{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Train Variational Quantum Circuits by using evovaq and Qiskit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## 1) Training a Variational Quantum Classifier through a Memetic Algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "#### Importing modules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import log_loss\n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "from sklearn.metrics import accuracy_score\n",
    "from qiskit.circuit.library import ZZFeatureMap, RealAmplitudes\n",
    "from qiskit import Aer, execute\n",
    "from evovaq.problem import Problem\n",
    "from evovaq.GeneticAlgorithm import GA\n",
    "from evovaq.HillClimbing import HC\n",
    "from evovaq.MemeticAlgorithm import MA\n",
    "import evovaq.tools.operators as op\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "#### Uploading the classical data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "iris = load_iris()\n",
    "\n",
    "# For the sake of simplicity, we consider all the four features but only two classes\n",
    "iris_data = iris.data[:100, :4]\n",
    "iris_target = iris.target[:100]   # 0 or 1\n",
    "\n",
    "# Split into train and test subsets\n",
    "train_data, test_data, train_labels, test_labels = train_test_split(iris_data, iris_target, test_size=0.2,\n",
    "                                                                    random_state=42)\n",
    "\n",
    "# Pre-process data\n",
    "scaler = MinMaxScaler()\n",
    "scaler.fit(train_data)\n",
    "\n",
    "train_data = scaler.transform(train_data)\n",
    "test_data = scaler.transform(test_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "#### Building the Variational Quantum Classifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# Encode classical data in a quantum system through a FeatureMap\n",
    "dim = train_data.shape[1]\n",
    "feature_map = ZZFeatureMap(dim, reps=1, entanglement='linear')\n",
    "\n",
    "# Define an Ansatz to be trained\n",
    "ansatz = RealAmplitudes(num_qubits=dim, reps=1, entanglement='circular')\n",
    "\n",
    "# Put together our quantum classifier\n",
    "circuit = feature_map.compose(ansatz)\n",
    "\n",
    "# Measure all the qubits to retrieve label information\n",
    "circuit.measure_all()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "def get_label_prediction(circuit, features, params):\n",
    "    # Bind the parameters to our quantum classifier\n",
    "    bound_circuit = circuit.bind_parameters(np.concatenate((features,params)))\n",
    "    backend = Aer.get_backend('qasm_simulator')\n",
    "    counts = execute(bound_circuit, backend).result().get_counts()\n",
    "    \n",
    "    # Read the label by considering the parity mapping of the final quantum state\n",
    "    parity_1 = 0\n",
    "    for state, count in counts.items():\n",
    "        if state.count('1') % 2 == 1:\n",
    "            parity_1 += count\n",
    "    return parity_1 / sum(counts.values())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Defining the cost function to be minimized"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "def cost_function(params):\n",
    "    predictions = [get_label_prediction(circuit, features, params) for features in train_data]\n",
    "    return log_loss(train_labels, predictions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "#### Setting up the problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "problem = Problem(ansatz.num_parameters, ansatz.parameter_bounds, cost_function)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "#### Defining a Memetic Algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# Define the global search method\n",
    "global_search = GA(selection=op.sel_tournament, crossover=op.cx_uniform, mutation=op.mut_gaussian, sigma=0.2, mut_indpb=0.15,\n",
    "               cxpb=0.9, tournsize=5)\n",
    "\n",
    "# Create a neighbour of a possibile solution\n",
    "def get_neighbour(problem, current_solution):\n",
    "    neighbour = current_solution.copy()\n",
    "    index = np.random.randint(0, len(current_solution))\n",
    "    _min, _max = problem.param_bounds[0]\n",
    "    neighbour[index] = np.random.uniform(_min, _max)\n",
    "    return neighbour\n",
    "\n",
    "# Define the local search method\n",
    "local_search = HC(generate_neighbour=get_neighbour)\n",
    "\n",
    "# Compose the global and local search method for a Memetic Algorithm \n",
    "optimizer = MA(global_search=global_search.evolve_population, sel_for_refinement=op.sel_best, local_search=local_search.stochastic_var, frequency=0.1, intensity=10)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Training our VQC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Generations:   0%|                                      | 0/10 [00:00<?, ?gen/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "********** Execution #1 **********\n",
      "gen    nfev    min       max      mean      std\n",
      "-----  ------  --------  -------  --------  --------\n",
      "0      10      0.574194  1.01087  0.777387  0.118212\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Generations:  10%|███                           | 1/10 [00:07<01:09,  7.68s/gen]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "1      20      0.549579  0.824715  0.724881  0.0867576\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Generations:  20%|██████                        | 2/10 [00:14<00:58,  7.29s/gen]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "2      18      0.519661  0.737288  0.624565  0.076709\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Generations:  30%|█████████                     | 3/10 [00:22<00:52,  7.46s/gen]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "3      20      0.512227  0.603781  0.554474  0.0314989\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Generations:  40%|████████████                  | 4/10 [00:29<00:44,  7.39s/gen]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "4      19      0.506354  0.553874  0.527675  0.0165829\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Generations:  50%|███████████████               | 5/10 [00:36<00:36,  7.36s/gen]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "5      19      0.487778  0.514964  0.507114  0.00765964\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Generations:  60%|██████████████████            | 6/10 [00:44<00:29,  7.34s/gen]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "6      19      0.487778  0.510338  0.499565  0.00927926\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Generations:  70%|█████████████████████         | 7/10 [00:51<00:22,  7.45s/gen]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "7      20      0.485524  0.500729  0.491166  0.00411343\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Generations:  80%|████████████████████████      | 8/10 [00:58<00:14,  7.27s/gen]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "8      18      0.485524  0.506184  0.493225  0.00625882\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Generations:  90%|███████████████████████████   | 9/10 [01:06<00:07,  7.28s/gen]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "9      19      0.485524  0.494877  0.490388  0.00262625\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Generations: 100%|█████████████████████████████| 10/10 [01:13<00:00,  7.28s/gen]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "10     19      0.4826  0.507815  0.491194  0.0067016\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "  fun: 0.48260042185591684\n",
       "  gen: 10\n",
       "  log: {'gen': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], 'nfev': [10, 20, 18, 20, 19, 19, 19, 20, 18, 19, 19], 'min': [0.5741943431806411, 0.5495792409760082, 0.5196605664809661, 0.5122270310580073, 0.5063544128367315, 0.48777758944625205, 0.48777758944625205, 0.4855235783395476, 0.4855235783395476, 0.4855235783395476, 0.48260042185591684], 'max': [1.0108700876409014, 0.8247149305827991, 0.7372875746767409, 0.6037810463616139, 0.5538735167983232, 0.5149636544597807, 0.5103379175913295, 0.5007291786843474, 0.5061838813178279, 0.49487692318985294, 0.5078148595811571], 'mean': [0.7773865786237139, 0.7248805833709737, 0.624564804037709, 0.5544738494343432, 0.5276751585322951, 0.5071143411368311, 0.49956486395235433, 0.491165859240668, 0.4932252838704291, 0.49038829387334315, 0.49119421090738113], 'std': [0.11821196539990832, 0.08675763260140516, 0.07670898880389071, 0.03149892902008803, 0.016582930547904655, 0.0076596415234313035, 0.00927925771628771, 0.004113433790050419, 0.006258821291836501, 0.002626253612978286, 0.006701596001080847]}\n",
       " nfev: 201\n",
       "    x: array([ 0.95180689, -1.57259719, -1.70411141, -0.58746966, -2.9748859 ,\n",
       "        3.05920085,  1.45586664,  0.85704908])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res = optimizer.optimize(problem, 10, max_gen=10, verbose=True, seed=42)\n",
    "res"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Testing the optimal solution found"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "pycharm": {
     "is_executing": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy on the test subset: 0.9\n"
     ]
    }
   ],
   "source": [
    "test_predictions = [1 if get_label_prediction(circuit, features, res.x) > 0.5 else 0 for features in test_data]\n",
    "test_accuracy = accuracy_score(test_labels, test_predictions)\n",
    "print(\"Accuracy on the test subset:\", test_accuracy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2) QAOA trained by a Particle Swarm Optimization algorithm to solve MaxCut problem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "#### Importing modules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "import numpy as np\n",
    "from qiskit import execute, Aer\n",
    "from qiskit.visualization import plot_histogram\n",
    "from qiskit_optimization.applications import Maxcut\n",
    "from qiskit.circuit.library import QAOAAnsatz\n",
    "from evovaq.problem import Problem\n",
    "from evovaq.ParticleSwarmOptimization import PSO"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "#### Defining the graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_nodes = 5\n",
    "edges = [(0, 1), (0, 2), (0, 3), (0, 4)]\n",
    "\n",
    "G = nx.Graph()\n",
    "G.add_nodes_from(range(num_nodes))\n",
    "G.add_edges_from(edges)\n",
    "nx.draw(G, with_labels=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Mapping the MaxCut problem in a QAOA circuit ansatz"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 1 - Trasforming the MaxCut instance in a quadratic problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "pycharm": {
     "is_executing": true
    }
   },
   "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_0*x_4 + 4*x_0 + x_1 + x_2 + x_3 + x_4\n",
      "\n",
      "Subject to\n",
      "  No constraints\n",
      "\n",
      "  Binary variables (5)\n",
      "    x_0 x_1 x_2 x_3 x_4\n",
      "\n"
     ]
    }
   ],
   "source": [
    "maxcut_prob = Maxcut(G)\n",
    "maxcut_qp = maxcut_prob.to_quadratic_program()\n",
    "print(maxcut_qp.prettyprint())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 2 - Defining the Hamiltonian by mapping the QUBO problem in an Ising Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "pycharm": {
     "is_executing": true
    }
   },
   "outputs": [],
   "source": [
    "# MaxCut problem to Hamiltonian operator\n",
    "hamiltonian, offset = maxcut_qp.to_ising()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 3 - Building the QAOA circuit based on the MaxCut instance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2252.61x1120.39 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# QAOA ansatz circuit\n",
    "qaoa_circuit = QAOAAnsatz(hamiltonian, reps=2)\n",
    "qaoa_circuit.measure_all()\n",
    "qaoa_circuit.decompose(reps=3).draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "is_executing": true
    }
   },
   "source": [
    "#### Defining the cost function to be minimized"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "pycharm": {
     "is_executing": true
    }
   },
   "outputs": [],
   "source": [
    "def cost_function(params):\n",
    "    backend = Aer.get_backend('qasm_simulator')\n",
    "    # Bind the parameters to the QAOA circuit\n",
    "    bound_qaoa_circuit = qaoa_circuit.bind_parameters(params)\n",
    "    counts = execute(bound_qaoa_circuit, backend, shots=512).result().get_counts()\n",
    "    cost_value = 0\n",
    "    # Compute the cost value by using the maxcut objective function\n",
    "    for bitstring, count in counts.items():\n",
    "        cost_value -= count * maxcut_qp.objective.evaluate([int(bit) for bit in bitstring[::-1]])\n",
    "    return cost_value / sum(counts.values())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Setting up the problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "qaoa_problem = Problem(qaoa_circuit.num_parameters, (0, 2 * np.pi), cost_function)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Defining the Particle Swarm Optimization algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "optimizer = PSO(vmin=-0.1, vmax=0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Training the QAOA circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      "Fitness Evaluations:   0%|                            | 0/100 [00:00<?, ?nfev/s]\u001b[A\n",
      "Fitness Evaluations:  20%|███▌              | 20/100 [00:00<00:00, 111.69nfev/s]\u001b[A"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "********** Execution #1 **********\n",
      "gen    nfev    min       max       mean     std\n",
      "-----  ------  --------  --------  -------  --------\n",
      "0      10      -3.59961  -1.21289  -2.0998  0.795261\n",
      "\n",
      "1      10      -3.69336  -1.16016  -2.06133  0.827515\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      "Fitness Evaluations:  40%|███████▌           | 40/100 [00:00<00:00, 70.74nfev/s]\u001b[A"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "2      10      -3.52539  -1.10156  -2.01016  0.748684\n",
      "\n",
      "3      10      -3.37695  -1.16602  -1.99609  0.70882\n",
      "\n",
      "4      10      -3.39062  -0.621094  -1.93848  0.725515\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      "Fitness Evaluations:  50%|█████████▌         | 50/100 [00:00<00:00, 66.07nfev/s]\u001b[A\n",
      "Fitness Evaluations:  60%|███████████▍       | 60/100 [00:00<00:00, 63.26nfev/s]\u001b[A\n",
      "Fitness Evaluations:  70%|█████████████▎     | 70/100 [00:01<00:00, 61.28nfev/s]\u001b[A"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "5      10      -3.56641  -0.810547  -2.06152  0.680007\n",
      "\n",
      "6      10      -3.74805  -1.32617  -2.1293  0.685094\n",
      "\n",
      "7      10      -3.72266  -1.22656  -2.19453  0.671043\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      "Fitness Evaluations:  80%|███████████████▏   | 80/100 [00:01<00:00, 59.48nfev/s]\u001b[A\n",
      "Fitness Evaluations:  90%|█████████████████  | 90/100 [00:01<00:00, 58.61nfev/s]\u001b[A\n",
      "Fitness Evaluations: 100%|██████████████████| 100/100 [00:01<00:00, 62.75nfev/s]\u001b[A"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "8      10      -3.75391  -0.927734  -2.15273  0.712836\n",
      "\n",
      "9      10      -3.69922  -0.908203  -2.10605  0.733891\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "  fun: -3.75390625\n",
       "  gen: 10\n",
       "  log: {'gen': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 'nfev': [10, 10, 10, 10, 10, 10, 10, 10, 10, 10], 'min': [-3.599609375, -3.693359375, -3.525390625, -3.376953125, -3.390625, -3.56640625, -3.748046875, -3.72265625, -3.75390625, -3.69921875], 'max': [-1.212890625, -1.16015625, -1.1015625, -1.166015625, -0.62109375, -0.810546875, -1.326171875, -1.2265625, -0.927734375, -0.908203125], 'mean': [-2.0998046875, -2.061328125, -2.01015625, -1.99609375, -1.9384765625, -2.0615234375, -2.129296875, -2.19453125, -2.152734375, -2.1060546875], 'std': [0.7952608162924764, 0.827514976527285, 0.748683944616005, 0.7088197122833735, 0.7255149590956633, 0.6800069124207058, 0.6850942237816521, 0.6710433852244695, 0.712836470545829, 0.7338907406430878]}\n",
       " nfev: 100\n",
       "    x: array([2.78906277, 4.94085891, 1.31774472, 3.20100144])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res = optimizer.optimize(qaoa_problem, 10, max_nfev=100, seed=42)\n",
    "res"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Testing the optimal angles found"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "backend = Aer.get_backend('qasm_simulator')\n",
    "trained_qaoa_circuit = qaoa_circuit.bind_parameters(res.x)\n",
    "counts = execute(trained_qaoa_circuit, backend, shots=512).result().get_counts()\n",
    "plot_histogram(counts, title='Distribution of the final counts')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal solution:  [0 1 1 1 1]\n"
     ]
    }
   ],
   "source": [
    "bitstring = maxcut_prob.sample_most_likely(counts)\n",
    "print('Optimal solution: ', bitstring)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "maxcut_prob.draw(bitstring)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}