max_cut_v4.ipynb

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      "source": [
        "The code is best run as a notebook in the IBM Quantum Experince!\n",
        "\n",
        "Modifications and changes to the original IBM QISKit file are indicated with #VGG whenever approprate\n",
        "\n",
        "Needs fixing: the IBM QISKit version update Ising\n",
        "\n",
        "June 28 summary of changes:\n",
        "1.   modified the brute force to select the smallest free sample number\n",
        "2.   for DOcplex runn - added x[i]/n term to split the degenerate states due to 1<->0 symetry to favor less free samples\n",
        "3.   added  panelties for free samples \n",
        "\n",
        "\n",
        "\n"
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      },
      "source": [
        "# Qiskit Aqua: Experimenting with Max-Cut problem with VQE"
      ]
    },
    {
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        "## Introduction and background informatoin\n",
        "\n",
        "Many problems in quantitative **fields** such as finance and engineering are optimization problems. Optimization problems lie at the core of complex decision-making and definition of strategies. \n",
        "\n",
        "Optimization (or combinatorial optimization) means searching for an optimal solution in a finite or countably infinite set of potential solutions. Optimality is defined with respect to some criterion function, which is to be minimized or maximized. This is typically called cost function or objective function. \n",
        "\n",
        "**Typical optimization problems**\n",
        "\n",
        "Minimization: cost, distance, length of a traversal, weight, processing time, material, energy consumption, number of objects\n",
        "\n",
        "Maximization: profit, value, output, return, yield, utility, efficiency, capacity, number of objects \n",
        "\n",
        "We consider here max-cut problems of practical interest in many fields, and show how they can be nmapped on quantum computers.\n",
        "\n",
        "\n",
        "### Weighted Max-Cut\n",
        "\n",
        "Max-Cut is an NP-complete problem, with applications in clustering, network science, and statistical physics. To grasp how practical applications are mapped into given Max-Cut instances, consider a system of many people that can interact and influence each other. Individuals can be represented by vertices of a graph, and their interactions seen as pairwise connections between vertices of the graph, or edges. With this representation in mind, it is easy to model typical marketing problems. For example, suppose that it is assumed that individuals will influence each other's buying decisions, and knowledge is given about how strong they will influence each other. The influence can be modeled by weights assigned on each edge of the graph. It is possible then to predict the outcome of a marketing strategy in which products are offered for free to some individuals, and then ask which is the optimal subset of individuals that should get the free products, in order to maximize revenues.\n",
        "\n",
        "The formal definition of this problem is the following:\n",
        "\n",
        "Consider an $n$-node undirected graph *G = (V, E)* where *|V| = n* with edge weights $w_{ij}>0$, $w_{ij}=w_{ji}$, for $(i, j)\\in E$. A cut is defined as a partition of the original set V into two subsets. The cost function to be optimized is in this case the sum of weights of edges connecting points in the two different subsets, *crossing* the cut. By assigning $x_i=0$ or $x_i=1$ to each node $i$, one tries to maximize the global profit function (here and in the following summations run over indices 0,1,...n-1)\n",
        "\n",
        "$$\\tilde{C}(\\textbf{x}) = \\sum_{i,j} w_{ij} x_i (1-x_j).$$\n",
        "\n",
        "In our simple marketing model, $w_{ij}$ represents the probability that the person $j$ will buy a product after $i$ gets a free one. Note that the weights $w_{ij}$ can in principle be greater than $1$, corresponding to the case where the individual $j$ will buy more than one product. Maximizing the total buying probability corresponds to maximizing the total future revenues. In the case where the profit probability will be greater than the cost of the initial free samples, the strategy is a convenient one. An extension to this model has the nodes themselves carry weights, which can be regarded, in our marketing model, as the likelihood that a person granted with a free sample of the product will buy it again in the future. With this additional information in our model, the objective function to maximize becomes \n",
        "\n",
        "$$C(\\textbf{x}) = \\sum_{i,j} w_{ij} x_i (1-x_j)+\\sum_i w_i x_i. $$\n",
        " \n",
        "In order to find a solution to this problem on a quantum computer, one needs first to map it to an Ising Hamiltonian. This can be done with the assignment $x_i\\rightarrow (1-Z_i)/2$, where $Z_i$ is the Pauli Z operator that has eigenvalues $\\pm 1$. Doing this we find that \n",
        "\n",
        "$$C(\\textbf{Z}) = \\sum_{i,j} \\frac{w_{ij}}{4} (1-Z_i)(1+Z_j) + \\sum_i \\frac{w_i}{2} (1-Z_i) = -\\frac{1}{2}\\left( \\sum_{i<j} w_{ij} Z_i Z_j +\\sum_i w_i Z_i\\right)+\\mathrm{const},$$\n",
        "\n",
        "where const = $\\sum_{i<j}w_{ij}/2+\\sum_i w_i/2 $. In other terms, the weighted Max-Cut problem is equivalent to minimizing the Ising Hamiltonian \n",
        "\n",
        "$$ H = \\sum_i w_i Z_i + \\sum_{i<j} w_{ij} Z_iZ_j.$$\n",
        "\n",
        "Aqua can generate the Ising Hamiltonian for the first profit function $\\tilde{C}$.\n",
        "\n",
        "\n",
        "### Approximate Universal Quantum Computing for Optimization Problems\n",
        "\n",
        "There has been a considerable amount of interest in recent times about the use of quantum computers to find a solution to combinatorial problems. It is important to say that, given the classical nature of combinatorial problems, exponential speedup in using quantum computers compared to the best classical algorithms is not guaranteed. However, due to the nature and importance of the target problems, it is worth investigating heuristic approaches on a quantum computer that could indeed speed up some problem instances. Here we demonstrate an approach that is based on the Quantum Approximate Optimization Algorithm by Farhi, Goldstone, and Gutman (2014). We frame the algorithm in the context of *approximate quantum computing*, given its heuristic nature. \n",
        "\n",
        "The Algorithm works as follows:\n",
        "1. Choose the $w_i$ and $w_{ij}$ in the target Ising problem. In principle, even higher powers of Z are allowed.\n",
        "2. Choose the depth of the quantum circuit $m$. Note that the depth can be modified adaptively.\n",
        "3. Choose a set of controls $\\theta$ and make a trial function $|\\psi(\\boldsymbol\\theta)\\rangle$, built using a quantum circuit made of C-Phase gates and single-qubit Y rotations, parameterized by the components of $\\boldsymbol\\theta$. \n",
        "4. Evaluate $C(\\boldsymbol\\theta) = \\langle\\psi(\\boldsymbol\\theta)~|H|~\\psi(\\boldsymbol\\theta)\\rangle = \\sum_i w_i \\langle\\psi(\\boldsymbol\\theta)~|Z_i|~\\psi(\\boldsymbol\\theta)\\rangle+ \\sum_{i<j} w_{ij} \\langle\\psi(\\boldsymbol\\theta)~|Z_iZ_j|~\\psi(\\boldsymbol\\theta)\\rangle$ by sampling the outcome of the circuit in the Z-basis and adding the expectation values of the individual Ising terms together. In general, different control points around $\\boldsymbol\\theta$ have to be estimated, depending on the classical optimizer chosen. \n",
        "5. Use a classical optimizer to choose a new set of controls.\n",
        "6. Continue until $C(\\boldsymbol\\theta)$ reaches a minimum, close enough to the solution $\\boldsymbol\\theta^*$.\n",
        "7. Use the last $\\boldsymbol\\theta$ to generate a final set of samples from the distribution $|\\langle z_i~|\\psi(\\boldsymbol\\theta)\\rangle|^2\\;\\forall i$ to obtain the answer.\n",
        "    \n",
        "It is our belief the difficulty of finding good heuristic algorithms will come down to the choice of an appropriate trial wavefunction. For example, one could consider a trial function whose entanglement best aligns with the target problem, or simply make the amount of entanglement a variable. In this tutorial, we will consider a simple trial function of the form\n",
        "\n",
        "$$|\\psi(\\theta)\\rangle  = [U_\\mathrm{single}(\\boldsymbol\\theta) U_\\mathrm{entangler}]^m |+\\rangle$$\n",
        "\n",
        "where $U_\\mathrm{entangler}$ is a collection of C-Phase gates (fully entangling gates), and $U_\\mathrm{single}(\\theta) = \\prod_{i=1}^n Y(\\theta_{i})$, where $n$ is the number of qubits and $m$ is the depth of the quantum circuit. The motivation for this choice is that for these classical problems this choice allows us to search over the space of quantum states that have only real coefficients, still exploiting the entanglement to potentially converge faster to the solution.\n",
        "\n",
        "One advantage of using this sampling method compared to adiabatic approaches is that the target Ising Hamiltonian does not have to be implemented directly on hardware, allowing this algorithm not to be limited to the connectivity of the device. Furthermore, higher-order terms in the cost function, such as $Z_iZ_jZ_k$, can also be sampled efficiently, whereas in adiabatic or annealing approaches they are generally impractical to deal with. \n",
        "\n",
        "\n",
        "References:\n",
        "- A. Lucas, Frontiers in Physics 2, 5 (2014)\n",
        "- E. Farhi, J. Goldstone, S. Gutmann e-print arXiv 1411.4028 (2014)\n",
        "- D. Wecker, M. B. Hastings, M. Troyer Phys. Rev. A 94, 022309 (2016)\n",
        "- E. Farhi, J. Goldstone, S. Gutmann, H. Neven e-print arXiv 1703.06199 (2017)"
      ]
    },
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      "cell_type": "markdown",
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        "id": "Rw2lBQvK6XZS",
        "colab_type": "text"
      },
      "source": [
        "#Main Code Cells "
      ]
    },
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      "cell_type": "markdown",
      "metadata": {
        "id": "kxbANBKN4-I5",
        "colab_type": "text"
      },
      "source": [
        "## Import libraries\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dPKtKtBOLpr3",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#%pip uninstall qiskit"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GsfRwjclGyHn",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "%pip install qiskit #==0.16"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BYV9mVvpJKIX",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 547
        },
        "outputId": "449e3956-3a5c-44cb-8897-97ed945029c7"
      },
      "source": [
        "import qiskit.tools.jupyter\n",
        "%qiskit_version_table\n",
        "%qiskit_copyright"
      ],
      "execution_count": 7,
      "outputs": [
        {
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          "data": {
            "text/html": [
              "<h3>Version Information</h3><table><tr><th>Qiskit Software</th><th>Version</th></tr><tr><td>Qiskit</td><td>0.19.6</td></tr><tr><td>Terra</td><td>0.14.2</td></tr><tr><td>Aer</td><td>0.5.2</td></tr><tr><td>Ignis</td><td>0.3.3</td></tr><tr><td>Aqua</td><td>0.7.3</td></tr><tr><td>IBM Q Provider</td><td>0.7.2</td></tr><tr><th>System information</th></tr><tr><td>Python</td><td>3.6.9 (default, Apr 18 2020, 01:56:04) \n",
              "[GCC 8.4.0]</td></tr><tr><td>OS</td><td>Linux</td></tr><tr><td>CPUs</td><td>1</td></tr><tr><td>Memory (Gb)</td><td>12.715869903564453</td></tr><tr><td colspan='2'>Wed Jul 01 02:28:29 2020 UTC</td></tr></table>"
            ],
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              "<IPython.core.display.HTML object>"
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              "<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 Qiskit</h3><p>&copy; Copyright IBM 2017, 2020.</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></div>"
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              "<IPython.core.display.HTML object>"
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          "metadata": {
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    {
      "cell_type": "code",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2019-12-12T17:59:38.109248Z",
          "start_time": "2019-12-12T17:59:38.098188Z"
        },
        "colab_type": "code",
        "id": "NYl6i6iKgJAA",
        "papermill": {
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      "source": [
        "# useful additional packages \n",
        "import matplotlib.pyplot as plt\n",
        "import matplotlib.axes as axes\n",
        "%matplotlib inline\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",
        "\n",
        "#VGG todo 1: the equivalent run_algorithm and EnergyInput versions updates\n",
        "#from qiskit.aqua.translators.ising import max_cut, tsp\n",
        "#from qiskit.aqua import run_algorithm\n",
        "#from qiskit.aqua.input import EnergyInput\n",
        "\n",
        "#old v0.16# from qiskit.optimization.ising import max_cut, tsp\n",
        "#old v0.16# from qiskit.optimization.ising.common import sample_most_likely\n",
        "#older# from qiskit.optimization.ising import docplex\n",
        "\n",
        "from qiskit.optimization.applications.ising import max_cut, tsp \n",
        "from qiskit.optimization.applications.ising.common import sample_most_likely\n",
        "from qiskit.optimization.applications.ising import docplex\n",
        "\n",
        "from qiskit.aqua.algorithms import VQE \n",
        "from qiskit.aqua.algorithms import NumPyEigensolver as ExactEigensolver  \n",
        "from qiskit.aqua.components.optimizers import SPSA\n",
        "#from qiskit.aqua.components.variational_forms import  RY #RealAmplitudes\n",
        "from qiskit.circuit.library import RealAmplitudes as RY\n",
        "from qiskit.aqua import QuantumInstance\n",
        "\n",
        "# setup aqua logging\n",
        "import logging\n",
        "from qiskit.aqua import set_qiskit_aqua_logging\n",
        "# set_qiskit_aqua_logging(logging.DEBUG)  # choose INFO, DEBUG to see the log"
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "4GqrhgSDgJAF",
        "papermill": {
          "duration": 0.265952,
          "end_time": "2020-03-12T03:56:22.589262",
          "exception": false,
          "start_time": "2020-03-12T03:56:22.323310",
          "status": "completed"
        },
        "tags": []
      },
      "source": [
        "## Setup token to run the experiment on a real device\n",
        "If you would like to run the experiment on a real device, you need to setup your account first.\n",
        "\n",
        "Note: If you do not store your token yet, use `IBMQ.save_account('MY_API_TOKEN')` to store it first."
      ]
    },
    {
      "cell_type": "code",
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        "ExecuteTime": {
          "end_time": "2019-12-12T17:59:38.838143Z",
          "start_time": "2019-12-12T17:59:38.836008Z"
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        "colab_type": "code",
        "id": "1a-_dBFBgJAH",
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          "end_time": "2020-03-12T03:56:26.244473",
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          "status": "completed"
        },
        "tags": [],
        "trusted": false,
        "colab": {}
      },
      "source": [
        "#from qiskit import IBMQ\n",
        "#provider = IBMQ.load_account()"
      ],
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "gBmv-6VbgJAL",
        "papermill": {
          "duration": 0.082241,
          "end_time": "2020-03-12T03:56:26.441082",
          "exception": false,
          "start_time": "2020-03-12T03:56:26.358841",
          "status": "completed"
        },
        "tags": [],
        "trusted": false,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "be3ebbcd-cdcb-4b28-e791-35b7e77c68f3"
      },
      "source": [
        "#VGG select the backend for coupling_map\n",
        "try: \n",
        "    backend = provider.get_backend('ibmq_16_melbourne')#'ibmq_16_melbourne')#'ibmq_essex')\n",
        "    #backend = provider.get_backend('ibmq_london')#'ibmq_16_melbourne')#'ibmq_essex')\n",
        "except:\n",
        "    backend = Aer.get_backend('qasm_simulator') #VGG it was 'BasicAer.get_backend' ibmq_16_melbourne\n",
        "    \n",
        "coupling_map = backend.configuration().coupling_map\n",
        "print(coupling_map)"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "None\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "UE1ETuhkgJAS",
        "papermill": {
          "duration": 0.072025,
          "end_time": "2020-03-12T03:56:26.587093",
          "exception": false,
          "start_time": "2020-03-12T03:56:26.515068",
          "status": "completed"
        },
        "tags": []
      },
      "source": [
        "# Stting up the code for the Max-Cut problem"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "85GE9gMBgJAT",
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        "tags": []
      },
      "source": [
        "### Generate Random Weighted Graph\n",
        "\n",
        "Given a list of edges, we generate a graph with random edge weights in the range \\[-1,1)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "onhnlv97gJAV",
        "papermill": {
          "duration": 0.082505,
          "end_time": "2020-03-12T03:56:26.930504",
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          "status": "completed"
        },
        "tags": [],
        "trusted": false,
        "colab": {}
      },
      "source": [
        "from typing import List, Tuple\n",
        "\n",
        "seed = 19120623\n",
        "np.random.seed(seed)\n",
        "\n",
        "#VGG: function adopted from the Rigetti's MaxCutQAOA.ipynb\n",
        "def generate_ising_graph(edges: List[Tuple[int, int]]) -> nx.Graph:\n",
        "    graph = nx.from_edgelist(edges)\n",
        "    weights:  np.ndarray =  np.random.rand(graph.number_of_edges()) #VGG the old [-1,1] range into [0,1]\n",
        "    weights /= np.linalg.norm(weights)\n",
        "    nx.set_edge_attributes(graph, {e: {'weight': w} for e, w in zip(graph.edges, weights)})\n",
        "    return graph"
      ],
      "execution_count": 11,
      "outputs": []
    },
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          "end_time": "2020-03-12T03:56:27.171022",
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          "start_time": "2020-03-12T03:56:27.004585",
          "status": "completed"
        },
        "tags": [],
        "trusted": false,
        "colab": {}
      },
      "source": [
        "if coupling_map != None:\n",
        "    G=generate_ising_graph(coupling_map)\n",
        "    n=G.number_of_nodes()\n",
        "    print(n)"
      ],
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2019-12-12T17:59:40.984512Z",
          "start_time": "2019-12-12T17:59:40.783157Z"
        },
        "colab_type": "code",
        "id": "zRStKm5jgJAh",
        "papermill": {
          "duration": 0.088352,
          "end_time": "2020-03-12T03:56:27.340782",
          "exception": false,
          "start_time": "2020-03-12T03:56:27.252430",
          "status": "completed"
        },
        "tags": [],
        "trusted": false,
        "colab": {}
      },
      "source": [
        "# Generating a graph if there were no coupling_map\n",
        "if coupling_map== None:\n",
        "    #define the edges / coupling_map\n",
        "    \n",
        "    #'ibmq_16_melbourne'\n",
        "    elist=[[0, 1], [0, 14], [1, 0], [1, 2], [1, 13], [2, 1], [2, 3], [2, 12], \n",
        "           [3, 2], [3, 4], [3, 11], [4, 3], [4, 5], [4, 10], [5, 4], [5, 6], \n",
        "           [5, 9], [6, 5], [6, 8], [7, 8], [8, 6], [8, 7], [8, 9], [9, 5], [9, 8], \n",
        "           [9, 10], [10, 4], [10, 9], [10, 11], [11, 3], [11, 10], [11, 12], [12, 2], \n",
        "           [12, 11], [12, 13], [13, 1], [13, 12], [13, 14], [14, 0], [14, 13]]\n",
        "   \n",
        "    \n",
        "    #elist=[[0,1],[0,2],[0,3],[1,2],[2,3],[0,4],[0,2], [4, 3],[1,5],[3,5]]\n",
        "    elist=[[0,1],[0,2],[0,3],[1,2],[2,3],[0,4],[0,2], [4, 3]]\n",
        "\n",
        "    G=generate_ising_graph(elist)\n",
        "    n=G.number_of_nodes()\n",
        "    \n",
        "#other ways to define the graph   \n",
        "    #n=5 # Number of nodes in graph\n",
        "    #G=nx.Graph()\n",
        "    #G.add_nodes_from(np.arange(0,n,1))\n",
        "    \n",
        "    #ewlist=[(0,1,1.),(0,2,.5),(0,3,0),(1,2,1.0),(0,3,1.0)]\n",
        "    #G1 = nx.from_edgelist(elist)\n",
        "    #G1.add_weighted_edges_from(ewlist)\n",
        "    \n",
        "    \n"
      ],
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "P-nfLK1ijEBX",
        "papermill": {
          "duration": 0.077867,
          "end_time": "2020-03-12T03:56:27.493563",
          "exception": false,
          "start_time": "2020-03-12T03:56:27.415696",
          "status": "completed"
        },
        "tags": []
      },
      "source": [
        "## Visulaize the Graph"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2019-12-12T17:59:40.984512Z",
          "start_time": "2019-12-12T17:59:40.783157Z"
        },
        "colab_type": "code",
        "id": "2-oriBdagJAk",
        "papermill": {
          "duration": 0.371556,
          "end_time": "2020-03-12T03:56:27.939545",
          "exception": false,
          "start_time": "2020-03-12T03:56:27.567989",
          "status": "completed"
        },
        "tags": [],
        "trusted": false,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "a706254b-ffc6-4463-96d8-e46c4077e5de"
      },
      "source": [
        "#Visulaize\n",
        "print(G.number_of_nodes(),G.number_of_edges())\n",
        "colors = ['r' for node in G.nodes()]\n",
        "pos = nx.spring_layout(G)\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)"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "5 7\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "VW3-NLq1gJAo",
        "papermill": {
          "duration": 0.272728,
          "end_time": "2020-03-12T03:56:28.313753",
          "exception": false,
          "start_time": "2020-03-12T03:56:28.041025",
          "status": "completed"
        },
        "tags": [],
        "trusted": false,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 319
        },
        "outputId": "f693db8e-cf1f-4f0c-e23a-94839bcd79db"
      },
      "source": [
        "nx.drawing.nx_pylab.draw(G)"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "3TPpoF6EgJAs",
        "papermill": {
          "duration": 0.088287,
          "end_time": "2020-03-12T03:56:28.514560",
          "exception": false,
          "start_time": "2020-03-12T03:56:28.426273",
          "status": "completed"
        },
        "tags": []
      },
      "source": [
        "##  Pepare for potential export of the graph's weights and edges\n",
        "G1 = nx.from_edgelist(elist);\n",
        "G1.add_weighted_edges_from(ewlist)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "br2VZc3SgJAt",
        "papermill": {
          "duration": 0.090566,
          "end_time": "2020-03-12T03:56:28.686420",
          "exception": false,
          "start_time": "2020-03-12T03:56:28.595854",
          "status": "completed"
        },
        "tags": [],
        "trusted": false,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "5737f13e-9849-4751-ae7b-aeff6a4bbfcc"
      },
      "source": [
        "elist=G.edges()\n",
        "print(\"elist=\",elist)"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "elist= [(0, 1), (0, 2), (0, 3), (0, 4), (1, 2), (2, 3), (3, 4)]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "YhhxZwW8gJA0",
        "papermill": {
          "duration": 0.092148,
          "end_time": "2020-03-12T03:56:28.862483",
          "exception": false,
          "start_time": "2020-03-12T03:56:28.770335",
          "status": "completed"
        },
        "tags": [],
        "trusted": false,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        },
        "outputId": "8b87cbe2-cdbe-44e2-d6da-15eada987556"
      },
      "source": [
        "ewlist=[(i,j,G.get_edge_data(i,j,default=0)['weight']) for i,j in G.edges()]\n",
        "print('ewlist=',ewlist)"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "ewlist= [(0, 1, 0.4489017820186629), (0, 2, 0.4615199431843579), (0, 3, 0.1261709331508631), (0, 4, 0.5054405671626448), (1, 2, 0.31275948656545793), (2, 3, 0.43912102962703636), (3, 4, 0.15313877934841572)]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IR61NU-_b1BD",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def issymmetric(Matrix):\n",
        "  dim=Matrix.shape[0]\n",
        "  if Matrix.shape[1] != dim:\n",
        "    print(\"Shape Error!\")\n",
        "    return False \n",
        "  for i in range(dim):\n",
        "    for j in range(i,dim):\n",
        "      if Matrix[i,j]!=Matrix[j,i]:\n",
        "        print(\"Shape Error:\",(i,j),Matrix[i,j],Matrix[j,i],\"difference:\",Matrix[i,j]-Matrix[j,i])\n",
        "        return False\n",
        "  return True\n",
        "  "
      ],
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2019-12-12T17:59:41.709471Z",
          "start_time": "2019-12-12T17:59:41.702848Z"
        },
        "colab_type": "code",
        "id": "wr6lQmHHgJA3",
        "papermill": {
          "duration": 0.095289,
          "end_time": "2020-03-12T03:56:29.038232",
          "exception": false,
          "start_time": "2020-03-12T03:56:28.942943",
          "status": "completed"
        },
        "tags": [],
        "trusted": false,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 136
        },
        "outputId": "286edb3a-f394-48bd-c8b2-998b80e7de44"
      },
      "source": [
        "# Computing the weight matrix from the random graph\n",
        "w = np.zeros([n,n])\n",
        "w = np.eye(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",
        "\n",
        "w/=np.linalg.det(w)**(1/n)\n",
        "print(\"Symmetric:\",issymmetric(w),\"Norm:\",np.linalg.norm(w))\n",
        "print(\"Eignvlues:\",np.linalg.eigvals(w),\"det:\",np.linalg.det(w))\n",
        "print(w)"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Symmetric: True Norm: 3.4017238241954932\n",
            "Eignvlues: [2.6475469  0.29188844 0.63645966 1.46395822 1.38880054] det: 1.0000000000000009\n",
            "[[1.28573075 0.57716683 0.59339038 0.16222185 0.64986048]\n",
            " [0.57716683 1.28573075 0.40212449 0.         0.        ]\n",
            " [0.59339038 0.40212449 1.28573075 0.56459141 0.        ]\n",
            " [0.16222185 0.         0.56459141 1.28573075 0.19689524]\n",
            " [0.64986048 0.         0.         0.19689524 1.28573075]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GeuV7JWWCwVL",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "63b8adeb-d18f-4262-efc0-3379fdb0b5ee"
      },
      "source": [
        "np.sum(w)/4 #the offset value"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "3.180288780364632"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "UQSv6WsUgJA7",
        "papermill": {
          "duration": 0.083057,
          "end_time": "2020-03-12T03:56:29.205519",
          "exception": false,
          "start_time": "2020-03-12T03:56:29.122462",
          "status": "completed"
        },
        "tags": []
      },
      "source": [
        "## Brute force approach to Max-Cut\n",
        "\n",
        "Try all possible $2^n$ combinations. For $n = 4$, as in this example, one deals with only 16 combinations, but for n = 1000, one has 1.071509e+30 combinations, which is impractical to deal with by using a brute force approach. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2019-12-12T17:59:42.618252Z",
          "start_time": "2019-12-12T17:59:42.418721Z"
        },
        "colab_type": "code",
        "id": "d_WTR1_OgJA8",
        "papermill": {
          "duration": 9.947705,
          "end_time": "2020-03-12T03:56:39.236869",
          "exception": false,
          "start_time": "2020-03-12T03:56:29.289164",
          "status": "completed"
        },
        "tags": [],
        "trusted": false,
        "colab": {}
      },
      "source": [
        "def Max_Cut_BF(W,*x0):\n",
        "  best_cost_brute = 0\n",
        "  xbest_brute=np.array([1]*n)\n",
        "\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 h in x0: \n",
        "        cost -= np.dot(h,x)/n #VGG don't give free samples to those with h==1\n",
        "      for i in range(n):\n",
        "          cost +=(2-np.dot(x,x))/n/2 #VGG try to favor fewer free samples \n",
        "          for j in range(n):\n",
        "              cost += W[i,j]*x[i]*(1-x[j])\n",
        "      \n",
        "              if np.isclose(cost,best_cost_brute):\n",
        "                if sum(x)<sum(xbest_brute):\n",
        "                  best_cost_brute = cost\n",
        "                  xbest_brute = x\n",
        "              else:\n",
        "                if best_cost_brute < cost:\n",
        "                  best_cost_brute = cost\n",
        "                  xbest_brute = x\n",
        "      if 1==2:\n",
        "          print('case = ' + str(x)+ ' cost = ' + str(cost))\n",
        "  return best_cost_brute, xbest_brute\n",
        "   "
      ],
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "H_fYHJU4HjiD",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 316
        },
        "outputId": "47628a4d-d46b-49ec-b789-b97539a7fee9"
      },
      "source": [
        "%%time \n",
        "if n < 10: \n",
        "  best_cost_brute, xbest_brute = Max_Cut_BF(w)\n",
        "\n",
        "  colors = ['r' if xbest_brute[i] == 0 else 'b' for i in range(n)]\n",
        "  nx.draw_networkx(G, node_color=colors, node_size=600, alpha=.8, pos=pos)\n",
        "  print('\\nBest solution = ' + str(xbest_brute) + ' cost = ' + str(best_cost_brute)) "
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\n",
            "Best solution = [1, 0, 0, 1, 0] cost = 2.581904340539446\n",
            "CPU times: user 48.5 ms, sys: 2.83 ms, total: 51.3 ms\n",
            "Wall time: 48.1 ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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lZDQaWbduHSEhIQQEBLBz5066d+8ugSsqZODAgRw5coTExEStSxE1RELXSoqi8NVXXzFw4EASExOJjY1lzJgx1K9fX+vSRB1Wr149RowYwapVq7QuRdQQaS9YISkpiaioKNLS0pg+fTpdunTRuiRhQ/r378/mzZv57bffuOuuu7QuR1QzGemWIScnhyVLljB69Gi6devG1q1bJXBFlXNycuKFF16Q0a6dkNAtgcViYffu3QwYMID8/Hx27NjB4MGDcXCQNwaievTr14+kpCSOHDmidSmimkmK3OTIkSMsWrQIR0dHli9fzp133ql1ScIOODk58eKLLxITE0N0dLTW5YhqJKH7p8uXL/POO+/w008/MX78eHr27CkzEkSN6tOnDxs2bCAhIYFOnTppXY6oJnbfXjAajWzatInBgwfj6+vLzp07eeaZZyRwRY1zcHBg1KhRxMTEoCiK1uWIamK3oasoCt9++y3BwcEcPnyYjRs3Mm7cOFxcXLQuTdixZ555hrS0NH788UetSxHVxC7bC2fOnGHx4sVcuHCBV199la5du2pdkhAAGAwGRo8eTUxMDJ07d5Z3XDbIrka6ubm5LF++nBdeeIEuXboQFxcngStqne7du3P16lUOHDigdSmiGthF6FosFj766CMGDBhAVlYW8fHxDB06FEdHR61LE+Jv9Hr9tdGu9HZtj823F3777TcWLlyITqdj8eLFcsWPqBOefPJJ1q1bx7fffku3bt20LkdUIZsN3StXrrBy5UoOHDjASy+9RK9evWSLc1Fn6PV6IiIiiImJ4ZFHHpHnrg2xuf/JoqIiYmNjCQoKwtPTk127dtGnTx950oo657HHHkOv1/PVV19pXYqoQjY10t2/fz+LFy/mtttuY/369TRv3lzrkoSoMJ1Ox5gxY1ixYgWPP/64DBxshE2E7rlz51i6dCmnTp1i8uTJPPLIIzLVRtiEhx9+mLVr17J37166d++udTmiCtTpX515eXmsXLmSESNG0KFDB7Zv386jjz4qgStsRvFod9WqVVgsFq3LEVWgToauoijs2bOHgQMHkpqaSlxcHMOHD8fJyUnr0oSocg888ACenp58+umnWpciqkCday/8/vvvLFq0iKKiIhYsWED79u21LkmIalU82p03bx49evSQXabruCoN3aws+P13OH8eiorA2RkCA+GOO6CySxpkZGQQHR3N119/zbhx4+jbt6+cWBB24/7778fPz4+PP/6Yfv36aV2OqIRKh25uLvznP7BmDZw6BY6OYDaDxQJ6PRgMagB37AgREfDEE+ptrGUymdixYwfr1q2jV69e7Nq1i4YNG1a2bCHqnDFjxjBz5kyeeeYZuZqyDqtw6CoKfPIJ/POfavA6OoKHB5R0DktR4JdfYNw48PGBFSvgvvtu/TMOHjxIVFQUjRs3ZvXq1bRs2bKi5QpR53Xs2JGAgAA++ugj+vfvr3U5ooIqFLoFBTB5Mnz2GdSrp4ZtWXQ6cHNTv75yBYKDYdQoePVVdTR8s+TkZJYuXUpiYiKTJ0/msccekxkJQqCOdl977TX69Olz7cRxUZH6LjMrS32teXqqbT1p/dZO5Q7dggIYMQIOHlTDtrxtVVdXtf2wejVkZsL8+X8dIz8/n40bN7Jjxw6GDh3K/PnzZUaCENe5++67adOmDdu2/QdHx/5s2QLHj6uvoeLXkcWivru8804IC4Nnnqn8ORVRdcodutOmwY8/qr9NKzr4NBjA3R22b4fmzSEiQuGLL75g+fLldOzYkbi4OHx8fCp2cCFsmMkEHh5TGTeuCD8/C46Oeho2/Pvgx2yGxET19Tpzpvp5yJDyD5JE1dOVtXTc/fffr/z000/X/rxvn9oWcHevmv+8oiLIzjbSpcscDIYkpkyZIntDCVGKc+dgzBg4dgyysy/QsGE9GjXyuuX9jEb1vMu990J0tHpeRVQvnU53SFGU+0v6ntUjXaMRpk5Vp4FVReCazSauXLlMerqZs2fH8N//NpUpYEKUIikJgoLUlpyHB7i4eHHmzFk8PDxv+bpxclJPdP/f/8Hzz8OOHdC0aQ0VLv7G6pTbt09t1Fe+N6SQkZHOyZNJgI42bZqQltaMEyckcIUoSWYmhIRAdvZfM4ScnevRoIELGRnpVh1Dp1Pvm5oKoaGQl1fNRYtSWZ1069dbd7sLF2bwxx89SEzsxsmT/cnM3H3te3l5uSQlJZGdnUPz5gH4+fnh4GDAYoFt28pduxB24c03IS3trxlAxRo39ubKlXQsFrPVx3J3V9sUb79dxUUKq1nVXjCZ1Lcmrq63vm3jxuE4Os5Ar3eisPA0Z86MxmBoQXa2F/n5+fj6+v55ccNfZ+Hq1YNvvqnoQxDCdu3fDx9/rIblzZydnWnQoAHp6Rk0btzY6mO6ucHWrTBgAMhV9DXPqpFuUpL69sSalquzc0v0enWal6IoFBUVce7cIZycnGnVqhUNG7pxfeCq94HTp6GwsLzlC2Hb3n237Neet3dj0tOvlGu0azCoU8rWrKmiIkW5WDXSTUkp3/SwlJQFpKV9QFFRLo6OrQkI6Iuzszsmk+naRQ7qZx06nfq1waAjJUUhIEAnF0IIgdoGOHgQyrrq3cnJGVfXhly+fIaiomiuXv0eBwcPvL1fwt29Z6n3a9gQPv1UvVjJ69YTIEQVsrq9UB5+ftPIyOiLxXIUvf4Ely5dAbIABUXhzx1O1a+LP5vN9enbdzxOTskYDIYbPvR6PQ4ODte+NhgMODg4XPu6rI+6cF9rbiszO+zPjz+qn2/1X+/t3Zhjx8bj4eFBmzafU1BwnHPnJlCvXhucnUu+dN5gUD9+/hmeeqqKCxdlsip069cv/4Hbtr2DS5c8uXLlAC4uB2jaNLzM22dlwRdf/BtvbwsWiwWz2XzDh8ViwWQyXfvabDZjMplKvG1V3regoECTn3v9fc1m9a1jbfklUZvua8u/jA4dUi9yuBWDwYyi/IiDw1r0ehdcXDrSsOFjZGV9jI/P+FLvV1iorokioVuzrArdVq3U0a6iWN9m0OsNNGnSFKOxARkZiSjKBfz8fDEY/v4jTSZ1LqGPD+h0+msvRPGX4qCuqeC/1W2NRmOt+KWotqbq7i+Nsu7744/NAWcKCxWub8UVf138ubDwFI6OzmRnN8DHx4TB4ICz8+3k5SWU+ZxydITffqv+5664kVXJ5u2tzlwoKlLDsTQmUzp5eT/h6voIOl09cnN/ID//S/z955Gf78DJk0n4+fni5nbjybSCAvUsqrRyS2fro7qKuj6YtQr+4vuaTKZrv4yq4ucePTqBnBxvMjMLr2vF3diWAwWT6RiFhXp0ujwuXkyhWbPb0OtdsVhyy/y3UwO72v+LxE2sCl2dDnr3hri4skMXdGRk7OTixUjAgqNjE3x9X8HN7XHc3MDNzY2LF5PJysqmSRM/HBzUNUHNZpB1mUVFFP8yssX1ZQcOVEeiDRqUfbvLl3M4fz4ff39/cnJyuHz5Mnp9Lnp92XdUlIq1DkXlWP0ePixMXaCmrBaDg4MnzZuvLvUY9evXp0WLFqSlXSEpKQkfHx9cXT0wGHQSukLcpF07SEgoPXQtFjMpKSnk5dXH2dmBhg3z8PDw59Sp0+j1R3B1LXv9aZMJ7rqrGgoXZbL6/WrbtvDII+oJr8rQ6fR4e3vTvHlzMjMzSUq6zLPPZvztahsh7F2nTqWviVtQkE9S0il0Oj0tW96Ju/tTXL4cg05XhLd3BtnZX+Ho+HiZx3dygnvuqfq6RdnK1SRcsEC9kKGgoPI/2Nm5Hl5egTRtCj/8EMLmzZuvnaUXQkCXLurnG3deV7hyJY2zZ8/h6+tDkyZN0Ov1+PlNw2Ip5Pjxp0lNnUXTpq9z+bIzhYUlv1jNf26pde+91f4wxE3KFbp+frBoEeTnq6uOVUZennomdscOH7ZsWceBAwcYMWIEx48fr9yBhbARTZtC167qQjcAJlMRZ8+e5erVq7Ro0eLPqztVBoMb/v6LueOO77j99o/x8XkOPz9fzp07h8lU9LdjZ2er52k8PWvq0Yhi5T4d3qsXREaqoVmRlYoURf0PVxTYsEF9e3PbbbcRHR3NwIEDGTt2LP/6178wVjbVhbAB48YVv2ZySEo6hYuLC82bN7fqxKGbmzuenp6cO3fuhsuEzWb1gotRo6qzclGaCs1BCg6GjRvVZR4zMqy/Ys1oVJepCwiA99+Hhx7663s6nY5nn32Wbdu2cfLkSYYMGcKRI0cqUp4QNqNjRyP+/j9w4UIOzZo1o3Fjb25eu6QsXl5e1KtXnwsXLgDqhgU5OfDCC+qJOlHzKjzx85FH1DV2hwxRe7yZmeoI1miE4s0oFEWdB5iZ+dcJuEmTYM8edf+mknh7e7No0aJrG/BFRUWRJ4t/CjuUlJTE8OHDuffePdxzjw9FRRVZzFqHn58figIpKSlkZiq0aKG+DoU2yrVdT2mys+E//1FD+PBhuHxZffuiKHDbbdCxo7o53lNPqSfirJWVlcWSJUv4+eefef3113nwwQetv7MQdZSiKHzwwQdER0czfvx4+vXrx/nzOgYNUl9bxQuZl4fZbOaPPy7TrBl8842fbNlTzcrarqdKQvdmRUXqh7Nz1WwDvX//fiIjI+ncuTOTJk3684o2IWxPdnY28+bN4/z580RGRhIYGHjteykp8NJL6iI1Li7WD2AKCtST35065ZORMZxp00bzlCy4UK3KCt1qua7U0VF9UlRF4AJ07dqV+Ph46tevT1BQEPv27auaAwtRiyQkJBASEoKfnx8bN268IXBBnT0UHw+zZql/zspS+7MlnVMxmdR3oFlZ4OCg7hQRH1+f6Oh5LFiwQM6XaKhaRrrV6fDhw8yZM4dWrVrx2muvlWvFfCFqI7PZzJo1a/jggw9488036dq16y3vU1AAn38OW7bAkSPqjITiQY7ZrF740KEDDB0K//jHjZfv79+/n9mzZ7N27Vr8/f2r6VHZtxpvL1Q3o9HI2rVr+eCDDxg/fjx9+/aVhc9FnZScnMz06dNxcXFh9uzZeFVgRXGLBZKT1VFt8QaUTZqU3fd9//33iY2NZf369Xh4eFTiEYiS2FzoFjt+/DizZ8/G3d2d6dOn01T2lRZ1yOeff86iRYsYPnw4oaGhNb6K3MqVK0lISCAmJgansleyEuVU4z3dmtKmTRs2b97MAw88wLBhw9i2bRuWG6+ZFKLWycvLY86cOcTExLBixQqGDh2qybKdY8eOxc/PjzfffFNeNzWoTocuqLspDB8+nA0bNrBv3z5GjhxJUlKS1mUJUaJjx44xdOhQAGJjY7mztAnrNUCv1zNr1ixSU1N59913NavD3tT50C0WEBDAqlWr6N27N6NHj2bt2rUUFf39mnMhtGCxWNiyZQvjx49nzJgxzJw5ExeXilzsULWcnJxYvHgxX375Je+//77W5dgFmwldUH9zDxw4kC1btvDLL78wbNgwjh49qnVZws6lp6czYcIE9u7dy6ZNm+jevbvWJd3Aw8OD5cuXExMTw/79+7Uux+bZVOgW8/X1ZdmyZYwYMYKJEyeyfPlyCqpiPUohymn//v2EhoZy5513smbNmlp7stff35+oqChmzpwpK/1VM5sMXVAX0OnZsyfbt2/n0qVLDB48mEOHDmldlrATRqORJUuWMG/ePObPn8/YsWNr/War7du3Z9q0aUycOJHU1FSty7FZNhu6xTw9PYmMjGTy5MnMmDGDyMhIrl69qnVZwoadOXOG8PBwkpOT2bZtG/fdd5/WJVntqaeeIiQkhAkTJpCbW/bGlqJibD50i3Xr1o34+HgAgoKC+OabbzSuSNgaRVH48MMPGTlyJP3792fRokW4u7trXVa5DR06lA4dOjB16lRM1q7bKqxWpy+OqKhDhw4xd+5c2rVrx5QpU2jUqJHWJYk6Licnh8jISE6dOkVkZCQtW5a9KWRtZzabmTx5Mt7e3rzxxhtyxWc52ezFERV13333ERcXh5+fH4MHD+aTTz6hrF8+QpTl8OHDhIaG4unpyaZNm+p84II6//2tt97i999/Z+PGjVqXY1PscqR7vaNHjzJnzhx8fX15/fXX8fX11bokUUdYLBbWrVvHjh07mD59Ot26ddO6pFAhyPQAABVhSURBVCp3+fJlwsPDGT9+PD169NC6nDpDRrplaNeuHe+99x7t27dnyJAh7Ny5Uy6JFLeUkpJCREQECQkJxMbG2mTggrqTy7Jly4iKiuLnn3/WuhybYPehC+Do6MjIkSNZvXo1H3/8MREREZw9e1brskQttW/fPsLCwnj44Yd599138bHxbRhat27NvHnzmDp1KmfOnNG6nDpPQvc6LVu2ZN26dfzjH/8gPDycTZs2YTabb31HYRcKCgqYP38+y5cvZ+nSpYwYMUKThWq08MADD/DSSy/x8ssvk56ernU5dZp9PGPKQa/XM3jwYN577z0OHjzI8OHD5QodwfHjxxk2bBiFhYVs3bqVu+66S+uSaly/fv3o2bMnkydPprCwUOty6iwJ3VI0bdqUlStXEhwczLhx44iOjsZoNGpdlqhhiqIQFxfH2LFjCQ8PZ86cOTRo0EDrsjQzZswYmjVrxowZM+TcRwVJ6JZBp9PRt29f4uLiOH36NCEhIRw+fFjrskQNycjIYNKkSezZs4cNGzbQq1cvrUvSnE6nY+bMmWRmZrJixQqty6mTJHSt4OXlxcKFCxk3bhxTp05l4cKF5OXlaV2WqEY//PADoaGhtGrVinXr1sleYtdxcnIiKiqKb7/99tpVnsJ6Errl8OSTTxIfH09BQQHBwcEcOHBA65JEFSsqKmLFihXMnj2b2bNnM378eBwdHbUuq9Zxc3NjxYoVrF+/nm+//VbrcuoUu784oqK+//57IiMjuffee5k8eXKdvMZe3OjcuXO88cYbeHl5MXPmTDw9PbUuqdb79ddfmThxIu+8846mu2DUNnJxRDV48MEHiYuLw83NjeDgYPbu3SuXEtdRiqLw8ccfEx4eTp8+fViyZIkErpXuvvtu3njjDSZPnszFixe1LqdOkJFuFThy5Ahz586lefPmTJ06FW9vb61LElbKzc3lrbfeIjExkcjISG6//XatS6qTtm7dyu7du1m3bh0NGzbUuhzNyUi3mrVv354tW7bQunVrQkND+fDDD2XUWwf88ssvhIaG4uLiwnvvvSeBWwkhISF07tyZ1157TfYmvAUZ6VaxP/74gzlz5uDq6sr06dO57bbbtC5J3MRisbBx40bi4uKYNm0aTz75pNYl2QSLxcKUKVNwd3dn5syZdr0cpIx0a9Dtt9/Oxo0b6dq1K2FhYWzdulUmkdciqampjB07lu+//5733ntPArcK6fV65s+fz4kTJ1i3bp3W5dRaErrVwGAwMGzYMDZu3MhXX33FCy+8wMmTJ7Uuy+59/fXXDB06lM6dOxMTEyPLeFaD+vXrs2zZMj788EP27NmjdTm1Uu3eKa+O8/f3JyYmht27dxMREUFQUBDh4eEy77OGFRYWsmzZMv773/8SFRVF+/bttS7Jpnl5ebF8+XIiIiLw9fWtU3vE1QQZ6VYzvV5P//792bp1K7///jtDhw7lt99+07osu3Hy5EnCwsLIyspiy5YtErg1pGXLlkRGRvLPf/6TU6dOaV1OrSKhW0N8fHxYsmQJI0eOZNKkSSxdupSCggKty7JZiqKwY8cOIiIiGDJkCPPnz5epTDWsc+fOTJgwgQkTJshykNeR0K1BOp2O7t27Ex8fT3p6OsHBwfz4449al2VzsrKymDJlCh9++CHr16+nX79+dn0mXUu9e/emT58+TJw4kfz8fK3LqRUkdDXg4eHB3LlzefXVV5k1axbz5s0jJydH67Jswk8//URISAj+/v6sX7+egIAArUuye6NGjaJFixZMnz5dZvIgoaupRx55hPj4eBwcHAgODubrr7/WuqQ6y2QyER0dzfTp05kxYwYTJ07EyclJ67IE6ju86dOnk5uby9KlS7UuR3NycUQtkZCQwLx582jbti2vvvoqjRo10rqkOuPChQu88cYbuLm5MWvWLPm3q6VycnIYOXIkzz//PCEhIVqXU63k4og6oFOnTmzbto2mTZsyePBg9uzZI5cSW+HTTz9l+PDhdO/enWXLlkng1mINGzZk2bJlbN682a7f1clItxb6/fffmTt3Lo0bN+b111/Hz89P65Jqnby8PN5++21++eUX3nrrLdq2bat1ScJKR48e5eWXX2bFihW0a9dO63KqhYx065g777yTzZs307FjR4YOHUp8fLycgLjO0aNHGTJkCAaDgdjYWAncOqZdu3bMnDmTyZMnk5ycrHU5NU5GurXc6dOnmTNnDnq9nhkzZtC8eXOtS9KMxWIhNjaW9957j9dee42nn35a65JEJcTHxxMfH8/69etxc3PTupwqJSPdOiwwMJC1a9fSvXt3XnjhBTZs2IDJZNK6rBqXlpbG+PHj+eqrr9i0aZMErg0ICgqia9euvPrqq3a107aEbh2g1+sJCgoiNjaWhIQEwsLCSExM1LqsGvPdd98xZMgQ2rdvz5o1a2jatKnWJYkqMnHiRNzc3Jg3b57dnDiW9kIdoygKe/bsYfny5fTr149Ro0bh7OysdVnVwmg0smLFCr788kvmzp1Lp06dtC5JVIOCggIiIiLo2rUrERERWpdTJaS9YEN0Oh29e/cmLi6O8+fPExISws8//6x1WVXu1KlTjBgxgtTUVLZt2yaBa8Pq1avH0qVL+fjjj/noo4+0Lqf6KYpS6sd9992niNpt3759Ss+ePZUFCxYoV69e1bqcSrNYLMr777+vPPnkk8quXbsUi8WidUmihpw6dUp5+umnlR9++EHrUioN+EkpJVdlpFvHPfHEE2zfvh2j0UhwcDD79+/XuqQKy87OZurUqcTHx7NmzRr69+8vC9XYkcDAQBYsWMAbb7xh04v+S+jaADc3N2bMmMHMmTNZsGABM2fOJDMzU+uyyuXnn38mNDQUHx8fNm3aRMuWLbUuSWigU6dOvPLKK0ycOJG0tDSty6kWEro2pEuXLmzfvh0PDw+Cg4P5/PPPa/0ZYbPZzKpVq5g6dSpTp05lypQpslCNnevZsyfPP/88EydOJC8vT+tyqpzMXrBRv/zyC3PnzqVZs2ZMmzYNHx8frUv6m4sXLzJ9+nScnZ2ZM2cOjRs31rokUUsoisLcuXNJT09n8eLFGAwGrUsqF5m9YIfuueceYmNjueOOOwgNDeWDDz6o/KjXaIRTpyAxEZKSoBI7X+zdu5ewsDAee+wxVq5cKYErbqDT6Xj99dcxGo1ERUXV+nds5SEjXTtw4sQJ5syZg4uLC9OnT6dZs2bW3zk5GbZtg88+U4PWYACdDhQFTCZo3hyeegpCQqBFi1seLj8/n6ioKA4dOkRkZKTNLngiqsbVq1cZOXIk/fr1Y8iQIVqXYzUZ6dq51q1bs3HjRh599FGGDx9ObGzsrRfQSUuDceOgWzeIjobz58HNDRo2BFdX9bO7O1y6BOvWwdNPw4gRcOFCqYdMTExk6NChmEwmtm7dKoErbsnV1ZXly5ezZcsW9u3bp3U5VUJGunbm/PnzzJ8/n9zcXGbOnEnr1q3/fqPPPoNXX4W8PDVo9Vb8blYUyMoCR0eYOxcGDrzuWwrbtm1j/fr1TJkyhZ49e1bhIxL2IDExkZdeeoklS5Zwzz33aF3OLclIV1zTrFkzoqOj6d+/P2PGjGHVqlU3LjayZQuMHQsWC3h4WBe4oLYcPDzAwQGmToUVKwBIT09nwoQJfPbZZ2zatEkCV1RI27ZtmTVrFlOmTOH8+fNal1MpMtK1Y6mpqSxYsIDz588zY8YM7klOVgPX1VUdsVaUyQQ5OfwRFsb4Awfo27cvERERODg4VF3xwi7t2rWLLVu2sGHDBtzd3bUup1RljXQldO2coijs3buXNZGRvHvsGF6enuhdXCp1TIuicCU5mcLsbK5s3UqHZ5+tomqFgBUrVnDkyBGio6Nr7ZxuaS+IUul0Op5++mnea9kSfWEhJ5OTyc3NrfDxCo1GTp8+TYHFQhNfXzrExlZhtULASy+9hJeXF7NmzaqTO6pI6Aq4cAHnr7/GKzCQJn5+JF+8SPLFi5jNZqsPoQCZWVmcPn0aDw8Pmvn7Y/D0hP/7Pzh6tPpqF3ZHr9czZ84cUlJSiImJ0bqccpPQFRAXp84+0OtxdXWlZcuW6HU6TiYlkZ2Tc+1mRouFOcnJ9Dlxgm6JiYQmJbH/6lXMFgsXLlzgypUrNG/enEaenuhAPblmscCmTZo9NGGbnJ2dWbx4MZ9//jm7d+/WupxykTMbQp0iVq/etT8a9Hr8/Pxwc3Mj+eJFsrOy8PPzw6zX4+foyOqAAPwcHfnv1au8du4cCwwGWrm50aJFC/Q3rwrWoAHs3VvDD0jYA09PT1asWMGLL76In58fDz74oNYlWUVGuvbOaFSvNCth9wkXFxdatmyJk5MTSUlJFObkMMrbm6ZOTuh0Ou4oLMTdaCTT3Z0mfn5/D1xQZ0FkZsKVKzXwYIS9CQgIYOHChcyYMYPjx49rXY5VJHTt3fnz6qW9pczH1et0+Pj4EBAQQHp6OufOniUvP58zZ86QnJNDupMTd3t4lH58nQ6cnNQ1G4SoBh07duTVV19l0qRJpKamal3OLUno2juj0aoLIOrVq0eLwEBcGjTg7NmzZOfmEpWXx2MGAw2ys8nMzORqbi6FRiOWkqYh2tFur6Lmde/enaCgoDqxHKT0dO2dk5N6Es0KOp2Oxl5eeHh68vq5c7iazbzi6YliMpGXl0eRyURRURFFRUXo9XocHR1xdHDARVH4/rPPcLx6FV9fX/z8/GjcuHGdW65P1G5hYWFcuHCBadOmsXTp0lr7/JLQtXdNm0JRkRq8VmyNoygK81NSyAJWBAbiXMIoWQHMJpMawkYjuuxsLhgMJO3bx6VLl0hJSSEjIwMvL69rIVz8UfxnX19f3N3dZbseYTWdTsfUqVOZNGkSb7/9Nv/85z9r5fNHrkgT8Pjj6qpi181gKE3kxYscLywkOiAAF2vWZSgO9MOHbwh1k8lEamrqtRAu6XNhYeENQVxSMNezomZhX/Ly8njxxRfp2bMnYWFhmtRQ1hVpMtIV6nq4GzbcMnQvFhXxfmYmTjodPf7449rfv+7nxzOlXQefmwvPPPO3UbSDgwNNmzaladOmpf68vLy8ayFcHMQJCQk3BHP9+vXLDGVvb+9a+zZTVA8XFxeWLVtGeHg4TZo04emnn9a6pBvISFeoU8a6d1fXx63Kt2OKAtnZsH07dOpUdce9dniFjIyMMkfL6enpNGrUqNRQ9vPzkzaGjTp+/Djjxo0jKiqKDh061OjPlgVvxK2FhcH+/eryjFUlOxtatoRPPqnaMC8Hk8nE5cuXbxgtl9TGKGu07OvrS/369TWpX1TOgQMHePPNN1m7di0BAQE19nMldMWtnTun7v7g5KR+VJbJpC6Cvns31PIdIq5vY5T2uV69emWOlqWNUXt98MEHbN68mfXr1+Pp6VkjP1NCV1hn+3b45z/V3SIqs/atxaLuIjFxIowfX3X1aURRFDIzM28IYWlj1C3vvvsuhw4d4l//+hfOJVx9WdUkdIX1li1Td31wda3YiPfPBcwZPBjmzdOsrVDTrm9jlDZavrmNcXMoSxuj+lgsFqZPn47FYiEyMhL9zTNv0tPh22/h0CF1ZbycHPVKzdtugwceUM9JdOli9U4qErrCeooCsbEwf74aoNaeXFMU9YkK6uh23Djrt/qxE+VtY5QU0NLGqDij0cjYsWNp3749L7/8svqXx4/DypXw6afqc9hsVmfxFD93jUb1deDgAI0awahRMHRoiWuVXE9CV5TfqVPwyivwyy9qu8DVVX3i3RzARUXqtDCdDlq1giVLan0Pt7YqqY1x8+eb2xgljZY9PDykjVGKrKwswsPDGRocTP/Ll9V3dWaz2lK71S+z/HwoKICAAFi+HNq3L/WmErqiYhQFfvsNNm6E//1fdTbC9S0Hkwnq14dHH4XwcLjvPrtpJ2ilvG2Mkj77+vriUsktmeqy84mJnHjsMR4wGKjfuHH59wPMzlY/L1wIzz1X4k0kdEXVuHwZTp9W33I5OoK/P/j5SdDWMsVtjNJCubQ2xs0XldjkRqKFhRAWRuH+/ZzJzCSgefOKXdVoNKrv8JYvhz59/vZtCV0hxDXlbWOUNmquk22MBQtgzRrw8CD76lUupaQQGBiIY0V2vy4sVN/tffaZ2nK4joSuEKJcitsYZY2WCwoKyhwt17o2xpEjMGCAupvJn6P4K+npZGZmEhgYiKEiJ34zM6FDB9ix44YTx7L2ghCiXBwcHGjSpAlNmjQp9TYltTEOHz7M559//rc2Rmmj5RptYyxYoJ6nuO7nNWrUCKPRyPnz5wnw9y//yN3dXV3Maf9+eOQRq+4ioSuEqBAXFxdatGhBixYtSvx+cRvj5lFyYmLi39oYN4dxlbcxTp+GgwfVWQrX0QF+fn6cO3eOiykpfOvszH+ysjhRWEgPNzdmlbEgk3qAP+tau1ZCVwihLZ1Oh6enJ56entxxxx0l3qakNsaZM2c4ePDg39oYZc3IuGUb47PP1KmPJbQQdMBtt93GmTNncDKZGNm4MQeuXqXQysX9cXOD775T56k3bHjLm0voCiE0Y00bIz8//2+j5SNHjlwL5eI2Rlmh7Pff/6Ivo41h0Ovx9/fHfPo0PorCUYOBVJPJugeh16sti2PHoHPnWz9m644qhBDaqF+/PoGBgQQGBpb4/dLaGMePH78Wyou//hpnvR5devq1baQcHR1xcHS89mcHBwf8/f05e+YMhS4u5buisqgIEhMldIUQts+aNobSti0mJyeKzOZre/kZjUZyc3Ov/dliseDo6IjeYCA9PR29l5f1RZjN6iJPVpDQFULYPJ1Op45uy1gzwWKxXAtgjytXyCnPyTtr+7/IFuxCCHvQqJF6IUMZ9Ho9zk5OuDZoQP3yXqXm5ATe3lbdVEJXCGH7OnRQF6u5BbOiYLRYsAAWwGixYLZmFGswQCmtjZtJ6AohbF/XruqUsVtYl5ZG18RENl65wp6sLLomJrIuLa3sO5nN6rHbtLGqFOnpCiFsX8+eMGeOGpBlLOE42tub0Va2Ca7JzlZXG7OyJSEjXSGE7fP2hh49/lqWsapYLOpVacOHW30XCV0hhH147TV1SVKjseqOmZ0NzzxT5oLmN5PQFULYh4AAeOMNdR1cK/q7t5Sbq172O3t2ue4moSuEsB9DhkD//uqSjJUJ3uItqtavV6ejlYOErhDCfuj18PbbEBKiXkGWn1+++ysKZGSobYrYWLj33nKXUOYi5jqd7jJwptxHFUII+9ZcUZQSp0GUGbpCCCGqlrQXhBCiBknoCiFEDZLQFUKIGiShK4QQNUhCVwghatD/A/sD4bt5I72fAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YAyvKB2ifErV",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        },
        "outputId": "9b4612c7-3a9c-4697-d6a6-bb03d64fd694"
      },
      "source": [
        "np.set_printoptions(precision=3)\n",
        "print(w)"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[1.286 0.577 0.593 0.162 0.65 ]\n",
            " [0.577 1.286 0.402 0.    0.   ]\n",
            " [0.593 0.402 1.286 0.565 0.   ]\n",
            " [0.162 0.    0.565 1.286 0.197]\n",
            " [0.65  0.    0.    0.197 1.286]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "s3h5cNojIqNZ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def market_simulations(m,*opt):\n",
        "\n",
        "  free_samples=0\n",
        "  boughten=0\n",
        "  Mw2 = np.zeros([n,n])+w\n",
        "  relations=np.zeros([n,n])\n",
        "  x_free_samples=np.zeros(n)\n",
        "  np.set_printoptions(precision=2)\n",
        "\n",
        "  if 'q' in opt: \n",
        "    print(\"Using Max_Cut option:\",'q')\n",
        "    print(\"submiting for results using:\",backend)\n",
        "  elif 'dcplx' in opt:\n",
        "    print(\"Using Max_Cut option:\",'Docplex')\n",
        "  else:\n",
        "    print(\"Using Max_Cut_BF\")\n",
        "    if n > 10 : \n",
        "      print(\"It may take too long to do Brute Force Calulations - skiping!\")\n",
        "      return\n",
        "            \n",
        "  print(\"day\",\" [free samples]\",\" [buyers distribution]\",\" [to be used as constrain]\",\" the two totals\",\" w-det\")\n",
        "  for i in range(m):\n",
        "    \n",
        "    if sum(x_free_samples)>n/3:\n",
        "      x_free_samples=np.zeros(n)\n",
        "      x=np.array([0]*n)\n",
        "      xbest_brute=np.array([0]*n)\n",
        "      tmp1=Mw2/np.linalg.norm(Mw2) #select only those rows that recived free samples\n",
        "      tmp=sum(tmp1[:,]) #sum probaility contributions  \n",
        "      tmp2=tmp\n",
        "\n",
        "    else:\n",
        "      \n",
        "      if 'q' in opt:\n",
        "        best_cost_brute, xbest_brute = Max_Cut_IBMQ(Mw2,x_free_samples)\n",
        "      elif 'dcplx' in opt:\n",
        "        best_cost_brute, xbest_brute = Max_Cut_Dcplx(Mw2,x_free_samples)\n",
        "      else:\n",
        "        best_cost_brute, xbest_brute = Max_Cut_BF(Mw2,x_free_samples)\n",
        "      \n",
        "      x=np.array(xbest_brute)\n",
        "      x_free_samples+=x\n",
        "      free_samples+=sum(x)\n",
        "      tmp1=Mw2[x==1]/np.linalg.norm(Mw2) #select only those rows that recived free samples\n",
        "      tmp=sum(tmp1[:,],(np.array([1]*n)-x)) #sum probaility contributions  \n",
        "      tmp-=np.array([1]*n) #push to negative those with free samples \n",
        "    \n",
        "    #print(tmp)\n",
        "    ab=sum(tmp[tmp > 0])\n",
        "\n",
        "    for j in range(n):\n",
        "      test=np.random.uniform()*ab/2\n",
        "      if tmp[j] > test: #buy the product\n",
        "        x[j]+=1\n",
        "        boughten+=1\n",
        "    \n",
        "    x0=np.array(xbest_brute)\n",
        "    x-=x0\n",
        "    relation_today=x.reshape(n,1) @ x0.reshape(1,n)\n",
        "    relation_today+=relation_today.T\n",
        "    relations+=relation_today\n",
        "    \n",
        "    #print(x0,x,\"\\n\",relation_today)\n",
        "    #print(x0,x,x_free_samples,tmp)\n",
        "    print(i,x0,x,x_free_samples,free_samples, boughten,np.linalg.det(Mw2))\n",
        "\n",
        "    if i%7==0 : #weekely updates of the w matrix \n",
        "      Mw2+=(np.eye(n)+relations)/n/100 #update the w matrix\n",
        "      relations=np.zeros([n,n])\n",
        "\n",
        "      if issymmetric(Mw2) and np.linalg.det(Mw2)>0.:\n",
        "        Mw2/=np.linalg.det(Mw2)**(1/n)\n",
        "      else:\n",
        "        Mw2/=np.linalg.norm(Mw2,ord='fro')\n",
        "\n",
        "  \n",
        "  print(\"\\nlast day configuration record:\\n\")\n",
        "  print(x0,tmp)\n",
        "  print()\n",
        "  print(x,free_samples, boughten, np.linalg.norm(Mw2),np.linalg.det(Mw2))\n",
        "  print()\n",
        "  print(Mw2)\n",
        "  return"
      ],
      "execution_count": 24,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AUCo-7IBDKPa",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 459
        },
        "outputId": "646d2f56-ba64-4499-9967-4dccea8654f4"
      },
      "source": [
        "%time market_simulations(10)"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Using Max_Cut_BF\n",
            "day  [free samples]  [buyers distribution]  [to be used as constrain]  the two totals  w-det\n",
            "0 [1 0 0 1 0] [0 1 1 0 1] [1. 0. 0. 1. 0.] 2 3 1.0000000000000009\n",
            "1 [0 0 0 0 0] [0 0 0 1 0] [0. 0. 0. 0. 0.] 2 4 0.9999999999999993\n",
            "2 [1 0 0 1 0] [0 1 1 0 0] [1. 0. 0. 1. 0.] 4 6 0.9999999999999993\n",
            "3 [0 0 0 0 0] [1 0 0 0 0] [0. 0. 0. 0. 0.] 4 7 0.9999999999999993\n",
            "4 [1 0 0 1 0] [0 1 1 0 0] [1. 0. 0. 1. 0.] 6 9 0.9999999999999993\n",
            "5 [0 0 0 0 0] [1 0 1 1 0] [0. 0. 0. 0. 0.] 6 12 0.9999999999999993\n",
            "6 [1 0 0 1 0] [0 0 1 0 0] [1. 0. 0. 1. 0.] 8 13 0.9999999999999993\n",
            "7 [0 0 0 0 0] [0 0 0 0 0] [0. 0. 0. 0. 0.] 8 13 0.9999999999999993\n",
            "8 [1 0 0 1 0] [0 0 1 0 1] [1. 0. 0. 1. 0.] 10 15 0.9999999999999991\n",
            "9 [0 0 0 0 0] [0 0 1 0 1] [0. 0. 0. 0. 0.] 10 17 0.9999999999999991\n",
            "\n",
            "last day configuration record:\n",
            "\n",
            "[0 0 0 0 0] [0.96 0.67 0.84 0.65 0.63]\n",
            "\n",
            "[0 0 1 0 1] 10 17 3.4227662096524827 0.9999999999999991\n",
            "\n",
            "[[1.29 0.58 0.6  0.16 0.65]\n",
            " [0.58 1.29 0.4  0.01 0.  ]\n",
            " [0.6  0.4  1.29 0.57 0.  ]\n",
            " [0.16 0.01 0.57 1.29 0.2 ]\n",
            " [0.65 0.   0.   0.2  1.29]]\n",
            "CPU times: user 181 ms, sys: 5.37 ms, total: 186 ms\n",
            "Wall time: 173 ms\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "XCr6nHa3gJBA",
        "papermill": {
          "duration": 0.084768,
          "end_time": "2020-03-12T03:56:39.412098",
          "exception": false,
          "start_time": "2020-03-12T03:56:39.327330",
          "status": "completed"
        },
        "tags": []
      },
      "source": [
        "## Mapping to the Ising problem"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2019-12-12T17:59:42.814360Z",
          "start_time": "2019-12-12T17:59:42.806413Z"
        },
        "colab_type": "code",
        "id": "g3CpUQmSgJBD",
        "papermill": {
          "duration": 0.10715,
          "end_time": "2020-03-12T03:56:39.603949",
          "exception": false,
          "start_time": "2020-03-12T03:56:39.496799",
          "status": "completed"
        },
        "tags": [],
        "trusted": false,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "b06fef3e-6bdb-4c55-be77-c5af73c8d6c7"
      },
      "source": [
        "#VGG qubitOp, offset = max_cut.get_max_cut_qubitops(w)\n",
        "qubitOp, offset = max_cut.get_operator(w)\n",
        "#algo_input = EnergyInput(qubitOp)\n",
        "offset"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "-1.5731253396959037"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "Di-nT72LgJBH",
        "papermill": {
          "duration": 0.086005,
          "end_time": "2020-03-12T03:56:39.790755",
          "exception": false,
          "start_time": "2020-03-12T03:56:39.704750",
          "status": "completed"
        },
        "tags": []
      },
      "source": [
        "### Checking that the full Hamiltonian gives the right cost "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2019-12-12T17:59:47.642069Z",
          "start_time": "2019-12-12T17:59:47.435702Z"
        },
        "colab_type": "code",
        "id": "sQT4-VAygJBH",
        "papermill": {
          "duration": 0.541471,
          "end_time": "2020-03-12T03:56:40.422029",
          "exception": false,
          "start_time": "2020-03-12T03:56:39.880558",
          "status": "completed"
        },
        "tags": [],
        "trusted": false,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 333
        },
        "outputId": "054caa7f-8067-48b9-f41c-3fb7df992b87"
      },
      "source": [
        "#Making the Hamiltonian in its full form and getting the lowest eigenvalue and eigenvector\n",
        "ee = ExactEigensolver(qubitOp, k=3)\n",
        "result = ee.run()\n",
        "\n",
        "print(\"energys:\",result['eigenvalues'].real)\n",
        "\n",
        "#VGG# x = max_cut.sample_most_likely(result['eigvecs'][0])\n",
        "x = sample_most_likely(result['eigenstates'][0]) \n",
        "\n",
        "print('energy:', result['eigenvalues'][0],', offset:',offset)\n",
        "print('max-cut objective:', result['eigenvalues'][0] + offset)\n",
        "print('solution:', max_cut.get_graph_solution(x))\n",
        "print('solution objective:', max_cut.max_cut_value(x, w))\n",
        "\n",
        "colors = ['r' if max_cut.get_graph_solution(x)[i] == 0 else 'b' for i in range(n)]\n",
        "nx.draw_networkx(G, node_color=colors, node_size=600, alpha = .8, pos=pos)\n",
        "\n",
        "#VGG note that the other runs had implemeneted soft constrains!"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "energys: [-1.01 -1.01 -0.83]\n",
            "energy: (-1.0087790008435424+0j) , offset: -1.5731253396959037\n",
            "max-cut objective: (-2.581904340539446+0j)\n",
            "solution: [1 0 0 1 0]\n",
            "solution objective: 2.581904340539446\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "Nk1VcD6VgJBL",
        "papermill": {
          "duration": 0.096524,
          "end_time": "2020-03-12T03:56:40.610762",
          "exception": false,
          "start_time": "2020-03-12T03:56:40.514238",
          "status": "completed"
        },
        "tags": []
      },
      "source": [
        "### [Optional] Using DOcplex for mapping to the Ising problem\n",
        "Using ```docplex.get_qubitops``` is a different way to create an Ising Hamiltonian of Max-Cut. ```docplex.get_qubitops``` can create a corresponding Ising Hamiltonian from an optimization model of Max-Cut. An example of using ```docplex.get_qubitops``` is as below. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2019-12-12T17:59:43.518965Z",
          "start_time": "2019-12-12T17:59:43.130559Z"
        },
        "colab_type": "code",
        "id": "Ee_79O6EgJBM",
        "papermill": {
          "duration": 12.591953,
          "end_time": "2020-03-12T03:56:53.313978",
          "exception": false,
          "start_time": "2020-03-12T03:56:40.722025",
          "status": "completed"
        },
        "tags": [],
        "trusted": false,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "92e65d34-05b0-4dfc-ca7d-8edfcac026ef"
      },
      "source": [
        "from docplex.mp.model import Model\n",
        "\n",
        "#VGG from qiskit.aqua.translators.ising import docplex\n",
        "#older# from qiskit.optimization.ising import docplex\n",
        "\n",
        "# Create an instance of a model and variables.\n",
        "mdl = Model(name='max_cut')\n",
        "y = {i: mdl.binary_var(name='x_{0}'.format(i)) for i in range(n)}\n",
        "\n",
        "# Object function\n",
        "#VGG added y[i]/100 term to split the degenerate 1<->0 states in favor of less free samples\n",
        "\n",
        "max_cut_func = mdl.sum(y[i]/50+w[i,j]* y[i] * ( 1 - y[j] ) for i in range(n) for j in range(n))\n",
        "mdl.maximize(max_cut_func)\n",
        "\n",
        "# No constraints for Max-Cut problems.\n",
        "\n",
        "qubitOp_docplex, offset_docplex = docplex.get_operator(mdl)\n",
        "offset_docplex"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "-1.8231253396959048"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "o7VVz_S0uEI-",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "93989aa9-cbb9-49fb-d819-920a5dd65fc2"
      },
      "source": [
        "#VGG define the above as a function \n",
        "def set_up_Dcplx_model(W,*c_x0):\n",
        "  mdl = Model(name='max_cut') \n",
        "  y = {i: mdl.binary_var(name='y_{0}'.format(i)) for i in range(n)}\n",
        "\n",
        "  #VGG try to favor fewer free samples using (2-np.dot(x,x))/n/2 \n",
        "  #VGG split the degenerate 1<->0 states in favor of less free samples using x[i]/n**2\n",
        "  max_cut_func=mdl.sum((-1)*(2-y[i])*0.5+(-0)*y[i]/100 for i in range(n)) \n",
        "  \n",
        "  #VGG don't give free samples to those with h==1\n",
        "  max_cut_func+=mdl.sum(h[i]*y[i]*0.5 for i in range(n) for h in c_x0) \n",
        "  \n",
        "  max_cut_func+=mdl.sum(W[i,j]* y[i] * ( 1 - y[j] ) for i in range(n) for j in range(n))\n",
        "  \n",
        "  mdl.maximize(max_cut_func)\n",
        "  qubitOp, offset = docplex.get_operator(mdl)\n",
        "  return qubitOp, offset\n",
        " \n",
        "qubitOp_docplex, offset_docplex = set_up_Dcplx_model(w)\n",
        "print(offset_docplex,x)"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "2.1768746603040965 [0 1 1 0 1]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "tPHlb2KpgJBV",
        "papermill": {
          "duration": 0.096382,
          "end_time": "2020-03-12T03:56:53.724708",
          "exception": false,
          "start_time": "2020-03-12T03:56:53.628326",
          "status": "completed"
        },
        "tags": []
      },
      "source": [
        "### Checking that the full Hamiltonian made by ```docplex.get_qubitops```  gives the right cost"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "BPSRHW9OgJBW",
        "papermill": {
          "duration": 0.48577,
          "end_time": "2020-03-12T03:56:54.307694",
          "exception": false,
          "start_time": "2020-03-12T03:56:53.821924",
          "status": "completed"
        },
        "tags": [],
        "trusted": false,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 350
        },
        "outputId": "e4447bf6-c082-42e1-b254-0a8f3cf3e03e"
      },
      "source": [
        "#Making the Hamiltonian in its full form and getting the lowest eigenvalue and eigenvector\n",
        "ee = ExactEigensolver(qubitOp_docplex, k=3)\n",
        "result = ee.run()\n",
        "\n",
        "print(\"energys:\",result['eigenvalues'].real)\n",
        "\n",
        "x = sample_most_likely(result['eigenstates'][0])\n",
        "\n",
        "print('energy:', result['eigenvalues'][0].real)\n",
        "print('max-cut objective:', result['eigenvalues'][0].real + offset_docplex)\n",
        "print('solution:', max_cut.get_graph_solution(x))\n",
        "print('solution objective:', max_cut.max_cut_value(x, w))\n",
        "\n",
        "colors = ['r' if max_cut.get_graph_solution(x)[i] == 0 else 'b' for i in range(n)]\n",
        "nx.draw_networkx(G, node_color=colors, node_size=600, alpha = .8, pos=pos)\n",
        "x=max_cut.get_graph_solution(x).tolist()\n",
        "\n",
        "qubitOp_docplex, offset_docplex = set_up_Dcplx_model(w,x)\n",
        "print(x,offset_docplex)\n",
        "\n",
        "#VGG note if you keep executing this cell you can see diferent configurations "
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "energys: [-1.26 -1.16 -1.08]\n",
            "energy: -1.258779000843542\n",
            "max-cut objective: 0.9180956594605545\n",
            "solution: [1 0 0 1 0]\n",
            "solution objective: 2.581904340539446\n",
            "[1, 0, 0, 1, 0] 1.6768746603040967\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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lZDQaWbduHSEhIQQEBLBz5066d+8ugSsqZODAgRw5coTExEStSxE1RELXSoqi8NVXXzFw4EASExOJjY1lzJgx1K9fX+vSRB1Wr149RowYwapVq7QuRdQQaS9YISkpiaioKNLS0pg+fTpdunTRuiRhQ/r378/mzZv57bffuOuuu7QuR1QzGemWIScnhyVLljB69Gi6devG1q1bJXBFlXNycuKFF16Q0a6dkNAtgcViYffu3QwYMID8/Hx27NjB4MGDcXCQNwaievTr14+kpCSOHDmidSmimkmK3OTIkSMsWrQIR0dHli9fzp133ql1ScIOODk58eKLLxITE0N0dLTW5YhqJKH7p8uXL/POO+/w008/MX78eHr27CkzEkSN6tOnDxs2bCAhIYFOnTppXY6oJnbfXjAajWzatInBgwfj6+vLzp07eeaZZyRwRY1zcHBg1KhRxMTEoCiK1uWIamK3oasoCt9++y3BwcEcPnyYjRs3Mm7cOFxcXLQuTdixZ555hrS0NH788UetSxHVxC7bC2fOnGHx4sVcuHCBV199la5du2pdkhAAGAwGRo8eTUxMDJ07d5Z3XDbIrka6ubm5LF++nBdeeIEuXboQFxcngStqne7du3P16lUOHDigdSmiGthF6FosFj766CMGDBhAVlYW8fHxDB06FEdHR61LE+Jv9Hr9tdGu9HZtj823F3777TcWLlyITqdj8eLFcsWPqBOefPJJ1q1bx7fffku3bt20LkdUIZsN3StXrrBy5UoOHDjASy+9RK9evWSLc1Fn6PV6IiIiiImJ4ZFHHpHnrg2xuf/JoqIiYmNjCQoKwtPTk127dtGnTx950oo657HHHkOv1/PVV19pXYqoQjY10t2/fz+LFy/mtttuY/369TRv3lzrkoSoMJ1Ox5gxY1ixYgWPP/64DBxshE2E7rlz51i6dCmnTp1i8uTJPPLIIzLVRtiEhx9+mLVr17J37166d++udTmiCtTpX515eXmsXLmSESNG0KFDB7Zv386jjz4qgStsRvFod9WqVVgsFq3LEVWgToauoijs2bOHgQMHkpqaSlxcHMOHD8fJyUnr0oSocg888ACenp58+umnWpciqkCday/8/vvvLFq0iKKiIhYsWED79u21LkmIalU82p03bx49evSQXabruCoN3aws+P13OH8eiorA2RkCA+GOO6CySxpkZGQQHR3N119/zbhx4+jbt6+cWBB24/7778fPz4+PP/6Yfv36aV2OqIRKh25uLvznP7BmDZw6BY6OYDaDxQJ6PRgMagB37AgREfDEE+ptrGUymdixYwfr1q2jV69e7Nq1i4YNG1a2bCHqnDFjxjBz5kyeeeYZuZqyDqtw6CoKfPIJ/POfavA6OoKHB5R0DktR4JdfYNw48PGBFSvgvvtu/TMOHjxIVFQUjRs3ZvXq1bRs2bKi5QpR53Xs2JGAgAA++ugj+vfvr3U5ooIqFLoFBTB5Mnz2GdSrp4ZtWXQ6cHNTv75yBYKDYdQoePVVdTR8s+TkZJYuXUpiYiKTJ0/msccekxkJQqCOdl977TX69Olz7cRxUZH6LjMrS32teXqqbT1p/dZO5Q7dggIYMQIOHlTDtrxtVVdXtf2wejVkZsL8+X8dIz8/n40bN7Jjxw6GDh3K/PnzZUaCENe5++67adOmDdu2/QdHx/5s2QLHj6uvoeLXkcWivru8804IC4Nnnqn8ORVRdcodutOmwY8/qr9NKzr4NBjA3R22b4fmzSEiQuGLL75g+fLldOzYkbi4OHx8fCp2cCFsmMkEHh5TGTeuCD8/C46Oeho2/Pvgx2yGxET19Tpzpvp5yJDyD5JE1dOVtXTc/fffr/z000/X/rxvn9oWcHevmv+8oiLIzjbSpcscDIYkpkyZIntDCVGKc+dgzBg4dgyysy/QsGE9GjXyuuX9jEb1vMu990J0tHpeRVQvnU53SFGU+0v6ntUjXaMRpk5Vp4FVReCazSauXLlMerqZs2fH8N//NpUpYEKUIikJgoLUlpyHB7i4eHHmzFk8PDxv+bpxclJPdP/f/8Hzz8OOHdC0aQ0VLv7G6pTbt09t1Fe+N6SQkZHOyZNJgI42bZqQltaMEyckcIUoSWYmhIRAdvZfM4ScnevRoIELGRnpVh1Dp1Pvm5oKoaGQl1fNRYtSWZ1069dbd7sLF2bwxx89SEzsxsmT/cnM3H3te3l5uSQlJZGdnUPz5gH4+fnh4GDAYoFt28pduxB24c03IS3trxlAxRo39ubKlXQsFrPVx3J3V9sUb79dxUUKq1nVXjCZ1Lcmrq63vm3jxuE4Os5Ar3eisPA0Z86MxmBoQXa2F/n5+fj6+v55ccNfZ+Hq1YNvvqnoQxDCdu3fDx9/rIblzZydnWnQoAHp6Rk0btzY6mO6ucHWrTBgAMhV9DXPqpFuUpL69sSalquzc0v0enWal6IoFBUVce7cIZycnGnVqhUNG7pxfeCq94HTp6GwsLzlC2Hb3n237Neet3dj0tOvlGu0azCoU8rWrKmiIkW5WDXSTUkp3/SwlJQFpKV9QFFRLo6OrQkI6Iuzszsmk+naRQ7qZx06nfq1waAjJUUhIEAnF0IIgdoGOHgQyrrq3cnJGVfXhly+fIaiomiuXv0eBwcPvL1fwt29Z6n3a9gQPv1UvVjJ69YTIEQVsrq9UB5+ftPIyOiLxXIUvf4Ely5dAbIABUXhzx1O1a+LP5vN9enbdzxOTskYDIYbPvR6PQ4ODte+NhgMODg4XPu6rI+6cF9rbiszO+zPjz+qn2/1X+/t3Zhjx8bj4eFBmzafU1BwnHPnJlCvXhucnUu+dN5gUD9+/hmeeqqKCxdlsip069cv/4Hbtr2DS5c8uXLlAC4uB2jaNLzM22dlwRdf/BtvbwsWiwWz2XzDh8ViwWQyXfvabDZjMplKvG1V3regoECTn3v9fc1m9a1jbfklUZvua8u/jA4dUi9yuBWDwYyi/IiDw1r0ehdcXDrSsOFjZGV9jI/P+FLvV1iorokioVuzrArdVq3U0a6iWN9m0OsNNGnSFKOxARkZiSjKBfz8fDEY/v4jTSZ1LqGPD+h0+msvRPGX4qCuqeC/1W2NRmOt+KWotqbq7i+Nsu7744/NAWcKCxWub8UVf138ubDwFI6OzmRnN8DHx4TB4ICz8+3k5SWU+ZxydITffqv+5664kVXJ5u2tzlwoKlLDsTQmUzp5eT/h6voIOl09cnN/ID//S/z955Gf78DJk0n4+fni5nbjybSCAvUsqrRyS2fro7qKuj6YtQr+4vuaTKZrv4yq4ucePTqBnBxvMjMLr2vF3diWAwWT6RiFhXp0ujwuXkyhWbPb0OtdsVhyy/y3UwO72v+LxE2sCl2dDnr3hri4skMXdGRk7OTixUjAgqNjE3x9X8HN7XHc3MDNzY2LF5PJysqmSRM/HBzUNUHNZpB1mUVFFP8yssX1ZQcOVEeiDRqUfbvLl3M4fz4ff39/cnJyuHz5Mnp9Lnp92XdUlIq1DkXlWP0ePixMXaCmrBaDg4MnzZuvLvUY9evXp0WLFqSlXSEpKQkfHx9cXT0wGHQSukLcpF07SEgoPXQtFjMpKSnk5dXH2dmBhg3z8PDw59Sp0+j1R3B1LXv9aZMJ7rqrGgoXZbL6/WrbtvDII+oJr8rQ6fR4e3vTvHlzMjMzSUq6zLPPZvztahsh7F2nTqWviVtQkE9S0il0Oj0tW96Ju/tTXL4cg05XhLd3BtnZX+Ho+HiZx3dygnvuqfq6RdnK1SRcsEC9kKGgoPI/2Nm5Hl5egTRtCj/8EMLmzZuvnaUXQkCXLurnG3deV7hyJY2zZ8/h6+tDkyZN0Ov1+PlNw2Ip5Pjxp0lNnUXTpq9z+bIzhYUlv1jNf26pde+91f4wxE3KFbp+frBoEeTnq6uOVUZennomdscOH7ZsWceBAwcYMWIEx48fr9yBhbARTZtC167qQjcAJlMRZ8+e5erVq7Ro0eLPqztVBoMb/v6LueOO77j99o/x8XkOPz9fzp07h8lU9LdjZ2er52k8PWvq0Yhi5T4d3qsXREaqoVmRlYoURf0PVxTYsEF9e3PbbbcRHR3NwIEDGTt2LP/6178wVjbVhbAB48YVv2ZySEo6hYuLC82bN7fqxKGbmzuenp6cO3fuhsuEzWb1gotRo6qzclGaCs1BCg6GjRvVZR4zMqy/Ys1oVJepCwiA99+Hhx7663s6nY5nn32Wbdu2cfLkSYYMGcKRI0cqUp4QNqNjRyP+/j9w4UIOzZo1o3Fjb25eu6QsXl5e1KtXnwsXLgDqhgU5OfDCC+qJOlHzKjzx85FH1DV2hwxRe7yZmeoI1miE4s0oFEWdB5iZ+dcJuEmTYM8edf+mknh7e7No0aJrG/BFRUWRJ4t/CjuUlJTE8OHDuffePdxzjw9FRRVZzFqHn58figIpKSlkZiq0aKG+DoU2yrVdT2mys+E//1FD+PBhuHxZffuiKHDbbdCxo7o53lNPqSfirJWVlcWSJUv4+eefef3113nwwQetv7MQdZSiKHzwwQdER0czfvx4+vXrx/nzOgYNUl9bxQuZl4fZbOaPPy7TrBl8842fbNlTzcrarqdKQvdmRUXqh7Nz1WwDvX//fiIjI+ncuTOTJk3684o2IWxPdnY28+bN4/z580RGRhIYGHjteykp8NJL6iI1Li7WD2AKCtST35065ZORMZxp00bzlCy4UK3KCt1qua7U0VF9UlRF4AJ07dqV+Ph46tevT1BQEPv27auaAwtRiyQkJBASEoKfnx8bN268IXBBnT0UHw+zZql/zspS+7MlnVMxmdR3oFlZ4OCg7hQRH1+f6Oh5LFiwQM6XaKhaRrrV6fDhw8yZM4dWrVrx2muvlWvFfCFqI7PZzJo1a/jggw9488036dq16y3vU1AAn38OW7bAkSPqjITiQY7ZrF740KEDDB0K//jHjZfv79+/n9mzZ7N27Vr8/f2r6VHZtxpvL1Q3o9HI2rVr+eCDDxg/fjx9+/aVhc9FnZScnMz06dNxcXFh9uzZeFVgRXGLBZKT1VFt8QaUTZqU3fd9//33iY2NZf369Xh4eFTiEYiS2FzoFjt+/DizZ8/G3d2d6dOn01T2lRZ1yOeff86iRYsYPnw4oaGhNb6K3MqVK0lISCAmJgansleyEuVU4z3dmtKmTRs2b97MAw88wLBhw9i2bRuWG6+ZFKLWycvLY86cOcTExLBixQqGDh2qybKdY8eOxc/PjzfffFNeNzWoTocuqLspDB8+nA0bNrBv3z5GjhxJUlKS1mUJUaJjx44xdOhQAGJjY7mztAnrNUCv1zNr1ixSU1N59913NavD3tT50C0WEBDAqlWr6N27N6NHj2bt2rUUFf39mnMhtGCxWNiyZQvjx49nzJgxzJw5ExeXilzsULWcnJxYvHgxX375Je+//77W5dgFmwldUH9zDxw4kC1btvDLL78wbNgwjh49qnVZws6lp6czYcIE9u7dy6ZNm+jevbvWJd3Aw8OD5cuXExMTw/79+7Uux+bZVOgW8/X1ZdmyZYwYMYKJEyeyfPlyCqpiPUohymn//v2EhoZy5513smbNmlp7stff35+oqChmzpwpK/1VM5sMXVAX0OnZsyfbt2/n0qVLDB48mEOHDmldlrATRqORJUuWMG/ePObPn8/YsWNr/War7du3Z9q0aUycOJHU1FSty7FZNhu6xTw9PYmMjGTy5MnMmDGDyMhIrl69qnVZwoadOXOG8PBwkpOT2bZtG/fdd5/WJVntqaeeIiQkhAkTJpCbW/bGlqJibD50i3Xr1o34+HgAgoKC+OabbzSuSNgaRVH48MMPGTlyJP3792fRokW4u7trXVa5DR06lA4dOjB16lRM1q7bKqxWpy+OqKhDhw4xd+5c2rVrx5QpU2jUqJHWJYk6Licnh8jISE6dOkVkZCQtW5a9KWRtZzabmTx5Mt7e3rzxxhtyxWc52ezFERV13333ERcXh5+fH4MHD+aTTz6hrF8+QpTl8OHDhIaG4unpyaZNm+p84II6//2tt97i999/Z+PGjVqXY1PscqR7vaNHjzJnzhx8fX15/fXX8fX11bokUUdYLBbWrVvHjh07mD59Ot26ddO6pFAhyPQAABVhSURBVCp3+fJlwsPDGT9+PD169NC6nDpDRrplaNeuHe+99x7t27dnyJAh7Ny5Uy6JFLeUkpJCREQECQkJxMbG2mTggrqTy7Jly4iKiuLnn3/WuhybYPehC+Do6MjIkSNZvXo1H3/8MREREZw9e1brskQttW/fPsLCwnj44Yd599138bHxbRhat27NvHnzmDp1KmfOnNG6nDpPQvc6LVu2ZN26dfzjH/8gPDycTZs2YTabb31HYRcKCgqYP38+y5cvZ+nSpYwYMUKThWq08MADD/DSSy/x8ssvk56ernU5dZp9PGPKQa/XM3jwYN577z0OHjzI8OHD5QodwfHjxxk2bBiFhYVs3bqVu+66S+uSaly/fv3o2bMnkydPprCwUOty6iwJ3VI0bdqUlStXEhwczLhx44iOjsZoNGpdlqhhiqIQFxfH2LFjCQ8PZ86cOTRo0EDrsjQzZswYmjVrxowZM+TcRwVJ6JZBp9PRt29f4uLiOH36NCEhIRw+fFjrskQNycjIYNKkSezZs4cNGzbQq1cvrUvSnE6nY+bMmWRmZrJixQqty6mTJHSt4OXlxcKFCxk3bhxTp05l4cKF5OXlaV2WqEY//PADoaGhtGrVinXr1sleYtdxcnIiKiqKb7/99tpVnsJ6Errl8OSTTxIfH09BQQHBwcEcOHBA65JEFSsqKmLFihXMnj2b2bNnM378eBwdHbUuq9Zxc3NjxYoVrF+/nm+//VbrcuoUu784oqK+//57IiMjuffee5k8eXKdvMZe3OjcuXO88cYbeHl5MXPmTDw9PbUuqdb79ddfmThxIu+8846mu2DUNnJxRDV48MEHiYuLw83NjeDgYPbu3SuXEtdRiqLw8ccfEx4eTp8+fViyZIkErpXuvvtu3njjDSZPnszFixe1LqdOkJFuFThy5Ahz586lefPmTJ06FW9vb61LElbKzc3lrbfeIjExkcjISG6//XatS6qTtm7dyu7du1m3bh0NGzbUuhzNyUi3mrVv354tW7bQunVrQkND+fDDD2XUWwf88ssvhIaG4uLiwnvvvSeBWwkhISF07tyZ1157TfYmvAUZ6VaxP/74gzlz5uDq6sr06dO57bbbtC5J3MRisbBx40bi4uKYNm0aTz75pNYl2QSLxcKUKVNwd3dn5syZdr0cpIx0a9Dtt9/Oxo0b6dq1K2FhYWzdulUmkdciqampjB07lu+//5733ntPArcK6fV65s+fz4kTJ1i3bp3W5dRaErrVwGAwMGzYMDZu3MhXX33FCy+8wMmTJ7Uuy+59/fXXDB06lM6dOxMTEyPLeFaD+vXrs2zZMj788EP27NmjdTm1Uu3eKa+O8/f3JyYmht27dxMREUFQUBDh4eEy77OGFRYWsmzZMv773/8SFRVF+/bttS7Jpnl5ebF8+XIiIiLw9fWtU3vE1QQZ6VYzvV5P//792bp1K7///jtDhw7lt99+07osu3Hy5EnCwsLIyspiy5YtErg1pGXLlkRGRvLPf/6TU6dOaV1OrSKhW0N8fHxYsmQJI0eOZNKkSSxdupSCggKty7JZiqKwY8cOIiIiGDJkCPPnz5epTDWsc+fOTJgwgQkTJshykNeR0K1BOp2O7t27Ex8fT3p6OsHBwfz4449al2VzsrKymDJlCh9++CHr16+nX79+dn0mXUu9e/emT58+TJw4kfz8fK3LqRUkdDXg4eHB3LlzefXVV5k1axbz5s0jJydH67Jswk8//URISAj+/v6sX7+egIAArUuye6NGjaJFixZMnz5dZvIgoaupRx55hPj4eBwcHAgODubrr7/WuqQ6y2QyER0dzfTp05kxYwYTJ07EyclJ67IE6ju86dOnk5uby9KlS7UuR3NycUQtkZCQwLx582jbti2vvvoqjRo10rqkOuPChQu88cYbuLm5MWvWLPm3q6VycnIYOXIkzz//PCEhIVqXU63k4og6oFOnTmzbto2mTZsyePBg9uzZI5cSW+HTTz9l+PDhdO/enWXLlkng1mINGzZk2bJlbN682a7f1clItxb6/fffmTt3Lo0bN+b111/Hz89P65Jqnby8PN5++21++eUX3nrrLdq2bat1ScJKR48e5eWXX2bFihW0a9dO63KqhYx065g777yTzZs307FjR4YOHUp8fLycgLjO0aNHGTJkCAaDgdjYWAncOqZdu3bMnDmTyZMnk5ycrHU5NU5GurXc6dOnmTNnDnq9nhkzZtC8eXOtS9KMxWIhNjaW9957j9dee42nn35a65JEJcTHxxMfH8/69etxc3PTupwqJSPdOiwwMJC1a9fSvXt3XnjhBTZs2IDJZNK6rBqXlpbG+PHj+eqrr9i0aZMErg0ICgqia9euvPrqq3a107aEbh2g1+sJCgoiNjaWhIQEwsLCSExM1LqsGvPdd98xZMgQ2rdvz5o1a2jatKnWJYkqMnHiRNzc3Jg3b57dnDiW9kIdoygKe/bsYfny5fTr149Ro0bh7OysdVnVwmg0smLFCr788kvmzp1Lp06dtC5JVIOCggIiIiLo2rUrERERWpdTJaS9YEN0Oh29e/cmLi6O8+fPExISws8//6x1WVXu1KlTjBgxgtTUVLZt2yaBa8Pq1avH0qVL+fjjj/noo4+0Lqf6KYpS6sd9992niNpt3759Ss+ePZUFCxYoV69e1bqcSrNYLMr777+vPPnkk8quXbsUi8WidUmihpw6dUp5+umnlR9++EHrUioN+EkpJVdlpFvHPfHEE2zfvh2j0UhwcDD79+/XuqQKy87OZurUqcTHx7NmzRr69+8vC9XYkcDAQBYsWMAbb7xh04v+S+jaADc3N2bMmMHMmTNZsGABM2fOJDMzU+uyyuXnn38mNDQUHx8fNm3aRMuWLbUuSWigU6dOvPLKK0ycOJG0tDSty6kWEro2pEuXLmzfvh0PDw+Cg4P5/PPPa/0ZYbPZzKpVq5g6dSpTp05lypQpslCNnevZsyfPP/88EydOJC8vT+tyqpzMXrBRv/zyC3PnzqVZs2ZMmzYNHx8frUv6m4sXLzJ9+nScnZ2ZM2cOjRs31rokUUsoisLcuXNJT09n8eLFGAwGrUsqF5m9YIfuueceYmNjueOOOwgNDeWDDz6o/KjXaIRTpyAxEZKSoBI7X+zdu5ewsDAee+wxVq5cKYErbqDT6Xj99dcxGo1ERUXV+nds5SEjXTtw4sQJ5syZg4uLC9OnT6dZs2bW3zk5GbZtg88+U4PWYACdDhQFTCZo3hyeegpCQqBFi1seLj8/n6ioKA4dOkRkZKTNLngiqsbVq1cZOXIk/fr1Y8iQIVqXYzUZ6dq51q1bs3HjRh599FGGDx9ObGzsrRfQSUuDceOgWzeIjobz58HNDRo2BFdX9bO7O1y6BOvWwdNPw4gRcOFCqYdMTExk6NChmEwmtm7dKoErbsnV1ZXly5ezZcsW9u3bp3U5VUJGunbm/PnzzJ8/n9zcXGbOnEnr1q3/fqPPPoNXX4W8PDVo9Vb8blYUyMoCR0eYOxcGDrzuWwrbtm1j/fr1TJkyhZ49e1bhIxL2IDExkZdeeoklS5Zwzz33aF3OLclIV1zTrFkzoqOj6d+/P2PGjGHVqlU3LjayZQuMHQsWC3h4WBe4oLYcPDzAwQGmToUVKwBIT09nwoQJfPbZZ2zatEkCV1RI27ZtmTVrFlOmTOH8+fNal1MpMtK1Y6mpqSxYsIDz588zY8YM7klOVgPX1VUdsVaUyQQ5OfwRFsb4Awfo27cvERERODg4VF3xwi7t2rWLLVu2sGHDBtzd3bUup1RljXQldO2coijs3buXNZGRvHvsGF6enuhdXCp1TIuicCU5mcLsbK5s3UqHZ5+tomqFgBUrVnDkyBGio6Nr7ZxuaS+IUul0Op5++mnea9kSfWEhJ5OTyc3NrfDxCo1GTp8+TYHFQhNfXzrExlZhtULASy+9hJeXF7NmzaqTO6pI6Aq4cAHnr7/GKzCQJn5+JF+8SPLFi5jNZqsPoQCZWVmcPn0aDw8Pmvn7Y/D0hP/7Pzh6tPpqF3ZHr9czZ84cUlJSiImJ0bqccpPQFRAXp84+0OtxdXWlZcuW6HU6TiYlkZ2Tc+1mRouFOcnJ9Dlxgm6JiYQmJbH/6lXMFgsXLlzgypUrNG/enEaenuhAPblmscCmTZo9NGGbnJ2dWbx4MZ9//jm7d+/WupxykTMbQp0iVq/etT8a9Hr8/Pxwc3Mj+eJFsrOy8PPzw6zX4+foyOqAAPwcHfnv1au8du4cCwwGWrm50aJFC/Q3rwrWoAHs3VvDD0jYA09PT1asWMGLL76In58fDz74oNYlWUVGuvbOaFSvNCth9wkXFxdatmyJk5MTSUlJFObkMMrbm6ZOTuh0Ou4oLMTdaCTT3Z0mfn5/D1xQZ0FkZsKVKzXwYIS9CQgIYOHChcyYMYPjx49rXY5VJHTt3fnz6qW9pczH1et0+Pj4EBAQQHp6OufOniUvP58zZ86QnJNDupMTd3t4lH58nQ6cnNQ1G4SoBh07duTVV19l0qRJpKamal3OLUno2juj0aoLIOrVq0eLwEBcGjTg7NmzZOfmEpWXx2MGAw2ys8nMzORqbi6FRiOWkqYh2tFur6Lmde/enaCgoDqxHKT0dO2dk5N6Es0KOp2Oxl5eeHh68vq5c7iazbzi6YliMpGXl0eRyURRURFFRUXo9XocHR1xdHDARVH4/rPPcLx6FV9fX/z8/GjcuHGdW65P1G5hYWFcuHCBadOmsXTp0lr7/JLQtXdNm0JRkRq8VmyNoygK81NSyAJWBAbiXMIoWQHMJpMawkYjuuxsLhgMJO3bx6VLl0hJSSEjIwMvL69rIVz8UfxnX19f3N3dZbseYTWdTsfUqVOZNGkSb7/9Nv/85z9r5fNHrkgT8Pjj6qpi181gKE3kxYscLywkOiAAF2vWZSgO9MOHbwh1k8lEamrqtRAu6XNhYeENQVxSMNezomZhX/Ly8njxxRfp2bMnYWFhmtRQ1hVpMtIV6nq4GzbcMnQvFhXxfmYmTjodPf7449rfv+7nxzOlXQefmwvPPPO3UbSDgwNNmzaladOmpf68vLy8ayFcHMQJCQk3BHP9+vXLDGVvb+9a+zZTVA8XFxeWLVtGeHg4TZo04emnn9a6pBvISFeoU8a6d1fXx63Kt2OKAtnZsH07dOpUdce9dniFjIyMMkfL6enpNGrUqNRQ9vPzkzaGjTp+/Djjxo0jKiqKDh061OjPlgVvxK2FhcH+/eryjFUlOxtatoRPPqnaMC8Hk8nE5cuXbxgtl9TGKGu07OvrS/369TWpX1TOgQMHePPNN1m7di0BAQE19nMldMWtnTun7v7g5KR+VJbJpC6Cvns31PIdIq5vY5T2uV69emWOlqWNUXt98MEHbN68mfXr1+Pp6VkjP1NCV1hn+3b45z/V3SIqs/atxaLuIjFxIowfX3X1aURRFDIzM28IYWlj1C3vvvsuhw4d4l//+hfOJVx9WdUkdIX1li1Td31wda3YiPfPBcwZPBjmzdOsrVDTrm9jlDZavrmNcXMoSxuj+lgsFqZPn47FYiEyMhL9zTNv0tPh22/h0CF1ZbycHPVKzdtugwceUM9JdOli9U4qErrCeooCsbEwf74aoNaeXFMU9YkK6uh23Djrt/qxE+VtY5QU0NLGqDij0cjYsWNp3749L7/8svqXx4/DypXw6afqc9hsVmfxFD93jUb1deDgAI0awahRMHRoiWuVXE9CV5TfqVPwyivwyy9qu8DVVX3i3RzARUXqtDCdDlq1giVLan0Pt7YqqY1x8+eb2xgljZY9PDykjVGKrKwswsPDGRocTP/Ll9V3dWaz2lK71S+z/HwoKICAAFi+HNq3L/WmErqiYhQFfvsNNm6E//1fdTbC9S0Hkwnq14dHH4XwcLjvPrtpJ2ilvG2Mkj77+vriUsktmeqy84mJnHjsMR4wGKjfuHH59wPMzlY/L1wIzz1X4k0kdEXVuHwZTp9W33I5OoK/P/j5SdDWMsVtjNJCubQ2xs0XldjkRqKFhRAWRuH+/ZzJzCSgefOKXdVoNKrv8JYvhz59/vZtCV0hxDXlbWOUNmquk22MBQtgzRrw8CD76lUupaQQGBiIY0V2vy4sVN/tffaZ2nK4joSuEKJcitsYZY2WCwoKyhwt17o2xpEjMGCAupvJn6P4K+npZGZmEhgYiKEiJ34zM6FDB9ix44YTx7L2ghCiXBwcHGjSpAlNmjQp9TYltTEOHz7M559//rc2Rmmj5RptYyxYoJ6nuO7nNWrUCKPRyPnz5wnw9y//yN3dXV3Maf9+eOQRq+4ioSuEqBAXFxdatGhBixYtSvx+cRvj5lFyYmLi39oYN4dxlbcxTp+GgwfVWQrX0QF+fn6cO3eOiykpfOvszH+ysjhRWEgPNzdmlbEgk3qAP+tau1ZCVwihLZ1Oh6enJ56entxxxx0l3qakNsaZM2c4ePDg39oYZc3IuGUb47PP1KmPJbQQdMBtt93GmTNncDKZGNm4MQeuXqXQysX9cXOD775T56k3bHjLm0voCiE0Y00bIz8//2+j5SNHjlwL5eI2Rlmh7Pff/6Ivo41h0Ovx9/fHfPo0PorCUYOBVJPJugeh16sti2PHoHPnWz9m644qhBDaqF+/PoGBgQQGBpb4/dLaGMePH78Wyou//hpnvR5devq1baQcHR1xcHS89mcHBwf8/f05e+YMhS4u5buisqgIEhMldIUQts+aNobSti0mJyeKzOZre/kZjUZyc3Ov/dliseDo6IjeYCA9PR29l5f1RZjN6iJPVpDQFULYPJ1Op45uy1gzwWKxXAtgjytXyCnPyTtr+7/IFuxCCHvQqJF6IUMZ9Ho9zk5OuDZoQP3yXqXm5ATe3lbdVEJXCGH7OnRQF6u5BbOiYLRYsAAWwGixYLZmFGswQCmtjZtJ6AohbF/XruqUsVtYl5ZG18RENl65wp6sLLomJrIuLa3sO5nN6rHbtLGqFOnpCiFsX8+eMGeOGpBlLOE42tub0Va2Ca7JzlZXG7OyJSEjXSGE7fP2hh49/lqWsapYLOpVacOHW30XCV0hhH147TV1SVKjseqOmZ0NzzxT5oLmN5PQFULYh4AAeOMNdR1cK/q7t5Sbq172O3t2ue4moSuEsB9DhkD//uqSjJUJ3uItqtavV6ejlYOErhDCfuj18PbbEBKiXkGWn1+++ysKZGSobYrYWLj33nKXUOYi5jqd7jJwptxHFUII+9ZcUZQSp0GUGbpCCCGqlrQXhBCiBknoCiFEDZLQFUKIGiShK4QQNUhCVwghatD/A/sD4bt5I72fAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zrWqYi3xBJlC",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#VGG define the above as a function \n",
        "def Max_Cut_Dcplx(W,*c_x0): \n",
        "\n",
        "  qubitOp_docplex, offset_docplex = set_up_Dcplx_model(W)\n",
        "  \n",
        "  for h in c_x0:\n",
        "    qubitOp_docplex, offset_docplex = set_up_Dcplx_model(W,h)\n",
        "\n",
        "  ee = ExactEigensolver(qubitOp_docplex,k=3)\n",
        "  result = ee.run()\n",
        "  x=sample_most_likely(result['eigenstates'][0])\n",
        "  x_dcplx=max_cut.get_graph_solution(x).tolist()\n",
        "  cost_dcplx=result['eigenvalues'][0].real\n",
        "  #cost_dcplx=max_cut.max_cut_value(x, W)\n",
        "\n",
        "  return cost_dcplx, x_dcplx"
      ],
      "execution_count": 31,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "M6DI-RqhB-yz",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 459
        },
        "outputId": "30cd0d41-aadd-41f7-9294-ce5b08a047aa"
      },
      "source": [
        "%time market_simulations(10,'dcplx')"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Using Max_Cut option: Docplex\n",
            "day  [free samples]  [buyers distribution]  [to be used as constrain]  the two totals  w-det\n",
            "0 [1 0 0 1 0] [0 1 1 0 0] [1. 0. 0. 1. 0.] 2 2 1.0000000000000009\n",
            "1 [0 0 0 0 0] [1 1 0 1 0] [0. 0. 0. 0. 0.] 2 5 1.0\n",
            "2 [1 0 0 1 0] [0 0 1 0 1] [1. 0. 0. 1. 0.] 4 7 1.0\n",
            "3 [0 0 0 0 0] [1 1 0 0 0] [0. 0. 0. 0. 0.] 4 9 1.0\n",
            "4 [1 0 0 1 0] [0 0 1 0 0] [1. 0. 0. 1. 0.] 6 10 1.0\n",
            "5 [0 0 0 0 0] [1 1 1 0 1] [0. 0. 0. 0. 0.] 6 14 1.0\n",
            "6 [1 0 0 1 0] [0 0 1 0 1] [1. 0. 0. 1. 0.] 8 16 1.0\n",
            "7 [0 0 0 0 0] [0 0 0 0 1] [0. 0. 0. 0. 0.] 8 17 1.0\n",
            "8 [1 0 0 1 0] [0 1 1 0 1] [1. 0. 0. 1. 0.] 10 20 0.9999999999999998\n",
            "9 [0 0 0 0 0] [1 0 0 0 1] [0. 0. 0. 0. 0.] 10 22 0.9999999999999998\n",
            "\n",
            "last day configuration record:\n",
            "\n",
            "[0 0 0 0 0] [0.96 0.67 0.84 0.65 0.63]\n",
            "\n",
            "[1 0 0 0 1] 10 22 3.423076333786 0.9999999999999998\n",
            "\n",
            "[[1.29 0.58 0.6  0.16 0.65]\n",
            " [0.58 1.29 0.4  0.   0.  ]\n",
            " [0.6  0.4  1.29 0.57 0.  ]\n",
            " [0.16 0.   0.57 1.29 0.2 ]\n",
            " [0.65 0.   0.   0.2  1.29]]\n",
            "CPU times: user 123 ms, sys: 10.7 ms, total: 134 ms\n",
            "Wall time: 129 ms\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "yGrp8wWKgJBc",
        "papermill": {
          "duration": 0.111064,
          "end_time": "2020-03-12T03:56:54.518671",
          "exception": false,
          "start_time": "2020-03-12T03:56:54.407607",
          "status": "completed"
        },
        "tags": []
      },
      "source": [
        "# Running it on a quantum computer\n",
        "We run the optimization routine using a feedback loop with a quantum computer that uses trial functions built with Y single-qubit rotations, $U_\\mathrm{single}(\\theta) = \\prod_{i=1}^n Y(\\theta_{i})$, and entangler steps $U_\\mathrm{entangler}$."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "S-lmsvcagJBh",
        "papermill": {
          "duration": 0.096835,
          "end_time": "2020-03-12T03:56:54.719354",
          "exception": false,
          "start_time": "2020-03-12T03:56:54.622519",
          "status": "completed"
        },
        "tags": []
      },
      "source": [
        "### First some results from runing on few simulater systems "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2019-12-12T18:00:12.595984Z",
          "start_time": "2019-12-12T17:59:52.126693Z"
        },
        "colab_type": "code",
        "id": "0N8v7qbngJBi",
        "papermill": {
          "duration": 203.982206,
          "end_time": "2020-03-12T04:00:18.796289",
          "exception": false,
          "start_time": "2020-03-12T03:56:54.814083",
          "status": "completed"
        },
        "scrolled": false,
        "tags": [],
        "trusted": false,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 367
        },
        "outputId": "2398b202-e152-4b59-e240-6b230f1db313"
      },
      "source": [
        "seed = 10598\n",
        "\n",
        "model=qubitOp_docplex\n",
        "#model=qubitOp\n",
        "\n",
        "spsa = SPSA(max_trials=30)\n",
        "ry = RY(model.num_qubits, entanglement='linear') #depth=5, \n",
        "vqe = VQE(model, ry, spsa)\n",
        "\n",
        "backend1 = Aer.get_backend('statevector_simulator')\n",
        "quantum_instance = QuantumInstance(backend1, seed_simulator=seed, seed_transpiler=seed)\n",
        "\n",
        "print(backend1)\n",
        "result = vqe.run(quantum_instance)\n",
        "\n",
        "#VGG# x = max_cut.sample_most_likely(result['eigvecs'][0])\n",
        "x = sample_most_likely(result['eigenstate'])\n",
        "\n",
        "print('energy:', result['eigenvalue'])\n",
        "print('time:', result['optimizer_time'])\n",
        "print('max-cut objective:', result['eigenvalue'] + offset)\n",
        "print('solution:', max_cut.get_graph_solution(x))\n",
        "print('solution objective:', max_cut.max_cut_value(x, w))\n",
        "\n",
        "colors = ['r' if max_cut.get_graph_solution(x)[i] == 0 else 'b' for i in range(n)]\n",
        "nx.draw_networkx(G, node_color=colors, node_size=600, alpha = .8, pos=pos)\n",
        "\n",
        "qubitOp_docplex, offset_docplex = set_up_Dcplx_model(w,x)\n",
        "print(x,offset_docplex)"
      ],
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "statevector_simulator\n",
            "energy: (-1.14620968659431+0j)\n",
            "time: 0.4005434513092041\n",
            "max-cut objective: (-2.7193350262902136+0j)\n",
            "solution: [0. 0. 1. 0. 1.]\n",
            "solution objective: 2.406862004554557\n",
            "[1. 1. 0. 1. 0.] 1.4268746603040965\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2019-12-12T18:00:40.238107Z",
          "start_time": "2019-12-12T18:00:12.618707Z"
        },
        "colab_type": "code",
        "id": "7lKJ0Em8gJBo",
        "papermill": {
          "duration": 1832.229602,
          "end_time": "2020-03-12T04:30:51.124712",
          "exception": false,
          "start_time": "2020-03-12T04:00:18.895110",
          "status": "completed"
        },
        "tags": [],
        "trusted": false,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 367
        },
        "outputId": "b16ea8c9-9ba6-4347-e90f-85e7a1aecb16"
      },
      "source": [
        "# run quantum algorithm with shots\n",
        "seed = 10598\n",
        "\n",
        "spsa = SPSA(max_trials=300)\n",
        "ry = RY(model.num_qubits,  entanglement='linear') #depth=5,\n",
        "vqe = VQE(model, ry, spsa)\n",
        "\n",
        "backend2 = Aer.get_backend('qasm_simulator') #VGG it was 'BasicAer.get_backend' ibmq_16_melbourne\n",
        "quantum_instance = QuantumInstance(backend2, shots=1024, seed_simulator=seed, seed_transpiler=seed)\n",
        "\n",
        "print(backend2)\n",
        "result = vqe.run(quantum_instance)\n",
        "\n",
        "\"\"\"declarative approach, update the param from the previous cell.\n",
        "params['backend']['provider'] = 'qiskit.BasicAer'\n",
        "params['backend']['name'] = 'qasm_simulator'\n",
        "params['backend']['shots'] = 1024\n",
        "result = run_algorithm(params, algo_input)\n",
        "\"\"\"\n",
        "\n",
        "#VGG# x = max_cut.sample_most_likely(result['eigvecs'][0])\n",
        "x = sample_most_likely(result['eigenstate'])\n",
        "\n",
        "print('energy:', result['eigenvalue'])\n",
        "print('time:', result['optimizer_time'])\n",
        "print('max-cut objective:', result['eigenvalue'] + offset)\n",
        "print('solution:', max_cut.get_graph_solution(x))\n",
        "print('solution objective:', max_cut.max_cut_value(x, w))\n",
        "plot_histogram(result['eigenstate'])\n",
        "\n",
        "colors = ['r' if max_cut.get_graph_solution(x)[i] == 0 else 'b' for i in range(n)]\n",
        "nx.draw_networkx(G, node_color=colors, node_size=600, alpha = .8, pos=pos)\n",
        "\n",
        "qubitOp_docplex, offset_docplex = set_up_Dcplx_model(w,x)\n",
        "print(x,offset_docplex)"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "qasm_simulator\n",
            "energy: (-1.57741525250531+0j)\n",
            "time: 11.721065282821655\n",
            "max-cut objective: (-3.1505405922012137+0j)\n",
            "solution: [0 0 1 0 1]\n",
            "solution objective: 2.406862004554557\n",
            "[1 1 0 1 0] 1.4268746603040965\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "AuUrMw1HgJBr",
        "papermill": {
          "duration": 0.10374,
          "end_time": "2020-03-12T04:30:51.338270",
          "exception": false,
          "start_time": "2020-03-12T04:30:51.234530",
          "status": "completed"
        },
        "tags": []
      },
      "source": [
        "## Results from runing on the IBMQ system "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "7117WBQAgJBv",
        "papermill": {
          "duration": 0.133988,
          "end_time": "2020-03-12T04:30:51.606039",
          "exception": false,
          "start_time": "2020-03-12T04:30:51.472051",
          "status": "completed"
        },
        "tags": [],
        "trusted": false,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "463e3e09-c54e-43e7-cf1e-829006a060ba"
      },
      "source": [
        "backend"
      ],
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<QasmSimulator('qasm_simulator') from AerProvider()>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 35
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "f-5STzregJBz",
        "papermill": {
          "duration": 12266.09723,
          "end_time": "2020-03-12T07:55:17.824722",
          "exception": false,
          "start_time": "2020-03-12T04:30:51.727492",
          "status": "completed"
        },
        "scrolled": true,
        "tags": [],
        "trusted": false,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "9452df53-40fc-49e6-cef4-851453ee00fd"
      },
      "source": [
        "# run quantum algorithm with shots\n",
        "seed = 10598\n",
        "\n",
        "spsa = SPSA(max_trials=30) #VGG 300\n",
        "ry = RY(model.num_qubits,  entanglement='linear') #depth=5,\n",
        "vqe = VQE(model, ry, spsa)\n",
        "\n",
        "#backend = provider.get_backend('ibmq_16_melbourne')#'ibmq_16_melbourne')#'ibmq_essex' # ibmq_london\n",
        "#backend = provider.get_backend('ibmq_qasm_simulator')\n",
        "quantum_instance = QuantumInstance(backend, shots=1024, seed_simulator=seed, seed_transpiler=seed)\n",
        "\n",
        "print(\"submiting for results using:\",backend)\n",
        "result = vqe.run(quantum_instance)\n"
      ],
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "submiting for results using: qasm_simulator\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "3Rt2smFtgJB2",
        "papermill": {
          "duration": 2.922226,
          "end_time": "2020-03-12T07:55:20.921701",
          "exception": false,
          "start_time": "2020-03-12T07:55:17.999475",
          "status": "completed"
        },
        "tags": [],
        "trusted": false,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 441
        },
        "outputId": "7b8901bc-5b0d-46bb-a5a9-da78e2b614ea"
      },
      "source": [
        "#VGG# x = max_cut.sample_most_likely(result['eigvecs'][0])\n",
        "x = sample_most_likely(result['eigenstate'])\n",
        "\n",
        "print('energy:', result['eigenvalue'])\n",
        "print('time:', result['optimizer_time'])\n",
        "print('max-cut objective:', result['eigenvalue'] + offset)\n",
        "print('solution:', max_cut.get_graph_solution(x))\n",
        "print('solution objective:', max_cut.max_cut_value(x, w))\n",
        "plot_histogram(result['eigenstate'])"
      ],
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "energy: (-0.57200142072691+0j)\n",
            "time: 1.9187567234039307\n",
            "max-cut objective: (-2.145126760422814+0j)\n",
            "solution: [0 1 1 0 1]\n",
            "solution objective: 2.581904340539446\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 504x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 37
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Xj66PNTl7rPZ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "outputId": "a5d407f2-9ecb-4309-b1b2-16d9a71f9822"
      },
      "source": [
        "colors = ['r' if max_cut.get_graph_solution(x)[i] == 0 else 'b' for i in range(n)]\n",
        "nx.draw_networkx(G, node_color=colors, node_size=600, alpha = .8, pos=pos)"
      ],
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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aIu2FcjIajaxevZrQ0FACAwPZvn07Xbt2lcAVFdK/f3+OHDlCUlKS1qWIGiKhayVFUfjyyy/p378/SUlJxMXFMWrUKOrVq6d1aaIOc3FxYdiwYSxfvlzrUkQNkfaCFZKTk4mOjiY9PZ2pU6fSqVMnrUsSNqRv375s2LCBX3/9lbvuukvrckQ1k5FuGXJzc1m4cCEjR46kS5cubN68WQJXVDknJydefPFFGe3aCQndElgsFnbt2kW/fv0oKChg27ZtDBw4EAcH+WAgqkefPn1ITk7myJEjWpciqpmkyE2OHDnC/PnzcXR0ZMmSJdx5551alyTsgJOTEy+99BKxsbHExMRoXY6oRhK6f7h8+TLvvfceP/74I2PHjqV79+4yI0HUqF69erF27VoSExPp0KGD1uWIamL37QWj0cj69esZOHAgfn5+bN++nWeffVYCV9Q4BwcHRowYQWxsLIqiaF2OqCZ2G7qKovDNN98QEhLC4cOHWbduHWPGjMHV1VXr0oQde/bZZ0lPT+eHH37QuhRRTeyyvXDmzBkWLFjAhQsXeO211+jcubPWJQkBgMFgYOTIkcTGxtKxY0f5xGWD7Gqkm5eXx5IlS3jxxRfp1KkT8fHxErii1unatStXr17lwIEDWpciqoFdhK7FYuGjjz6iX79+ZGdnk5CQwODBg3F0dNS6NCH+Rq/XXx/tSm/X9th8e+HXX39l3rx56HQ6FixYIFf8iDrhqaeeYvXq1XzzzTd06dJF63JEFbLZ0L1y5QrLli3jwIEDvPzyy/To0UO2OBd1hl6vJzIyktjYWB599FF57doQm/s/WVxcTFxcHMHBwXh6erJjxw569eolL1pR5zz++OPo9Xq+/PJLrUsRVcimRrr79+9nwYIF3HbbbaxZs4ZmzZppXZIQFabT6Rg1ahRLly7liSeekIGDjbCJ0D137hyLFi3i1KlTTJw4kUcffVSm2gib8Mgjj7Bq1Sr27t1L165dtS5HVIE6/aszPz+fZcuWMWzYMO699162bt3KY489JoErbMa10e7y5cuxWCxalyOqQJ0MXUVR2L17N/379yctLY34+HiGDh2Kk5OT1qUJUeUefPBBPD09+fTTT7UuRVSBOtde+O2335g/fz7FxcXMnTuXdu3aaV2SENXq2mh39uzZdOvWTXaZruOqNnSzs+G33+D8eSguBmdnCAqCO+6ASq5pkJmZSUxMDF999RVjxoyhd+/ecmJB2I0HHngAf39/Pv74Y/r06aN1OaISKh+6eXnwn//AypVw6hQ4OoLZDBYL6PVgMKgB3L49REbCk0+q97GSyWRi27ZtrF69mh49erBjxw4aNmxY6bKFqGtGjRrF9OnTefbZZ+Vqyjqs4qGrKPDJJ/DPf6rB6+gIHh5Q0kksRYGff4YxY8DXF5Yuhfvvv+WPOHjwINHR0Xh7e7NixQpatGhR4XKFqOvat29PYGAgH330EX379tW6HFFBFQvdwkKYOBH27AEXFzVsy6LTgZub+ucrVyAkBEaMgNdeU0fDN0lJSWHRokUkJSUxceJEHn/8cZmRIATqaPf111+nV69ef544Li5WP2VmZ6vvNU9Pta0nvd9aqfyhW1gIw4bBwYNq2Ja3r9qggdp+WLECsrJgzpzrxygoKGDdunVs27aNwYMHM2fOHJmRIMRf3H333bRu3Zr/bNlCX0dH2LQJjh9X30PX3osWi/rp8s47ITwcnn220udURNUpf+hOmQI//KD+Nq3o6NNgAHd32LoVmjVDiYzk888/Z8mSJbRv3574+Hh8fX0rdmwhbJnJxGQPD4rHjMHi74/e0REaNvz74MdshqQk9f06fbr6fdCg8g+SRJXTlbV03AMPPKD8+OOPf/7Dvn1qW8DdvWr+5xUXY8zJYWanTiQbDEyaNEn2hhKiNOfOwahRcOwYF3JycGnYEK9GjW79OKNRPe9y330QE6OeVxHVSqfTHVIU5YGSbrN+pGs0wuTJ6jSwKghck9nM5StXMGdkMOrsWZr8978yBUyI0iQnQ3Cw2pLz8MDL1ZWzZ87g6eFx6/eNk5N6ovt//4MXXoBt26BJk5qpW/yN9Sm3b5/aqK9kb0gBMjIzST55Eh3QuHVrmqanoz9xolLHFcJmZWVBaCjk5FyfIeTi7Ixr/fpkZGZadwydTn1sWhqEhUF+fvXWLEplfeiuWWPV3aZduEC333+nS1ISfU+eZFdW1vXb8vLzSU5OJjcnh8BmzfD398fg4KA2/rdsKXfxQtiFt96C9PQ/ZwD9wcfbm4wrVzCXZ00Gd3e1TfHuu1VcpLCWde0Fk0n9aNKgwS3vGuHtzTRHR5z0ek4XFTHyzBmaGwx45eRQUFCAn58fDRs25IZTcC4u8PXXFXsGQtiy/fvh44/VsLyJs7Mz9evXJzMjA29vb+uP6eYGmzdDv34gl9HXOOtGusnJ6scTK3quLZydcfrjfoqiUFxczKFz53B2cqJly5a43Ry4oPaJT5+GoqLyVS+ErXv//TLfe94+PlzJyCjfaNdgUKeUrVxZRUWK8rBupJuaWq7pYXNTU9mZnk5ecTGtHB3pHRiIu7MzJpPp+kUOOp1ODV+dTv2zwYCSmoouMFAuhBAC1DbAwYPqlLBSODs50bBBA85cvkxMcTHfXb2Kh4MDL/v40L2E0fF1DRvCp5+qFyt5eVVD8aI01rcXymGKvz+9MzM5arFwQq/nyqVLZKOeRENRUBTlzz//8b2e2czY3r1JcXLCYDDc8KXX63FwcLj+Z4PBgIODw/U/l/VVFx5rzX1lZocd+uEH9fst/t97+/gw9tgxPDw8+Kx1a44XFjLu3Dlau7jQwtm55AcZDOrXTz/B009XceGiLNaFbr165T7wHW3a4HnpEgeuXOGAqysRt5qikp3Nvz//HIuPDxaLBbPZfMOXxWLBZDJd/7PZbMZkMpV436p8bGFhoSY/96+PNZvNALXml0RteqxN/zI6dEi9yOEWzAYDPygKqxwccNXrae/qyuMNG/JxdjZjy5qTW1SkrokioVujrAvdli3V0a6iWN1mMOj1NGncmPpGI0mZmVxQFPz8/XEo6Xpwk0mdS+jri16nu/5GFH+6FtQ1Ffy3uq/RaKwVvxR1Op3mwV9dj232ww84A0pR0Y2tuGt//uP7qaIinB0dqZ+Tg8nXFweDgdudnUm81bQwR0f49ddqfuWKm1mXbD4+6syF4mI1HEuRYTLxY34+jzZogItOx/d5eXxRUMDsgAAcCgpIPnkSP39/3NzcbjyZVlionkWVXm6pbH5UV0F/DWatgv/aY00m0/VfRlXxc8cdPYpPbi5FWVnXW3GKotzQllOAYyYT+qIi8nU6Ui9e5LamTWmg15N3q5NrOp2cvNaAdaGr00HPnhAfX2bo6oDtmZlEXbyIBWjs6Mirfn484eYGbm64ubmRcvEiOdnZ+DdujOO10azZDLIws6iAa7+MbHJ92f791ZFo/fpl3i338mUKzp8nICCA3NxcLl++TJ5eT/1b/ZJWlAq1DkXlWP8ZPjxcXaCmjBaDp4MDK8rY9rxevXo0b96cK+npJCcn4+vri0eDBugMBgldIW7Wti0kJpYaumaLhdTUVOrl5+Pg7Ex+w4YEeHhw+tQpjuj1tLjVvHqTCe66qxoKF2Wx/vNqmzbw6KPqpcCV+YE6HT4+PjRr1oysrCwuJyeT+dxzf7vaRgi716FDqWviFhQWcio5Gb1Ox50tWvC0uzuxly9TrNOR6ePDlzk5PHGr0b+TE9xzTzUULspSvibh3LnqhQyFhZX+wS7OzgR5eUGTJoR+/z0bNmy4fpZeCAF06qR+/0tvVgHSr1zh3Nmz+Pr50bhxY/R6PVP8/SmyWHjm+HHeTkvjjSZNcL58mcLSerbmP7bUuu++6n8e4gblC11/f5g/HwoK1FXHKiM/H51Oh++2bazetIkDBw4wbNgwjh8/XrnjCmErmjSBzp3VhW6AYpOJs2fPcvXqVZo3b47bXy6acDMYWBAQwLd33MHHt9/O876++Pn7c+7cOYpLmmefk6Oep/H0rKlnI/5Q/tPhPXpAVJS6SlFFVipSFPV/uKLA2rVwzz3cdtttxMTE0L9/f0aPHs2//vUvjJUNdSFswZgxoCjk5uRwKjkZV1dXmjVrZtWJQ3c3Nzw9PTl37tyNlwmbzeoFFyNGVGPhojQVm4MUEgLr1qnLPGZmWn/FmtGoLlMXGAgffAAPP3z9Jp1Ox3PPPceWLVs4efIkgwYN4siRIxUqTwhbYWzfnu8DAsi9cIGmTZvi4+3997VLyuDl5UU9FxcuXLjA9e0KcnPhxRfVE3WixlV84uejj6pr7A4apPZ4s7LUEazRqI5iQf1eVKTedu0E3IQJsHu3un9TCXx8fJg/f/71Dfiio6PJl7U/hR1KTk5m6NCh7L7vPnzvuQfX4uJyH0MH+Pv7g6KQmpqKkpUFzZur70OhifJt11OanBz4z3/UED58GC5fVj++KArcdhu0b69ujvf00+qJOCtlZ2ezcOFCfvrpJ9544w0eeughqx8rRF2lKAo7d+4kJiaGsWPH0qdPH3Tnz8OAAep764+FzMvDbDZz+fffoWlT/L/+WrbsqWZlbddTNaF7s+Ji9cvZuUq2gd6/fz9RUVF07NiRCRMm4CbTy4SNysnJYfbs2Zw/f56oqCiCgoL+vDE1FV5+WV2kxtXV+gFMYSEUFFDQoQNDMzMZOWUKT8t6C9WqrNCtnutKHR3VF0UVBC5A586dSUhIoF69egQHB7Nv374qOa4QtUliYiKhoaH4+/uzbt26GwMX1NlDCQnw9tvq37Oz1f5sSedUTCb1E2h2Njg4wLvvUi8hgdkxMcydO1fOl2ioeka61ejw4cPMnDmTli1b8vrrr5dvxXwhaiGz2czKlSvZuXMnb731Fp07d771gwoL4bPPYNMmOHJEnZFwbZBjNqsXPtx7LwweDP/4xw2X7+/fv58ZM2awatUqAgICqulZ2beaby9UM6PRyKpVq9i5cydjx46ld+/esvC5qJNSUlKYOnUqrq6uzJgxA6+KLChusUBKijqqvbYBZePGZfZ9P/jgA+Li4lizZg0eHh6VeAaiJDYXutccP36cGTNm4O7uztSpU2ki20qLOuSzzz5j/vz5DB06lLCwsBpfRW7ZsmUkJiYSGxuLUxkLWYnyq/mebg1p3bo1GzZs4MEHH2TIkCFs2bIFS3n2ihJCA/n5+cycOZPY2FiWLl3K4MGDNVm2c/To0fj7+/PWW2/J+6YG1enQBXU3haFDh7J27Vr27dvH8OHDSU5O1rosIUp07NgxBg8eDEBcXBx3ljJfvSbo9Xrefvtt0tLSeP/99zWrw97U+dC9JjAwkOXLl9OzZ09GjhzJqlWrKK7AZHIhqoPFYmHTpk2MHTuWUaNGMX36dFxdXbUuCycnJxYsWMAXX3zBBx98oHU5dsFmQhfU39z9+/dn06ZN/PzzzwwZMoSjR49qXZawcxkZGYwbN469e/eyfv16unbtqnVJN/Dw8GDJkiXExsayf/9+rcuxeTYVutf4+fmxePFihg0bxvjx41myZAmFVbAcpRDltX//fsLCwrjzzjtZuXJlrT3ZGxAQQHR0NNOnT5eV/qqZTYYuqAvodO/ena1bt3Lp0iUGDhzIoUOHtC5L2Amj0cjChQuZPXs2c+bMYfTo0bV+s9V27doxZcoUxo8fT1pamtbl2CybDd1rPD09iYqKYuLEiUybNo2oqCiuXr2qdVnChp05c4aIiAhSUlLYsmUL999/v9YlWe3pp58mNDSUcePGkZeXp3U5NsnmQ/eaLl26kJCQAEBwcDBff/21xhUJW6MoCh9++CHDhw+nb9++zJ8/H3d3d63LKrfBgwdz7733MnnyZEzWLtsqrFanL46oqEOHDjFr1izatm3LpEmTaNSokdYliTouNzeXqKgoTp06RVRUFC1atNC6pEoxm81MnDgRHx8f3nzzTbnis5xs9uKIirr//vuJj4/H39+fgQMH8sknn1DWLx8hynL48GHCwsLw9PRk/fr1dT5wQZ3//s477/Dbb7+xbt06rcuxKXY50v2ro0ePMnPmTPz8/HjjjTfw8/PTuiRRR1gsFlavXs22bduYOnUqXbp00bqkKnf58mUiIoieutYAABVhSURBVCIYO3Ys3bp107qcOkNGumVo27YtGzdupF27dgwaNIjt27fLJZHillJTU4mMjCQxMZG4uDibDFxQd3JZvHgx0dHR/PTTT1qXYxPsPnQBHB0dGT58OCtWrODjjz8mMjKSs2fPal2WqKX27dtHeHg4jzzyCO+//z6+Nr4LQ6tWrZg9ezaTJ0/mzJkzWpdT50no/kWLFi1YvXo1//jHP4iIiGD9+vWYzWatyxK1RGFhIXPmzGHJkiUsWrSIYcOGabJQjRYefPBBXn75ZV555RUyMjK0LqdOs49XTDno9XoGDhzIxo0bOXjwIEOHDpUrdATHjx9nyJAhFBUVsXnzZu666y6tS6pxffr0oXv37kycOJGioiKty6mzJHRL0aRJE5YtW0ZISAhjxowhJiYGo9GodVmihimKQnx8PKNHjyYiIoKZM2dSv359rcvSzKhRo2jatCnTpk2Tcx8VJKFbBp1OR+/evYmPj+f06dOEhoZy+PBhrcsSNSQzM5MJEyawe/du1q5dS48ePbQuSXM6nY7p06eTlZXF0qVLtS6nTpLQtYKXlxfz5s1jzJgxTJ48mXnz5pGfn691WaIaff/994SFhdGyZUtWr14te4n9hZOTE9HR0XzzzTfXr/IU1pPQLYennnqKhIQECgsLCQkJ4cCBA1qXJKpYcXExS5cuZcaMGcyYMYOxY8fi6OiodVm1jpubG0uXLmXNmjV88803WpdTp9j9xREV9d133xEVFcV9993HxIkT6+Q19uJG586d480338TLy4vp06fj6empdUm13i+//ML48eN57733NN0Fo7aRiyOqwUMPPUR8fDxubm6EhISwd+9euZS4jlIUhY8//piIiAh69erFwoULJXCtdPfdd/Pmm28yceJELl68qHU5dYKMdKvAkSNHmDVrFs2aNWPy5Mn4+PhoXZKwUl5eHu+88w5JSUlERUVx++23a11SnbR582Z27drF6tWradiwodblaE5GutWsXbt2bNq0iVatWhEWFsaHH34oo9464OeffyYsLAxXV1c2btwogVsJoaGhdOzYkddff132JrwFGelWsd9//52ZM2fSoEEDpk6dym233aZ1SeImFouFdevWER8fz5QpU3jqqae0LskmWCwWJk2ahLu7O9OnT7fr5SBlpFuDbr/9dtatW0fnzp0JDw9n8+bNMom8FklLS2P06NF89913bNy4UQK3Cun1eubMmcOJEydYvXq11uXUWhK61cBgMDBkyBDWrVvHl19+yYsvvsjJkye1LsvuffXVVwwePJiOHTsSGxsry3hWg3r16rF48WI+/PBDdu/erXU5tVLt3imvjgsICCA2NpZdu3YRGRlJcHAwERERMu+zhhUVFbF48WL++9//Eh0dTbt27bQuyaZ5eXmxZMkSIiMj8fPzq1N7xNUEGelWM71eT9++fdm8eTO//fYbgwcP5tdff9W6LLtx8uRJwsPDyc7OZtOmTRK4NaRFixZERUXxz3/+k1OnTmldTq0ioVtDfH19WbhwIcOHD2fChAksWrSIwsJCrcuyWYqisG3bNiIjIxk0aBBz5syRqUw1rGPHjowbN45x48bJcpB/IaFbg3Q6HV27diUhIYGMjAxCQkL44YcftC7L5mRnZzNp0iQ+/PBD1qxZQ58+fez6TLqWevbsSa9evRg/fjwFBQVal1MrSOhqwMPDg1mzZvHaa6/x9ttvM3v2bHJzc7Uuyyb8+OOPhIaGEhAQwJo1awgMDNS6JLs3YsQImjdvztSpU2UmDxK6mnr00UdJSEjAwcGBkJAQvvrqK61LqrNMJhMxMTFMnTqVadOmMX78eJycnLQuS6B+wps6dSp5eXksWrRI63I0JxdH1BKJiYnMnj2bNm3a8Nprr9GoUSOtS6ozLly4wJtvvombmxtvv/22/LerpXJzcxk+fDgvvPACoaGhWpdTreTiiDqgQ4cObNmyhSZNmjBw4EB2794tlxJb4dNPP2Xo0KF07dqVxYsXS+DWYg0bNmTx4sVs2LDBrj/VyUi3Fvrtt9+YNWsW3t7evPHGG/j7+2tdUq2Tn5/Pu+++y88//8w777xDmzZttC5JWOno0aO88sorLF26lLZt22pdTrWQkW4dc+edd7Jhwwbat2/P4MGDSUhIkBMQf3H06FEGDRqEwWAgLi5OAreOadu2LdOnT2fixImkpKRoXU6Nk5FuLXf69GlmzpyJXq9n2rRpNGvWTOuSNGOxWIiLi2Pjxo28/vrrPPPMM1qXJCohISGBhIQE1qxZg5ubm9blVCkZ6dZhQUFBrFq1iq5du/Liiy+ydu1aTCaT1mXVuPT0dMaOHcuXX37J+vXrJXBtQHBwMJ07d+a1116zq522JXTrAL1eT3BwMHFxcSQmJhIeHk5SUpLWZdWYb7/9lkGDBtGuXTtWrlxJkyZNtC5JVJHx48fj5ubG7Nmz7ebEsbQX6hhFUdi9ezdLliyhT58+jBgxAmdnZ63LqhZGo5GlS5fyxRdfMGvWLDp06KB1SaIaFBYWEhkZSefOnYmMjNS6nCoh7QUbotPp6NmzJ/Hx8Zw/f57Q0FB++uknrcuqcqdOnWLYsGGkpaWxZcsWCVwb5uLiwqJFi/j444/56KOPtC6n+imKUurX/fffr4jabd++fUr37t2VuXPnKlevXtW6nEqzWCzKBx98oDz11FPKjh07FIvFonVJooacOnVKeeaZZ5Tvv/9e61IqDfhRKSVXZaRbxz355JNs3boVo9FISEgI+/fv17qkCsvJyWHy5MkkJCSwcuVK+vbtKwvV2JGgoCDmzp3Lm2++adOL/kvo2gA3NzemTZvG9OnTmTt3LtOnTycrK0vrssrlp59+IiwsDF9fX9avX0+LFi20LklooEOHDrz66quMHz+e9PR0rcupFhK6NqRTp05s3boVDw8PQkJC+Oyzz2r9GWGz2czy5cuZPHkykydPZtKkSbJQjZ3r3r07L7zwAuPHjyc/P1/rcqqczF6wUT///DOzZs2iadOmTJkyBV9fX61L+puLFy8ydepUnJ2dmTlzJt7e3lqXJGoJRVGYNWsWGRkZLFiwAIPBoHVJ5SKzF+zQPffcQ1xcHHfccQdhYWHs3Lmz0qNeoxFOnYKkJEhOhspsfLF3717Cw8N5/PHHWbZsmQSuuIFOp+ONN97AaDQSHR1d6z+xlYeMdO3AiRMnmDlzJq6urkydOpWmTZta/diUFNiyBfbsUYPWYACdDhQFTCZo1gyefhpCQ6F581sfr6CggOjoaA4dOkRUVJTNLngiqsbVq1cZPnw4ffr0YdCgQVqXYzUZ6dq5Vq1asW7dOh577DGGDh1KXFzcLRfQSU+HMWOgSxeIiYHz58HNDRo2hAYN1O/u7nDpEqxeDc88A8OGwYULpR8zKSmJwYMHYzKZ2Lx5swSuuKUGDRqwZMkSNm3axL59+7Qup0rISNfOnD9/njlz5pCXl8f06dNp1arV3+6zZw+89hrk56tBq7fiV7OiQHY2ODrCrFnQv/9fb1PYsmULa9asYdKkSXTv3r0Kn5GwB0lJSbz88sssXLiQe+65R+tybklGuuK6pk2bEhMTQ9++fRk1ahTLly+/YbGRTZtg9GiwWMDDw7rABbXl4OEBDg4weTIsXar+e0ZGBuPGjWPPnj2sX79eAldUSJs2bXj77beZNGkS58+f17qcSpGRrh1LS0tj7ty5nD9/nmnTppGScg+jR6vtA0fHih/XZILcXAgP/50DB8bSu3dvIiMjcXBwqLrihV3asWMHmzZtYu3atbi7u2tdTqnKGulK6No5RVHYu3cvUVErOXbsfTw9vXB1rdwHIEWxkJJyhZycIjZvvsJzz91bRdUKAUuXLuXIkSPExMTU2jnd0l4QpdLpdDzzzDO0aLGRoiI9KSknycvLq/DxjMYiTp8+jcVSiJ9fY+LiJHBF1Xr55Zfx8vLi7bffrpM7qkjoCi5cgK++ciYoyAt//8ZcvJjCxYspmM3mchxFITs7i9OnT+Ph4UFAQFM8PQ38739w9Gi1lS7skF6vZ+bMmaSmphIbG6t1OeUmoSuIj1dnH+j16hSdFi1aoNPpSU4+SW5uzvX7WSxGUlJmcuJEL5KSupCcHMbVq/uxWMxcuHCBK1eu0KxZMzw9GwE6dDr1hNz69do9N2GbnJ2dWbBgAZ999hm7du3SupxykTMbgj17wMXlz7/r9Qb8/f1xc3Pj4sUUsrNz8Pf3R6834+joT2DgChwd/bl69b+cO/c6BsNc3Nxa0rx5c3S6G3+P168Pe/fW8BMSdsHT05OlS5fy0ksv4e/vz0MPPaR1SVaRka6dMxrVK81K2nzC1dWVFi1a4OTkRHJyMrm5Rfj4jMDJqQk6nY6iojswGt1xd8/C37/x3wIX1FkQWVlw5UoNPBlhdwIDA5k3bx7Tpk3j+PHjWpdjFQldO3f+vHppb2nzcXU6Pb6+vgQGBpKRkcHZs+coKMjnzJkz5Oam4OSUgYfH3aUeX6cDJyd1zQYhqkP79u157bXXmDBhAmlpaVqXc0sSunbOaLTuAggXFxeCgppTv74rZ8+eJS8vh/z8aAyGx8nJqU9WVhZ5eVcxGotQlL+fUbajzV6FBrp27UpwcHCdWA5Serp2zslJPYlmDZ1Oh5eXN56eHpw79wZmcwM8PV/FZFLIz8/HZCqmuFj90uv1ODo64uDgiKK4smfPd1y96oifnx/+/v54e3vXueX6RO0WHh7OhQsXmDJlCosWLaq1ry8JXTvXpAkUF6vBa83OOIqikJo6B8gmKGgpen1JOxErmExmTKZijMZicnJ0GAwX2LcvmUuXLpGamkpmZiZeXl7XQ/ja17W/+/n54e7uLtv1CKvpdDomT57MhAkTePfdd/nnP/9ZK18/ckWa4Ikn1FXF/jqDoTQXL0ZRVHScwMAY9HrXW97/WqAfPnxjqJtMJtLS0q6HcEnfi4qKbgjikoLZxZqihV3Jz8/npZdeonv37oSHh2tSQ1lXpMlIV/D007B27a1Dt7j4IllZH6DTOfH7792u/7u//xu4uz9b4mPy8uDZZ/8+inZwcKBJkyY0adKk1J+Xn59/PYSvBXFiYuINwVyvXr0yQ9nHx6fWfswU1cPV1ZXFixcTERFB48aNeeaZZ7Qu6QYy0hUkJ0PXrur6uFX5aUxRICcHtm6FDh2q7rh/Hl8hMzOzzNFyRkYGjRo1KjWU/f39pY1ho44fP86YMWOIjo7m3ntr9nJ0WfBG3FJ4OOzfry7PWFVycqBFC/jkk6oN8/IwmUxcvnz5htFySW2MskbLfn5+1KtXT5snICrlwIEDvPXWW6xatYrAwMAa+7kSuuKWzp1Td39wclK/KstkUhdB37ULavsGEX9tY5T23cXFpczRsrQxaq+dO3eyYcMG1qxZg6enZ438TAldYZWtW+Gf/1R3i6jM0rcWi7qLxPjxMHZs1dWnFUVRyMrKuiGEpY1Rt7z//vscOnSIf/3rXziXdPllFZPQFVZbvFjd9aFBg4qNeK8tYD5wIMyerV1boab9tY1R2mj55jbGzaEsbYzqY7FYmDp1KhaLhaioKPQ3XRGUkQHffAOHDsH//qe+hg0GuO02ePBB9ZxEp07l2UlFQldYSVEgLg7mzFED1NqTa4qivlBBHd2OGWP9C9RelLeNUVJASxuj4oxGI6NHj6Zdu3a88sorABw/DsuWwaefqq9hs1mdxXPttWs0qu8DBwdo1AhGjIDBg0teq+SvJHRFuZ06Ba++Cj//rLYLGjRQX3g3B3BxsTotTKeDli1h4cLa38OtrUpqY9z8/eY2RkmjZQ8PD2ljlCI7O5uIiAhCQgZz+XJfli5Vg9bNTR3ZlqWgAAoLITAQliyBdu1Kv6+ErqgQRYFff4V16+D//k+djfDXloPJBPXqwWOPQUQE3H+//bQTtFLeNkZJ3/38/HB1vfWFLbYqKek8jz9+AoPhQby965V7P8CcP5aYnjcPnn++5PtI6IoqcfkynD6tfuRydISAAPD3l6Ctba61MUoL5dLaGDdfVGKLG4kWFV2bHllEVtYZmjULrNBVjUaj+glvyRLo1evvt0voCiGuK28bo7RRc11sY8ydCytXqvPRr17NITX1EkFBQThWYPvroiL1096ePWrL4a8kdIUQ5XKtjVHWaLmwsLDM0XJta2McOQL9+qm7mVwbxGdkXCErK4ugoCD0+vKfoMzKgnvvhW3bbjxxLGsvCCHKxcHBgcaNG9O4ceNS71NSG+Pw4cN89tlnf2tjlDZarsk2xty56nmKv/64Ro0aYTQaOX/+PAEBgeUeubu7q4s57d8Pjz5q3WMkdIUQFeLq6krz5s1p3rx5ibdfa2PcPEpOSkr6Wxvj5jCu6jbG6dNw8KA6S+FGOvz9/Tl37hypqRdxdv6G7Oz/UFR0Aje3bjRp8naZx71W1qpVErpCCI3pdDo8PT3x9PTkjjvuKPE+JbUxzpw5w8GDB//WxihrRsat2hh79qhTH0ueO67jtttu48yZM5hMTnh7D+fq1QMoSpFVz9PNDb79Vp2n3rDhre8voSuE0Iw1bYyCgoK/jZaPHDlyPZSvtTHKCuX//tcfB4fSr9bR6w0EBARw+rQZRfHFYDiKyWTdfmt6vdqyOHYMOna04jlbdVQhhNBIvXr1CAoKIigoqMTbS2tjHD9+/Hoof/XVAvR6ZzIydNe3kXJ0dMTR0eH63x0cHAgICODMmbO4uhaV64rK4mJISpLQFULYAWvaGG3aKDg5mTCbi6/v5Wc0GsnLy7v+d4vFgqOjIwaDnoyMDLy8rE9ds1ld5MkaErpCCJun0+lwcHDE2bn0+bgWi+V6AF+54oFOl2v18a3d3BVkC3YhhB1o1Ei9kKEser0eJydn6tdvgItL+VZ7c3ICHx/r7iuhK4Sweffeqy5WcyuKYsZiMQIWwILFYkRRzLd8nMEApXQ2/kZCVwhh8zp3VqeM3Up6+mqSkjpz5co6srN3k5TUmfT01WU+xmxWj926tXW1SE9XCGHzuneHmTPVgCxrCUcfn5H4+Iws17FzctTVxqxdN0dGukIIm+fjA926/bksY1WxWNSr0oYOtf4xErpCCLvw+uvqkqRGY9UdMycHnn227AXNbyahK4SwC4GB8Oab6jq41vR3byUvT73sd8aM8j1OQlcIYTcGDYK+fdUlGSsTvNe2qFqzRp2OVh4SukIIu6HXw7vvQmioegVZQUH5Hq8okJmptini4uC++8pfQ5mLmOt0usvAmfIfVggh7FozRVFKvFyizNAVQghRtaS9IIQQNUhCVwghapCErhBC1CAJXSGEqEESukIIUYP+P4vy4bsJj3e4AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7LO-UVXs7FWE",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#VGG define the above as a function \n",
        "\n",
        "def Max_Cut_IBMQ(W,*c_x0): \n",
        "\n",
        "  qubitOp_docplex, offset_docplex = set_up_Dcplx_model(W)\n",
        "  \n",
        "  for h in c_x0:\n",
        "    qubitOp_docplex, offset_docplex = set_up_Dcplx_model(W,h)\n",
        "\n",
        "  model=qubitOp_docplex\n",
        "\n",
        "  spsa = SPSA(max_trials=30) #VGG 300\n",
        "  ry = RY(model.num_qubits,  entanglement='linear') #depth=5,\n",
        "  vqe = VQE(model, ry, spsa)\n",
        "\n",
        "  quantum_instance = QuantumInstance(backend, shots=1024, seed_simulator=seed, seed_transpiler=seed)\n",
        "\n",
        "  result = vqe.run(quantum_instance)\n",
        "  x = sample_most_likely(result['eigenstate'])\n",
        "  cost_vqe=max_cut.max_cut_value(x, W)\n",
        "  x_vqe =np.int_(max_cut.get_graph_solution(x)).tolist()\n",
        "\n",
        "  return cost_vqe, x_vqe"
      ],
      "execution_count": 39,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oZC9L_SRDnpb",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 459
        },
        "outputId": "892bb9f3-4d0a-4bc4-d0e8-dd237a5ef397"
      },
      "source": [
        "%time market_simulations(10)"
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Using Max_Cut_BF\n",
            "day  [free samples]  [buyers distribution]  [to be used as constrain]  the two totals  w-det\n",
            "0 [1 0 0 1 0] [0 0 1 0 1] [1. 0. 0. 1. 0.] 2 2 1.0000000000000009\n",
            "1 [0 0 0 0 0] [0 0 1 1 1] [0. 0. 0. 0. 0.] 2 5 1.000000000000001\n",
            "2 [1 0 0 1 0] [0 0 1 0 0] [1. 0. 0. 1. 0.] 4 6 1.000000000000001\n",
            "3 [0 0 0 0 0] [0 1 0 1 0] [0. 0. 0. 0. 0.] 4 8 1.000000000000001\n",
            "4 [1 0 0 1 0] [0 0 1 0 1] [1. 0. 0. 1. 0.] 6 10 1.000000000000001\n",
            "5 [0 0 0 0 0] [1 0 0 0 1] [0. 0. 0. 0. 0.] 6 12 1.000000000000001\n",
            "6 [1 0 0 1 0] [0 1 1 0 0] [1. 0. 0. 1. 0.] 8 14 1.000000000000001\n",
            "7 [0 0 0 0 0] [0 0 0 1 1] [0. 0. 0. 0. 0.] 8 16 1.000000000000001\n",
            "8 [1 0 0 1 0] [0 0 1 0 0] [1. 0. 0. 1. 0.] 10 17 1.0\n",
            "9 [0 0 0 0 0] [1 1 0 0 0] [0. 0. 0. 0. 0.] 10 19 1.0\n",
            "\n",
            "last day configuration record:\n",
            "\n",
            "[0 0 0 0 0] [0.96 0.67 0.84 0.65 0.63]\n",
            "\n",
            "[1 1 0 0 0] 10 19 3.4230628351014545 1.0\n",
            "\n",
            "[[1.29 0.58 0.6  0.16 0.65]\n",
            " [0.58 1.29 0.4  0.   0.  ]\n",
            " [0.6  0.4  1.29 0.57 0.  ]\n",
            " [0.16 0.   0.57 1.29 0.2 ]\n",
            " [0.65 0.   0.   0.2  1.29]]\n",
            "CPU times: user 212 ms, sys: 11.4 ms, total: 223 ms\n",
            "Wall time: 213 ms\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PTk0dxdxDxdi",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 459
        },
        "outputId": "d96f190c-081a-4458-eb85-07a17fae15a7"
      },
      "source": [
        "%time market_simulations(10,'dcplx')"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Using Max_Cut option: Docplex\n",
            "day  [free samples]  [buyers distribution]  [to be used as constrain]  the two totals  w-det\n",
            "0 [1 0 0 1 0] [0 1 1 0 1] [1. 0. 0. 1. 0.] 2 3 1.0000000000000009\n",
            "1 [0 0 0 0 0] [1 1 1 0 0] [0. 0. 0. 0. 0.] 2 6 0.9999999999999993\n",
            "2 [1 0 0 1 0] [0 1 1 0 1] [1. 0. 0. 1. 0.] 4 9 0.9999999999999993\n",
            "3 [0 0 0 0 0] [1 0 0 0 0] [0. 0. 0. 0. 0.] 4 10 0.9999999999999993\n",
            "4 [1 0 0 1 0] [0 0 1 0 1] [1. 0. 0. 1. 0.] 6 12 0.9999999999999993\n",
            "5 [0 0 0 0 0] [0 0 1 1 0] [0. 0. 0. 0. 0.] 6 14 0.9999999999999993\n",
            "6 [1 0 0 1 0] [0 0 1 0 1] [1. 0. 0. 1. 0.] 8 16 0.9999999999999993\n",
            "7 [0 0 0 0 0] [1 0 1 0 0] [0. 0. 0. 0. 0.] 8 18 0.9999999999999993\n",
            "8 [1 0 0 1 0] [0 1 1 0 0] [1. 0. 0. 1. 0.] 10 20 1.0000000000000007\n",
            "9 [0 0 0 0 0] [0 0 0 0 1] [0. 0. 0. 0. 0.] 10 21 1.0000000000000007\n",
            "\n",
            "last day configuration record:\n",
            "\n",
            "[0 0 0 0 0] [0.96 0.67 0.84 0.65 0.63]\n",
            "\n",
            "[0 0 0 0 1] 10 21 3.4345884086636813 1.0000000000000007\n",
            "\n",
            "[[1.3  0.58 0.6  0.16 0.66]\n",
            " [0.58 1.3  0.4  0.   0.  ]\n",
            " [0.6  0.4  1.3  0.58 0.  ]\n",
            " [0.16 0.   0.58 1.3  0.21]\n",
            " [0.66 0.   0.   0.21 1.3 ]]\n",
            "CPU times: user 132 ms, sys: 10.3 ms, total: 142 ms\n",
            "Wall time: 135 ms\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "D6nVmQc780iT",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 476
        },
        "outputId": "19b3b00c-9b2b-4cab-97c1-4e6b96d06e06"
      },
      "source": [
        "#backend = provider.get_backend('ibmq_16_melbourne')#'ibmq_16_melbourne')#'ibmq_essex' # ibmq_london\n",
        "#backend = provider.get_backend('ibmq_qasm_simulator')\n",
        "#backend = Aer.get_backend('qasm_simulator')\n",
        "#backend = Aer.get_backend('statevector_simulator')\n",
        "%time market_simulations(10,'q')"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Using Max_Cut option: q\n",
            "submiting for results using: statevector_simulator\n",
            "day  [free samples]  [buyers distribution]  [to be used as constrain]  the two totals  w-det\n",
            "0 [1 0 0 0 0] [0 1 0 1 1] [1. 0. 0. 0. 0.] 1 3 1.0000000000000009\n",
            "1 [0 0 1 0 0] [1 0 0 0 0] [1. 0. 1. 0. 0.] 2 4 1.0000000000000002\n",
            "2 [0 0 0 0 0] [1 0 1 0 1] [0. 0. 0. 0. 0.] 2 7 1.0000000000000002\n",
            "3 [1 0 0 1 0] [0 0 1 0 1] [1. 0. 0. 1. 0.] 4 9 1.0000000000000002\n",
            "4 [0 0 0 0 0] [0 1 0 1 0] [0. 0. 0. 0. 0.] 4 11 1.0000000000000002\n",
            "5 [0 1 1 0 0] [1 0 0 1 0] [0. 1. 1. 0. 0.] 6 13 1.0000000000000002\n",
            "6 [0 0 0 0 0] [0 1 1 0 0] [0. 0. 0. 0. 0.] 6 15 1.0000000000000002\n",
            "7 [0 1 1 0 1] [1 0 0 1 0] [0. 1. 1. 0. 1.] 9 17 1.0000000000000002\n",
            "8 [0 0 0 0 0] [0 1 1 0 0] [0. 0. 0. 0. 0.] 9 19 0.9999999999999992\n",
            "9 [0 1 1 0 0] [1 0 0 1 0] [0. 1. 1. 0. 0.] 11 21 0.9999999999999992\n",
            "\n",
            "last day configuration record:\n",
            "\n",
            "[0 1 1 0 0] [ 0.35 -0.51 -0.51  0.17  0.  ]\n",
            "\n",
            "[1 0 0 1 0] 11 21 3.4281866860962196 0.9999999999999992\n",
            "\n",
            "[[1.29 0.58 0.6  0.16 0.66]\n",
            " [0.58 1.29 0.4  0.   0.  ]\n",
            " [0.6  0.4  1.29 0.57 0.  ]\n",
            " [0.16 0.   0.57 1.29 0.2 ]\n",
            " [0.66 0.   0.   0.2  1.29]]\n",
            "CPU times: user 2.65 s, sys: 73.5 ms, total: 2.73 s\n",
            "Wall time: 2.75 s\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "B-s4-BJTkauc",
        "papermill": {
          "duration": 0.114454,
          "end_time": "2020-03-12T07:55:21.151502",
          "exception": false,
          "start_time": "2020-03-12T07:55:21.037048",
          "status": "completed"
        },
        "tags": []
      },
      "source": [
        "\n",
        "\n",
        "# **Acknowlegments**\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mVna1OYNJUA6",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "2babf7fc-ffff-49f3-9a18-2bcd93f9e7a9"
      },
      "source": [
        "import qiskit.tools.jupyter\n",
        "%qiskit_version_table\n",
        "%qiskit_copyright"
      ],
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<h3>Version Information</h3><table><tr><th>Qiskit Software</th><th>Version</th></tr><tr><td>Qiskit</td><td>0.19.6</td></tr><tr><td>Terra</td><td>0.14.2</td></tr><tr><td>Aer</td><td>0.5.2</td></tr><tr><td>Ignis</td><td>0.3.3</td></tr><tr><td>Aqua</td><td>0.7.3</td></tr><tr><td>IBM Q Provider</td><td>0.7.2</td></tr><tr><th>System information</th></tr><tr><td>Python</td><td>3.6.9 (default, Apr 18 2020, 01:56:04) \n",
              "[GCC 8.4.0]</td></tr><tr><td>OS</td><td>Linux</td></tr><tr><td>CPUs</td><td>1</td></tr><tr><td>Memory (Gb)</td><td>12.715869903564453</td></tr><tr><td colspan='2'>Wed Jul 01 02:28:50 2020 UTC</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 Qiskit</h3><p>&copy; Copyright IBM 2017, 2020.</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></div>"
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              "<IPython.core.display.HTML object>"
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    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "5bI3CphPgJB5",
        "papermill": {
          "duration": 0.297616,
          "end_time": "2020-03-12T07:55:21.640494",
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          "status": "completed"
        },
        "tags": [],
        "trusted": false,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "2d704c34-be5f-4f87-9b0f-46afe52dfacb"
      },
      "source": [
        "import qiskit.tools.jupyter\n",
        "%qiskit_version_table\n",
        "%qiskit_copyright"
      ],
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<h3>Version Information</h3><table><tr><th>Qiskit Software</th><th>Version</th></tr><tr><td>Qiskit</td><td>0.19.6</td></tr><tr><td>Terra</td><td>0.14.2</td></tr><tr><td>Aer</td><td>0.5.2</td></tr><tr><td>Ignis</td><td>0.3.3</td></tr><tr><td>Aqua</td><td>0.7.3</td></tr><tr><td>IBM Q Provider</td><td>0.7.2</td></tr><tr><th>System information</th></tr><tr><td>Python</td><td>3.6.9 (default, Apr 18 2020, 01:56:04) \n",
              "[GCC 8.4.0]</td></tr><tr><td>OS</td><td>Linux</td></tr><tr><td>CPUs</td><td>1</td></tr><tr><td>Memory (Gb)</td><td>12.715869903564453</td></tr><tr><td colspan='2'>Wed Jul 01 02:28:50 2020 UTC</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 Qiskit</h3><p>&copy; Copyright IBM 2017, 2020.</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></div>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
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}