26dJ776Wz6VLPnvF3dTGAdwec7Onrs+dpuOnVMzteG4GAOxXl+2bXF37/Y/rJbrghvv5RR6kYsTMAAClB06W4LjslwLM1Np/+knYZ1if+Qt4qKCQfGThp4dFHc6xtrB2OCQAAWUtd0yWftey9d0QGq6xS+O17X2r9D9mjR/RO9pFEHeCYAACQNd+0umdOdUOjltZ06V//yr7pkj/uQKJoeNt+5MjY6qhXB+f4mSMDj/m86y7pxBNVTNgZAACkq+mSmz9su200Eqrr5kATJkS1wssv10kPAnYGAAAF54u87/r9WLKcfmlNl/77X+nppxNsuvT449ELwNFJDmbNm6fbJ03S05WVqpo7V+s0bqzj2rfXFrmMSXRugo8LnnlG2n9/FQuCAQBAwQIFX+T92HTT7JouuVugJxAWrOmSIxS3GPbickxwuPjbb/V8VZUObtNGqzVqpCcrK3XS6NG6Y401tEm2EYvPSvyXHz6cYAAAkG4+QvdF3o9NNsmu6dIXX8Tueq2aLn31VTxyPPL+aPp0PVtVpZPbt9ehXrSkvSsqdMCoUbppwgQNrS7ZYmkcwbz/fvxF3OWwCBAMAACKii/gvsj7sdFG2Tddev315Tdd6vblCK05bbrq53gRfn7qVLmicn8vaoFG9evrN61a6ZaJEzV+9mytnG2GZNOmUePoKYhbbqliQDAAAEhN06Xe4z9R3x/qqWWORwSfzJihNRo10opLfN4GvrBL+nTGjOyDAf85l2AQDAAAkH8+uu/aNR7VNV2a0X+0mj81N+evO2nOHLWtZl5B5mP+/Zy2PvxwlFIkCAYAAKngPj9NGk2XVsi9heLMefPUsJpgoPGCpIQZy6/SX5z/vEsbi0QJN5UEAKBuNK5fX7OrueDPXPCxJjVpXFREk6IIBgAA6TpHyPUuXnEcUN1RQOZj1R0hLDcQqKOWxNkgGAAApEfnzjWatLRu48b6atYs/ehxxIv4cEHnpHVzubA7GPFjrbVULAgGAADpsf768TaXhD9Jv2rZUp7V9Jg7Fy7SkfCvlZXasGnT7CsJzLkC/vOZtRQBEggBAOnhekSXA/qO3o0IsrRh06bauUUL3Txhgr6fO1edGjb8qQPh2FmzdMEaa+S2Bpc1eA3rrqtiwc4AACA9PK7YAcHUqTl/6qUdO/7UivipykpdN3685syfrxtXW009ch2e4F7LW20l5TLToMDYGQAApIcT9w45RHrnHWn27JzmKjeqX18nr7zyT48a8xGBGxf16qViws4AACBd9torpictcv5fZ9wv2XMMdtxRxYRgAACQLh4U1Ldv7AzUZeOfadPibf/+Oe1I1AWCAQBA+hxzjNSjhzRxYo36DuTMo5O9K+AdgSI7IjCCAQBA+jRuLF1xRYwQnjixsM/lYGP8eKldO2ngwBr1OSi04lsRAAB1oXt36cILI6lw0qTCBQIel+imRFddFfkCRYhgAACQXr17S+efH7/23Xs+jwx8NDBunNSokXT11ZG4WKQIBgAA6Xb00dKVV0Zi4Zgx0RQoH8mCY8dKbdpIgwdLPXuqmBEMAADQq5f0+OPS1ltHop/v6GtSaeBAwkFAVZW0667Sk09Ke+6pYkfTIQAAzO2BH3pIuv9+acgQ6csvY6vfnQJ95u+kwyXHDvv3HTQ4CPBugKcXdu0qHXusdOCBRZksWJ168+cv/4CkqqpKFRUVqqysVMuWLetmZQAAJGXWLOn556Xhw6W33ooLvfsSOBjwZTMTFDgYcJDglsTbbBM7DNtvH10Gi0C21292BgAAWJKT/vbYIx4OBEaOlEaMkEaPXnh84N0CVwd4+qB3AxwUlCiCAQAAlsV3/ZtsEo8yVRqHGQAAoGAIBgAASDmCAQAAUo5gAACAlCMYAAAg5QgGAABIOYIBAABSjmAAAICUIxgAACDlCAYAAEg5ggEAAFKOYAAAgJTLalBRZsqxRyECAIDSkLluZ67jtQoGpk6d+tPb1VZbLR9rAwAAdcjX8YqKiqX+fr35ywsXJM2bN09jx45VixYtVK9evXyvEQAAFIAv8Q4EOnbsqPr169cuGAAAAOWLBEIAAFKOYAAAgJQjGAAAIOUIBgAASDmCAQAAUo5gAACAlCMYAABA6fb/APQbOIyKfmcuAAAAAElFTkSuQmCC",
      "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\n",
    "ee = NumPyMinimumEigensolver()\n",
    "result = ee.compute_minimum_eigenvalue(qubitOp)\n",
    "\n",
    "print(\"energy:\", result.eigenvalue.real)\n",
    "print(\"tsp objective:\", result.eigenvalue.real + offset)\n",
    "x = tsp.sample_most_likely(result.eigenstate)\n",
    "print(\"feasible:\", qubo.is_feasible(x))\n",
    "z = tsp.interpret(x)\n",
    "print(\"solution:\", z)\n",
    "print(\"solution objective:\", tsp.tsp_value(z, adj_matrix))\n",
    "draw_tsp_solution(tsp.graph, z, colors, pos)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8876177-f41a-4528-82f8-9d0252e34c6e",
   "metadata": {},
   "source": [
    "# Running it on quantum computer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "1557fe0d-73ca-4c5f-9c87-57b6f049c402",
   "metadata": {},
   "outputs": [],
   "source": [
    "algorithm_globals.random_seed = 123\n",
    "seed = 10598"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "2ff44b09-2e89-4323-a73d-0b3c70b9b086",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "energy: -7337.3740234375\n",
      "time: 131.1148111820221\n",
      "feasible: True\n",
      "solution: [0, 2, 1]\n",
      "solution objective: 202.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "optimizer = SPSA(maxiter=300)\n",
    "ry = TwoLocal(qubitOp.num_qubits, \"ry\", \"cz\", reps=5, entanglement=\"linear\")\n",
    "vqe = SamplingVQE(sampler=Sampler(backend = qr_backend), ansatz=ry, optimizer=optimizer)\n",
    "\n",
    "result = vqe.compute_minimum_eigenvalue(qubitOp)\n",
    "\n",
    "print(\"energy:\", result.eigenvalue.real)\n",
    "print(\"time:\", result.optimizer_time)\n",
    "x = tsp.sample_most_likely(result.eigenstate)\n",
    "print(\"feasible:\", qubo.is_feasible(x))\n",
    "z = tsp.interpret(x)\n",
    "print(\"solution:\", z)\n",
    "print(\"solution objective:\", tsp.tsp_value(z, adj_matrix))\n",
    "draw_tsp_solution(tsp.graph, z, colors, pos)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "eca980e7-2aa4-44d4-8007-fff607467548",
   "metadata": {},
   "outputs": [],
   "source": [
    "algorithm_globals.random_seed = 123\n",
    "seed = 10598"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "fa87c098-cffb-4da9-9868-31a92752ac43",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "objective function value: 202.0\n",
      "variable values: x_0_0=0.0, x_0_1=0.0, x_0_2=1.0, x_1_0=1.0, x_1_1=0.0, x_1_2=0.0, x_2_0=0.0, x_2_1=1.0, x_2_2=0.0\n",
      "status: SUCCESS\n",
      "solution: [0, 2, 1]\n",
      "solution objective: 202.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# create minimum eigen optimizer based on SamplingVQE\n",
    "vqe_optimizer = MinimumEigenOptimizer(vqe)\n",
    "\n",
    "# solve quadratic program\n",
    "result = vqe_optimizer.solve(qp)\n",
    "print(result.prettyprint())\n",
    "\n",
    "z = tsp.interpret(x)\n",
    "print(\"solution:\", z)\n",
    "print(\"solution objective:\", tsp.tsp_value(z, adj_matrix))\n",
    "draw_tsp_solution(tsp.graph, z, colors, pos)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "4d834a9c-0f0e-4e94-b6b2-c4af0f1e798f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<h3>Version Information</h3><table><tr><th>Software</th><th>Version</th></tr><tr><td><code>qiskit</code></td><td>2.2.1</td></tr><tr><td><code>qiskit_algorithms</code></td><td>0.4.0</td></tr><tr><td><code>qiskit_ibm_runtime</code></td><td>0.40.1</td></tr><tr><td><code>qiskit_optimization</code></td><td>0.7.0</td></tr><tr><td><code>qiskit_aer</code></td><td>0.17.1</td></tr><tr><th colspan='2'>System information</th></tr><tr><td>Python version</td><td>3.12.9</td></tr><tr><td>OS</td><td>Windows</td></tr><tr><td colspan='2'>Tue Oct 21 15:36:05 2025 Mountain Daylight Time</td></tr></table>"
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       "<h3>Quantum Rings Version Information</h3><table><tr><th>Software</th><th>Version</th></tr><tr><td><code>QuantumRingsLib</code></td><td>0.11.0</td></tr><tr><td><code>quantumrings-toolkit-qiskit</code></td><td>0.2.0</td></tr></table>"
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      "text/html": [
       "<div style='width: 100%; background-color:#d5d9e0;padding-left: 10px; padding-bottom: 10px; padding-right: 10px; padding-top: 5px'><h3>This code is a part of a Qiskit project</h3><p>&copy; Copyright IBM 2017, 2025.</p><p>This code is licensed under the Apache License, Version 2.0. You may<br>obtain a copy of this license in the LICENSE.txt file in the root directory<br> of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.<p>Any modifications or derivative works of this code must retain this<br>copyright notice, and modified files need to carry a notice indicating<br>that they have been altered from the originals.</p><p>Modifications (c) Copyright Quantum Rings Inc, 2025<br>Modified from the originals<br>Added support for Quantum Rings toolkit for Qiskit. </p></div>"
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   "source": [
    "import tutorial_magics\n",
    "\n",
    "%qiskit_version_table\n",
    "%quantumrings_version_table\n",
    "%qiskit_copyright"
   ]
  }
 ],
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