Colab_10b_Superdense_coding.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyPQlDWOv9STjR+0lmJeOI4c",
      "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_10b_Superdense_coding.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "e56EbQHF9eC0",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0ddcfb13-51c3-48d6-e5e5-667c149ac657"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "  Installing build dependencies ... \u001b[?25l\u001b[?25hdone\n",
            "  Getting requirements to build wheel ... \u001b[?25l\u001b[?25hdone\n",
            "  Installing backend dependencies ... \u001b[?25l\u001b[?25hdone\n",
            "  Preparing metadata (pyproject.toml) ... \u001b[?25l\u001b[?25hdone\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m6.0/6.0 MB\u001b[0m \u001b[31m29.6 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m12.8/12.8 MB\u001b[0m \u001b[31m60.7 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m241.5/241.5 kB\u001b[0m \u001b[31m21.2 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m129.9/129.9 kB\u001b[0m \u001b[31m12.4 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m1.9/1.9 MB\u001b[0m \u001b[31m78.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m49.6/49.6 kB\u001b[0m \u001b[31m5.6 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m110.5/110.5 kB\u001b[0m \u001b[31m13.4 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m49.6/49.6 kB\u001b[0m \u001b[31m5.0 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m37.5/37.5 MB\u001b[0m \u001b[31m21.2 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m112.7/112.7 kB\u001b[0m \u001b[31m13.3 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25h  Building wheel for qiskit (pyproject.toml) ... \u001b[?25l\u001b[?25hdone\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m162.6/162.6 kB\u001b[0m \u001b[31m1.8 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25h  Preparing metadata (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Building wheel for pylatexenc (setup.py) ... \u001b[?25l\u001b[?25hdone\n"
          ]
        }
      ],
      "source": [
        "!pip install qiskit --quiet && pip install pylatexenc --quiet"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from qiskit import QuantumCircuit, Aer, execute, transpile\n",
        "from qiskit.visualization import plot_histogram\n",
        "from qiskit.visualization.state_visualization import array_to_latex"
      ],
      "metadata": {
        "id": "HWvTt_uy9k0X"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def get_state(circuit):\n",
        "  state_vector_simulator = Aer.get_backend(\"statevector_simulator\")\n",
        "  job = execute(circuit, backend=state_vector_simulator)\n",
        "  result = job.result()\n",
        "  return result.get_statevector()"
      ],
      "metadata": {
        "id": "UVLIKk6L90j6"
      },
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Step 1: creazione dello stato di Bell\n",
        "qc = QuantumCircuit(2)\n",
        "qc.h(1)\n",
        "qc.cx(1, 0)\n",
        "\n",
        "qc.barrier()\n",
        "\n",
        "# Step 2: codifica del messaggio\n",
        "msg = '01'\n",
        "if msg == \"00\":\n",
        "    qc.i(1)\n",
        "if msg == \"01\":\n",
        "    qc.x(1)\n",
        "if msg == \"10\":\n",
        "    qc.z(1)\n",
        "if msg == \"11\":\n",
        "    qc.y(1)\n",
        "\n",
        "qc.barrier()\n",
        "\n",
        "# Step 3: decodifica del messaggio\n",
        "qc.cx(1, 0)\n",
        "qc.h(1)\n",
        "\n",
        "qc.measure_all()\n",
        "\n",
        "qc.draw(output=\"mpl\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 255
        },
        "id": "3FQZYhT1_x3W",
        "outputId": "de337b88-8eca-4f49-b810-272576b03d98"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 998.442x284.278 with 1 Axes>"
            ],
            "image/png": 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4Nl9p/5vaOo9UeFuXFlJDm/e3C/eq7/0gODhYhw8fVkZGhsuhaNGiRS6HiTLHjh3TyZMndepU9RdGgDkIFCbYt2+fHA6HEhMTK52MNX78eMXGxmrkyJFatWqVli1bpvvvv189e/bUyJEjTaoYv9Q3yfvbbB8rNQ33/nYBVNYoVOrcwvvbNWPfA/xSdna2EhMTFR8fr7Fjx7q07Pfffy/J9TAhSbfccotatmyp66+/3qVtwvM4KdsEe/bskVR5uJPkPIy4fv16TZkyRWPGjFFgYKCGDRumP/7xj1y1oA6Jj5Y6xUt7vXRepEXSHZ29sy0AtTMwWdpz0nmStjckNme4E+q/uXPnyuFw6OTJky6FCdRtBAoTXClQSFLbtm21atUqb5YEA0b3lI7+LBVc8vy2bmkvteaDBFCnxEdLA5Klv+/1/LaCA6UxN0kWE4ZZAe42b948s0uAm/GVtwlqChSoHxo1kO6+wbVlLlyUcgpqd636Mk3DpaE+9FJp3ry5ZsyYoebNfeAMc7jM19r/9k5SXJRryxjZD4y8Xmpc9dU7UQ/5Wj8ALA4jdyIBUG7tbmntHs+sO6KBNOX2uv1BwtXrrxvRvn17j28Dxvn7ayCnQHr779LZ6u95eVX6d5BGXM/RibrMV/vAle5DUVfl5eVxHwoTcIQCuEp3dJYGd3H/eqPCpMkD6naYMOL8+fNau3atzp8/b3YpMIEvtn9kqDR5oGcumvCrjoQJX+SL/QD+jUABXCWLxRkqHr3FfZdz7NpSemaQ1DTCPeurS9LT0/X0009XuDQy/Ievtn9UmPSbO6QbEtyzvtBg6aHe0nDChE/y1X4A/8VJ2YCbdGnhvALL33ZIO9MkI2MJIxpId3WXrm/l7uoAeFpYiPRgH+m6VtKybc6hUEZ0bSHd08O5PwCA+oBAAbhRQ5v0UB9pSFfp20PSliNSflHNy7VrLvVNdF7XPoDjhkC91ile6nCNtC9D2nxQ+jGr5mVCg6Ub20q92/nmkUkAvo1AAXhA44bOoQpDu0o/50onz0jp55who7hUCgpwDpNqEe289GRYiNkVA3CnAKvzqGWXFs5LS6efdf78fEHakebcDwQHSKN6OvcDzSL4MgFA/UWgADzIapViGjl/ekhKOS6dv+j8NnJAstnVmcNms6lDhw6y2dx0wgnqFX9s/9BgKSnG+SNJ+0859wMNgqWebcytDebwx34A30agAOBVbdu21YoVK8wuAyah/QH6AXwPB1gBAAAAGEagAOBVqamp6tKli1JTU80uBSag/QH6AXwPgQKAVzkcDhUXF8vhMHJhXdR3tD9AP4DvIVAAAAAAMIyTsgEAAFBJaGio8vLy3La+1xd8rAv5BYoIC9W0CWMqPXaH0NBQt6wHriFQAAAAoBKLxaKwsDC3rS84xKbg4lIFh9gUFhZW6THqLwIFAK9q27atVq5cqRYtWphdCkxA+wP0A/geAgUAr7LZbEpMTDS7DJiE9gfoB/A9nJQNwKsyMjL0/PPPKyMjw+xSYALaH6AfwPcQKAB4VU5OjpYvX66cnByzS4EJaH+AfgDfQ6AAAAAAYBiBAgAAAIBhBAoAAAAAhhEoAHhVkyZN9Nhjj6lJkyZmlwIT0P4A/QC+h0ABwKssFouCg4NlsVjMLgUmoP0B+gF8D4ECgFedPn1a8+bN0+nTp80uBSag/QH6AXwPgQIAAACAYQQKAAAAAIYRKAAAAAAYRqAA4FWNGjXS8OHD1ahRI7NLgQlof4B+AN8TaHYBAPxLfHy8XnvtNbPLgElof4B+AN/DEQoAXlVUVKTjx4+rqKjI7FJgAtofoB/A9xAoAHjV4cOHNWjQIB0+fNjsUmAC2h+gH8D3MOQJVXI4pEulZlfhmuAAiXsEwV0cDocK7PWrE4RaA7hRFtyG9wH4O4fDoYKCArPLcEloaKgp7wMEClTpUqk0Y6nZVbhm9n1SCK9ouEmBvVRR69eZXYZLzt02UGEBdAK4B+8D8HcFBQVq2LCh2WW4JC8vT2FhYV7fLkOeAAAAABhGoAAAAABgGAcGAXhVcnKy9u/fb3YZMAntD9AP4Hs4QgEAAADAMAIFAK86duyYxowZo2PHjpldCkxA+wP0A/geAgUAryooKNCuXbvq3aX44B60P0A/gO8hUAAAAAAwjEABAAAAwDACBQAAAADDCBQAvCouLk6zZ89WXFyc2aXABLQ/QD+A7+E+FAC8KjIyUiNGjDC7DJiE9gfoBzAuOjpaRUVFys/PN7uUCggUALzq7Nmz+vLLLzV48GBFR0ebXQ68jPYH6Af+JjIyUj179lT37t3VrVs3NW7cWIGBgSosLNSxY8e0Y8cObd++XSkpKbLb7dWup3Hjxvrqq6904cIFDRkypE6FCgIFAK/KzMzUzJkzdd111/FG6odof4B+4C9uvPFGTZw4Uffee69sNluN8x8/flwLFizQX/7yF/38888VppWFieuuu06S9Je//EVjxozxRNmGcA6FF2RnZ2v69Olq166dbDabWrRooSlTpig/P1/jxo2TxWLR3LlzzS4THnYuXyoudf6/pFQqrf5LCAA+qNQuHf353/uBK3wRCaAeS0hI0Lp167RlyxY9/PDDtQoTktSqVSvNmjVLJ06c0AsvvKDAQOf3/r8MExkZGXrhhRc8Vb4hBAoPS0lJUefOnfX6668rKytLHTt2VHFxsd5++23dd9992r9/vySVv0h8TXrq1/rTgxbtWD2n2nn+9KBFn88Z5sWqvGv/Kem9DdLvP5MKLjmfy78kvfw3ac0u6cJFU8uDh5W+v0jFtw+Rfe3fK01zOBwq+a8ZKh46Qo5jad4vDl6RVyj9fY/0h8+lt9f9ez+QWyS9s17amy45HObW6Em8D8CfTJgwQXv27NGAAQPKnztz5ozmzp2rBx54QO3bt1doaKiCg4MVFRWlvn37asqUKVq9enX5cKeQkBD9/ve/19atW9WnT59KYaJ///46dOiQGb9etRjy5EHZ2dkaPny4srKyNHXqVL344osKDw+XJL322muaMWOGAgMDZbFY1KVLF5Orhbs5HNLnO6WvD1Q9/UKh9Pe90pYj0oT+UlyUd+uDd1gfekD2LVtVuuB/ZOneTZamTcqn2Vd8JsfuPbI++ogsrRPMKxIe89N56d0NziOUVfkx0/nTu500qodk5Ws+oF6yWCx666239NRTT5U/d/z4cb344otaunSpCgsLKy2Tk5OjzZs3a/PmzXr77beVkJCgp556SpMnT1ZgYKC6deumjRs3KiAgQFLdDRMSRyg86qmnnlJ6eromTZqkOXPmlIcJSZo+fbq6du2qkpISJSQkKCIiwsRK4Qlf7q4+TFzuwkXnt5TZuZ6vqS4ICwtTnz59FBYWZnYpXmEJClLgtKlSYaFK33yr/HnHyXTZF/1VlvbXyjr6HvMK9DJ/av+cAmn+P6oPE5f79rD02U7P14S6wZ/6gb/4ZZhYsGCBOnfurA8//LDKMFGVtLQ0PfPMM7rpppvKR7CUhYnTp0/X2TAhESg8Zv/+/Vq6dKmaNGmiV155pcp5unfvLknq2rVr+XNlAaRnz54KCQmRxWLxSr1wr+xcad3e2s+fVyit3uW5euqShIQELVy4UAkJCWaX4jWWxHayjrlXjh07ZV/9pRylpSp9bY7kcChg2lRZ/vWG4Q/8qf3X7pbOuzCk8Z8/SqfOea4e1B3+1A/8wWOPPVYeJkpLSzV27Fg9/vjjys019k1hWlqaLl26VOG5gIAAnT9//qpr9RQChYcsWbJEdrtdDzzwgBo2bFjlPA0aNJBUMVAcPnxYy5cvV0xMjHr06OGVWr2h5FKBLuZmV/nji749JLk6JHr3Sf84n6K0tFR5eXkqLS01uxSvsj5wv9SmjUr/Z6Hs896V48eDsj7ysCwt4s0uzav8pf0LLkk70lxf7pu6+eWjW/jb+8CV+Es/8ActW7bUG2+8Uf543Lhx+utf/2p4fWUnYJd9Niw7uhEdHa133nnn6or1IM6h8JD169dLkvr371/tPOnp6ZIqBopbbrlFmZmZkqSXXnpJmzdv9mCV3rNl+YvasvxFs8vwmu+Pur5MqV3amSbd2sHt5dQpBw4c0KhRo7Rs2TIlJyebXY7XWAIDFTjtGZVM/o3sq1bL0ilZ1rvvNLssr/OX9t914t9Xc3LFjmPSqBt881wKf3sfuBJ/6Qf+YMGCBeVD2hcuXKgPP/zQ8LqquprT3XffrS+++ELNmjXT3XffrdGjR+vTTz91R+luRaDwkOPHj0tyXgKsKiUlJeVh4fJAYfXAu8gNN9ygrKwsl5YJCGqgu2a676uyTv3HK/HG0VVO+9urA92yjaTERJUWm/8VvzUgWHfPMpAoJL32p/f04Krfu7kiz3rkkUdcmr8sMK9Zs0Y//PBDrZZZtGiRi1VdPUdwsLRgnntXGhYmBQVJJSWy9LhBFjf396TEJFl+cZjcG1x5DRhpf8mc18DV6DhwqjoOeNrl5YpKpHbtO+tSgfljn3gfqD1f3Q+6213/8RuFNYxQZlam4uPjKz2ua650kzlJ6tatmwYNGiRJOnnypKZOnWp4W1WFibJzJiZOnKhly5ZJkp577rkrBorExETDnyVjYmK0fft2Q8sSKDyk7O6FFy9WvWNbunSpsrOzFR4ertatW3u0lqysLGVkZLi0TGBIqFtriIxJVMtOA2qe8SqcyjylkqICj26jNqwBQYaXzcvNdbmtzFZQ4NrfvOzwbWFhYa2XNeVvYguR8ZaszOFwqPSNP0olxVLLFrL/78ey9rtFlmti3baNU5mnpMIit62vtlx5DRhpf8mk18BVaHHhguFlMzNPqTDvrBurMYb3gdrz2f2gm9n/NcTLXlqqjIyMSo/rmyeeeKL8/zNnztQFg/3+SmFCkpYvX66tW7fqxhtv1PXXX6+bbrpJW7ZsqXJdZWHV2wgUHhITE6Nz585p586d6tWrV4VpmZmZmjZtmiSpS5cuHj/xOiYmxuVlAoIaeKASz7om9po6cYRCkgpzT8sW3tTl5aylFxQXF+eBijwnNNS1Dx1lN/ix2Wy1XtaMv4kjOFin3bg++2cr5di1W9b/GCtrr5tU8uRklb7xRwXMme22fcA1sdeYcoTCldeAkfaXzHkNXI0Au7GTMYuL8tQ4MkxqZP4+mPeB2vPV/aC7Wf91AQprQIDi4uIqPa5r7HZ7tR/Qw8LC9Otf/1qSdP78eS1evNjQNmoKE2Xmz5+vG2+8UZI0fvz4agNFbGzsVR2hMIpA4SEDBgzQ/v37NXv2bA0cOFBJSUmSpG3btumhhx5SdrbzJDRv3NDOyOGrohJpxlIPFONBBw8dUkgdeUV/8YP0j1TXlgmwSl8selnhtpc9U5SHHDhQi2vjXmbfvn16//33NWTIkFqPHZ45c6aR0q5KfmmJotavc8u6HBkZsr+/SJZrk2S9d5QsAQGyPviA7B98KPtnKxVw10i3bOfgoYMKC/B+J3DlNWCk/SVzXgNX4+Il6cUV0iUXz6Po36mh5p084ZmiXMT7QO356n7Q3WbNW6wLefmKjYlVenp6pcd1TX5+frUX1unevXt5GPz000/LR6a4orZhQpI++eQTvfPOOwoNDdXNN99c7ToPHTpkyuWIffC0r7ph+vTpaty4sU6ePKnk5GR17txZiYmJ6tmzp9q0aaPbbrtNUsXzJ+A7eidKrn7nfF1LKdzmkXLqlKSkJG3evLk8ZPs6h92u0tfflOx2BUx7pvwSsdZ7R8mSlCj7+4vkOGXOIWoz+Ev7NwiWuhsYzdrHt/8s+Bd/6Qe+rOzS/5KqPVpwJa6ECck5PG7XLuf15du1a6fIyEiXt+lJBAoPiY+P16ZNmzR06FDZbDalpaUpOjpaCxYs0OrVq3Xw4EFJBApf1bihdEfn2s8fYZOG+MlLISgoSNHR0QoKcucZCnWXfdkKOVL3yzr2QVlatix/3hIQoID/ekayl6r0jT/K4XD1QsP1kz+1/6AuUpQLI2FubS/FRnqsHNQh/tQPfNXlI0x27Njh0rKuhokyl4848cYIF1cQKDyoQ4cOWrVqlXJzc5Wbm6utW7dq/Pjxys/PV1pamqxWqzp16mR2mfCQOzpLv+pY83yRodITv3KGEH9w4sQJTZw4USdO1I1hHZ7kOHFC9g8/kqVDe1nvubvSdEtCK1kffECOPXtl/2ylCRV6nz+1f6MG0sRa9u2bk6QR3TxfE+oGf+oHvqpx48bl/3elHY2GCcl5JakyUVFRtS/WC+rIiHP/sm/fPjkcDiUlJVV5MlbZpcFSU1MrPE5ISNANN9zgvULdIL7jrZry/678zWtN0+sri0Uafr10baz0zUFpT7p0+ZfQkaFS73bO4VEN/WCoU5nc3Fxt2LBBTz75pNmleJylZUsFrf78ivME3H+fAu6/z0sVmc+f2l+SmkZIzwySvjvsvOHl2cuGWVskdbhG6pvk/NfD1+cwjT+/D1TH3/qBL5oxY4befPNN2Ww2l67uNGjQIENhQnJe7Wn37t0qLCzU3r17jZTtMQQKE+zZs0dS9cOdRo8eXeXjsWPH+sR1qP1NUozzJ6dA+vmC82ZXYSFSi2jnidgAfFtYiDQgWbqtg3TyrJRXJAVapWYRUpT3z50E4Ab79u3Tvn37XF5u8eLFio6O1owZM1wKE5J09OhRHT1q7D5XnkagMEFNgcJfxlL7m8hQ5w8A/2S1Sq2amF0FALP9+c9/1qJFi5Sba+zy0nUR34+aoKZAAQAAAN/lS2FC4giFKdavX292CYBpmjdvrhkzZqh58+ZmlwIT0P4A/QC+h0ABwKuaNGmiRx55xOwyYBLaH6AfwPcw5AmAV50/f15r167V+fPnzS4FJqD9AfoBfA+BAoBXpaen6+mnn1Z6errZpcAEtD9AP4DvIVAAAAAAMIxAAQAAAMAwAgUAAAAAwwgUALzKZrOpQ4cOstlsZpcCE9D+AP0AvofLxgLwqrZt22rFihVmlwGT0P4A/QC+hyMUAAAAAAwjUADwqtTUVHXp0kWpqalmlwIT0P4A/QC+h0ABwKscDoeKi4vlcDjMLgUmoP0B+gF8D+dQoErBAdLs+8yuwjXBAWZXAF8Sag3QudsGml2GS0KtdAK4D+8D8HehoaHKy8tz2/peX/CxLuQXKCIsVNMmjKn02B1CQ0Pdsh5XEShQJYtFCuHVAT9msVgUFkAngP/ifQD+zmKxKCwszG3rCw6xKbi4VMEhNoWFhVV6XJ8x5AkAAACAYXz3AMCr2rZtq5UrV6pFixZmlwIT0P4A/QC+h0ABwKtsNpsSExPNLgMmof0B+gF8D0OeAHhVRkaGnn/+eWVkZJhdCkxA+wP0A/geAgUAr8rJydHy5cuVk5NjdikwAe0P0A/gewgUAAAAAAwjUAAAAAAwjEABAAAAwDCu8gTgqrRv396l+Rs1aqQXX3xRvXv3VmxsrIeqgje58hqg/eGL2A/C3xEoAHhVbGysXnrpJbPLgElof4B+AN/DkCcAAAAAhhEoAAAAABhGoAAAAABgGIECAAAAgGEECgAAAACGESgAAAAAGEagAAAAAGAYgQIAAACAYQQKAAAAAIYRKAAAAAAYRqAAAAAAYBiBAgAAAIBhBApIkl5//XX16tVLUVFRioyMVN++fbV27VqzywIAAKjWmjVrdN111ykkJEQJCQl68803zS7Jq/75z39q5MiRatWqlSwWi2bOnGlKHQQKSJLWr1+vRx99VBs2bND333+v3r17a9iwYdq8ebPZpQEAAFSyfft2jRw5UoMHD1ZKSopeeukl/fa3v9W7775rdmlek5eXp44dO+q1115TTEyMaXUEmrZl1Clffvllhcevvfaa1q5dqxUrVqhPnz4mVQUAAFC1N998Uz169NArr7wiSerQoYP27dunV199VY8//rjJ1XnHkCFDNGTIEEnSjBkzTKuDQIEq2e12XbhwQWFhYWaXAgAA6pELeQXKOn220vMlpaXl/x48ll7p8eVaXtNMtpDgK25n8+bNGjduXIXnBg0apDlz5ig9PV3x8fFX82sY5nA4dOT4KdkdjgrPu/L7R4aHqVmTKO8U7AYEClRp1qxZysnJ0fjx480uBQAA1CMhwUH67O+bdDYnt8rpBRcL9f4na6p93LpFrB4bM7TG7WRmZlYa5lP2ODMz07RAYbFYdPh4hr7eklLl9Jp+/4AAqyaPvdvTZboV51Cgkvnz52vWrFlatmyZaZ0RAADUTyHBQbpvaH9ZLBZDy44eequs1vr9EXVA3+6KbdbY0LJ33NJTMU2j3VyRZ9Xv1oLbzZkzR9OmTdPKlSs1YMAAs8sBAAD1UKv4GN16U1eXlxs+oLeiG4XXat7Y2FhlZWVVeO6nn34qn2amwIAA3TesvwICXPuo3aZlrPr26OyhqjyHQIFy//3f/62XX35Za9asIUwAAICr8qs+3XVN89p/S5+clKDunZJqPX+fPn30f//3fxWeW7t2rVq1alUnRljENI3WoFt61nr+kOAgjR5yq6wGjuyYjUABSdJvfvMbvf766/roo4907bXXKisrS1lZWTp//rzZpQEAgHooMCBA9w3tr8CAgBrnbRjWQHfdcbNLw6Sefvppff/99/rd736nAwcO6MMPP9Sf//xnPfvss1dTtlv16dFZbVrW7mjJiIF9FFXLozNl8vLylJKSopSUFF26dElZWVlKSUnR4cOHjZRrmMXh+MUp6PBL1XXgsWPHatGiRd4tBgAA+IxN23Zr9fotV5xn7D13qEO7Vi6ve/Xq1frtb3+rAwcOKCYmRlOmTNEzzzxjtFSPOHc+V2+9v0xFl4qrnSc5KUEP3jnQ5fNOvv76a/Xv37/S8/369dPXX3/taqmGESjgkoKLhTqbk6v42KZmlwIAAOoBu8OhhR+v1tETp6qc3rNre9096BYvV+VdO/Ye1Kerv65yWsOwBnr60dEKC7V5tyg3YsgTXLJp2x7N/evfavymAQAAQJKsFovuHXqrQoKDKk2LjgzX0Nt6mVCVd3VLTlSnpNZVThs1uF+9DhMSgQIuyL9YqG937JUkJcSbd3t3AABQv0RGNNSdt/et8JzFYtF9Q/tXGTR8jcVi0V133KyGYQ0qPH/jdR3Uvm1Lk6pyH58JFBaLpXzc2RdffKGbb75ZERERatKkiUaNGqUjR46Uz7tq1Sr169dPkZGRioiI0MiRI3Xo0KFq111UVKQ//elP6t27tyIjI2Wz2XTttddq2rRpys7OrnKZrVu3asaMGerRo4diYmIUEhKiuLg43Xvvvdq2bVu121qzZo2GDBmiZs2aKSgoSI0bN1aHDh306KOPavPmzQb/Ou7xzbY9KrpUrNhmjdUx0fVxjgAAwH9d17GdOl/772/pb72pq1r50ReUYaE2jRrcr/xx48gIDel/k4kVuY/PnENRFibmzp2rSZMm6ZprrlHz5s114MABXbx4UXFxcfrhhx+0ePFiPf3004qNjVVMTEz59JiYGO3evVtNm1Y8N+Cnn37S4MGD9cMPP8hqtapFixaKiIjQwYMHVVRUpJYtW2rDhg1q06ZNheXatWunI0eOKDo6WrGxsQoODtaJEyd05swZBQYG6uOPP9Y999xTYZn58+frySeflCQ1btxYrVq10sWLF3Xy5Enl5eVpwoQJevfddz34V6xe/sVCvfbuEhVdKtZDd92u5KQEU+oAAAD1V/7FQr31/jKFhzXQxIfurNUVoHzN3/5vk77fdUCPPzBCreKam12OW/hcoAgNDdU777yjhx9+WJJ09uxZDRo0SNu2bdOwYcP0j3/8Q++++2759DNnzuiOO+7Qjh07NGPGDL366qvl63Q4HOrfv782btyooUOHau7cuUpISJDkvEzXlClT9P7776tXr1769ttvK9Tz17/+Vb1791a7du3Kn7Pb7fr888/18MMPKzAwUCdPnlTDhg0lSSUlJWrWrJnOnTun+fPna/z48Qr4VydzOBzatGmTzpw5o7vuusvlv82fP1yh3LyLLi93ucKiS7pUXCyr1aqwBjZDd78EAAAoKS2V1WKp93fDNs6hS8UlCg6qW0O9whs20OSxdxta1ucCxeTJk/X2229XmLZ27VoNHjy42ulffvmlhgwZoi5dumjXrl3lz69Zs0ZDhw5Vp06dtG3bNtlsFU+YKS0tVc+ePbVz505988036tOnT61qfeGFFzRz5kwtWbJEY8aMkSRlZWUpNjZWUVFROnv2rGu/fA1mzVusC3n5bl0nAAAAfEdEwzD99skHDC0b6OZaTPef//mflZ7r1q1braYfPXq0wvPLly+X5LwXwy/DhCQFBARoxIgR2rlzp77++utKgeLQoUP6+OOPtWvXLp05c0bFxc7rD//888+SpJSUlPJA0bRpU9lsNuXk5GjdunUaOHBgrX/nmoQ3bFDzTFfA0QkAAADfdjWfF30uULRt27bSc5efF1HV9GbNmklyDmO63O7duyVJH3zwgT777LMqt/fTTz9JkjIyMio8/8Ybb+jZZ59VSUlJtbWeOXOm/P8BAQGaMmWKZs+erdtvv13dunXTgAED1LdvX/Xr108RERHVrqcmRg9fSf8+d0KSHhg5gHMnAAAAUIHPDXmq7tcxMj0xMbHWty6//I7SmzdvVt++fRUQEKCXX35ZI0eOVEJCgsLCwmSxWPT+++9r3Lhxle5CbbfbNX/+fM2bN08HDhwofz4kJES//vWvNWfOHEVHR9eqnstdzTkUHJ0AAADwfVdzDoXPHaFwp7ITpleuXKnhw4fXermPPvpIkjR16lT97ne/qzT98iMTl7NarZo0aZImTZqk9PR0bdq0SevWrdMnn3yiDz74QCdPntS6detc/j1y8y5e9TkUdrtdufkFV7UOAAAA+B4CxRUkJycrJSVFe/fudSlQHDt2TJLUt2/fKqdv2VLzXabj4+N1//336/7779fUqVPVuXNnffXVVzp27Jhat676TovVMTomjqMTAAAA/oFzKDxk1KhRWrx4sd577z1Nnjy5/IhFTRo0cDZIVlZWpWmHDh3SqlWrXKojOTlZjRo1Uk5Ojk6dOuVyoDBy+IpzJwAAAFAb/noB4FoZOXKk+vXrp7S0NN1+++3au3dvhel2u13fffedHn/88QpXiLr55pslSa+88kqFO3Tv27dPw4cPr/K6y6mpqXrssce0ZcuWCudxlJaW6q233lJOTo5sNpuSk5Pd/WtWibtiAwAAoDY4KbuG6dnZ2Ro5cmT5jetatWqlmJgYXbx4UUeOHFF+vvPchP3796t9+/aSpNzcXHXr1k2HDx9WUFCQrr32Wtntdu3fv1+xsbGaOHGinn/++QonZaekpOj666+XJIWHh6tt27YKCAhQWlpa+TkX8+fP1xNPPGHo7+MK7ooNAACA2uIIRQ2aNGmijRs3atGiRRo4cKDy8/O1fft2HTt2TO3atdOUKVO0ceNGJSUllS8THh6ub775Ro8++qiioqL0448/Ki8vTxMmTNDOnTsVFxdXaTtJSUlauHCh7rvvPsXGxuro0aPatWuXbDabRo8erU2bNnklTEjOcydaXtOMoxMAAACokc8coYD7FRZdki0k2OwyAAAAUIcRKAAAAAAYxpAnAAAAAIYRKAAAAAAYRqAAAAAAYBiBAgAAAIBhBAoAAAAAhhEoAAAAABhGoAAAAABgGIECAAAAgGEECgAAAACGESgAAAAAGEagAAAAAGAYgQIAAACAYQQKAAAAAIYRKAAAAAAYRqAAAAAAYBiBAgAAAIBhBAoAAAAAhhEoAAAAABhGoAAAAABgGIECAAAAgGEECgAAAACGESgAAAAAGEagAAAAAGAYgQIAAACAYQQKAAAAAIYRKAAAAAAYRqAAAAAAYBiBAgAAAIBhBAoAAAAAhhEoAAAAABhGoAAAAABgGIECAAAAgGEECgAAAACGESgAAAAAGEagAAAAAGAYgQIAAACAYQQKAAAAAIYRKAAAAAAYRqAAAAAAYNj/B7IpDdvN9t/UAAAAAElFTkSuQmCC\n"
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "aer_sim = Aer.get_backend('aer_simulator')\n",
        "result = aer_sim.run(qc).result()\n",
        "counts = result.get_counts(qc)\n",
        "plot_histogram(counts)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 461
        },
        "id": "atbFy0Zh_31W",
        "outputId": "482fc1ae-cd87-43c3-be35-e1cda60aaab2"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 700x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "Jjz6dVaAFtJp"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}