max_cut_v4-5q-YorkTown-ibmqx2.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"
   },
   "source": [
    "#Main Code Cells "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "kxbANBKN4-I5"
   },
   "source": [
    "## Import libraries\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "Ghbqos6FsC2v"
   },
   "outputs": [],
   "source": [
    "import warnings\n",
    "#warnings.filterwarnings('ignore', 'DeprecationWarning')\n",
    "warnings.filterwarnings('once')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "dPKtKtBOLpr3"
   },
   "outputs": [],
   "source": [
    "#%pip uninstall qiskit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "GsfRwjclGyHn"
   },
   "outputs": [],
   "source": [
    "#%pip install qiskit #==0.16"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 547
    },
    "colab_type": "code",
    "id": "BYV9mVvpJKIX",
    "outputId": "bd9dc120-053e-4856-992b-e6e892b1097e"
   },
   "outputs": [
    {
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       "<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>3.7.6 | packaged by conda-forge | (default, Jun  1 2020, 18:57:50) \n",
       "[GCC 7.5.0]</td></tr><tr><td>OS</td><td>Linux</td></tr><tr><td>CPUs</td><td>8</td></tr><tr><td>Memory (Gb)</td><td>31.416831970214844</td></tr><tr><td colspan='2'>Wed Jul 01 07:45:23 2020 UTC</td></tr></table>"
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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>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import qiskit.tools.jupyter\n",
    "%qiskit_version_table\n",
    "%qiskit_copyright"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-12T17:59:38.109248Z",
     "start_time": "2019-12-12T17:59:38.098188Z"
    },
    "colab": {},
    "colab_type": "code",
    "id": "NYl6i6iKgJAA",
    "papermill": {
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     "end_time": "2020-03-12T03:56:22.244228",
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     "status": "completed"
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    "tags": []
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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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "4GqrhgSDgJAF",
    "papermill": {
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     "end_time": "2020-03-12T03:56:22.589262",
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     "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",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-12T17:59:38.838143Z",
     "start_time": "2019-12-12T17:59:38.836008Z"
    },
    "colab": {},
    "colab_type": "code",
    "id": "1a-_dBFBgJAH",
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     "duration": 3.557514,
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     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from qiskit import IBMQ\n",
    "provider = IBMQ.load_account()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "gBmv-6VbgJAL",
    "outputId": "c587a915-d329-4a3c-faf8-7b88656b4b98",
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     "duration": 0.082241,
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     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0, 1], [0, 14], [1, 0], [1, 2], [1, 13], [2, 1], [2, 3], [2, 12], [3, 2], [3, 4], [3, 11], [4, 3], [4, 5], [4, 10], [5, 4], [5, 6], [5, 9], [6, 5], [6, 8], [7, 8], [8, 6], [8, 7], [8, 9], [9, 5], [9, 8], [9, 10], [10, 4], [10, 9], [10, 11], [11, 3], [11, 10], [11, 12], [12, 2], [12, 11], [12, 13], [13, 1], [13, 12], [13, 14], [14, 0], [14, 13]]\n"
     ]
    }
   ],
   "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",
    "    #backend = provider.get_backend('ibmq_5_yorktown')#'ibmq_london')#'ibmq_16_melbourne')#'ibmq_essex')\n",
    "    \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)\n",
    "\n",
    "#VGG we will generate a diferent coupling_map for the graph\n",
    "#coupling_map=None"
   ]
  },
  {
   "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",
    "papermill": {
     "duration": 0.110541,
     "end_time": "2020-03-12T03:56:26.771374",
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     "start_time": "2020-03-12T03:56:26.660833",
     "status": "completed"
    },
    "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",
   "execution_count": 8,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "onhnlv97gJAV",
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     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "5Oj_Y52XgJAa",
    "papermill": {
     "duration": 0.166437,
     "end_time": "2020-03-12T03:56:27.171022",
     "exception": false,
     "start_time": "2020-03-12T03:56:27.004585",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15\n"
     ]
    }
   ],
   "source": [
    "if coupling_map != None:\n",
    "    G=generate_ising_graph(coupling_map)\n",
    "    n=G.number_of_nodes()\n",
    "    print(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-12T17:59:40.984512Z",
     "start_time": "2019-12-12T17:59:40.783157Z"
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    "tags": []
   },
   "outputs": [],
   "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",
    "coupling_map = backend.configuration().coupling_map\n"
   ]
  },
  {
   "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",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-12T17:59:40.984512Z",
     "start_time": "2019-12-12T17:59:40.783157Z"
    },
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 265
    },
    "colab_type": "code",
    "id": "2-oriBdagJAk",
    "outputId": "46a2f08a-e1b3-4e4f-f801-dc3de8208211",
    "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": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15 20\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.7/site-packages/networkx/drawing/nx_pylab.py:402: DeprecationWarning: Using or importing the ABCs from 'collections' instead of from 'collections.abc' is deprecated since Python 3.3,and in 3.9 it will stop working\n",
      "  if isinstance(alpha, collections.Iterable):\n",
      "/opt/conda/lib/python3.7/site-packages/networkx/drawing/nx_pylab.py:579: MatplotlibDeprecationWarning: \n",
      "The iterable function was deprecated in Matplotlib 3.1 and will be removed in 3.3. Use np.iterable instead.\n",
      "  if not cb.iterable(width):\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "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)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 319
    },
    "colab_type": "code",
    "id": "VW3-NLq1gJAo",
    "outputId": "c5c06bd6-003d-4b6d-dd71-1b410bf69082",
    "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": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.drawing.nx_pylab.draw(G)"
   ]
  },
  {
   "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",
   "execution_count": 13,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "br2VZc3SgJAt",
    "outputId": "4938c45a-8fbf-4065-ab79-f287efa7fbc4",
    "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": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "elist= [(0, 1), (0, 14), (1, 2), (1, 13), (14, 13), (2, 3), (2, 12), (13, 12), (3, 4), (3, 11), (12, 11), (4, 5), (4, 10), (11, 10), (5, 6), (5, 9), (10, 9), (6, 8), (9, 8), (8, 7)]\n"
     ]
    }
   ],
   "source": [
    "elist=G.edges()\n",
    "print(\"elist=\",elist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 54
    },
    "colab_type": "code",
    "id": "YhhxZwW8gJA0",
    "outputId": "e31c73cb-3e8a-4a49-b539-cc9a45a0c2ee",
    "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": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ewlist= [(0, 1, 0.28490602228659206), (0, 14, 0.2929144335923414), (1, 2, 0.08007733569368065), (1, 13, 0.32078968554105974), (14, 13, 0.19850012813283252), (2, 3, 0.27869843886748114), (2, 12, 0.09719311045231566), (13, 12, 0.29945197426165837), (3, 4, 0.05178331155590488), (3, 11, 0.3039894114840758), (12, 11, 0.11399146540365047), (4, 5, 0.18749621089199975), (4, 10, 0.2526570803700687), (11, 10, 0.12170438447222447), (5, 6, 0.08868902586635545), (5, 9, 0.303983757675792), (10, 9, 0.28639001119989677), (6, 8, 0.12900947266197205), (9, 8, 0.08511376848255917), (8, 7, 0.2818718963302103)]\n"
     ]
    }
   ],
   "source": [
    "ewlist=[(i,j,G.get_edge_data(i,j,default=0)['weight']) for i,j in G.edges()]\n",
    "print('ewlist=',ewlist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "IR61NU-_b1BD"
   },
   "outputs": [],
   "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",
    "  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-12T17:59:41.709471Z",
     "start_time": "2019-12-12T17:59:41.702848Z"
    },
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 136
    },
    "colab_type": "code",
    "id": "wr6lQmHHgJA3",
    "outputId": "782865b5-9cc1-43f8-a989-7fdacbbf5ec0",
    "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": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Symmetric: True Norm: 4.459766923226844\n",
      "Eignvlues: [0.41811893 0.48497963 1.74518579 1.67832509 0.62863542 1.5346693\n",
      " 0.75143879 0.86094303 1.41186593 1.30236168 0.98368174 1.17962297\n",
      " 1.04847602 1.11482869 1.08165236] det: 0.9999999999999996\n",
      "[[1.08165236 0.30816927 0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.31683159]\n",
      " [0.30816927 1.08165236 0.08661584 0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.34698292 0.        ]\n",
      " [0.         0.08661584 1.08165236 0.30145482 0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.10512916 0.         0.        ]\n",
      " [0.         0.         0.30145482 1.08165236 0.05601154 0.\n",
      "  0.         0.         0.         0.         0.         0.32881086\n",
      "  0.         0.         0.        ]\n",
      " [0.         0.         0.         0.05601154 1.08165236 0.20280572\n",
      "  0.         0.         0.         0.         0.27328713 0.\n",
      "  0.         0.         0.        ]\n",
      " [0.         0.         0.         0.         0.20280572 1.08165236\n",
      "  0.09593069 0.         0.         0.32880475 0.         0.\n",
      "  0.         0.         0.        ]\n",
      " [0.         0.         0.         0.         0.         0.09593069\n",
      "  1.08165236 0.         0.1395434  0.         0.         0.\n",
      "  0.         0.         0.        ]\n",
      " [0.         0.         0.         0.         0.         0.\n",
      "  0.         1.08165236 0.3048874  0.         0.         0.\n",
      "  0.         0.         0.        ]\n",
      " [0.         0.         0.         0.         0.         0.\n",
      "  0.1395434  0.3048874  1.08165236 0.09206351 0.         0.\n",
      "  0.         0.         0.        ]\n",
      " [0.         0.         0.         0.         0.         0.32880475\n",
      "  0.         0.         0.09206351 1.08165236 0.30977443 0.\n",
      "  0.         0.         0.        ]\n",
      " [0.         0.         0.         0.         0.27328713 0.\n",
      "  0.         0.         0.         0.30977443 1.08165236 0.13164183\n",
      "  0.         0.         0.        ]\n",
      " [0.         0.         0.         0.32881086 0.         0.\n",
      "  0.         0.         0.         0.         0.13164183 1.08165236\n",
      "  0.12329914 0.         0.        ]\n",
      " [0.         0.         0.10512916 0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.12329914\n",
      "  1.08165236 0.32390293 0.        ]\n",
      " [0.         0.34698292 0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.32390293 1.08165236 0.21470813]\n",
      " [0.31683159 0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.21470813 1.08165236]]\n"
     ]
    }
   ],
   "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)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "GeuV7JWWCwVL",
    "outputId": "0266374f-cf1f-4e5b-baf2-327981644906"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.251523878337194"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(w)/4 #the offset value"
   ]
  },
  {
   "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",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-12T17:59:42.618252Z",
     "start_time": "2019-12-12T17:59:42.418721Z"
    },
    "colab": {},
    "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": []
   },
   "outputs": [],
   "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",
    "   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 316
    },
    "colab_type": "code",
    "id": "H_fYHJU4HjiD",
    "outputId": "4446ef7e-7490-4fcb-a085-7c13d291edcc"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n",
      "Wall time: 13.4 µs\n"
     ]
    }
   ],
   "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)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 102
    },
    "colab_type": "code",
    "id": "YAyvKB2ifErV",
    "outputId": "7383af96-bbc5-448c-bcc0-68e7a54cd0fe"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.082 0.308 0.    0.    0.    0.    0.    0.    0.    0.    0.    0.\n",
      "  0.    0.    0.317]\n",
      " [0.308 1.082 0.087 0.    0.    0.    0.    0.    0.    0.    0.    0.\n",
      "  0.    0.347 0.   ]\n",
      " [0.    0.087 1.082 0.301 0.    0.    0.    0.    0.    0.    0.    0.\n",
      "  0.105 0.    0.   ]\n",
      " [0.    0.    0.301 1.082 0.056 0.    0.    0.    0.    0.    0.    0.329\n",
      "  0.    0.    0.   ]\n",
      " [0.    0.    0.    0.056 1.082 0.203 0.    0.    0.    0.    0.273 0.\n",
      "  0.    0.    0.   ]\n",
      " [0.    0.    0.    0.    0.203 1.082 0.096 0.    0.    0.329 0.    0.\n",
      "  0.    0.    0.   ]\n",
      " [0.    0.    0.    0.    0.    0.096 1.082 0.    0.14  0.    0.    0.\n",
      "  0.    0.    0.   ]\n",
      " [0.    0.    0.    0.    0.    0.    0.    1.082 0.305 0.    0.    0.\n",
      "  0.    0.    0.   ]\n",
      " [0.    0.    0.    0.    0.    0.    0.14  0.305 1.082 0.092 0.    0.\n",
      "  0.    0.    0.   ]\n",
      " [0.    0.    0.    0.    0.    0.329 0.    0.    0.092 1.082 0.31  0.\n",
      "  0.    0.    0.   ]\n",
      " [0.    0.    0.    0.    0.273 0.    0.    0.    0.    0.31  1.082 0.132\n",
      "  0.    0.    0.   ]\n",
      " [0.    0.    0.    0.329 0.    0.    0.    0.    0.    0.    0.132 1.082\n",
      "  0.123 0.    0.   ]\n",
      " [0.    0.    0.105 0.    0.    0.    0.    0.    0.    0.    0.    0.123\n",
      "  1.082 0.324 0.   ]\n",
      " [0.    0.347 0.    0.    0.    0.    0.    0.    0.    0.    0.    0.\n",
      "  0.324 1.082 0.215]\n",
      " [0.317 0.    0.    0.    0.    0.    0.    0.    0.    0.    0.    0.\n",
      "  0.    0.215 1.082]]\n"
     ]
    }
   ],
   "source": [
    "np.set_printoptions(precision=3)\n",
    "print(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "s3h5cNojIqNZ"
   },
   "outputs": [],
   "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.int_(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*2/3:\n",
    "      #VGG In the future one can consider giving out to these who have not recived yet!\n",
    "\n",
    "      x_free_samples = np.array([1]*n)-np.int_(x_free_samples!=0)\n",
    "      \n",
    "      if (x_free_samples==0).all:\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",
    "      else:\n",
    "        x=x_free_samples\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",
    "    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,'{:6.4f}'.format(np.linalg.det(Mw2)))\n",
    "\n",
    "    if i%4==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, '{:6.4f}'.format(np.linalg.norm(Mw2)),'{:6.4f}'.format(np.linalg.det(Mw2)))\n",
    "  print()\n",
    "  print(Mw2)\n",
    "  return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 459
    },
    "colab_type": "code",
    "id": "AUCo-7IBDKPa",
    "outputId": "7fceffe2-8ae6-4f8e-8f5a-b8636cb2f95d"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using Max_Cut_BF\n",
      "It may take too long to do Brute Force Calulations - skiping!\n",
      "CPU times: user 4 ms, sys: 0 ns, total: 4 ms\n",
      "Wall time: 770 µs\n"
     ]
    }
   ],
   "source": [
    "%time market_simulations(10)"
   ]
  },
  {
   "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",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-12T17:59:42.814360Z",
     "start_time": "2019-12-12T17:59:42.806413Z"
    },
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "g3CpUQmSgJBD",
    "outputId": "0656f214-bcce-4757-c719-d966f1756d62",
    "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": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.1953275349327455"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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"
   ]
  },
  {
   "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",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-12T17:59:47.642069Z",
     "start_time": "2019-12-12T17:59:47.435702Z"
    },
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 333
    },
    "colab_type": "code",
    "id": "sQT4-VAygJBH",
    "outputId": "392c8e40-45f2-4910-fcb2-94e9103a1935",
    "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": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "energys: [-2.2  -2.2  -2.01]\n",
      "energy: (-2.1953275349327455+0j) , offset: -2.1953275349327455\n",
      "max-cut objective: (-4.390655069865491+0j)\n",
      "solution: [0 1 0 1 0 1 0 0 1 0 1 0 1 0 1]\n",
      "solution objective: 4.390655069865491\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Making the Hamiltonian in its full form and getting the lowest eigenvalue and eigenvector\n",
    "ee = 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!"
   ]
  },
  {
   "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",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-12T17:59:43.518965Z",
     "start_time": "2019-12-12T17:59:43.130559Z"
    },
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "Ee_79O6EgJBM",
    "outputId": "a9b2c0f0-526e-4822-e69f-8af087e1889b",
    "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": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-4.4453275349327495"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "o7VVz_S0uEI-",
    "outputId": "d4be9be3-e723-4f92-fae5-f48e26b76f52"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.054672465067256 [1 0 1 0 1 0 1 1 0 1 0 1 0 1 0]\n"
     ]
    }
   ],
   "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]*0.55 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)"
   ]
  },
  {
   "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",
   "execution_count": 27,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 350
    },
    "colab_type": "code",
    "id": "BPSRHW9OgJBW",
    "outputId": "5f087978-0bfd-4302-d96e-55a53898bfef",
    "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": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "energys: [-2.63 -2.59 -2.51]\n",
      "energy: -2.6302834014392342\n",
      "max-cut objective: 6.424389063628022\n",
      "solution: [1 0 0 1 0 1 0 0 1 0 1 0 0 1 0]\n",
      "solution objective: 4.075610936371979\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.7/site-packages/networkx/drawing/nx_pylab.py:579: MatplotlibDeprecationWarning: \n",
      "The iterable function was deprecated in Matplotlib 3.1 and will be removed in 3.3. Use np.iterable instead.\n",
      "  if not cb.iterable(width):\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0] 7.404672465067255\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Making the Hamiltonian in its full form and getting the lowest eigenvalue and eigenvector\n",
    "ee = 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 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "zrWqYi3xBJlC"
   },
   "outputs": [],
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 459
    },
    "colab_type": "code",
    "id": "M6DI-RqhB-yz",
    "outputId": "2f9df8c3-f444-4927-cd3d-eaafab88ab96"
   },
   "outputs": [
    {
     "name": "stdout",
     "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 1 0 0 1 0 1 0 0 1 0] [0 0 0 0 0 0 0 0 0 1 0 1 0 0 0] [1 0 0 1 0 1 0 0 1 0 1 0 0 1 0] 6 2 1.0000\n",
      "1 [0 1 0 0 1 0 0 0 0 1 0 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0] [1 1 0 1 1 1 0 0 1 1 1 1 0 1 1] 11 3 1.0000\n",
      "2 [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 1 0 0 0 0] [0 0 1 0 0 0 1 1 0 0 0 0 1 0 0] 11 5 1.0000\n",
      "3 [1 0 0 1 0 1 0 0 1 0 1 0 0 1 0] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 1] [1 0 1 1 0 1 1 1 1 0 1 0 1 1 0] 17 7 1.0000\n",
      "4 [0 1 0 0 1 0 0 0 0 1 0 1 0 0 1] [0 0 0 0 0 1 0 0 1 0 0 0 0 0 0] [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] 22 9 1.0000\n",
      "5 [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 1 0 0 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] 22 12 1.0000\n",
      "6 [1 0 0 1 0 1 0 0 1 0 1 0 0 1 0] [0 0 0 0 0 0 1 0 0 1 0 0 0 0 0] [1 0 0 1 0 1 0 0 1 0 1 0 0 1 0] 28 14 1.0000\n",
      "7 [0 1 0 0 1 0 0 0 0 1 0 1 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [1 1 0 1 1 1 0 0 1 1 1 1 0 1 1] 33 15 1.0000\n",
      "8 [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0] [0 0 1 0 0 0 1 1 0 0 0 0 1 0 0] 33 16 1.0000\n",
      "9 [1 0 0 1 0 1 0 0 1 0 1 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 1] [1 0 1 1 0 1 1 1 1 0 1 0 1 1 0] 39 18 1.0000\n",
      "\n",
      "last day configuration record:\n",
      "\n",
      "[1 0 0 1 0 1 0 0 1 0 1 0 0 1 0] [-0.76  0.15  0.07 -0.76  0.12 -0.76  0.05  0.07 -0.76  0.17 -0.76  0.1\n",
      "  0.07 -0.76  0.12]\n",
      "\n",
      "[0 0 0 0 0 0 0 0 0 0 0 0 1 0 1] 39 18 4.4614 1.0000\n",
      "\n",
      "[[1.08e+00 3.08e-01 0.00e+00 0.00e+00 1.33e-03 0.00e+00 6.66e-04 0.00e+00\n",
      "  0.00e+00 2.00e-03 0.00e+00 1.33e-03 0.00e+00 0.00e+00 3.18e-01]\n",
      " [3.08e-01 1.08e+00 8.65e-02 0.00e+00 0.00e+00 6.66e-04 0.00e+00 0.00e+00\n",
      "  6.66e-04 0.00e+00 6.66e-04 0.00e+00 0.00e+00 3.46e-01 0.00e+00]\n",
      " [0.00e+00 8.65e-02 1.08e+00 3.01e-01 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n",
      "  0.00e+00 0.00e+00 0.00e+00 0.00e+00 1.05e-01 0.00e+00 0.00e+00]\n",
      " [0.00e+00 0.00e+00 3.01e-01 1.08e+00 5.66e-02 0.00e+00 6.66e-04 0.00e+00\n",
      "  0.00e+00 1.33e-03 0.00e+00 3.29e-01 0.00e+00 0.00e+00 6.66e-04]\n",
      " [1.33e-03 0.00e+00 0.00e+00 5.66e-02 1.08e+00 2.04e-01 0.00e+00 0.00e+00\n",
      "  1.33e-03 0.00e+00 2.74e-01 0.00e+00 0.00e+00 6.66e-04 0.00e+00]\n",
      " [0.00e+00 6.66e-04 0.00e+00 0.00e+00 2.04e-01 1.08e+00 9.64e-02 0.00e+00\n",
      "  0.00e+00 3.30e-01 0.00e+00 1.33e-03 0.00e+00 0.00e+00 1.33e-03]\n",
      " [6.66e-04 0.00e+00 0.00e+00 6.66e-04 0.00e+00 9.64e-02 1.08e+00 0.00e+00\n",
      "  1.40e-01 0.00e+00 6.66e-04 0.00e+00 0.00e+00 6.66e-04 0.00e+00]\n",
      " [0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 1.08e+00\n",
      "  3.04e-01 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00]\n",
      " [0.00e+00 6.66e-04 0.00e+00 0.00e+00 1.33e-03 0.00e+00 1.40e-01 3.04e-01\n",
      "  1.08e+00 9.39e-02 0.00e+00 1.33e-03 0.00e+00 0.00e+00 1.33e-03]\n",
      " [2.00e-03 0.00e+00 0.00e+00 1.33e-03 0.00e+00 3.30e-01 0.00e+00 0.00e+00\n",
      "  9.39e-02 1.08e+00 3.11e-01 0.00e+00 0.00e+00 1.33e-03 0.00e+00]\n",
      " [0.00e+00 6.66e-04 0.00e+00 0.00e+00 2.74e-01 0.00e+00 6.66e-04 0.00e+00\n",
      "  0.00e+00 3.11e-01 1.08e+00 1.33e-01 0.00e+00 0.00e+00 1.33e-03]\n",
      " [1.33e-03 0.00e+00 0.00e+00 3.29e-01 0.00e+00 1.33e-03 0.00e+00 0.00e+00\n",
      "  1.33e-03 0.00e+00 1.33e-01 1.08e+00 1.23e-01 6.66e-04 0.00e+00]\n",
      " [0.00e+00 0.00e+00 1.05e-01 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n",
      "  0.00e+00 0.00e+00 0.00e+00 1.23e-01 1.08e+00 3.23e-01 0.00e+00]\n",
      " [0.00e+00 3.46e-01 0.00e+00 0.00e+00 6.66e-04 0.00e+00 6.66e-04 0.00e+00\n",
      "  0.00e+00 1.33e-03 0.00e+00 6.66e-04 3.23e-01 1.08e+00 2.15e-01]\n",
      " [3.18e-01 0.00e+00 0.00e+00 6.66e-04 0.00e+00 1.33e-03 0.00e+00 0.00e+00\n",
      "  1.33e-03 0.00e+00 1.33e-03 0.00e+00 0.00e+00 2.15e-01 1.08e+00]]\n",
      "CPU times: user 1.22 s, sys: 180 ms, total: 1.4 s\n",
      "Wall time: 4.83 s\n"
     ]
    }
   ],
   "source": [
    "%time market_simulations(10,'dcplx')"
   ]
  },
  {
   "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",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "warnings.filterwarnings('once')\n",
    "model=qubitOp_docplex\n",
    "#model=qubitOp\n",
    "\n",
    "backend1 = Aer.get_backend('statevector_simulator')\n",
    "backend2 = Aer.get_backend('qasm_simulator') #VGG it was 'BasicAer.get_backend' ibmq_16_melbourne\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-12T18:00:12.595984Z",
     "start_time": "2019-12-12T17:59:52.126693Z"
    },
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 367
    },
    "colab_type": "code",
    "id": "0N8v7qbngJBi",
    "outputId": "484d6c0f-4c08-4d99-ab55-00d6ad9eb4ef",
    "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": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "qasm_simulator\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.7/site-packages/qiskit/aqua/operators/state_fns/dict_state_fn.py:209: DeprecationWarning: The Python built-in `round` is deprecated for complex scalars, and will raise a `TypeError` in a future release. Use `np.round` or `scalar.round` instead.\n",
      "  ndigits=EVAL_SIG_DIGITS)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "energy: (-0.9220142546533701+0j)\n",
      "time: 117.87839531898499\n",
      "max-cut objective: (-3.1173417895861153+0j)\n",
      "solution: [0 0 0 1 1 1 0 0 1 0 1 0 0 1 0]\n",
      "solution objective: 2.918505691087315\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.7/site-packages/networkx/drawing/nx_pylab.py:579: MatplotlibDeprecationWarning: \n",
      "The iterable function was deprecated in Matplotlib 3.1 and will be removed in 3.3. Use np.iterable instead.\n",
      "  if not cb.iterable(width):\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0] 7.404672465067256\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "seed = 10598\n",
    "\n",
    "spsa = SPSA(max_trials=10)\n",
    "ry = RY(model.num_qubits, entanglement='linear') #depth=5, \n",
    "vqe = VQE(model, ry, spsa)\n",
    "\n",
    "#VGG backend1 = Aer.get_backend('statevector_simulator')\n",
    "quantum_instance = QuantumInstance(backend2, seed_simulator=seed, seed_transpiler=seed)\n",
    "print(backend2)\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",
    "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-12-12T18:00:40.238107Z",
     "start_time": "2019-12-12T18:00:12.618707Z"
    },
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 367
    },
    "colab_type": "code",
    "id": "7lKJ0Em8gJBo",
    "outputId": "6abbb320-6659-45f7-8009-8edfb4323e74",
    "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": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "qasm_simulator\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.7/site-packages/qiskit/aqua/operators/state_fns/dict_state_fn.py:209: DeprecationWarning: The Python built-in `round` is deprecated for complex scalars, and will raise a `TypeError` in a future release. Use `np.round` or `scalar.round` instead.\n",
      "  ndigits=EVAL_SIG_DIGITS)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "energy: (-1.2718138233776304+0j)\n",
      "time: 150.87189292907715\n",
      "max-cut objective: (-3.467141358310376+0j)\n",
      "solution: [0 1 0 0 0 0 0 0 0 0 0 1 0 1 0]\n",
      "solution objective: 1.5171480113823086\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.7/site-packages/qiskit/visualization/counts_visualization.py:187: PendingDeprecationWarning: \n",
      "The label function will be deprecated in a future version. Use Tick.label1 instead.\n",
      "  tick.label.set_fontsize(14)\n",
      "/opt/conda/lib/python3.7/site-packages/networkx/drawing/nx_pylab.py:579: MatplotlibDeprecationWarning: \n",
      "The iterable function was deprecated in Matplotlib 3.1 and will be removed in 3.3. Use np.iterable instead.\n",
      "  if not cb.iterable(width):\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0] 8.229672465067257\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#warnings.filterwarnings('ignore', 'DeprecationWarning')\n",
    "warnings.filterwarnings('once')\n",
    "\n",
    "# run quantum algorithm with shots\n",
    "seed = 10598\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",
    "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",
    "x=max_cut.get_graph_solution(x).tolist()\n",
    "qubitOp_docplex, offset_docplex = set_up_Dcplx_model(w,x)\n",
    "print(x,offset_docplex)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 356
    },
    "colab_type": "code",
    "id": "wX8XbexL4zZs",
    "outputId": "62f6dcb4-d560-4641-f6c1-a003a425c741"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_histogram(result['eigenstate'])"
   ]
  },
  {
   "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",
   "execution_count": 37,
   "metadata": {
    "colab": {},
    "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": []
   },
   "outputs": [],
   "source": [
    "backend_old=backend\n",
    "#backend=backend2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "f-5STzregJBz",
    "outputId": "6fb1a389-2a66-4d4e-91e7-888bd9a06925",
    "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": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "submiting for results using: qasm_simulator\n"
     ]
    }
   ],
   "source": [
    "#warnings.filterwarnings('ignore', 'DeprecationWarning')\n",
    "# run quantum algorithm with shots\n",
    "seed = 10598\n",
    "\n",
    "spsa = SPSA(max_trials=10) #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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 672
    },
    "colab_type": "code",
    "id": "3Rt2smFtgJB2",
    "outputId": "c0f6ee2f-ec38-452e-ca39-274c0bc02b8f",
    "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": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "energy: (-0.6859390571738+0j)\n",
      "time: 43.64244818687439\n",
      "max-cut objective: (-2.8812665921065452+0j)\n",
      "solution: [0 1 0 0 0 0 0 1 1 0 1 0 0 0 1]\n",
      "solution objective: 2.219618050317786\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.7/site-packages/qiskit/visualization/counts_visualization.py:187: PendingDeprecationWarning: \n",
      "The label function will be deprecated in a future version. Use Tick.label1 instead.\n",
      "  tick.label.set_fontsize(14)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "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",
    "\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",
    "plot_histogram(result['eigenstate'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "7LO-UVXs7FWE"
   },
   "outputs": [],
   "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=10) #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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 459
    },
    "colab_type": "code",
    "id": "oZC9L_SRDnpb",
    "outputId": "6fd47302-ebcc-4b69-e7bb-9edbbe16caaa"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using Max_Cut_BF\n",
      "It may take too long to do Brute Force Calulations - skiping!\n",
      "CPU times: user 4 ms, sys: 0 ns, total: 4 ms\n",
      "Wall time: 931 µs\n"
     ]
    }
   ],
   "source": [
    "%time market_simulations(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 459
    },
    "colab_type": "code",
    "id": "PTk0dxdxDxdi",
    "outputId": "58c12b76-401d-4cc3-9890-a23302abee35"
   },
   "outputs": [
    {
     "name": "stdout",
     "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 1 0 0 1 0 1 0 0 1 0] [0 1 0 0 1 0 0 0 0 1 0 0 1 0 0] [1 0 0 1 0 1 0 0 1 0 1 0 0 1 0] 6 4 1.0000\n",
      "1 [0 1 0 0 1 0 0 0 0 1 0 1 0 0 1] [1 0 0 1 0 0 0 0 0 0 0 0 0 0 0] [1 1 0 1 1 1 0 0 1 1 1 1 0 1 1] 11 6 1.0000\n",
      "2 [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 1 0 1 0 0 0 0 0] [0 0 1 0 0 0 1 1 0 0 0 0 1 0 0] 11 8 1.0000\n",
      "3 [1 0 0 1 0 1 0 0 1 0 1 0 0 1 0] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0] [1 0 1 1 0 1 1 1 1 0 1 0 1 1 0] 17 9 1.0000\n",
      "4 [0 1 0 0 1 0 0 0 0 1 0 1 0 0 1] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0] [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] 22 10 1.0000\n",
      "5 [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] 22 11 1.0000\n",
      "6 [1 0 0 1 0 1 0 0 1 0 1 0 0 1 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0] [1 0 0 1 0 1 0 0 1 0 1 0 0 1 0] 28 12 1.0000\n",
      "7 [0 1 0 0 1 0 0 0 0 1 0 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0] [1 1 0 1 1 1 0 0 1 1 1 1 0 1 1] 33 13 1.0000\n",
      "8 [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 1 0 0 0 0 0 0] [0 0 1 0 0 0 1 1 0 0 0 0 1 0 0] 33 15 1.0000\n",
      "9 [1 0 0 1 0 1 0 0 1 0 1 0 0 1 0] [0 1 0 0 1 0 0 0 0 0 0 0 0 0 0] [1 0 1 1 0 1 1 1 1 0 1 0 1 1 0] 39 17 1.0000\n",
      "\n",
      "last day configuration record:\n",
      "\n",
      "[1 0 0 1 0 1 0 0 1 0 1 0 0 1 0] [-0.76  0.15  0.07 -0.76  0.12 -0.76  0.05  0.07 -0.76  0.17 -0.76  0.1\n",
      "  0.07 -0.76  0.12]\n",
      "\n",
      "[0 1 0 0 1 0 0 0 0 0 0 0 0 0 0] 39 17 4.4619 1.0000\n",
      "\n",
      "[[1.08e+00 3.10e-01 0.00e+00 0.00e+00 1.33e-03 0.00e+00 0.00e+00 0.00e+00\n",
      "  0.00e+00 2.00e-03 0.00e+00 6.66e-04 6.66e-04 0.00e+00 3.17e-01]\n",
      " [3.10e-01 1.08e+00 8.65e-02 2.00e-03 0.00e+00 2.00e-03 0.00e+00 0.00e+00\n",
      "  1.33e-03 0.00e+00 2.00e-03 0.00e+00 0.00e+00 3.48e-01 0.00e+00]\n",
      " [0.00e+00 8.65e-02 1.08e+00 3.01e-01 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n",
      "  0.00e+00 0.00e+00 0.00e+00 0.00e+00 1.05e-01 0.00e+00 0.00e+00]\n",
      " [0.00e+00 2.00e-03 3.01e-01 1.08e+00 5.73e-02 0.00e+00 0.00e+00 0.00e+00\n",
      "  0.00e+00 2.00e-03 0.00e+00 3.29e-01 6.66e-04 0.00e+00 6.66e-04]\n",
      " [1.33e-03 0.00e+00 0.00e+00 5.73e-02 1.08e+00 2.04e-01 0.00e+00 0.00e+00\n",
      "  6.66e-04 0.00e+00 2.74e-01 0.00e+00 0.00e+00 6.66e-04 0.00e+00]\n",
      " [0.00e+00 2.00e-03 0.00e+00 0.00e+00 2.04e-01 1.08e+00 9.58e-02 0.00e+00\n",
      "  0.00e+00 3.30e-01 0.00e+00 6.66e-04 6.66e-04 0.00e+00 6.66e-04]\n",
      " [0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 9.58e-02 1.08e+00 0.00e+00\n",
      "  1.39e-01 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00]\n",
      " [0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 1.08e+00\n",
      "  3.04e-01 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00]\n",
      " [0.00e+00 1.33e-03 0.00e+00 0.00e+00 6.66e-04 0.00e+00 1.39e-01 3.04e-01\n",
      "  1.08e+00 9.33e-02 0.00e+00 0.00e+00 6.66e-04 0.00e+00 0.00e+00]\n",
      " [2.00e-03 0.00e+00 0.00e+00 2.00e-03 0.00e+00 3.30e-01 0.00e+00 0.00e+00\n",
      "  9.33e-02 1.08e+00 3.11e-01 0.00e+00 0.00e+00 1.33e-03 0.00e+00]\n",
      " [0.00e+00 2.00e-03 0.00e+00 0.00e+00 2.74e-01 0.00e+00 0.00e+00 0.00e+00\n",
      "  0.00e+00 3.11e-01 1.08e+00 1.32e-01 6.66e-04 0.00e+00 6.66e-04]\n",
      " [6.66e-04 0.00e+00 0.00e+00 3.29e-01 0.00e+00 6.66e-04 0.00e+00 0.00e+00\n",
      "  0.00e+00 0.00e+00 1.32e-01 1.08e+00 1.23e-01 0.00e+00 0.00e+00]\n",
      " [6.66e-04 0.00e+00 1.05e-01 6.66e-04 0.00e+00 6.66e-04 0.00e+00 0.00e+00\n",
      "  6.66e-04 0.00e+00 6.66e-04 1.23e-01 1.08e+00 3.24e-01 0.00e+00]\n",
      " [0.00e+00 3.48e-01 0.00e+00 0.00e+00 6.66e-04 0.00e+00 0.00e+00 0.00e+00\n",
      "  0.00e+00 1.33e-03 0.00e+00 0.00e+00 3.24e-01 1.08e+00 2.14e-01]\n",
      " [3.17e-01 0.00e+00 0.00e+00 6.66e-04 0.00e+00 6.66e-04 0.00e+00 0.00e+00\n",
      "  0.00e+00 0.00e+00 6.66e-04 0.00e+00 0.00e+00 2.14e-01 1.08e+00]]\n",
      "CPU times: user 1.63 s, sys: 212 ms, total: 1.84 s\n",
      "Wall time: 5.25 s\n"
     ]
    }
   ],
   "source": [
    "%time market_simulations(10,'dcplx')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "qasm_simulator\n",
      "ibmq_16_melbourne\n"
     ]
    }
   ],
   "source": [
    "print(backend)\n",
    "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",
    "print(backend)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 476
    },
    "colab_type": "code",
    "id": "D6nVmQc780iT",
    "outputId": "fb987ab8-dc2a-440c-b91b-5d818c222346"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using Max_Cut option: q\n",
      "submiting for results using: qasm_simulator\n",
      "day  [free samples]  [buyers distribution]  [to be used as constrain]  the two totals  w-det\n",
      "0 [0 0 1 1 0 0 1 1 1 0 1 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0] [0 0 1 1 0 0 1 1 1 0 1 1 0 1 1] 9 1 1.0000\n",
      "1 [1 0 0 0 0 0 0 1 0 0 0 0 0 1 0] [0 1 0 0 0 0 0 0 1 0 0 0 1 0 0] [1 0 1 1 0 0 1 2 1 0 1 1 0 2 1] 12 4 1.0000\n",
      "2 [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [1 1 1 1 1 0 0 0 1 0 0 0 0 0 1] [0 1 0 0 1 1 0 0 0 1 0 0 1 0 0] 12 11 1.0000\n",
      "3 [0 0 0 1 0 0 1 1 0 0 0 1 1 0 1] [1 0 0 0 0 0 0 0 1 0 0 0 0 0 0] [0 1 0 1 1 1 1 1 0 1 0 1 2 0 1] 18 13 1.0000\n",
      "4 [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [1 0 0 0 0 0 0 0 1 1 0 1 0 0 0] [1 0 1 0 0 0 0 0 1 0 1 0 0 1 0] 18 17 1.0000\n",
      "5 [1 0 0 0 0 0 1 1 0 0 1 0 0 0 0] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0] [2 0 1 0 0 0 1 1 1 0 2 0 0 1 0] 22 18 1.0000\n",
      "6 [0 0 1 0 0 1 0 1 1 1 0 1 0 0 0] [0 0 0 1 0 0 1 0 0 0 0 0 0 0 0] [2 0 2 0 0 1 1 2 2 1 2 1 0 1 0] 28 20 1.0000\n",
      "7 [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 1 0 1 1 0 1 0 0] [0 1 0 1 1 0 0 0 0 0 0 0 1 0 1] 28 24 1.0000\n",
      "8 [0 1 1 0 0 1 0 1 1 1 1 1 0 1 0] [1 0 0 0 0 0 0 0 0 0 0 0 0 0 1] [0 2 1 1 1 1 0 1 1 1 1 1 1 1 1] 37 26 1.0000\n",
      "9 [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [1 0 0 1 0 0 0 0 0 0 0 0 0 0 0] [1 0 0 0 0 0 1 0 0 0 0 0 0 0 0] 37 28 1.0000\n",
      "\n",
      "last day configuration record:\n",
      "\n",
      "[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0.39 0.41 0.35 0.4  0.36 0.38 0.3  0.31 0.37 0.41 0.4  0.37 0.37 0.44\n",
      " 0.36]\n",
      "\n",
      "[1 0 0 1 0 0 0 0 0 0 0 0 0 0 0] 37 28 4.4604 1.0000\n",
      "\n",
      "[[1.08e+00 3.09e-01 6.66e-04 6.66e-04 0.00e+00 6.66e-04 6.66e-04 1.33e-03\n",
      "  2.00e-03 6.66e-04 6.66e-04 1.33e-03 1.33e-03 6.66e-04 3.17e-01]\n",
      " [3.09e-01 1.08e+00 8.65e-02 0.00e+00 0.00e+00 0.00e+00 0.00e+00 6.66e-04\n",
      "  0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 3.47e-01 6.66e-04]\n",
      " [6.66e-04 8.65e-02 1.08e+00 3.02e-01 0.00e+00 0.00e+00 6.66e-04 0.00e+00\n",
      "  0.00e+00 0.00e+00 0.00e+00 0.00e+00 1.06e-01 0.00e+00 6.66e-04]\n",
      " [6.66e-04 0.00e+00 3.02e-01 1.08e+00 5.59e-02 6.66e-04 0.00e+00 6.66e-04\n",
      "  1.33e-03 6.66e-04 0.00e+00 3.29e-01 6.65e-04 0.00e+00 0.00e+00]\n",
      " [0.00e+00 0.00e+00 0.00e+00 5.59e-02 1.08e+00 2.02e-01 0.00e+00 0.00e+00\n",
      "  0.00e+00 0.00e+00 2.73e-01 0.00e+00 0.00e+00 0.00e+00 0.00e+00]\n",
      " [6.66e-04 0.00e+00 0.00e+00 6.66e-04 2.02e-01 1.08e+00 9.64e-02 0.00e+00\n",
      "  0.00e+00 3.28e-01 0.00e+00 0.00e+00 0.00e+00 0.00e+00 6.66e-04]\n",
      " [6.66e-04 0.00e+00 6.66e-04 0.00e+00 0.00e+00 9.64e-02 1.08e+00 6.66e-04\n",
      "  1.41e-01 6.66e-04 0.00e+00 6.66e-04 6.65e-04 0.00e+00 0.00e+00]\n",
      " [1.33e-03 6.66e-04 0.00e+00 6.66e-04 0.00e+00 0.00e+00 6.66e-04 1.08e+00\n",
      "  3.06e-01 0.00e+00 0.00e+00 0.00e+00 1.33e-03 0.00e+00 6.66e-04]\n",
      " [2.00e-03 0.00e+00 0.00e+00 1.33e-03 0.00e+00 0.00e+00 1.41e-01 3.06e-01\n",
      "  1.08e+00 9.19e-02 6.66e-04 6.66e-04 1.33e-03 6.66e-04 1.33e-03]\n",
      " [6.66e-04 0.00e+00 0.00e+00 6.66e-04 0.00e+00 3.28e-01 6.66e-04 0.00e+00\n",
      "  9.19e-02 1.08e+00 3.09e-01 0.00e+00 0.00e+00 0.00e+00 6.66e-04]\n",
      " [6.66e-04 0.00e+00 0.00e+00 0.00e+00 2.73e-01 0.00e+00 0.00e+00 0.00e+00\n",
      "  6.66e-04 3.09e-01 1.08e+00 1.31e-01 6.65e-04 0.00e+00 6.66e-04]\n",
      " [1.33e-03 0.00e+00 0.00e+00 3.29e-01 0.00e+00 0.00e+00 6.66e-04 0.00e+00\n",
      "  6.66e-04 0.00e+00 1.31e-01 1.08e+00 1.24e-01 0.00e+00 6.66e-04]\n",
      " [1.33e-03 0.00e+00 1.06e-01 6.65e-04 0.00e+00 0.00e+00 6.65e-04 1.33e-03\n",
      "  1.33e-03 0.00e+00 6.65e-04 1.24e-01 1.08e+00 3.25e-01 6.65e-04]\n",
      " [6.66e-04 3.47e-01 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00\n",
      "  6.66e-04 0.00e+00 0.00e+00 0.00e+00 3.25e-01 1.08e+00 2.15e-01]\n",
      " [3.17e-01 6.66e-04 6.66e-04 0.00e+00 0.00e+00 6.66e-04 0.00e+00 6.66e-04\n",
      "  1.33e-03 6.66e-04 6.66e-04 6.66e-04 6.65e-04 2.15e-01 1.08e+00]]\n",
      "CPU times: user 7min 30s, sys: 1.44 s, total: 7min 32s\n",
      "Wall time: 5min 56s\n"
     ]
    }
   ],
   "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')"
   ]
  },
  {
   "cell_type": "markdown",
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    "colab_type": "text",
    "id": "B-s4-BJTkauc",
    "papermill": {
     "duration": 0.114454,
     "end_time": "2020-03-12T07:55:21.151502",
     "exception": false,
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     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "\n",
    "\n",
    "# **Acknowlegments**\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 0
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    "colab_type": "code",
    "id": "mVna1OYNJUA6",
    "outputId": "2babf7fc-ffff-49f3-9a18-2bcd93f9e7a9"
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    "import qiskit.tools.jupyter\n",
    "%qiskit_version_table\n",
    "%qiskit_copyright"
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  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
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    "colab_type": "code",
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       "<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>3.7.6 | packaged by conda-forge | (default, Jun  1 2020, 18:57:50) \n",
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