Colab_22_Costo_e_Optimization_Loop.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyPfW/xdkbPer4Gwuhj1cD+A",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/EmmanueleVilla/quantum_computing/blob/main/Colab_22_Costo_e_Optimization_Loop.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "pfMQ6HZkfF56"
      },
      "outputs": [],
      "source": [
        "!pip install qiskit --quiet && pip install pylatexenc --quiet && pip install qiskit-aer --quiet && pip install qiskit[nature] --quiet && pip install pyscf --quiet"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Esempio di funzioni di costo"
      ],
      "metadata": {
        "id": "e6GPPw6WA8tj"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from qiskit.circuit.library import TwoLocal\n",
        "from qiskit import QuantumCircuit\n",
        "from qiskit.primitives import Sampler, Estimator\n",
        "from qiskit.quantum_info import SparsePauliOp\n",
        "import numpy as np\n",
        "\n",
        "# Funzione di costo\n",
        "def cost_function_vqe(theta):\n",
        "\n",
        "  # Osservabile\n",
        "  observable = SparsePauliOp.from_list([(\"XX\", 1), (\"YY\", -3)])\n",
        "\n",
        "  # Circuito di riferimento\n",
        "  reference_circuit = QuantumCircuit(2)\n",
        "  reference_circuit.x(0)\n",
        "  reference_circuit.barrier()\n",
        "\n",
        "  # Variational form N-Locale\n",
        "  variational_form = TwoLocal(\n",
        "      2,\n",
        "      rotation_blocks=[\"rz\", \"ry\"],\n",
        "      entanglement_blocks=\"cx\",\n",
        "      entanglement=\"linear\",\n",
        "      reps=1,\n",
        "  )\n",
        "\n",
        "  # Ansatz\n",
        "  ansatz = reference_circuit.compose(variational_form)\n",
        "\n",
        "  # Mostra il circuito\n",
        "  display(ansatz.decompose().draw(\"mpl\"))\n",
        "\n",
        "\n",
        "  # Usa Estimator per ottenere l'expected value dell'ansatz\n",
        "  estimator = Estimator()\n",
        "  job = estimator.run(ansatz, observable, theta)\n",
        "  values = job.result().values\n",
        "\n",
        "  return values\n",
        "\n",
        "# Lista di parametri theta casuali\n",
        "theta_list = (2 * np.pi * np.random.rand(1, 8)).tolist()\n",
        "\n",
        "# Expected value\n",
        "cost_function_vqe(theta_list)"
      ],
      "metadata": {
        "id": "Kbk09UgtfJdj",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 209
        },
        "outputId": "9ae07beb-b708-435c-b39b-0b985406d082"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 705.35x200.667 with 1 Axes>"
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjMAAACuCAYAAADDNYx2AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAmnklEQVR4nO3deXhU5d3G8e9MFiYEEggBgmFJCImBQAh7WVxQqKCAQkVBRaFWtIhYF8C6FH2LC0v1FZciBYpWRRSQIu6vgKKigkJEEoRgWLIBIQkEQvZ5/4hEAwnOJDNzODP357q4IDPnzLmf55xn+OWsFrvdbkdERETEpKxGBxARERFpCBUzIiIiYmoqZkRERMTUVMyIiIiIqamYEREREVNTMSMiIiKmpmJGRERETE3FjIiIiJiaihkRERExNRUzIiIiYmoqZkRERMTUVMyIiIiIqamYEREREVNTMSMiIiKmpmJGRERETE3FjIiIiJiaihkRERExNRUzIiIiYmoqZkRERMTUVMyIiIiIqamYEREREVNTMSMiIiKmpmJGRERETE3FjIiIiJiaihkRERExNRUzIiIiYmoqZkRERMTUVMyIiIiIqfkbHUCkIXbt2uXU9IcPH+bNN9/kuuuuo1WrVg7NEx8fX59oIiLiIdozIz7lyJEjvPDCCxw5csToKCIi4iIqZkRERMTUVMyIiIiIqamYEREREVNTMSM+JTQ0lJEjRxIaGmp0FBERcRGL3W63Gx1CpL6cvZqpPnQ1k4jI+U17ZsSnlJSUsH//fkpKSoyOIiIiLqJiRnxKWloaw4YNIy0tzegoIiLiIrpp3nnIbrdDWYXRMZwT4IfFYjE6hdew26GyzOgUzrEGgCs3AbP1gavb7+vMtv5BYwCMGwcqZs5HZRWUP/SW0Smc4v/4WAjU5uQqlWWwYYHRKZwzeBr4Bbru88zWB65uv68z2/oHjQEwbhzoMJOIiIiYmooZERERMTUdFxCfkpCQQGpqqtExRETEhbRnRkRERExNxYz4lPT0dMaNG0d6errRUURExEVUzIhPKSoqIjk5maKiIqOjiIiIi6iYEREREVPTCcBe5JUfPuVPH7zE4mG3c3PXS856f9+xI8T9624mJFzMkuF3GJBQ3C1570buXzi4xmu2wGDatoxjSM8JXDPwLvz8vHfY+3r7RduAr7bf+1okIgxOGk/f+CuxYye/MIePv32Fhe/cy4HDqdxz7SKj47mdr7dftA34WvtVzIhPiYyMZM6cOURGRhodxa1iI3sypNdN1T+PHDCFW+fG8/43i5k07HGaNWlpYDr38/X2i7YBX2u/zpkRn9KsWTNGjRpFs2bNjI7iUUGBwcR3+B12u52so3uNjuNxvt5+0Tbg7e1XMSM+JS8vj9dee428vDyjo3hc9s9fYCGNwwxOYgxfb79oG/Dm9uswk/iU7OxsZs+eTVJSEmFh3jegTysuK+LYyVzs9qrj5e9sXkha5jbi2/Wlbcs4o+O5na+3X7QN+Fr7vb6Yyc3NZe7cuaxevZqMjAxatmzJmDFjeOKJJ5g2bRpLly7lueeeY+rUqUZHFXGZVz6axSsfzarx2qCuY7hr9AsGJfIsX29/bSrtcOAonCgGqwXCm0KrEKNTuY+vbwO+1n6vLma2b9/O8OHDycnJITg4mC5dupCVlcWCBQvYu3dv9aGGpKQkY4N6mOVX/77r46W8+9N3HCs5RdNAG3+I68eTl9xAoBdeuudLruo3mYsTx1JeWUZ69g5WbJxD7rEMAgNs1dPs+GkTDy4Zfta85RWlVFZW8OHcCk9GdilH2v/4q+OotFfyyIQ3q187XpTHbfMTmDxiPpf3vNGI6C53qhQ2p8GXeyD3RM33YlrBwFhI6lBV4HgTjQHfGgNe+z9Wbm4uI0eOJCcnh/vuu49Zs2bRtGlTAObOncvMmTPx9/fHYrGQmJhocFrXsPkHAlBUVlrr+yfLSgAI+nk6gD/3+D1PXXIDwYE2couOM/6dBTz11Rr+NvBa9wcWt4kMj6Vn3BAA+sYPp2v0IO55cRDPrrqDh256A4BuHS/incdr/u+WeyyLOxf05uoB5t5T6Uj77xrzIpP/0Y3125ZzWY/xADz39p0kRA8y1Zf4ueSfhIXr4dDx2t/fe7jqz/cH4aYB4O/n2XzupDHgW2PAa08AnjZtGhkZGUydOpX58+dXFzIAM2bMoHv37pSXlxMVFUVIiHfsa40OrbrUbldeZq3v7zpa9XpU6C+X5HUJb0twYFWlbgesFgtpBTnuDWqg4OBgBg4cSHBwsNFRPCohagBDek5gY/IKdu77stZpSstLeOyVMXSNGsQNlz/o4YTuVVv7QxqHcd/YJTy/Ziq5x7L47PuVfL93I38Zs9DgtK5xsgT+eY5C5te2H4DlX4Hd7v5cRtEY8O4x4JXFTGpqKitWrCA8PJwnn3yy1ml69eoFQPfu3Wu8np6ezqhRo2jatCnNmzfn5ptv5ujRo27P7Ao9WkfTrmkL3ty1mawT+TXeK60o55/bPsKChRGdetV4b+7Xa2n+7CQiX7yD74/sZ1rPs3e7eouoqCgWL15MVFSU0VE87sYhj2C1+vHyh3+r9f1nV91BaVkx069f5tlgHlJb+/vED+OSxOuYs/wmnls9hXvHLiYkuIWBKV1nQyocdqCQOe3bfZB2yG1xzgsaA947BryymFm+fDmVlZXceOONNGnSpNZpgoKCgJrFTGFhIYMHDyYjI4Ply5ezaNEiNm3axIgRI6isrPRI9obwt/rx3JA/cqykiF4vz+Svny5ncfInPL55NX1feZDPMlKZ0W8UF4ZdUGO+Gf1GkX/3v0meNI/bug8hokkzYxrgARUVFZw4cYKKCvMeC6+vyPBODO4+jm1pn7Djp0013nv78wV8nbqOxyauwRbY2KCE7lVX+yePnE/m0TT6xA+nX+erDEzoOuUV8FWa8/N9vsf1Wc4nGgPeOwa8sphZv349AIMHD65zmoyMDKBmMbNo0SIyMzNZs2YNI0aMYOzYsbz++ut89dVXrF271r2hXeTKmB58Ov5RLmnXhVd3fsa0T5bxv1vfo2XjEF4bMY2/X3R9nfN2bhFJYsv2THrvnx5M7Fm7du2iT58+7Nq1y+gohhh/+UNYLVZe/uiX38y2p21g8bszeWTCW0SERRkXzgNqa39QYDBtwjoSHdHNwGSulZIFJ0qcn2/HQSiq/ZQ7r6Ex4J1jwCtPAN6/fz8AHTp0qPX98vJyvvjiC6BmMbNu3ToGDRpE+/btq1/r378/HTt25J133uGaa66pV57evXuTk+P4eShBfgGkXPdEvZYF0LtNDG+M+ku95i2rrGBPfrbT88XFxnKqoqxey2yIiRMnOjV9dnZV29577z22bdvm0DzLli1zMlXDBfoHsWiq878md4+5lI/n1X3iQ4fWnWtcoZGTt4/Zr17HbSPm0T3m0vpErRYbF0tp+akGfcav1acPnG2/K7m6/Q0RM2ASPa7+u9PzVdqhV79LKDxi/B1iNQbMNwagYX0QERHB1q1b6zWvVxYzJ0+eBODUqdo7dMWKFeTm5tK0aVOio6OrX09JSWHs2LFnTZ+QkEBKSkq98+Tk5JCZWftJubVpHNCo3styxrGSIv67ZwujOvUmtFFjduQe5MnNaxga5fzVXVnZ2RSV1eNXwQYqKipyavri4uLqvx2d15l15yq2APfv5i4uLWLWsmvo32UU1wxs+JUb2VlZFJc5tz7OxRN94Equbn9DtCjI/+2J6pBzKIeCbM9v82fSGDDfGADjxoFXFjMRERHk5+fz3Xff0b9//xrvZWdnM336dAASExOxWH65uUJ+fn6tz+wJCwvjxx9/bFAeZwT5BdR7Wc6wAK+nfM70ja9SWlFOq8YhXBPbl78N+IPTn3VBmzaG7Jlp3Ni5wW6z2ar/dnReIx5KGegf5PZlbNqxip+yk8nM3c3G5BVnvb/k/hRaNW9fy5y1a3PBBS7/rdRMXN3+hgikfv+ZVFaUEdrYSvB58CBWjQHzjQFoWB84+3/lr3llMTNkyBBSU1OZM2cOQ4cOJS6u6tbNW7ZsYcKECeTm5gKeu1mes7vN7KXllD/0lpvS/CKkUWM+uO4hl3zW7j17sAR6fnNy9tyXnTt3snTpUq688koSEhIcmmf27Nn1idYgFaWwYYF7lzG01wSG9prgss/bs3sPfoG/PZ2jPNEHp/3jzxsb/Bmubn9DlFfAo2uq7vbrjJ7RASxIS3VLJmdpDJhvDIBx48ArTwCeMWMGLVq04ODBgyQkJNCtWzdiY2Pp27cvHTt25LLLLgPOviy7efPmFBQUnPV5eXl5Xv0cH18SFxfHF198UV3gingjfz/oH+P8fIM0LMSkvLKYadu2LZs2beKqq67CZrOxb98+wsLCeOmll3j33XfZvXs3cHYx07lz51rPjUlJSaFz584eyS7uFRAQQFhYGAEBnjmUJ2KUwV0gItTx6ft0rHq8gYgZeWUxA1WFybp16ygsLKSwsJCvv/6ayZMnc/LkSfbt24fVaqVr16415hkxYgSff/559WXbAF9//TV79+5l5MiRnm6CuMGBAweYMmUKBw4cMDqKiFs1DoQ7LoM2zX572l5RcH1fsHjZ85nEd3htMVOXnTt3YrfbiY2NPesE0MmTJ9OmTRuuvvpq1q1bx8qVKxk/fjx9+/bl6quvNiixuFJhYSEbNmygsLDQ6CgibtesMdz9exjdq/YnZMdFwKSLvO+5TOJ7vPIE4HPZsWMHcPYhJoCQkBDWr1/P3Xffzbhx4/D392fEiBE888wzWK0+V/eJiBewBcAl8XDxhZCRV/W8pqJSaNIIplxudDoR11Axc4aYmBjWrVvnyUgiIm5nsUC7FhDw8x4YP/1+Jl5ExYwP2JOfza3vLyT3VCGhgY1ZPPwOEsLbGh1LXGxvVjLPrLyNopJCWjfrwMzx/2H/oZ08uHg4bVteyFOTP6J5k1YUlxbxj7duZffBLVgsVv44/AkuTrwWgEXrprMxeQWxkT15bOIaYxtUD472wZL3H+SLHasJ8G+En18Ak4Y9Tp8LrwBg1WfPsPbLF7AFNuGle7cb2yBxiqPr/7T9h1K589leXNlvMlOu/l/A/OvfmT5Y++WLrPniOfys/lgtVp6762sCA2ym/B7wuWLm9HObfMmdHy3hT4mXcXPXS1j149f86f2FbJ7g+XunnA9at27NzJkzad26tdFRXG7eioncf92/6RSZxAffLGXRuvu5os8k2ra8sMaX8lufzifArxEvP5BGdl460xb0IylmMCHBLZg8Yh4dWifw5c41hrWjIRztg27RF3HTkEdoFBDE3qxk7v3nxbzxSBZBgcH84eJ76BTZgxf/+xfD2iH14+j6ByivKON/V01mYNfRNV43+/p3tA++/OG/fPLdazw39SuCg0IpOHEEv59v2GrG7wHtaDSRguKTRC+cSsTzk+n98l/ptvR+mjxzM7d/uKjOeQ6fPMa3h9K5ocsgAMbE9SWj8Chp+ed+VlR9lmUG4eHhTJw4kfDwcKOjuFRa5jaCGjWhU2QSAEN738LmlLWUlZ/91MBPk1cwov8dALQJiyYx5lI+/+FtT8Z1C2f6oG/8cBoFVN1dNTqiG9jtHDtxxJNxxcWcWf8Ar378P1ycOJbI8FgPpnQvZ/rgzU/nMWHoLIKDqq7fb9akJX5W854F7nN7ZsysmS2Y6zsPoGmgjYf6j+Gj9GTmfP1fXrpicp3zZBQeJSK4Gf4/b6QWi4V2IS04WHiUTs3rvnV0fZZlBseOHWPz5s3079+f0FAnbsJxnsvOSyc9ewe3P51U/VpJaRG5x89+xs7hggO0bv7LQ1gjmkdxuMD8l6o70we/9uHWfxMR1rFGn4j5OLP+Uw98Tcr+zcyZ/DH/+fgxD6Z0L2f64MChFHZnbOU/Hz9GWUUJQ3vdzOhB0zyY1rVUzJjM94f3c2fPqmP73x1KJ6lVlFcsy1MyMjK45557WLlypVcVMwDx7fvx1G0fVv987aMtDUxjDGf74Ls9n/Cfjx9jzm0f13hOm5iTI+u/uLSI51ZP4ZGbV3rlOnd0DFRUlpOTl87TUz7jxKl87vvnJbQJ68jvuozwVFSXUjFjMsmH91cXFd8dSmdETK9zTt+2aQtyThZQXlmBv9UPu93OweNHade0hcuXJcZpE9axxt6Vk8XHKS49SXjI2Q8MbNWsPYfy99MipA0AOfn76BX3e49ldRdn+gAgee+nzH9zEn+f9A7tWl3oqZjiJo6u/+yjezlccIDpCwcDcOJUAXZ7JSdO5TNj3Msezexqzn4PDO4xHj+rH6HB4fSNv5LUA1+ZtpjROTMmklmYh8UCkU2rnhP1w5EDdGvZDoBJ773Imj1bzpqnVXAoPVpF8XrK5wCs3v0NkU3Dqg8x1TXfuZYl559OkUn4WwP4dvfHALzz5Ytc0v16AvzPfuLbxYljWbd5IVC1W/r7vRsZ2PUaT8Z1C2f64PufPmPOGxP4n4n/JeYC37my0Zs5uv6j23Rj5aNHePXBfbz64D7GXPQXrujzR9MXMuDcGBjc4wa27voAgJKyUyTv3UjHNuYdCypmTGT74X01DvWENgpm4faqjfbbnPQ697a88Ptb+VfyJ3RZci/zvlnLv4bdXv1eXfOda1lyfvrrDa+x5P2/cstTnUjeu5HJI+bVOt3YS6dTWn6Km5+M4a//uoKpo58nNNg7Toh2tA/+8datlJWXMG/FJG5/Oonbn04iPXuHh9OKqzm6/r2Zo31w7cX3kn/iELfO68Kdz/amT/xwLuk+1sNpXUeHmUzkqpieXBXTs/rn05dXHyk6TmTT5vSK6FjrfBeGXcCmG//nrNfPNV9dyzI7m81G586dsdlsRkdxueg23Xjx7q2/OV1QYDAP37TCA4k8z9E+eHnmHg+kEU9zdP3/2s2/f9Q9YQziaB8EBti8Ym/Uadoz4wVaNg7h/bEPemw+M4uJiWH16tXExMQYHcUj/P0CKSw6yu1PJ5F/4vBvTr9o3XTe2PAkTYKaeyCdZzjbB6s+e4YFq6d4zd4qX6f17xvfAxa73W43OoTUZC8tp/yht4yO4RT/x8diCfT8jr5du3a5fRnx8fFuX8aZKkphwwKPL7ZBBk8Dv7MPzdeb2frA1e13l1mr4dgpCA2Cx8YYnaZuZlv/oDEAxo0D7ZkRn5KSkkJiYiIpKSlGRxERERdRMSM+xW63U1ZWhnZIioh4D50AfD4K8MP/cZOdVR5g3ttgn4+sAVW7a83EGuD6zzNTH7i6/b7ObOsfNAbAuHGgYuY8ZLFYwIDzT+T8YbGY4/wLd1If+Datf/WBM3SYSURERExNv/6LT4mJiWHt2rW0a6e7GYuIeAsVM+JTbDYbsbGxRscQEREX0mEm8SmZmZk8/PDDZGZmGh1FRERcRMWM+JSCggJWrVpFQUGB0VFERMRFVMyIiIiIqamYEREREVNTMSMiIiKmpmJGfIrVaqVPnz5Yrdr0RUS8hb7RxadUVlayZcsWKisrjY4iIiIuomJGRERETE3FjIiIiJiaihkRERExNRUz4lNCQ0MZOXIkoaGhRkcREREX0bOZxKe0bduWuXPnGh1DRERcSHtmxKeUlJSwf/9+SkpKjI4iIiIuomJGfEpaWhrDhg0jLS3N6CgiIuIiOswkch6y26GyzOgUzrEGgMXius8zWx+4uv2+zmzrHzQGwLhxoGJG5DxUWQYbFhidwjmDp4FfoOs+z2x94Or2+zqzrX/QGADjxoEOM4mIiIipqZgRERERU9NhJvEpCQkJpKamGh1DRERcSHtmRERExNRUzIhPSU9PZ9y4caSnpxsdRUREXESHmcSnFBUVkZycTFFRkdFRRDyiqAQO5lX9OXwcikqrXj9VCp/vhnZhcEFzCPAzNqdIQ6iYERHxMpWVkJJVVazsyq59mtIKWLml6t+BftAzCgbFQdswj8UUcRkVMyIiXmRXNrz1DRw94fg8pRXw1d6qP3ERcF1fCG/qvowirqZiRsSLJO/dyP0LB9d4zRYYTNuWcQzpOYFrBt6Fn5/3Dntfbn9xGaz5tqogaYjdOTD3XRjRo2pPjdVkdzX25W0AfLf93tcikXOIjIxkzpw5REZGGh3FrQYnjadv/JXYsZNfmMPH377Cwnfu5cDhVO65dpHR8dzO19p//BQsXA9ZBa75vNIKWL216jybcf3Az4SXivjaNnAmX2u/ihnxKc2aNWPUqFFGx3C72MieDOl1U/XPIwdM4da58bz/zWImDXucZk1aGpjO/Xyp/SeK4YX/g0PHXf/ZW36qOv/mxgHm20PjS9tAbXyt/Sast0XqLy8vj9dee428vDyjo3hUUGAw8R1+h91uJ+toA49DmJC3tr/SDks/c08hc9q3++CjHe77fE/x1m3AUd7efhUz4lOys7OZPXs22dl1XOLhxbJ//gILaeybl6t4Y/s/+xF+OuLcPPcOg0dHV/3tqI9+gAwvqP+9cRtwhje33yeKmdzcXGbMmEGnTp2w2Wy0a9eOu+++m5MnT3LrrbdisVh4/vnnjY4p4jLFZUUcO5lLwYkjpGfvYMHqO0nL3EZ8u760bRlndDy384X25xbCu9udny8kCJo1rvrbUZV2eP0rqKh0fnlG8YVt4Fx8rf1ef87M9u3bGT58ODk5OQQHB9OlSxeysrJYsGABe/furT7ckJSUZGxQERd65aNZvPLRrBqvDeo6hrtGv2BQIs/yhfavT4GyCs8tLysffsiA7u09t8yG8IVt4Fx8rf1eXczk5uYycuRIcnJyuO+++5g1axZNm1bdPGHu3LnMnDkTf39/LBYLiYmJBqcVcZ2r+k3m4sSxlFeWkZ69gxUb55B7LIPAAFv1NDt+2sSDS4afNW95RSmVlRV8ONeD/1O6mCPtf/zVcVTaK3lkwpvVrx0vyuO2+QlMHjGfy3veaER0h5wqha37PL/cz3ebp5jRGPDuMXAmry5mpk2bRkZGBlOnTmX+/Pk13psxYwavv/46ycnJREdHExISYlBK8aTg4GAGDhxIcHCw0VHcKjI8lp5xQwDoGz+crtGDuOfFQTy76g4euukNALp1vIh3Hq95Z7XcY1ncuaA3Vw+Y6vHMruRI++8a8yKT/9GN9duWc1mP8QA89/adJEQPOu+/xL/dB6Xlnl/unkNVj0RoZYKvS40B7x4DZ/Lac2ZSU1NZsWIF4eHhPPnkk7VO06tXLwC6d+9e/drp4qdv3740atQIi8Vk1yPKOUVFRbF48WKioqKMjuJRCVEDGNJzAhuTV7Bz35e1TlNaXsJjr4yha9Qgbrj8QQ8ndK/a2h/SOIz7xi7h+TVTyT2WxWffr+T7vRv5y5iFBqf9bXsOGbfsNAOX3RAaA941Bs7ktcXM8uXLqays5MYbb6RJkya1ThMUVHUG3K+LmbS0NFatWkVERAR9+vTxSFbxnIqKCk6cOEFFhXl3H9fXjUMewWr14+UP/1br+8+uuoPSsmKmX7/Ms8E8pLb294kfxiWJ1zFn+U08t3oK945dTEhwCwNTOsbIK4sOmviqJo0B7xkDZ/LaYmb9+vUADB48uM5pMjIygJrFzMUXX0x2djZr165lyJAh7g0pHrdr1y769OnDrl27jI7icZHhnRjcfRzb0j5hx0+barz39ucL+Dp1HY9NXIMtsLFBCd2rrvZPHjmfzKNp9IkfTr/OVxmY0DFFJc49d8nVzHyJtsaAd4yB2njtOTP79+8HoEOHDrW+X15ezhdffAHULGasVtfXd7179yYnJ8flnyswceJEp6Y/fX+Z9957j23btjk0z7Jly5xM1XCB/kEsmrrH5Z87/vKH2LB9OS9/9Dfm37EBgO1pG1j87kye+NP7RIRF1fuzY+NiKS0/5aKk7umD2tofFBhMm7COREd0a9Bnu7r9dWnSIpphMzbV+t69w377kusQ2y9/Pzq67umOn4KnPzj79V1pB2nbtr+DaetPY8B8YwAa1gcRERFs3bq1XvN6bTFz8uRJAE6dqr1TV6xYQW5uLk2bNiU6OtqtWXJycsjMzHTrMnxVUVGRU9MXFxdX/+3ovEasO1tA/X4z7B5zKR/Ps9f5fofWnWtcoZGTt4/Zr17HbSPm0T3m0not87TsrCyKy5xbH+dSnz5wtv2u5Or21yXMXvfZt6fvIeMIq9XxaX/NjtUjY0JjwHxjADw3Ds7ktcVMREQE+fn5fPfdd/TvX/O3iOzsbKZPnw5AYmKi20/yjYiIcOvn+7LGjZ0b7DabrfpvR+c14qGUgf5O3NGsnopLi5i17Br6dxnFNQMbfuVGmwsucPlvpWbi6vbXJTisWZ3vHXdg8SG2qkKmshKOF9c9XZ2fZS/3yJjQGDDfGICG9UFD/q/02mJmyJAhpKamMmfOHIYOHUpcXNUdD7ds2cKECRPIzc0FPHOzvPruNpPf5uy5Lzt37mTp0qVceeWVJCQkODTP7Nmz6xOtQSpKYcMC9y5j045V/JSdTGbubjYmrzjr/SX3p9CqueM3Fdmzew9+ga7L54k+cCVXt78upeXwwJtVd+U9U22Hhc706OiqPTLHi+HRt51fflKXDiz++XxDd9IYMN8YAM+NgzN5bTFz+j4yBw8eJCEhgfj4eIqLi0lLS2P48OFERUXx4Ycf1jhfRrxfXFwcX3zxRfXNE33Z0F4TGNprgtExzgv/+PNGoyM4LNAfIkIhq8CY5bfzosf6aAz8wkxjoDZeezVT27Zt2bRpE1dddRU2m419+/YRFhbGSy+9xLvvvsvu3bsBVMz4mICAAMLCwggICDA6iki9tTWwoDBy2SJ18do9MwCdO3dm3bp1Z71+4sQJ9u3bh9VqpWvXrgYkE6McOHCAp556igceeID27U1yX3aRM3RtC9/85Pnl+lnhQp0CKOchry5m6rJz507sdjtxcXG1ngS6cuVKAFJSUmr8HBUVRe/evT0XVFyusLCQDRs2cOeddxodRaTeEiIhNAiOuf984xp6dIAmtt+eTsTTfLKY2bFjB1D3IaaxY8fW+vMtt9xiyD1HRER+zc8KA2Lh/e89u9yBsZ5dnoijVMzUwm6v+xp9EZHzwSXx8FUa5Hvolh5J7SG6pWeWJeIsFTMiXmJvVjLPrLyNopJCWjfrwMzx/2H/oZ08uHg4bVteyFOTP6J5k1Z88M1SVm16hgOHU7l9xHzGXPSX6s9YtG46G5NXEBvZk8cmrjGsLfXlaB8sff8hNqesxWrxA2DcZQ8wOGkcYJ4+sAXAuN/BP9e7f1nBjeBakzyqztFtYO4bE/luz8eEBldVaL3ihjJ5xDzAPNtAbRxt/6PLRpOdl149X3rO9zx6yxoGJIxi1WfPsPbLF7AFNuGle7cb1xgn+GQxc/q5TeJ7WrduzcyZM2ndurXRUVxu3oqJ3H/dv+kUmcQH3yxl0br7uaLPJNq2vLDGF1Js2148fNObvLH+7KfJTx4xjw6tE/hy5xrPBXchR/vgukun88fhjwOQeyyTW+d1pmfsEEKDw03VBxe2gYsuhE0/Oj7P6ZvhOXKDPQALcH0/85wr4+g2AFXbwa+L+dPMtA2cydH2Pzrxl5sM/XhwKw8uHkafC4cB8IeL76FTZA9e/O9fPJy+/rz20myR2oSHhzNx4kTCw8ONjuJSaZnbCGrUhE6RSQAM7X0Lm1PWUlZeeta0MRd0p0Przlgs3jX8nemDJkHNqv99quQEduxU2is9lNS1RvesOjHXUU9/UHWzPEdusAdVe2QS29Uvm6c5sw14o/q2/4NvlnB5z5sI8Dfgbncu4pN7ZsR3HTt2jM2bN9O/f39CQ0ONjuMy2XnppGfv4Pank6pfKyktIve47zwTzNk+ePvzBaz98gVyCzK4Z+ximjdp5aGkrmW1wk0DoJE/fLXXhZ9rqdoj0y/GdZ/pbk5vA5ue5YNvltKqeXsmXjG7uggwq/p8D5SUnWLD9uU8M6X2h5eahYoZ8SkZGRncc889rFy50quKGYD49v146rYPq3++9lHfO1vTmT4YPWgaowdNY29WMk8tv4necb8nJLiFJ2K6nJ+1qvCIi4BVW+FkScM+74LmcMPvzHmDPEe3gT8Of5ywpm2wWq18vuNtHloynGUz9xDUqImnorqFs98Dn32/krYt44hu0/AnZhvJu/Yzi/ioNmEdOVxwoPrnk8XHKS49SXiI5x+SaZT69kHMBd0JD4kkee9GNyd0L4sFekbBA1dB347gX49v96Y2uKo73HuFOQsZZ7aB8NBIrNaqThrUbTSNbSEcPOLEyUfnofqMgQ++WcKwPrd6Ip5bqZgR8QKdIpPwtwbw7e6PAXjnyxe5pPv1pj4G7ixn+mD/oZTqf2fl7iUtaxvtW3fxWFZ3ahoEN/SHx8bAqB5VRYnfOb7pG/lX3dX35oEw6xoY2hX8/TwW16Wc2QaOFPzysMyU/V9x/ORRIlt08lhWd3D2eyAzN43dGVsZ3GO8J2O6hQ4ziXiJv97wGvPenMSC1X/mghadeOCGV9mX88NZ0324ZRnLPnyYE0X5fLlzDW99Op+/T3qHTpE9DEjtWo72wb/enUFOXjp+1gD8/PyZes3zdGjd2YDE7hPcCC7rUvWnvKLqwZSHj0NZRdVeHJt/1eGk8KZV58d4C0e3gXkrJpJ/4hBWix+NAoJ4ZMJbBAeZ/9Czo+0H+GDLUi7q9geCbSEeTul6KmbEp9hsNjp37ozNZpLrTJ0Q3aYbL9699Tenu6LPRK7oM9H9gQzgaB/M/uPZz2zzZv5+0L5F1R9v5+g2MPf2//NAGs9ztP0Atw5/ws1pPEeHmcSnxMTEsHr1amJiTHSJRgP4+wVSWHSU259OIv/E4d+cftG66byx4UmaBDX3QDrPUB+Ir28DzrZ/1WfPsGD1FEKDzXMLC4td9+4XE9u1a5fblxEfH+/2ZZypohQ2LPD4Yhtk8DTwc+EpOmbrA1e339eZbf2DxgAYNw60Z0Z8SkpKComJidVPRBcREfNTMSM+xW63U1ZWpoeJioh4EZ0ALHIesgZU7a41E2uA6z/PTH3g6vb7OrOtf9AYAOPGgYoZkfOQxaLzL9QHvk3rX33gDB1mEhEREVPTnhnxKTExMaxdu5Z27UzyGGAREflNKmbEp9hsNmJjY42OISIiLqTDTOJTMjMzefjhh8nMzDQ6ioiIuIiKGfEpBQUFrFq1ioKCAqOjiIiIi6iYEREREVNTMSMiIiKmpmJGRERETE3FjPiU8PBwbrvtNsLDzfM0WBEROTc9NVtERERMTXtmRERExNRUzIiIiIipqZgRERERU1MxIyIiIqamYkZERERMTcWMiIiImJqKGRERETE1FTMiIiJiaipmRERExNRUzIiIiIipqZgRERERU1MxIyIiIqamYkZERERMTcWMiIiImJqKGRERETG1/wdgOcPvfJqhSQAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.73277923])"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install qiskit-optimization"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9woowIxu8EdT",
        "outputId": "6b2f0f58-91ac-4c5a-d41f-cb4c004d8c4d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Requirement already satisfied: qiskit-optimization in /usr/local/lib/python3.10/dist-packages (0.5.0)\n",
            "Requirement already satisfied: qiskit-terra>=0.22.4 in /usr/local/lib/python3.10/dist-packages (from qiskit-optimization) (0.25.0)\n",
            "Requirement already satisfied: scipy>=1.4 in /usr/local/lib/python3.10/dist-packages (from qiskit-optimization) (1.10.1)\n",
            "Requirement already satisfied: numpy>=1.17 in /usr/local/lib/python3.10/dist-packages (from qiskit-optimization) (1.22.4)\n",
            "Requirement already satisfied: docplex!=2.24.231,>=2.21.207 in /usr/local/lib/python3.10/dist-packages (from qiskit-optimization) (2.25.236)\n",
            "Requirement already satisfied: setuptools>=40.1.0 in /usr/local/lib/python3.10/dist-packages (from qiskit-optimization) (67.7.2)\n",
            "Requirement already satisfied: networkx>=2.6.3 in /usr/local/lib/python3.10/dist-packages (from qiskit-optimization) (3.1)\n",
            "Requirement already satisfied: six in /usr/local/lib/python3.10/dist-packages (from docplex!=2.24.231,>=2.21.207->qiskit-optimization) (1.16.0)\n",
            "Requirement already satisfied: rustworkx>=0.13.0 in /usr/local/lib/python3.10/dist-packages (from qiskit-terra>=0.22.4->qiskit-optimization) (0.13.1)\n",
            "Requirement already satisfied: ply>=3.10 in /usr/local/lib/python3.10/dist-packages (from qiskit-terra>=0.22.4->qiskit-optimization) (3.11)\n",
            "Requirement already satisfied: psutil>=5 in /usr/local/lib/python3.10/dist-packages (from qiskit-terra>=0.22.4->qiskit-optimization) (5.9.5)\n",
            "Requirement already satisfied: sympy>=1.3 in /usr/local/lib/python3.10/dist-packages (from qiskit-terra>=0.22.4->qiskit-optimization) (1.11.1)\n",
            "Requirement already satisfied: dill>=0.3 in /usr/local/lib/python3.10/dist-packages (from qiskit-terra>=0.22.4->qiskit-optimization) (0.3.7)\n",
            "Requirement already satisfied: python-dateutil>=2.8.0 in /usr/local/lib/python3.10/dist-packages (from qiskit-terra>=0.22.4->qiskit-optimization) (2.8.2)\n",
            "Requirement already satisfied: stevedore>=3.0.0 in /usr/local/lib/python3.10/dist-packages (from qiskit-terra>=0.22.4->qiskit-optimization) (5.1.0)\n",
            "Requirement already satisfied: symengine<0.10,>=0.9 in /usr/local/lib/python3.10/dist-packages (from qiskit-terra>=0.22.4->qiskit-optimization) (0.9.2)\n",
            "Requirement already satisfied: typing-extensions in /usr/local/lib/python3.10/dist-packages (from qiskit-terra>=0.22.4->qiskit-optimization) (4.7.1)\n",
            "Requirement already satisfied: pbr!=2.1.0,>=2.0.0 in /usr/local/lib/python3.10/dist-packages (from stevedore>=3.0.0->qiskit-terra>=0.22.4->qiskit-optimization) (5.11.1)\n",
            "Requirement already satisfied: mpmath>=0.19 in /usr/local/lib/python3.10/dist-packages (from sympy>=1.3->qiskit-terra>=0.22.4->qiskit-optimization) (1.3.0)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Da funzione di costo a osservabile"
      ],
      "metadata": {
        "id": "JvY84BHTBAOj"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Calcolo il valore atteso dello stato |0>\n",
        "\n",
        "from qiskit import QuantumCircuit\n",
        "from qiskit.quantum_info import SparsePauliOp\n",
        "from qiskit.primitives import Sampler, Estimator\n",
        "from qiskit.circuit.library import IGate, ZGate\n",
        "import numpy as np\n",
        "\n",
        "# Creo lo stato |0>\n",
        "original_circuit = QuantumCircuit(1)\n",
        "\n",
        "# Creo l'osservabile\n",
        "H = SparsePauliOp([\"Z\"], [1])\n",
        "\n",
        "# Creo circuiti aggiuntivi per ogni porta della scomposizione dell'osservabile\n",
        "aux_circuits = []\n",
        "for pauli in H.paulis:\n",
        "    aux_circ = original_circuit.copy()\n",
        "    aux_circ.barrier()\n",
        "    if str(pauli) == \"X\":\n",
        "        aux_circ.h(0)\n",
        "    else:\n",
        "        aux_circ.i(0)\n",
        "    aux_circ.measure_all()\n",
        "    aux_circuits.append(aux_circ)\n",
        "\n",
        "display(original_circuit.draw(\"mpl\"))\n",
        "\n",
        "# Sampler\n",
        "sampler = Sampler()\n",
        "job = sampler.run(aux_circuits)\n",
        "probability_dists = job.result().quasi_dists\n",
        "\n",
        "expvals = []\n",
        "for dist, pauli in zip(probability_dists, H.paulis):\n",
        "    val = 0\n",
        "    if str(pauli) == \"I\":\n",
        "        Lambda = IGate().to_matrix().real\n",
        "    else:\n",
        "        Lambda = ZGate().to_matrix().real\n",
        "    val += Lambda[0][0] * dist.get(0, 0)\n",
        "    val += Lambda[1][1] * dist.get(1, 0)\n",
        "    expvals.append(val)\n",
        "\n",
        "# Estimator\n",
        "observables = [\n",
        "    *H.paulis,\n",
        "    H,\n",
        "]\n",
        "\n",
        "estimator = Estimator()\n",
        "job = estimator.run([original_circuit] * len(observables), observables)\n",
        "estimator_expvals = job.result().values\n",
        "\n",
        "for (obs, expval) in zip(observables, estimator_expvals):\n",
        "    if obs is H:\n",
        "        print(f\"  >> Valore atteso: {expval:.5f}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 145
        },
        "id": "HevLM1jI8Wc4",
        "outputId": "dda27e14-9d4b-4a4c-f074-edd1e1d8333d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 143.647x117.056 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "  >> Valore atteso: 1.00000\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Il problema del taglio massimo"
      ],
      "metadata": {
        "id": "qHoEnlW6BECs"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Stampo il grafo del problema\n",
        "\n",
        "import networkx as nx\n",
        "\n",
        "n = 4\n",
        "G = nx.Graph()\n",
        "G.add_nodes_from(range(n))\n",
        "edge_list = [(0, 1, 1.0), (0, 2, 1.0), (0, 3, 1.0), (1, 2, 1.0), (2, 3, 1.0)]\n",
        "G.add_weighted_edges_from(edge_list)\n",
        "\n",
        "colors = [\"red\" for i in range(n)]\n",
        "\n",
        "layout = nx.shell_layout(G)\n",
        "nx.draw_networkx(G, node_color=colors, pos=layout)\n",
        "edge_labels = nx.get_edge_attributes(G, \"weight\")\n",
        "nx.draw_networkx_edge_labels(G, pos=layout, edge_labels=edge_labels)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 495
        },
        "id": "M96J8mX_79lW",
        "outputId": "ce22112f-16f0-461e-b467-89b6728389b7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{(0, 1): Text(-0.4999999940375597, -0.5000000437113883, '1.0'),\n",
              " (0, 2): Text(0.0, 4.371138828673793e-08, '1.0'),\n",
              " (0, 3): Text(-0.500000168883119, 0.4999999562886117, '1.0'),\n",
              " (1, 2): Text(0.5000000059624403, -0.4999999125772234, '1.0'),\n",
              " (2, 3): Text(0.49999983111688096, 0.5000000874227766, '1.0')}"
            ]
          },
          "metadata": {},
          "execution_count": 13
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Osservabile"
      ],
      "metadata": {
        "id": "oBsS61yaBHfy"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from qiskit_optimization.applications import Maxcut\n",
        "from qiskit.algorithms.optimizers import COBYLA\n",
        "\n",
        "# Trasformo il grafo in array numpy\n",
        "w = nx.to_numpy_array(G)\n",
        "\n",
        "# Importo il modulo per il Maxcut problem\n",
        "max_cut = Maxcut(w)\n",
        "quadratic_program = max_cut.to_quadratic_program()\n",
        "observable, offset = quadratic_program.to_ising()\n",
        "print(f\"osservabile: {observable}\")\n",
        "print(f\"offset: {offset}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YbxiqUBK0tWW",
        "outputId": "1b797417-fde6-4826-cdde-4a2ec3bba37a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "osservabile: 0.5 * IIZZ\n",
            "+ 0.5 * IZIZ\n",
            "+ 0.5 * IZZI\n",
            "+ 0.5 * ZIIZ\n",
            "+ 0.5 * ZZII\n",
            "offset: -2.5\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Funzione di costo"
      ],
      "metadata": {
        "id": "C24gjcl7BI-c"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "def cost_function_max_cut_vqe(theta):\n",
        "\n",
        "  # Creo l'ansatz\n",
        "  ansatz = TwoLocal(\n",
        "    observable.num_qubits, \"rx\", reps=1\n",
        "  )\n",
        "\n",
        "  # Eseguo la stima\n",
        "  estimator = Estimator()\n",
        "  job = estimator.run(ansatz, observable, theta)\n",
        "  values = job.result().values\n",
        "\n",
        "  return values"
      ],
      "metadata": {
        "id": "nz4hxhCO9ZS1"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Ottimizzazione"
      ],
      "metadata": {
        "id": "TxY28t4HBLnk"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Funzione di ottimizzazione classica\n",
        "optimizer = COBYLA()\n",
        "\n",
        "# Inizio con tutti 1\n",
        "initial_theta = np.ones(8)\n",
        "\n",
        "# Eseguo l'ottimizzazione\n",
        "optimizer_result = optimizer.minimize(fun=cost_function_max_cut_vqe, x0=initial_theta)\n",
        "\n",
        "optimal_parameters = optimizer_result.x\n",
        "print(optimal_parameters)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rEcM2U9KBMYQ",
        "outputId": "d08da14a-b130-4106-fa46-a82c73a4b3a7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[ 1.21912639  0.25498488  1.20580137  0.70140314  1.92243514 -0.25503671\n",
            "  1.93575092 -0.70140044]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Verifica"
      ],
      "metadata": {
        "id": "5c7ZrM6uFllI"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from qiskit.primitives import Estimator\n",
        "from qiskit.algorithms.minimum_eigensolvers import VQE\n",
        "from qiskit.algorithms.optimizers import COBYLA\n",
        "from qiskit.circuit.library import TwoLocal\n",
        "import numpy as np\n",
        "\n",
        "# Creo ansatz, estimator e optimizer\n",
        "ansatz = TwoLocal(observable.num_qubits, \"rx\", reps=1)\n",
        "optimizer = COBYLA()\n",
        "estimator = Estimator()\n",
        "\n",
        "# Passo tutto al VQE\n",
        "vqe = VQE(\n",
        "    estimator=estimator,\n",
        "    ansatz=ansatz,\n",
        "    optimizer=optimizer,\n",
        "    initial_point=np.zeros(ansatz.num_parameters),\n",
        ")\n",
        "\n",
        "result = vqe.compute_minimum_eigenvalue(observable)\n",
        "\n",
        "print(result)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "LIoQ6lmJGxIo",
        "outputId": "5933a669-f648-4f9b-e3e7-674c9d6d4bf7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "{   'aux_operators_evaluated': None,\n",
            "    'cost_function_evals': 139,\n",
            "    'eigenvalue': -1.4999999987811397,\n",
            "    'optimal_circuit': <qiskit.circuit.library.n_local.two_local.TwoLocal object at 0x7dc9d2a22830>,\n",
            "    'optimal_parameters': {   ParameterVectorElement(θ[5]): 1.8411976315784566,\n",
            "                              ParameterVectorElement(θ[4]): 0.28862929295473855,\n",
            "                              ParameterVectorElement(θ[1]): 1.3004366844636701,\n",
            "                              ParameterVectorElement(θ[2]): -1.236293455691152,\n",
            "                              ParameterVectorElement(θ[0]): -0.28862642231947017,\n",
            "                              ParameterVectorElement(θ[3]): 2.715586863505642,\n",
            "                              ParameterVectorElement(θ[7]): 0.42597963418539364,\n",
            "                              ParameterVectorElement(θ[6]): 1.2362882193563711},\n",
            "    'optimal_point': array([-0.28862642,  1.30043668, -1.23629346,  2.71558686,  0.28862929,\n",
            "        1.84119763,  1.23628822,  0.42597963]),\n",
            "    'optimal_value': -1.4999999987811397,\n",
            "    'optimizer_evals': None,\n",
            "    'optimizer_result': <qiskit.algorithms.optimizers.optimizer.OptimizerResult object at 0x7dc9d2a20ca0>,\n",
            "    'optimizer_time': 0.38790225982666016}\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from qiskit.quantum_info import Statevector\n",
        "\n",
        "# Ottengo il circuito ottimizzato\n",
        "optimal_circuit = result.optimal_circuit.bind_parameters(result.optimal_parameters)\n",
        "optimal_circuit.decompose().draw(\"mpl\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 320
        },
        "id": "pMwrnaYpFmSE",
        "outputId": "46d42f82-2450-4c0c-b058-14b734fb05da"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 287.496x367.889 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {},
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from qiskit.visualization.state_visualization import array_to_latex\n",
        "\n",
        "# Ottengo lo state vector\n",
        "state_vector = Statevector(optimal_circuit)\n",
        "array_to_latex(state_vector, max_size=24)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        },
        "id": "RtAJu0WlH96w",
        "outputId": "4b46ff97-0c46-49cc-f472-fcab765c0c3f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<IPython.core.display.Latex object>"
            ],
            "text/latex": "$$\n\n\\begin{bmatrix}\n-3.0 \\cdot 10^{-10} & 0 & - 1.30779 \\cdot 10^{-5} i & 0 & 0 & 0 & 0 & 0 & 2.08312 \\cdot 10^{-5} i & 0 & -1 & 1.4353 \\cdot 10^{-6} i & -1.0 \\cdot 10^{-10} & 0 & - 2.6182 \\cdot 10^{-6} i & 0  \\\\\n \\end{bmatrix}\n$$"
          },
          "metadata": {},
          "execution_count": 30
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from qiskit import Aer, transpile\n",
        "from qiskit.visualization import plot_histogram\n",
        "\n",
        "#Misurazione\n",
        "simulator = Aer.get_backend(\"aer_simulator\")\n",
        "qc = optimal_circuit.copy()\n",
        "qc.measure_all()\n",
        "qc_t = transpile(qc, simulator)\n",
        "result = simulator.run(qc_t).result()\n",
        "counts = result.get_counts()\n",
        "plot_histogram(counts)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 484
        },
        "id": "SCmqMkTwIhgR",
        "outputId": "65aa9ce0-f91b-4b15-e588-baea254014b1"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 700x500 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {},
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Disegno i due sottografi\n",
        "\n",
        "x = max_cut.sample_most_likely(state_vector)\n",
        "\n",
        "colors = [\"red\" if x[i] == 0 else \"orange\" for i in range(n)]\n",
        "\n",
        "layout = nx.shell_layout(G)\n",
        "nx.draw_networkx(G, node_color=colors, pos=layout)\n",
        "edge_labels = nx.get_edge_attributes(G, \"weight\")\n",
        "nx.draw_networkx_edge_labels(G, pos=layout, edge_labels=edge_labels)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 495
        },
        "id": "lIFxCyNUFynI",
        "outputId": "85f44143-fbc0-4e71-8ae4-8b03940bcd58"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{(0, 1): Text(-0.4999999940375597, -0.5000000437113883, '1.0'),\n",
              " (0, 2): Text(0.0, 4.371138828673793e-08, '1.0'),\n",
              " (0, 3): Text(-0.500000168883119, 0.4999999562886117, '1.0'),\n",
              " (1, 2): Text(0.5000000059624403, -0.4999999125772234, '1.0'),\n",
              " (2, 3): Text(0.49999983111688096, 0.5000000874227766, '1.0')}"
            ]
          },
          "metadata": {},
          "execution_count": 36
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}