GSE.ipynb

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  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyPO5gOmhDRohK0aKmkMo+u3",
      "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/Sabarikirishwaran/GSE/blob/main/GSE.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": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Wpu-gc6SNTkE",
        "outputId": "414dd56d-5468-4f2a-a76c-b8d851864d0b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Collecting qiskit\n",
            "  Downloading qiskit-1.2.4-cp38-abi3-manylinux_2_17_x86_64.manylinux2014_x86_64.whl.metadata (12 kB)\n",
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            "\u001b[?25hInstalling collected packages: symengine, rustworkx, pbr, dill, stevedore, qiskit\n",
            "Successfully installed dill-0.3.9 pbr-6.1.0 qiskit-1.2.4 rustworkx-0.15.1 stevedore-5.3.0 symengine-0.13.0\n"
          ]
        }
      ],
      "source": [
        "!pip install qiskit"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install qiskit-aer"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ztFjITzwOjvF",
        "outputId": "885774e6-d357-41e1-be0e-4d00cc72fc60"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Collecting qiskit-aer\n",
            "  Downloading qiskit_aer-0.15.1-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl.metadata (8.0 kB)\n",
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            "Requirement already satisfied: numpy>=1.16.3 in /usr/local/lib/python3.10/dist-packages (from qiskit-aer) (1.26.4)\n",
            "Requirement already satisfied: scipy>=1.0 in /usr/local/lib/python3.10/dist-packages (from qiskit-aer) (1.13.1)\n",
            "Requirement already satisfied: psutil>=5 in /usr/local/lib/python3.10/dist-packages (from qiskit-aer) (5.9.5)\n",
            "Requirement already satisfied: rustworkx>=0.15.0 in /usr/local/lib/python3.10/dist-packages (from qiskit>=1.1.0->qiskit-aer) (0.15.1)\n",
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            "Requirement already satisfied: mpmath<1.4,>=1.1.0 in /usr/local/lib/python3.10/dist-packages (from sympy>=1.3->qiskit>=1.1.0->qiskit-aer) (1.3.0)\n",
            "Downloading qiskit_aer-0.15.1-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (12.3 MB)\n",
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            "\u001b[?25hInstalling collected packages: qiskit-aer\n",
            "Successfully installed qiskit-aer-0.15.1\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install pylatexenc"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "oIXSFdMyVH_p",
        "outputId": "4e5e0e93-c69a-4ee3-cf28-0c15358274fa"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Collecting pylatexenc\n",
            "  Downloading pylatexenc-2.10.tar.gz (162 kB)\n",
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            "\u001b[?25h  Preparing metadata (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "Building wheels for collected packages: pylatexenc\n",
            "  Building wheel for pylatexenc (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for pylatexenc: filename=pylatexenc-2.10-py3-none-any.whl size=136817 sha256=15a3652d26bb6870e4c49f5bee317e91344c79f9a1934e653426953a3a429c31\n",
            "  Stored in directory: /root/.cache/pip/wheels/d3/31/8b/e09b0386afd80cfc556c00408c9aeea5c35c4d484a9c762fd5\n",
            "Successfully built pylatexenc\n",
            "Installing collected packages: pylatexenc\n",
            "Successfully installed pylatexenc-2.10\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from qiskit import QuantumCircuit, transpile\n",
        "from qiskit_aer import AerSimulator, noise\n",
        "from qiskit.visualization import plot_histogram, plot_state_city\n",
        "from qiskit.quantum_info import Statevector\n",
        "\n",
        "# Number of qubits: 3 for GHZ state\n",
        "shots = 1000\n",
        "\n",
        "# Create a Quantum Circuit with 3 system qubits for GHZ\n",
        "qc = QuantumCircuit(3, 3)\n",
        "\n",
        "# Step 1: Prepare the GHZ state\n",
        "qc.h(0)\n",
        "qc.cx(0, 1)\n",
        "qc.cx(1, 2)\n",
        "\n",
        "# Introduce noise (same noise model as in GSE circuit)\n",
        "noise_model = noise.NoiseModel()\n",
        "\n",
        "# Define single-qubit depolarizing error\n",
        "single_qubit_error = noise.depolarizing_error(0.01, 1)\n",
        "# Define two-qubit depolarizing error\n",
        "two_qubit_error = noise.depolarizing_error(0.02, 2)\n",
        "\n",
        "# Add errors to the noise model\n",
        "noise_model.add_all_qubit_quantum_error(single_qubit_error, ['h'])\n",
        "noise_model.add_all_qubit_quantum_error(two_qubit_error, ['cx'])\n",
        "\n",
        "# Step 2: Measure all qubits in the computational basis\n",
        "qc.measure([0, 1, 2], [0, 1, 2])\n",
        "\n",
        "qc.draw(output='mpl')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 320
        },
        "id": "59dhXzXwRDcP",
        "outputId": "0ae9d09f-386e-4e07-8140-6e00e3ec7233"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 621.941x367.889 with 1 Axes>"
            ],
            "image/png": 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7dzZ4HkmSsGnTJuzZswdHjhzBq6++Ci8vL2u8BGqBVtEi12g0iI+PR/fu3eHi4oIuXbpg0aJFKC0txdy5cyGTybBu3Tpbl0lGKCqpxFNvJBt9nJ+vGwI6usPPt+WhXFBUiflvHTWq9UJkSykpKVi1ahUWL16MpKQknDt3zmBLuri4GOfPn8e2bduwZMkSvPXWWzhz5ky93/W6IQ4A169fR1oa54/YE4dvkaekpCAmJgZqtRru7u6IiIhAbm4uPvjgA2RkZCA/Px8A0K9fP9sWSkZZ+2Uqfs0rtdr1dhz+Fcln1BgxsJPVrmlOOTdK8cm2dFy4UoDyCh182jrjkQe7YeLwACgUreLzfKtQVFSEzz77DMeOHWuwrab1XdOSLikpQVZWFgoLC2v3uXjxIi5evIjBgwdjzpw5aNOmTb0Ql8lkmDdvHu6//37rvCBqEYcOco1Gg8mTJ0OtVmPJkiVYsWIFPD09AQBr1qzBsmXLoFQqIZPJEBkZaeNqqaW0Wj02bL1k9et+uOWScEGuKSjHc28fQ9LBrAaL4nz2zS8I9PfAn5+9D09MCbVRhWQuFy9exAcffFAvmDt06ICxY8figQcegK+vb4PvCpckCbdu3cKJEydw4MABqNVqAMDJkyeRmpqK8PBwnDp1CsB/Qzw6Otp6L4paxKGDfOHChcjOzsaCBQuQkJBQb1t8fDy+/PJLnDt3DkFBQRzvEcju5Ou4rrZea7xG0sEsqDVlRnXL21Leb2UY8eRuXPm18clJ13JLMPvVH5BzswzLn+prxerInH7++We89957qKqqXoLY3d0ds2fPxrBhwyCXN97jIpPJ4Ovri9jYWMTExOCnn37Cp59+iuLiYpSUlDDEBeGwfWppaWlITEyEr68vVq1aZXCfAQMGAAD69v3vG1hN8A8ePBjOzs4NPsGS7e068qtNrlul1ePA8RybXNtYer2EyX860GSI1/XyB6ex9VvLzf4ny7l06VK9EI+MjERCQgJGjBjRZIjfTS6XY8iQIUhISECHDh3qbZs4cSJD3I45bJBv3rwZer0eM2fOhIeHh8F9XF1dAdQP8itXriApKQl+fn4YNGiQVWol45xJvdUqr22MfUezcSZVY9Qxf/k4hRP6BFNWVoa1a9fWhvgDDzyA+Ph4tGvXzqTzSZKEb775Bjdv3qz3/I8//oji4uJ7rpcsw2GD/NChQwDQ5KfI7OxsAPWDfMSIEcjLy8OOHTswZswYyxZJRquo1OHClQKbXd/YcLSVfyQaP6s45VI+fvq/m83vSHbjX//6F27dqv5wGRERgQULFkCpNG3E9O7Z6TKZDF26dAEAFBYW4rPPPjNLzWR+Dhvk165dAwAEBgYa3K7VanH06FEA9YPcmK4osj61pgxVWuPXUTeXX9UlNrt2S0mShP3Hsk06du+Pph1H1vfLL7/UNlhcXFzwzDPPmDXE582bh+XLl8Pd3R0AcPToUVy4cME8xZNZOexkt9LS6slQd+7cMbg9MTERGo0Gnp6eCAoKsmgtAwcOrJ0NSvemSu4DtF3Y6PaaBV8a4+frWvvz+oHpje7X2IIx2Tk3EBAQYETF1qeHE7Ter5p07Hv/ux4bV+01c0X24eEnF8Pdwwt56jwEBAQ0eGxvVCpVo/N7AGD//v21/54+fTrat29v0nUaC/Ga3sxZs2Zh/fr1tdfs3bvxJYvDwsJQWXnv33fQGvn5+eH06dMmHeuwQe7n54eCggKcPXsWUVFR9bbl5eVh6dKlAKonhlh6QptarUZOjhiTpOyeUwXQtvHNNQu+NEepkLdov7vptZUC/L+UAd6mHVladAulN+z99ZlGr9PV/szJyWnw2N44Ozs3uq2wsBA//fQTAMDDwwOjR4826RrNhTgADBs2DImJiSgoKMDp06eh0Wjg6+tr8Hy5ubmoqKgwqRYyncMG+ZgxY5CWlobVq1dj7NixCAsLAwCcOnUKs2bNgkZTPdZpjYVg/Pz8LH6N1kIPFfKa2K7WlDV5vJ+vK5QKObQ6PdQaw701TZ3HSV6ODo0sY2lPbmpzUKU0vk5v1yK4CvD6TCFXKGp/du7cucFje6NSqRrddurUKWi1WgDV84Ca2rcxLQlxAFAqlXjwwQexdetWSJKEEydOIDY21uA5/f392SI30b3khMMGec194tevX0evXr3Qs2dPlJeX48qVK4iJiUG3bt2wf//+euPjlmJqdwkZ1mPyVqRfKzS4rbn1068fmI6Aju5Qa+6gy9ivjL727MdH4Z9vvGb0cdb26fZ0zHnduCVsAzq6I/Pst1AqHXOeyNt//zeKSkrRya8TsrOzGzy2N1qtFklJSQa3ZWRk1P574MCBRp+7pSFe9xpbt25tcO27paenmzxOT6ZzzL9YAAEBAUhOTkZsbCxcXFyQlZUFb29vbNiwAbt370Z6ejoAWCXIybwGRPjY8NqGuxTtzbTxwejo42rUMX+aEeGwIe5oMjOr7/mXyWSNTuhtjLEhDlS/nzo5OdW7NtkPh/7oFB4ejl27djV4vmaNYblc3uTEDbJP0YM6YfNe23y16KhBYizR6uaqxI4PxmL0U3tQekfb7P6PPNgNS2bzb0EUNWP6nTp1gouLS4uPMyXEgeru9S5duuDq1avIy8uDXq/nHT52pFX+n7h48SIkSUJoaCjc3BrOcN66dSu2bt2K1NTUeo/ZRW4fZkwMgae7k9WvO2pQJ/QMamv165pqcJ/2OPJpLLr5G14QCQDkchmeebwnvloTzS9PEYQkSfDx8YG3t7fRM9X//e9/Gx3iNXx9feHt7Y2OHTvWLkBD9sGhW+SNOX/+PIDGu9Ufe+wxg49nz57NRRHsgIebE2ZPCcW6zcZ9F/m9enZauFWvZw4DInxxZfdj2JOcjfX/ScP+oznQ6SUoFTIsmxOJeY/2RNdOjQc92R+ZTIa//e1vJh0bHBxce5eOsWunv/DCCyZdkyyPQW4Al6m0f0ue6I1Pt6e3qNvYHCLDvPFQtHFjkfZCoZBj8qiumDyqKwLGbEbOzTJ09HHFyj8ZP0mKxDZkyBAAQEVFBddOdyCtsi+tuSAn+9etsyfWPG+dtfCVShk+e2s4nJxa5Z8LOZghQ4YwxB1Mq2yR1yxrSGKb/3g4th26hoM/5bb4mJr7w5u737yuV57qh/7hYsxWJ6LWp1UGOTkGuVyGLQmjMWrOHvxfen6LjmnuPvO7zZrUHa/P729KeUREVsG+QhJaOy9nfPfPGIvc3/3kQ6HY+OfhkMv5nfREZL8Y5CQ833YuOLJxIhbMiDDL+dxdlfj7y1H4+I3hXCCFiOwe36XIIbi7OWHt8ih8/8lE9OjWxuTzjBvSGeeTHsGz0yPYEiciIXCMnBzKqEGdkLo9Dgd/ysE/EtOw88h16PVN307o4eaEWZNC8Mzj4egTZuLXhhER2QiDnByOXC7DuCEBGDckAMWllUi5lI/TqRpcyryNsnItFHI5PN2d0DfMGwMifNCrezuonBS2LpuIyCQMcnJonu4qDB/gh+ED+FWyROSYOEZOREQkMAY5ERGRwBjkREREAmOQExERCYxBTkREJDDOWiciskMKhQJxcXFmO9+7GxJRXFoKT3d3LP2faQ0em4NCwds4bYFBTkRkh2QyGZRK871FSwD0UvVPpVLZ4DGJi13rREREAmOQExERCYxBTkREJDAGORERkcAY5ERERAJjkBMREQmMQU5ERCQwBjkREZHAGOREREQCY5ATEREJjEFOREQkMAY5ERGRwBjkREREAmOQExERCYxBTkREJDAGORERkcAY5ERERAJT2roAIiKiu0mSBJ1OZ+syjKJQKCCTyax+XQY5ERHZHZ1Oh6SkJFuXYZS4uDgoldaPVXatExERCYxBTkREJDAGORERkcAY5ERERAJjkBO1EpIkQZKk2n8TkWPgrHUiB1VZpcOO739F8lk1zqTdQsqlWyi9owUA5P52B0ETEjGwly8GRPji4dGB6BHU1rYFE5FJGOREDib3Zin+/lUaPv76Mm7mlze6X1ZuCbJyS7D1QBaW/+9pPHi/P56bHo6HRgfa5F5YIjINg5zIQUiShE++TscLCSdQXFpl9PHfncjFdydy8eD9/vjkzWEI9Pe0QJVEZG4cIydyAPmFFZj47Ld4+s0fTQrxur47kYvej2zDv3ZdMVN1RGRJbJETCe7GrTsY8/ReXLhSYLZzlpRVYdbLR6ApKMfiWb3Ndl4iMj+2yIkEVlhcifHz95k1xOt6/t0T+OfWSxY5N5FoysvLUVRUZOsyGmCLnEhgC985jnOX8y16jefePo4HIjugT5i3Ra9DZAl37txBRkYGrl69iszMTBQVFUGr1cLJyQk+Pj4ICgpCSEgIgoKCmlwnvby8HKtXr0ZpaSleffVVeHl5WfFVNI1BTiSonYd/xRc7jRvHPrV5Cvx83aDWlGHQjB0tOqZKq8f/e+0H/PSvKXByYiceieHatWs4cOAAkpOTUVFR0eh+R44cAQC0adMGo0ePxoMPPghfX996+9SEeFpaGgDg/fffx+uvv243d3e0ir9KjUaD+Ph4dO/eHS4uLujSpQsWLVqE0tJSzJ07FzKZDOvWrbN1mUQtVlGpw/yVR40+zs/XDQEd3eHn62bUcWfTbmHdV6lGX4/I2m7fvo2//vWvWLZsGQ4ePNhkiNdVWFiIbdu24U9/+hO++OKL2uPuDnF3d3f88Y9/tJsQB1pBizwlJQUxMTFQq9Vwd3dHREQEcnNz8cEHHyAjIwP5+dXdkv369bNtoURG2HogE7k3y6x6zbVfpmLhHyKgULSKz/8koGPHjmHjxo0oKSmpfc7FxQVDhgxBWFgYgoOD0aFDByiVSlRWViInJweZmZm4cOECzpw5A51OB0mSsGfPHpw9exZPPfUUkpKS6oX4yy+/jJCQEFu9RIMcOsg1Gg0mT54MtVqNJUuWYMWKFfD0rL43ds2aNVi2bBmUSiVkMhkiIyNtXC1Ry/39qzSrXzMzpxj7jmYjdkRXq1+bqCmSJGH79u1ITEysfc7LywtxcXEYMWIEXF1dGxyjVCoRGhqK0NBQjBs3Dvn5+Thw4AB27dqFqqoqqNVqrFy5snZ/ew1xwMG71hcuXIjs7GwsWLAACQkJtSEOAPHx8ejbty+0Wi26detmVxMXiJqScb0Ix8/dtMm1jR2TJ7KGb775pl6IP/DAA0hISMD48eMNhrgh3t7emDZtGt555x0EBwfX2+bs7Gy3IQ44cJCnpaUhMTERvr6+WLVqlcF9BgwYAADo27dv7XNbt25FXFwcAgMD4ebmhp49e+KVV16p11VDZEsnz/9ms2ufuqCx2bWJDDl9+jS++uqr2sczZ87E4sWLTW6c+fj4QKVS1XtOp9PBzc24eSXW5LBBvnnzZuj1esycORMeHh4G96n5pFY3yBMSEqBQKPD2229j7969eOaZZ/Dhhx9iwoQJ0Ov1VqmdqCmnU20Xppk5xbh1u/H124msqaSkBB9//HHt4xkzZmDy5Mkmn69mYtulS9VrJygUCgCAVqvF+vXr7TYDHHaM/NChQwCA6OjoRvfJzs4GUD/Id+7cifbt29c+HjlyJNq3b4+ZM2fixx9/xIgRIyxUMVHLXLTQ4i8tlZpxG8MH+Nm0BiIA+OKLL3D79m0AQP/+/TFlyhSTz2VodvqLL76I9evX48aNG7h8+TL279+PmJgYc5RuVg4b5NeuXQMABAYGGtyu1Wpx9Gj17Tt1g7xuiNcYOHAgACAnJ8ekWgYOHAi1Wm3SsUR3+81zDuBk+Pe65j7xxvj5utb+vH5gepPXaexe84cfnQ6XKvHGyh9+cjHcPbyQp85DQEBAg8eOTrTXr1KpGh0WBaonMycnJwMA3Nzc8PTTT5t8S5ihEK8ZE58/fz7efPNNANUNvXHjxtW21O8WFhaGyspKk2rw8/PD6dOnTTrWYYO8tLQUQPWqPoYkJiZCo9HA09MTQUFBTZ7r+++/BwCEh4ebVItarTb5QwBRA8EVgJPhTTX3iTdHqZC3aD9Dbmk0QIl4v896na72Z05OToPHjk601+/s7Nzk9u+++w6SJAEAJk6cCG9v01YebCrEger3/QEDBuDMmTPIz8/HmTNnMHjwYIPnys3NbfF96+bksEHu5+eHgoICnD17FlFRUfW25eXlYenSpQCAyMjIJj/F5eTk4LXXXsOECRNMvtfcz4/dkGQ+GicZGnurUGuavrfcz9cVSoUcWp0eao3hD7nNncvXxwvObTq3pFS7Iv+9FSVXKNC5c+cGjx2daK//7glnden1+trhU4VCgdGjR5t0jeZCvMa4ceNw5swZANUfIBoLcn9//3tqkZvKYYN8zJgxSEtLw+rVqzF27FiEhYUBAE6dOoVZs2ZBo6meMNRUOJeUlGDq1KlQqVTYuHGjybWY2l1CZMiLCSfw1y8uGNzW3LKr1w9MR0BHd6g1d9Bl7FdN7tuYy+e+h3ebpltL9ujtv/8bRSWl6OTXCdnZ2Q0eOzrRXr9Wq0VSUpLBbWq1GoWFhQCqG2OmtMZbGuIA0KdPH7Rr1w4FBQVIT0+HXq+HXN5wrnh6enqT67VbisPOWo+Pj4ePjw+uX7+OXr16oU+fPggNDcXgwYMRHBxc+wmu7vh4XXfu3MHkyZORmZmJb7/9Fp06dbJm+USNGhDh2/xOFhLU2VPIECfHcvXq1dp/h4aGGn28MSEOAHK5HN27dwdQnQ32NufJYYM8ICAAycnJiI2NhYuLC7KysuDt7Y0NGzZg9+7dSE9PB2A4yKuqqvDoo4/i9OnT2Lt3LyIiIqxdPlGj7o9sOCHTWgb3sd2HCKIaNZOZATQ7x+luxoZ4jbqLxGRmZhp1TUtz2K51oHqSwq5duxo8X1JSgqysLMjlcvTu3bvetpp7z7/77jvs2bOn0bEQIlsJDvDC0P4dcfTnG1a/9uzJxrd+iMytuLi49t93f1NZU0wNcaB6oZgaNZOp7YVDB3ljLl68CEmSEBYW1mC1nueeew7/+c9/8NJLL8HNzQ0//fRT7baQkBCDt6cRWduzj4dbPciDAzwxfqj93aZErc+UKVMwbNgwVFVVGfWefPny5drFXoxdO71Xr15YtmwZVCqV3Q21OmzXelPOnz8PwHC3+t69ewEA77zzDqKiour9t3v3bqvWSdSYuLHdTL59zFQL/xABudx+vrqRWi9/f3/07t0b/fv3h4uLS4uP69u3LxYsWABPT0+j10738fFB//790atXL5NvdbOUVtkibyrIs7KyrFwNkfGcVQp89PpQTHzuW6tcb1BvXzw3nXNFSHxDhw5F//797XrtdGOxRU4kqJjhXfDkQ8aNWas1Zci+Udrs/eZ1qZzk+OytEVAqW+XbBTkgRwpxoJW2yGsWEiAS3d/iH8C5y/k4m3arRfs3d5+5IetfG4qIkHZGH0dE1sGP2EQC8/JQYd+H49G3h2XG7NYuj8KTD4VZ5NxEZB4MciLBtfd2xeFPJmLSiC5mO6eXhxM2rx6FBTM4Lk5k7xjkRA6grZczdqwdi89XjkBbz8bXqG6JCUMDcPHrOEyPafmMXiKynVY5Rk7kiGQyGZ6YEorxQwOwfksaPkq6jNybLZvUJpNVB/iz08IRO6KLyV8HSUTWxyAncjAdfVyx4pn78PJT/bDnx+v48ewNnEnV4OdLt3C7uPqbmRQKGUICvDAgwgcDInzx0OhAhHTxsnHlRGQKBjmRg3JykmNqdCCmRgfWPqfXS9DpJDg5cVSNyFEwyIlaEblcxtXZiBwMP5YTEREJjEFOREQkMAY5ERGRwBjkREREAuNkNyIisjsKhQJxcXFmO9+7GxJRXFoKT3d3LP2faQ0em4NCoTDLeYzFICciIrsjk8mgVJovoiQAeqn6p1KpbPBYZOxaJyIiEhiDnIiISGAMciIiIoExyImIiATGICciIhIYg5yIiEhgDHIiIiKBMciJiIgExiAnIiISGIOciIhIYAxyIiIigTHIiYiIBMYgJyIiEhiDnIiISGAMciIiIoExyImIiATGICciIhIYg5yIiEhgDHIiIiKBMciJiIgExiAnIiISGIPcDmzatAkDBgxAu3bt4OrqivDwcLz33nuQJMnWpRFRE/bs2YN+/frB2dkZ3bp1w3vvvWfrkqzqhx9+wNSpUxEYGAiZTIaVK1fauiSreffddxEVFYV27dqhbdu2GDZsGPbt22eTWpQ2uSrV06FDB7z22mvo0aMHnJ2dkZycjGeffRYKhQKLFi2ydXlEZMDp06cxdepUvPjii9i8eTNOnDiB+fPnw83NDfPnz7d1eVZRUlKCiIgI/OEPf8DixYttXY5VHTp0CHPmzMGgQYPg5uaGjz/+GJMmTcKRI0cwdOhQq9bCILcD48ePr/c4ODgY27dvx+HDhxnkRHbqvffew6BBg7Bq1SoAQHh4OC5evIh33nmn1QT5xIkTMXHiRADAsmXLbFyNde3du7fe4zVr1mDfvn34+uuvrR7k7Fq3M5Ik4eTJkzh69Ciio6NtXQ4RNeLo0aOYMGFCvecmTJiAa9euITs720ZVka3o9XoUFRXB3d3d6tdmi9xOFBYWonPnzqisrIRer8eKFSuwcOFCW5dFJBz1b/koKilr8LxWp6v9mZ6Z3eBxDYVcjuCunSCTyZq8Tl5eHvz8/Oo9V/M4Ly8PAQEB9/Q6TFV2pxzZak2D51v6+gHAv6MPPNxcLV+shWRez0OVVlfvOWNev4ebC/w7+hp1zbfffhu3b9/GvHnz7qFy0zDI7YSnpydSUlJQVlaGY8eOYfny5fD398fcuXNtXRqRUKqqtPjsP3uhb2SyaNmdcmzcsqfRx+NHDEJIoL/F67QUZ5UK+384iRwDYQ40//o7+rbDgtkPW7xOS8q5ocGu744b3Nbc65cBeHrGJKOu949//ANvv/02duzYYZMPcOxatxNyuRzdu3dHZGQk5s+fj/j4eLzyyiu2LotIOF38OyB6SH+Tjg3s3BEj7+/bon07deoEtVpd77kbN27UbrMVhUKOaZNGQ6lUGH+sXI5pk6LhpBS7jTdkQG90D+xs0rHDB0ciuGvLP8glJCRg6dKl2LFjB8aMGWPSNe8Vg9xO6fV6lJeX27oMIiGNjroPAX7tjTpG5aTE47HRkMtb9rY4dOhQ7N+/v95z+/btQ2BgoM261Wt08GmLmFH3G33c2OEDje5StkdymQyPThwJF2eVUcf5tffGuOGDWrz/66+/jjfffBN79uyxWYgDDHK7sGLFChw8eBBXr17F5cuX8c9//hOrV6/G7NmzbV0akZCqW6XRcDKiVTppdBR82nm1eP/nn38eJ0+exCuvvIJLly7h888/x9q1a/HSSy+ZUrLZRd3Xy6hWaWDnjhgxONKoa5SUlCAlJQUpKSmorKyEWq1GSkoKrly5Ymy5ZtfWywMPjRvW4v0VcjkenxTd4p6MxYsX491338WmTZvQo0cPqNVqqNVqFBYWmlqyyWQSVx2xueeffx47d+5ETk4OXFxcEBwcjDlz5mD+/PlQKIzvHiOiasfOXMCOg8ea3a9nSFfMjhvf7AS3u+3evRsvv/wyLl26BD8/PyxatAgvvPCCqeWaXWFRCd7fuBXlFZVN7qdSOWHRk3HwadvyDzIAcPjwYYN314wcORKHDx826lyWIEkSNu/4Dv936Wqz+8aMGoyR9/dr8bkb+12ZPXs2PvvssxafxxwY5ETksPSShE+37MUvWY3fDubu6oLFcx+Fp7ubFSuznpTUK/hq56Em94mbMAKD+va0UkXWVXanHO9v3IpiA3cy1OgW4Id5Mya1eFjF3ohZdSt2Pe8mysorbF0GkRBqxkpdXZwb3efhCcMdNsQBoF9Ed/QND2l0e3j3rhgY2cOKFVmXm6sLHosZ2eh2lcoJj8eOEjbEAQa5ULQ6Hf617QBWf/glfs25YetyiITQxtO90bHSAb3D0DssyMoVWd/UsUPh5dHww4q7mwsemTDC6CEF0YQFd0HUfREGt01+MAreRg4p2BsG+V10Oh02bdqEcePGoX379nB2dkbXrl0xYcIEfPzxx9DpdM2fxELOnL+MwuJSqFRO6NTBx2Z1EImmb3hIg1ZpWy8PTB4zxEYVWZebqwsemziqwfOPTBjh0L0RdcWMegC+3m3qPRcRGoiBfcTvjWCQ11FUVISxY8fiiSeewIEDB6BSqdC3b1/o9Xp8++23ePrpp1FcXGyT2rQ6HQ4d+xkAMOr+fnByEvs+TyJrmzpuGLw8qpfPlAF4fFK00bcniSw0KABR9/WqfTywTw/0Cu1mu4KsTOWkxLTYaMh/733wcHPFI+MdozeCQV7H3Llz8f333yMgIACHDh1CTk4OTp48iezsbOTl5eEvf/kLnJycbFJbTWvc08MNgx10UgqRJbm5OOOx2Oqx0uGDIxHcxXaLtthKzKj70d67Ddq18cSkB6NsXY7V1V0s6JEJw+HhLu4ytHVx1vrvzpw5g4EDB0KpVOLnn39G7969zXbutZ9/jeKSO/dwBgnFpXcgSRJcnFVQ2ejDBJEjqKyqgpNS6RAtMVPodDpIAJSt9NZWSZJQVaWFSmVf76OeHq740+xHTDqW/bO/2759OwAgNjbWrCEOAMUld1BUUmqWc5VXVDZ7TygRNY1/Q1Re6Ti/Awzy36WmpgIAoqLM393k6XEv3TdsjRMRObp7yQkG+e+KiooAAG3atGlmT+OZ2l0CACdS0rBtfzI8PdwQP286J7kREVE9TIXfeXlV30doiXVyTR8jr26NA9VfzfjuR4nmLYyIiOwCx8jNoFevXvj6669x/Ljh77C9F+YYI+fYOBERGcIg/93DDz+Mt956C3v27EFqaioiIgyvAmQK08Y+ODZORNRa3MsYOW8/q2PatGnYsmULunbtii+++AIjR/53fd4bN25g48aNWLhwIdzd3S1eC8fGiYioJRjkdRQVFWHq1Km1X7/XuXNn+Pv7Iy8vDzk5OZAkCQUFBWjbtq1F69DqdEj4KBG3i0ow+cEhGDrQvLfDERGR4+DKbnV4eXnh4MGD+OSTTzBq1CiUlZXh3LlzkMvlGD9+PD755BN4enpavI4z59Nxu6iEq7gREVGz2CK3Qz9f/AV7D5/EyPv7sjVORERNYpDbqSqtFjLIoFS2zmUUiYioZRjkREREAuMYORERkcAY5ERERAJjkBMREQmMQU5ERCQwBjkREZHAGOREREQCY5ATEREJjEFOREQkMAY5ERGRwBjkREREAmOQExERCYxBTkREJDAGORERkcAY5ERERAJjkBMREQmMQU5ERCQwBjkREZHAGOREREQCY5ATEREJjEFOREQkMAY5ERGRwBjkREREAmOQExERCYxBTkREJDAGORERkcAY5ERERAJjkBMREQmMQU5ERCQwBjkREZHAGOREREQCY5ATEREJjEFOREQkMAY5ERGRwBjkREREAmOQExERCYxBTkREJDAGORERkcAY5ERERAJjkBMREQns/wMX+/aIrRWeTwAAAABJRU5ErkJggg==\n"
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "# Transpile and execute the circuit\n",
        "simulator = AerSimulator(noise_model=noise_model)\n",
        "qc_transpiled = transpile(qc, simulator)\n",
        "result = simulator.run(qc_transpiled, shots=shots).result()\n",
        "\n",
        "# Get the counts and display the results\n",
        "counts = result.get_counts()\n",
        "plot_histogram(counts, title=\"Counts for Noisy GHZ State Without GSE\")\n",
        "\n",
        "# # Optional: Visualize the state\n",
        "# state = Statevector(qc)\n",
        "# plot_state_city(state.data, title=\"Statevector of Noisy GHZ State Without GSE\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 468
        },
        "id": "RJT9ONA-hNdj",
        "outputId": "aa886fea-dfbb-4dd6-fa1a-32f752228d9d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#overlap matrix\n",
        "from qiskit import QuantumCircuit, transpile\n",
        "from qiskit_aer import AerSimulator, noise\n",
        "from qiskit.visualization import plot_histogram, circuit_drawer\n",
        "from qiskit.quantum_info import Statevector\n",
        "import matplotlib.pyplot as plt\n",
        "from qiskit.circuit.library import SwapGate\n",
        "\n",
        "# Set the matplotlib backend to inline for Colab\n",
        "%matplotlib inline\n",
        "\n",
        "# Number of qubits: 1 ancilla + 3 system qubits (GHZ) + 3 system qubits for copies\n",
        "shots = 1000\n",
        "\n",
        "# Create a Quantum Circuit with 1 ancilla + 3 system qubits for GHZ + 3 system qubits for copies\n",
        "qc = QuantumCircuit(10, 1)\n",
        "\n",
        "# Step 1: Prepare the GHZ state\n",
        "qc.h(1)\n",
        "qc.cx(1, 2)\n",
        "qc.cx(2, 3)\n",
        "\n",
        "# Create copies of the GHZ state\n",
        "qc.h(4)\n",
        "qc.cx(4, 5)\n",
        "qc.cx(5, 6)\n",
        "\n",
        "# Create copies of the GHZ state\n",
        "qc.h(7)\n",
        "qc.cx(7, 8)\n",
        "qc.cx(8, 9)\n",
        "\n",
        "# Introduce noise (corrected implementation)\n",
        "noise_model = noise.NoiseModel()\n",
        "\n",
        "# Define single-qubit depolarizing error\n",
        "single_qubit_error = noise.depolarizing_error(0.01, 1)\n",
        "# Define two-qubit depolarizing error\n",
        "two_qubit_error = noise.depolarizing_error(0.01, 2)\n",
        "\n",
        "# Add errors to the noise model\n",
        "noise_model.add_all_qubit_quantum_error(single_qubit_error, ['h'])\n",
        "noise_model.add_all_qubit_quantum_error(two_qubit_error, ['cx'])\n",
        "\n",
        "# Step 2: Prepare the ancilla qubit\n",
        "qc.h(0)\n",
        "\n",
        "# Step 4: Implement derangement using swap operators\n",
        "qc.append(SwapGate().control(1),[0,1,4])\n",
        "qc.append(SwapGate().control(1),[0,2,5])\n",
        "qc.append(SwapGate().control(1),[0,3,6])\n",
        "qc.append(SwapGate().control(1),[0,4,7])\n",
        "qc.append(SwapGate().control(1),[0,5,8])\n",
        "qc.append(SwapGate().control(1),[0,6,9])\n",
        "\n",
        "# Step 3: Apply different Pauli operators (example: U1 = X, V1 = Z)\n",
        "# Apply to first copy\n",
        "qc.cx(0, 1)  # Controlled-X on the first copy\n",
        "qc.cx(0, 2)\n",
        "qc.cx(0, 3)\n",
        "\n",
        "# Apply to second copy\n",
        "qc.cz(0, 4)  # Controlled-Z on the fifth qubit\n",
        "qc.cz(0, 4)  # Controlled-Z on the second qubit\n",
        "qc.cz(0, 5)  # Controlled-Z on the fifth qubit\n",
        "qc.cz(0, 5)  # Controlled-Z on the second qubit\n",
        "qc.cz(0, 6)  # Controlled-Z on the fifth qubit\n",
        "qc.cz(0, 6)  # Controlled-Z on the second qubit\n",
        "#qc.cx(0, 4)  # Controlled-X on the second copy\n",
        "\n",
        "\n",
        "qc.cx(0, 7)  # Controlled-X on the first copy\n",
        "qc.cx(0, 8)\n",
        "qc.cx(0, 9)\n",
        "\n",
        "\n",
        "# Step 5: Apply Pauli operator Pa on the ancilla qubit (e.g., Pa = X)\n",
        "#qc.y(0)  # Example: Applying Pauli-X operator as Pa\n",
        "\n",
        "# Step 6: Measure in the X basis (for real part)\n",
        "qc.h(0)\n",
        "qc_vec = qc.copy()\n",
        "qc.measure(0, 0)\n",
        "\n",
        "# qc.sdg(0)\n",
        "# qc.h(0)\n",
        "\n",
        "# qc.measure(0, 1)\n",
        "# Draw the circuit\n",
        "qc.draw(output=\"mpl\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 770
        },
        "id": "tmgtGUI0UW_2",
        "outputId": "f0a7b203-1b0d-46ab-b6ca-acc4c9689102"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 2126.94x953.167 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Transpile and execute\n",
        "simulator = AerSimulator(noise_model=noise_model)\n",
        "qc_transpiled = transpile(qc, simulator)\n",
        "result = simulator.run(qc_transpiled, shots=shots).result()\n",
        "\n",
        "counts = result.get_counts()\n",
        "plot_histogram(counts, title=\"Counts for GSE QEM on GHZ state with Pa and Derangement\")\n",
        "\n",
        "# # Optional: Visualize the state\n",
        "# state = Statevector(qc_vec)\n",
        "# print(state)\n",
        "#plot_state_city(state.data, title=\"Statevector of GHZ after GSE QEM with Pa and Derangement\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 451
        },
        "id": "69604QVBVgPB",
        "outputId": "27857393-36ba-4b6f-8ed0-7b8824e951b4"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Hamiltonian matrix\n",
        "from qiskit import QuantumCircuit, transpile\n",
        "from qiskit_aer import AerSimulator, noise\n",
        "from qiskit.visualization import plot_histogram, circuit_drawer\n",
        "from qiskit.quantum_info import Statevector\n",
        "import matplotlib.pyplot as plt\n",
        "from qiskit.circuit.library import SwapGate\n",
        "\n",
        "# Set the matplotlib backend to inline for Colab\n",
        "%matplotlib inline\n",
        "\n",
        "# Number of qubits: 1 ancilla + 3 system qubits (GHZ) + 3 system qubits for copies\n",
        "shots = 1000\n",
        "\n",
        "# Create a Quantum Circuit with 1 ancilla + 3 system qubits for GHZ + 3 system qubits for copies\n",
        "qc = QuantumCircuit(10, 1)\n",
        "\n",
        "# Step 1: Prepare the GHZ state\n",
        "qc.h(1)\n",
        "qc.cx(1, 2)\n",
        "qc.cx(2, 3)\n",
        "\n",
        "# Create copies of the GHZ state\n",
        "qc.h(4)\n",
        "qc.cx(4, 5)\n",
        "qc.cx(5, 6)\n",
        "\n",
        "# Create copies of the GHZ state\n",
        "qc.h(7)\n",
        "qc.cx(7, 8)\n",
        "qc.cx(8, 9)\n",
        "\n",
        "# Introduce noise (corrected implementation)\n",
        "noise_model = noise.NoiseModel()\n",
        "\n",
        "# Define single-qubit depolarizing error\n",
        "single_qubit_error = noise.depolarizing_error(0.01, 1)\n",
        "# Define two-qubit depolarizing error\n",
        "two_qubit_error = noise.depolarizing_error(0.01, 2)\n",
        "\n",
        "# Add errors to the noise model\n",
        "noise_model.add_all_qubit_quantum_error(single_qubit_error, ['h'])\n",
        "noise_model.add_all_qubit_quantum_error(two_qubit_error, ['cx'])\n",
        "\n",
        "# Step 2: Prepare the ancilla qubit\n",
        "qc.h(0)\n",
        "\n",
        "# Step 4: Implement derangement using swap operators\n",
        "qc.append(SwapGate().control(1),[0,1,4])\n",
        "qc.append(SwapGate().control(1),[0,2,5])\n",
        "qc.append(SwapGate().control(1),[0,3,6])\n",
        "qc.append(SwapGate().control(1),[0,4,7])\n",
        "qc.append(SwapGate().control(1),[0,5,8])\n",
        "qc.append(SwapGate().control(1),[0,6,9])\n",
        "\n",
        "# Step 3: Apply different Pauli operators (example: U1 = X, V1 = Z)\n",
        "# Apply to first copy\n",
        "qc.cy(0, 1)  # Controlled-X on the first copy\n",
        "qc.cy(0, 2)\n",
        "qc.cy(0, 3)\n",
        "\n",
        "# Apply to second copy\n",
        "qc.cz(0, 4)  # Controlled-Z on the fifth qubit\n",
        "qc.cx(0, 4)  # Controlled-Z on the fifth qubit\n",
        "qc.cz(0, 4)  # Controlled-Z on the second qubit\n",
        "qc.cz(0, 5)  # Controlled-Z on the fifth qubit\n",
        "qc.cx(0, 5)  # Controlled-Z on the fifth qubit\n",
        "qc.cz(0, 5)  # Controlled-Z on the second qubit\n",
        "qc.cz(0, 6)  # Controlled-Z on the fifth qubit\n",
        "qc.cx(0, 6)  # Controlled-Z on the fifth qubit\n",
        "qc.cz(0, 6)  # Controlled-Z on the second qubit\n",
        "#qc.cx(0, 4)  # Controlled-X on the second copy\n",
        "\n",
        "\n",
        "qc.cx(0, 7)  # Controlled-X on the first copy\n",
        "qc.cx(0, 8)\n",
        "qc.cx(0, 9)\n",
        "\n",
        "\n",
        "# Step 5: Apply Pauli operator Pa on the ancilla qubit (e.g., Pa = X)\n",
        "#qc.y(0)  # Example: Applying Pauli-X operator as Pa\n",
        "\n",
        "# Step 6: Measure in the X basis (for real part)\n",
        "qc.h(0)\n",
        "qc_vec = qc.copy()\n",
        "qc.measure(0, 0)\n",
        "\n",
        "# qc.sdg(0)\n",
        "# qc.h(0)\n",
        "\n",
        "# qc.measure(0, 1)\n",
        "# Draw the circuit\n",
        "qc.draw(output=\"mpl\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 399
        },
        "id": "65ZjOnrEUvFb",
        "outputId": "601598ae-27fe-49bf-86e6-398b1df02182"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "error",
          "ename": "ModuleNotFoundError",
          "evalue": "No module named 'qiskit'",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-1-567178a2dbb8>\u001b[0m in \u001b[0;36m<cell line: 2>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m#Hamiltonian matrix\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mQuantumCircuit\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtranspile\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mqiskit_aer\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mAerSimulator\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnoise\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvisualization\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mplot_histogram\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcircuit_drawer\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mqiskit\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mquantum_info\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mStatevector\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'qiskit'",
            "",
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0;32m\nNOTE: If your import is failing due to a missing package, you can\nmanually install dependencies using either !pip or !apt.\n\nTo view examples of installing some common dependencies, click the\n\"Open Examples\" button below.\n\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n"
          ],
          "errorDetails": {
            "actions": [
              {
                "action": "open_url",
                "actionText": "Open Examples",
                "url": "/notebooks/snippets/importing_libraries.ipynb"
              }
            ]
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Transpile and execute\n",
        "simulator = AerSimulator(noise_model=noise_model)\n",
        "qc_transpiled = transpile(qc, simulator)\n",
        "result = simulator.run(qc_transpiled, shots=shots).result()\n",
        "\n",
        "# Get the counts and display the results\n",
        "counts = result.get_counts()\n",
        "plot_histogram(counts, title=\"Counts for GSE QEM on GHZ state with Pa and Controlled Derangement\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 451
        },
        "id": "SOdjyXP5gs0U",
        "outputId": "1526558a-d19a-4e8e-e284-70ac80745efd"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "state = Statevector(qc_vec)\n",
        "print(state)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TYKsD3lAgxOF",
        "outputId": "4303ad27-3e56-4c56-ebc5-7117b17cdfe2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Statevector([ 0.25+0.j,  0.25+0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,\n",
            "              0.  +0.j,  0.25+0.j,  0.25+0.j,  0.  +0.j,  0.  +0.j,\n",
            "              0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,\n",
            "              0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,\n",
            "              0.25+0.j, -0.25+0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,\n",
            "              0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,\n",
            "             -0.25+0.j,  0.25+0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,\n",
            "              0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,\n",
            "              0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,\n",
            "              0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,\n",
            "              0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,\n",
            "              0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,\n",
            "              0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,\n",
            "              0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,\n",
            "              0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,\n",
            "              0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,\n",
            "              0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,\n",
            "              0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,\n",
            "              0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,\n",
            "              0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,\n",
            "             -0.25+0.j,  0.25+0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,\n",
            "              0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,\n",
            "              0.25+0.j, -0.25+0.j,  0.25+0.j,  0.25+0.j,  0.  +0.j,\n",
            "              0.  +0.j,  0.  +0.j,  0.  +0.j,  0.25+0.j,  0.25+0.j,\n",
            "              0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,  0.  +0.j,\n",
            "              0.  +0.j,  0.  +0.j,  0.  +0.j],\n",
            "            dims=(2, 2, 2, 2, 2, 2, 2))\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#ESD demo\n",
        "from qiskit import QuantumCircuit, transpile\n",
        "from qiskit_aer import AerSimulator, noise\n",
        "from qiskit.visualization import plot_histogram, circuit_drawer\n",
        "from qiskit.quantum_info import Statevector\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Step 1: Define the noise model\n",
        "noise_model = noise.NoiseModel()\n",
        "\n",
        "# Define errors\n",
        "prob_1 = 0.01  # 1% chance of error on single-qubit gates\n",
        "prob_2 = 0.02  # 2% chance of error on two-qubit gates\n",
        "\n",
        "# Depolarizing error on single qubit gates\n",
        "error_1 = noise.depolarizing_error(prob_1, 1)\n",
        "\n",
        "# Depolarizing error on two qubit gates\n",
        "error_2 = noise.depolarizing_error(prob_2, 2)\n",
        "\n",
        "# Thermal relaxation error\n",
        "thermal_error = noise.thermal_relaxation_error(50, 100, 0.03)\n",
        "\n",
        "# Add errors to the noise model\n",
        "noise_model.add_all_qubit_quantum_error(error_1, ['h', 'x', 'y', 'z'])\n",
        "noise_model.add_all_qubit_quantum_error(error_2, ['cx'])\n",
        "noise_model.add_all_qubit_quantum_error(thermal_error, ['h'])\n",
        "\n",
        "# Step 2: Create a quantum circuit for the GHZ state\n",
        "n = 3  # Number of qubits\n",
        "\n",
        "ghz_circuit = QuantumCircuit(n)\n",
        "ghz_circuit.h(0)  # Apply Hadamard gate to the first qubit\n",
        "\n",
        "# Apply CNOT gates to entangle the qubits\n",
        "for i in range(1, n):\n",
        "    ghz_circuit.cx(0, i)\n",
        "\n",
        "# Add a barrier for visualization purposes\n",
        "ghz_circuit.barrier()\n",
        "ghz_circuit.draw(output='mpl')\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 272
        },
        "id": "9QHLOXCkpMlp",
        "outputId": "352bf24e-12f3-4d50-c2d7-acf6ed5fdb74"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "WARNING:qiskit_aer.noise.noise_model:WARNING: all-qubit error already exists for instruction \"h\", composing with additional error.\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 454.719x284.278 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Assuming ghz_circuit and n are predefined\n",
        "copies = 2  # Number of copies\n",
        "ghz_circuits = []\n",
        "\n",
        "# Step 4: Create multiple copies of the noisy GHZ state for ESD\n",
        "for _ in range(copies):\n",
        "    ghz_copy = ghz_circuit.copy()\n",
        "    ghz_circuits.append(ghz_copy)\n",
        "\n",
        "# Create a deranged circuit by applying swap operations between the copies\n",
        "deranged_circuit = QuantumCircuit(n * copies + 1, 3)  # +1 for the ancilla qubit\n",
        "ancilla_index = 0  # Using q0 as the ancilla qubit\n",
        "\n",
        "# Apply a Hadamard gate to the ancilla qubit\n",
        "deranged_circuit.h(ancilla_index)\n",
        "\n",
        "# Apply the GHZ state preparation to each copy\n",
        "for i in range(copies):\n",
        "    deranged_circuit.compose(ghz_circuits[i], qubits=range(1 + i * n, 1 + (i + 1) * n), inplace=True)\n",
        "\n",
        "# Step 5: Add an ancilla qubit and apply controlled swap operations\n",
        "for i in range(copies - 1):\n",
        "    for j in range(n):\n",
        "        deranged_circuit.cswap(ancilla_index, j + 1, j + 1 + (i + 1) * n)\n",
        "\n",
        "# Add controlled CNOT gates from the ancilla to q1, q2, and q3 (i.e X1 X2 X3 which is pauli decomposition of Hamiltonian of GHZ)\n",
        "for i in range(1, 4):\n",
        "    deranged_circuit.cx(ancilla_index, i)\n",
        "\n",
        "# Add H to ancilla before measuring (this is equivalent of measuring using pauli-X)\n",
        "deranged_circuit.h(ancilla_index)\n",
        "\n",
        "# Measure the ancilla qubit\n",
        "#deranged_circuit.measure(ancilla_index, 0)\n",
        "deranged_circuit.measure(1, 0)\n",
        "deranged_circuit.measure(2, 1)\n",
        "deranged_circuit.measure(3, 2)\n",
        "\n",
        "# Visualize the circuit\n",
        "deranged_circuit.draw(output='mpl')\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 577
        },
        "id": "mTvQjz7d3sQu",
        "outputId": "137f6e97-42e0-4fd0-d1c5-6968ed09c227"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 1207.22x702.333 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Step 6: Simulate the deranged circuit with noise\n",
        "simulator = AerSimulator(noise_model=noise_model)\n",
        "result_deranged = simulator.run(deranged_circuit).result()\n",
        "counts = result_deranged.get_counts()\n",
        "# Plot the measurement results\n",
        "plot_histogram(counts)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 446
        },
        "id": "K06XWUxu8zjR",
        "outputId": "4979fe00-bd6b-4bb0-c7b4-21b0af96ff85"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(counts)"
      ],
      "metadata": {
        "id": "2xOMGRkeXmXP",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "cc8fd88f-d305-4669-82be-7198cdf3c7dc"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "{'1': 76, '0': 948}\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "y3_OTLBFWbo1"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}