BZ_Algo.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/NSPFD/IBM_-QUANTUM/blob/main/BZ_Algo.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "8a533677",
      "metadata": {
        "tags": [],
        "id": "8a533677"
      },
      "source": [
        "# Bernstein-Vazirani"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "bb529d8f",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bb529d8f",
        "outputId": "ca606fe3-e315-44fe-c60a-cb6cc9c54f9c"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
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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-ibm-runtime) (1.3.0)\n",
            "Requirement already satisfied: pycparser in /usr/local/lib/python3.10/dist-packages (from cffi>=1.12->cryptography>=1.3->requests-ntlm>=1.1.0->qiskit-ibm-runtime) (2.22)\n",
            "Downloading qiskit_ibm_runtime-0.26.0-py3-none-any.whl (2.9 MB)\n",
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            "\u001b[?25hDownloading requests_ntlm-1.3.0-py3-none-any.whl (6.6 kB)\n",
            "Downloading urllib3-2.2.2-py3-none-any.whl (121 kB)\n",
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            "\u001b[?25hDownloading pyspnego-0.11.1-py3-none-any.whl (130 kB)\n",
            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m130.5/130.5 kB\u001b[0m \u001b[31m8.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hBuilding wheels for collected packages: ibm-platform-services, ibm-cloud-sdk-core\n",
            "  Building wheel for ibm-platform-services (pyproject.toml) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for ibm-platform-services: filename=ibm_platform_services-0.55.2-py3-none-any.whl size=339687 sha256=9575ad7d7e5ea205010f15d91910988d1176fb036f868ac69353b0293a2e7a5e\n",
            "  Stored in directory: /root/.cache/pip/wheels/af/ef/67/6c17a948d54c37e26b0c927dc206d95a258e9a3f7ba7014c67\n",
            "  Building wheel for ibm-cloud-sdk-core (pyproject.toml) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for ibm-cloud-sdk-core: filename=ibm_cloud_sdk_core-3.20.4-py3-none-any.whl size=102561 sha256=e1a92d3eb7410f424b21bd123c7180f76452f0356ac8bf614623e8a757687350\n",
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            "Successfully built ibm-platform-services ibm-cloud-sdk-core\n",
            "Installing collected packages: urllib3, pyspnego, ibm-cloud-sdk-core, requests-ntlm, ibm-platform-services, qiskit-ibm-runtime\n",
            "  Attempting uninstall: urllib3\n",
            "    Found existing installation: urllib3 2.0.7\n",
            "    Uninstalling urllib3-2.0.7:\n",
            "      Successfully uninstalled urllib3-2.0.7\n",
            "Successfully installed ibm-cloud-sdk-core-3.20.4 ibm-platform-services-0.55.2 pyspnego-0.11.1 qiskit-ibm-runtime-0.26.0 requests-ntlm-1.3.0 urllib3-2.2.2\n"
          ]
        }
      ],
      "source": [
        "### For people using Google-colab un-comment this cell and run it!\n",
        "!pip install qiskit\n",
        "!pip install qiskit_aer\n",
        "!pip install qiskit[visualization]\n",
        "!pip install qiskit-ibm-runtime"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "44205c1e-e76f-4390-a73c-db8af35d8373",
      "metadata": {
        "id": "44205c1e-e76f-4390-a73c-db8af35d8373"
      },
      "source": [
        "###  Importing the required libraries"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "b9e61404-c9c1-4582-bf4f-0fcfb5ad0861",
      "metadata": {
        "id": "b9e61404-c9c1-4582-bf4f-0fcfb5ad0861"
      },
      "outputs": [],
      "source": [
        "import time\n",
        "import numpy as np\n",
        "from qiskit import *\n",
        "from qiskit.circuit import Parameter\n",
        "from qiskit.quantum_info import Statevector, Pauli, SparsePauliOp\n",
        "from qiskit.circuit.library import RealAmplitudes\n",
        "import matplotlib.pyplot as plt\n",
        "import matplotlib.ticker as tck\n",
        "from qiskit.visualization import plot_histogram\n",
        "# %config InlineBackend.figure_format='retina'"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "e863ea74-249e-45d2-9e5e-007200606b3c",
      "metadata": {
        "id": "e863ea74-249e-45d2-9e5e-007200606b3c"
      },
      "source": [
        "# Part II: Getting Started with Qiskit Runtime"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "c72f9aec-de6a-4668-8de6-da61c8c378c1",
      "metadata": {
        "id": "c72f9aec-de6a-4668-8de6-da61c8c378c1"
      },
      "source": [
        "We shall get started with Qiskit Runtime. Qiskit Runtime is already installed and setup for you in the IBM Quantum Lab instance of the IBM Quantum Challenge you are in.\n",
        "\n",
        "If you are running on your local systems, you may need to install Qiskit Runtime packages which can be dones uing: `pip install qiskit-ibm-runtime`. If you have navigated to the IBM Quantum Lab throught the IBM Quantum Challenge portal, then everything should already be setup for you.\n",
        "\n",
        "To start off, the first thing to do here is to define `QiskitRuntimeService` instance to run the program on. We can use this to call the currently available two primitives as needed; `Sampler` and `Estimator` and run them on Qiskit Runtime."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "a08d9314",
      "metadata": {
        "id": "a08d9314"
      },
      "outputs": [],
      "source": [
        "from qiskit_ibm_runtime import QiskitRuntimeService, Session, Options, Sampler, Estimator"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "e1a8f7ea-5967-404f-ab43-3675a4c0c10a",
      "metadata": {
        "id": "e1a8f7ea-5967-404f-ab43-3675a4c0c10a"
      },
      "source": [
        "The block below saves your Runtime account credentials for your current environment. The `channel` keyword argument lets the Runtime know whether you are using the regular IBM Quantum (`channel='ibm_quantum'`) or IBM Cloud (`channel='ibm_cloud'`). We will be using the `ibm_quantum` channel for all our runs. This cell can be run just once and your credentials should be saved for that environment. And for the `token` keyword argument, your API token value is found in this link: **[quantum-computing.ibm.com/account](https://quantum-computing.ibm.com/account)**.\n",
        "\n",
        "If you are on the IBM Quantum Lab, you can simply call the `QiskitRuntimeService` with just the channel in your subsequent runs."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "b9ffbb87-f5a5-453c-892e-d870f8bd7297",
      "metadata": {
        "id": "b9ffbb87-f5a5-453c-892e-d870f8bd7297"
      },
      "outputs": [],
      "source": [
        "# Save the Runtime account credentials if you have not done so already\n",
        "# If you need to overwrite the account info, please add `overwrite=True`\n",
        "# QiskitRuntimeService.save_account(channel='ibm_quantum', token='my_token', overwrite=True)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "0bf9aa54-94ec-4497-baac-3407d26a595f",
      "metadata": {
        "tags": [],
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "id": "0bf9aa54-94ec-4497-baac-3407d26a595f",
        "outputId": "ac056ff3-dee2-465f-a6cd-4bd7a0ae6dd7"
      },
      "outputs": [
        {
          "output_type": "error",
          "ename": "AccountNotFoundError",
          "evalue": "'Unable to find account.'",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mAccountNotFoundError\u001b[0m                      Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-4-ed94ecbd37ce>\u001b[0m in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mservice\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mQiskitRuntimeService\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mchannel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'ibm_quantum'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/qiskit_ibm_runtime/qiskit_runtime_service.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, channel, token, url, filename, name, instance, proxies, verify, channel_strategy, private_endpoint)\u001b[0m\n\u001b[1;32m    127\u001b[0m         \u001b[0msuper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__init__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    128\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 129\u001b[0;31m         self._account = self._discover_account(\n\u001b[0m\u001b[1;32m    130\u001b[0m             \u001b[0mtoken\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mtoken\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    131\u001b[0m             \u001b[0murl\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0murl\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/qiskit_ibm_runtime/qiskit_runtime_service.py\u001b[0m in \u001b[0;36m_discover_account\u001b[0;34m(self, token, url, instance, channel, filename, name, proxies, verify, channel_strategy)\u001b[0m\n\u001b[1;32m    239\u001b[0m                 \u001b[0;32mif\u001b[0m \u001b[0murl\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    240\u001b[0m                     \u001b[0mlogger\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mwarning\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Loading default %s account. Input 'url' is ignored.\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mchannel\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 241\u001b[0;31m                 \u001b[0maccount\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mAccountManager\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfilename\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mfilename\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mchannel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mchannel\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    242\u001b[0m         \u001b[0;32melif\u001b[0m \u001b[0many\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mtoken\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0murl\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    243\u001b[0m             \u001b[0;31m# Let's not infer based on these attributes as they may change in the future.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/qiskit_ibm_runtime/accounts/management.py\u001b[0m in \u001b[0;36mget\u001b[0;34m(cls, filename, name, channel)\u001b[0m\n\u001b[1;32m    195\u001b[0m                 \u001b[0;32mreturn\u001b[0m \u001b[0mAccount\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfrom_saved_format\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mall_config\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0maccount_name\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    196\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 197\u001b[0;31m         \u001b[0;32mraise\u001b[0m \u001b[0mAccountNotFoundError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Unable to find account.\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    198\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    199\u001b[0m     \u001b[0;34m@\u001b[0m\u001b[0mclassmethod\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mAccountNotFoundError\u001b[0m: 'Unable to find account.'"
          ]
        }
      ],
      "source": [
        " service = QiskitRuntimeService(channel='ibm_quantum')"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "26b7d75e-ebed-49bc-9e31-3d570dd2242d",
      "metadata": {
        "id": "26b7d75e-ebed-49bc-9e31-3d570dd2242d"
      },
      "source": [
        "Now that your service is setup, the service allows you to view all the backends that you have access to. Let's run the command below to display all the available backends that can utilize Qiskit Runtime."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "37f4ac11-f69d-4d2b-acd6-86230ffdd2b2",
      "metadata": {
        "id": "37f4ac11-f69d-4d2b-acd6-86230ffdd2b2",
        "outputId": "5901d813-f168-4773-aaa8-e3c7c64b2685"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[<IBMBackend('ibmq_qasm_simulator')>,\n",
              " <IBMBackend('ibmq_lima')>,\n",
              " <IBMBackend('ibmq_belem')>,\n",
              " <IBMBackend('ibmq_quito')>,\n",
              " <IBMBackend('simulator_statevector')>,\n",
              " <IBMBackend('simulator_mps')>,\n",
              " <IBMBackend('simulator_extended_stabilizer')>,\n",
              " <IBMBackend('simulator_stabilizer')>,\n",
              " <IBMBackend('ibmq_manila')>,\n",
              " <IBMBackend('ibm_nairobi')>,\n",
              " <IBMBackend('ibm_oslo')>]"
            ]
          },
          "execution_count": 4,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# service.backends()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "b9005172-89b5-41f3-b391-781c38951a76",
      "metadata": {
        "tags": [],
        "id": "b9005172-89b5-41f3-b391-781c38951a76"
      },
      "source": [
        "# Example using Sampler"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "b88b9d10-6cf6-4723-b33b-1e0494efed12",
      "metadata": {
        "tags": [],
        "id": "b88b9d10-6cf6-4723-b33b-1e0494efed12"
      },
      "source": [
        "### Bernstein-Vazirani algorithm\n",
        "\n",
        "This algorithm is one of special quantum algorithms which showed that there can be advantages in using a quantum computer as a computational tool for more complex problems.\n",
        "\n",
        "There is a function returning the bitwise product of the input with a hidden string of bits $ s $. Its length is $ n $.\n",
        "\n",
        "$$ f(x) = s ⋅ x (\\mathrm{mod} 2) $$\n",
        "\n",
        "To find the hidden string, we would need to call the function $f$ for $ n $ times. However, using a quantum computer, we can solve this problem with 100% confidence after **only one call** to the function . The quantum Bernstein-Vazirani algorithm to find the hidden bit string is very simple:\n",
        "\n",
        "1. Initialize the inputs qubits to the state $|0\\rangle^{\\otimes n}$, and output qubit to $|-\\rangle$.\n",
        "2. Apply Hadamard gates to the input register\n",
        "3. Query the oracle\n",
        "4. Apply Hadamard gates to the input register\n",
        "5. Measure\n",
        "\n",
        "For more in detailed information about the Bernstein-Vazirani algorithm, feel free to check out this helpful chapter in the Qiskit textbook: **https://learn.qiskit.org/course/ch-algorithms/bernstein-vazirani-algorithm**. Or you may refer Ep. 6 of Coding with Qiskit Season 1 in Qiskit Youtube: **[Bernstein-Vazirani Algorithm](https://youtu.be/sqJIpHYl7oo)**.\n",
        "\n",
        "In the below, there is an example for the Bernstein Vazirani algorithm to find the hidden bit string \"001\"."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "c4c73a73-965c-40fb-a710-a890b40c9f8b",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "c4c73a73-965c-40fb-a710-a890b40c9f8b",
        "outputId": "646d8f9e-d912-42c2-e149-527a0d90e9a2"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "3\n"
          ]
        }
      ],
      "source": [
        "hidden = \"001\"\n",
        "print(len(hidden))"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "4ad9114a-cfd5-43de-9319-263fae1ca9ba",
      "metadata": {
        "id": "4ad9114a-cfd5-43de-9319-263fae1ca9ba"
      },
      "source": [
        "For this hidden string, we need 3 input qubits and 1 output qubit."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "43b61779-5c84-4026-afde-dd24bffa0515",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 384
        },
        "id": "43b61779-5c84-4026-afde-dd24bffa0515",
        "outputId": "3ddb1e87-8b82-42f8-ad0d-acd678bf0e67"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 162.08x451.5 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# Make a quantum circuit\n",
        "qc = QuantumCircuit(4, 3)\n",
        "display(qc.draw(output=\"mpl\"))"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "03f0b1e9-3891-4556-a6c3-d3d48b81e14e",
      "metadata": {
        "id": "03f0b1e9-3891-4556-a6c3-d3d48b81e14e"
      },
      "source": [
        "Step 1. Initialize the inputs qubits to the state $|0\\rangle^{\\otimes n}$, and output qubit to $|-\\rangle$.\n",
        "\n",
        "At first every qubit is initialized as $|0\\rangle$ so we don't have to apply any gate for input qubits. However, the output qubit state should be changed as $|-\\rangle$. For it, we will apply X-gate and then H-gate (Hadamard gate)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "e972546d-7945-48b1-a0c8-64be4211afe4",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 384
        },
        "id": "e972546d-7945-48b1-a0c8-64be4211afe4",
        "outputId": "54036bc1-5acb-4126-a73b-ca35adafea82"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 287.496x451.5 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "qc.x(3)\n",
        "qc.h(3)\n",
        "display(qc.draw(output=\"mpl\"))"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "749bd8b3-f80e-4405-ac8a-e4d8ce1e3f35",
      "metadata": {
        "id": "749bd8b3-f80e-4405-ac8a-e4d8ce1e3f35"
      },
      "source": [
        "Step 2. Apply Hadamard gates to the input register.\n",
        "\n",
        "We will apply Hadamard gates to each input qubit."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "05a42af6-1c97-463a-b0df-e12622bb360a",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 384
        },
        "id": "05a42af6-1c97-463a-b0df-e12622bb360a",
        "outputId": "3aa8924f-7d4f-41a8-dbd8-dea8b2c08571"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 287.496x451.5 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "qc.h(0)\n",
        "qc.h(1)\n",
        "qc.h(2)\n",
        "display(qc.draw(output=\"mpl\"))"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "3dbfb8d2-3da8-4567-9e64-d7e10b650c4a",
      "metadata": {
        "id": "3dbfb8d2-3da8-4567-9e64-d7e10b650c4a"
      },
      "source": [
        "Step 3. Query the oracle.\n",
        "\n",
        "We will use CNOT gate to query the oracle. As our hidden circuit is \"001\", we will apply CNOT gate to qubit 0 and the output gate. Note: In Qiskit, numbers are assigned to the bits in a string **from right to left**."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "620eaa24-860c-42dc-93b0-14a58ed1ff21",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 384
        },
        "id": "620eaa24-860c-42dc-93b0-14a58ed1ff21",
        "outputId": "f0299519-7425-4ee3-c889-c486229026cd"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 371.107x451.5 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "qc.cx(0,3)\n",
        "display(qc.draw(output=\"mpl\"))"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "4ecb4a1c-4a2a-4de0-81b4-486819305665",
      "metadata": {
        "id": "4ecb4a1c-4a2a-4de0-81b4-486819305665"
      },
      "source": [
        "Step 4. Apply Hadamard gates to the input register.\n",
        "\n",
        "We will apply Hadamard gates to each input qubit again."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "ca75b927-0cb5-477d-a530-0b5fc0ce5001",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 384
        },
        "id": "ca75b927-0cb5-477d-a530-0b5fc0ce5001",
        "outputId": "eee0182d-7166-4ed1-acaf-2fa83e8a992d"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 538.33x451.5 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "qc.barrier()\n",
        "qc.h(0)\n",
        "qc.h(1)\n",
        "qc.h(2)\n",
        "display(qc.draw(output=\"mpl\"))"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "1b7d1e11-f6b0-41df-a974-56b83b140b2b",
      "metadata": {
        "id": "1b7d1e11-f6b0-41df-a974-56b83b140b2b"
      },
      "source": [
        "Step 5. Measure.\n",
        "\n",
        "We will measure all the input qubits with [`measure`](https://qiskit.org/documentation/stubs/qiskit.circuit.QuantumCircuit.measure.html) method."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "1ab053c0-7c10-41ba-8dd8-0cf37109e6c2",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 384
        },
        "id": "1ab053c0-7c10-41ba-8dd8-0cf37109e6c2",
        "outputId": "d9a235da-e580-40d0-c038-e804ff79a4b4"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 789.163x451.5 with 1 Axes>"
            ],
            "image/png": 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rwoQJhp1vwUtLdbyyUlGRkXr4Z7ed9doIdrvdkPMAniLM+SibzSaFhZldBgCTBHobYLPZ5HAY90+UW5LLffpPh8Nx1mvAyhhmBQAAsDA+jgAIKF27dlVOTo6SkpLMLgUADEGYAxBQwsLC1L17d7PLAADDMMwKIKAUFRVp9uzZKioqMrsUADAEYQ5AQCkrK9M777yjsrIys0sBAEMQ5gAAACyMMAcAAGBhhDkAAAALI8wBCChBQUG65JJLFBRE8wfAP9CaAQgoLpdL27Ztk8vlMrsUADAEYQ4AAMDCCHMAAAAWRpgDAACwMMIcgIASFRWlsWPHKioqyuxSAMAQPJsVQEBJSkrSrFmzzC4DAAxDzxyAgFJdXa1Dhw6purra7FIAwBCEOQABJT8/XxMmTFB+fr7ZpQCAIRhm9VFut1uyUs9BaKhsNpvZVQB+w3JtgEQ7YDC32y2n02l2GR6x2+38DJiAMOerqqtVO3Ga2VU0m+P116SwMLPLAPyHxdoAiXbAaE6nU8uWLTO7DI9MmDBBDgfRorUxzAoAAGBhhDkAAAALoy8UQEDp0aOHvvjiC7PLAADD0DMHAABgYYQ5AAHl4MGDuuOOO3Tw4EGzSwEAQxDmAASUqqoq7dixQ1VVVWaXAgCGIMwBAABYGGEOAADAwghzAAAAFkaYAxBQEhISNHPmTCUkJJhdCgAYgnXmAASUtm3bKjMz0+wyAEtyuVwKCqIfyNcQ5gAElNLSUq1atUqjR49W+/btzS4HaHEul0tHjhxRfn6+ioqKVFNTo6CgIEVGRqpLly7q1q2bIiMjz3ue3NxcvfTSS3r44Yfp2fYxhDkAAeXIkSNasGCB+vTpQ5iDX9u/f78+/PBDffHFFzpx4sQ5901OTtaoUaM0YsSIRoNdbm6u5syZo5MnT2rWrFmaOXOmOnbs2FKlw0MB0VdaUlKi7OxspaamKiwsTJ06dVJWVpYqKyt15513ymaz6cUXXzS7TAAALti+ffs0Y8YMPfbYY1qzZs15g5wkFRQUaPHixbr33nu1ZMkSnTx5sn7bmUFOkjp16qR27dq1VPnwgt/3zG3fvl2ZmZkqLi5WZGSkevbsqcLCQj3//PPat2+fjh07Jknq37+/uYW2kLUlRzXmszWa27Ovftm9R6P7hLz7uq7tmKC3h1zRytUBaGm0AYGjpqZGb775pt599125XK7698PDw9WzZ0+lpKSoc+fOCgsLk8vlUmlpqfbv36+vv/5a+/fvlyRVV1drxYoV2rx5s+655x4FBQU1CHJ9+/bVr371K4WEhJjyNaJxfh3mSkpKNG7cOBUXF2v69Ol66qmnFBUVJUmaP3++HnnkETkcDtlsNvXt29fkagEA8E5FRYXmzZunvXv31r+XnJyszMxMDRs2TGFhYY0ed+WVV0qSDh06pFWrVmn16tWqqanRkSNHNHPmTDkcDtXW1koiyPkyvx5mfeCBB1RQUKD7779fCxcurA9ykpSdna1+/fqptrZWXbt2VXR0tImVAmgtERERGjJkiCIiIswuBTBEZWWlZs+eXR/k7Ha7Jk6cqLlz5+qqq65qMsidqVOnTrr99ts1f/58paen179PkLMGvw1zu3fv1tKlS9WhQwfNmTOn0X0GDBggSerXr1/9e3Xhb/DgwQoNDZXNZmuVegG0js6dO+uFF15Q586dzS4FuGAul0vPPvusDhw4IOn00juzZ8/WzTffLIfD88G3hIQETZo0SXa7vcH7I0aMIMj5ML8dZs3JyZHL5dLkyZPVpk2bRvcJDw+X1DDMff3111q2bJkGDRqkkJAQbdiwoVXqbWknnE6VVFebXQZgOqfTqaqqKoWHh5/1D5Y/ow3wT++//7527twpSYqOjtaTTz6ppKQkr8+Xm5urefPmyel0Nnj/tddeU58+fRjF8lF+G+ZWr14tSRo5cmST+xQUFEhqGOaGDx+uoqIiSdLTTz/tN2FuVu5OzcrdaXYZgOn27t2rqVOnavHixerRo/EbAvwRbYD/KS4u1t///vf611lZWRcc5L5/s0NwcLC2bNmi8vJyvfrqq3rwwQcvtGy0AL8NcwcPHpQkdenSpdHttbW19UHtzDDXEitbDxw4UMXFxR4dEx4UpF39hxpWw087p2hCYqdGt2V+vvaCz5+WlqaqM+6egm8qavdLKaitioqLlJycbHY5hrjllls82v/o0aOSpJUrV2rLli3NOmb8+PEe13WhrNYGSL7dDoy//UFFtomu/9n//mtfFBIS0uQ0IUl66623dOrUKUnS1VdfrV69enl9rcaC3K9+9SudOHFCubm5qqio0Oeff678/Hx169atyfOkpaXV1wTPxMfHa/PmzV4d67dhrrKyUpJUVVXV6PalS5eqpKREUVFR5/zBNEJxcbEOHz7s0TERdrvU37gaUtu00VVxFxl3wu8pLCzUie91y8MHRTmlIMnldHr8M+mr6n7Xm6uuTaiqqmr2sWZ8r6zWBki+3Q64vqur7mf/+699UWhoaJPbjh8/rs8++0zS6Zt6fvjDH3p9naaCXEhIiEJCQjRx4kS9+uqrkqSPPvpId999d5PnKiwsVDXD+a3Ob8NcfHy8SktLtXXrVg0d2vDTbVFRkR5++GFJp39oW/omh/j4eI+PCbfYs+8SExN99hM5/qvIbpdLUpDdroQLGI7xJc15DNGZ6gJceHh4s4+9kKErb1mtDZB8ux0I+m5+ZJDdrqSkpLNe+6Jz3XCwbt061dTUSDp9c0LdHHBPnSvI1bniiiuUk5OjqqoqbdiwQT/+8Y+bvBs8MTGRnjkveZMV6vhtmBs9erR2796tefPmacyYMUpLS5Mkbdq0SVOmTFFJSYmk1lks2JtuU/fJk6qdOK0FqmkZeXl5sjXj9neYK3l0jg4fPaGE+AQV7CgwuxxDbNq0yaP99+zZo5ycHGVmZjZ7ztxzzz3nRWUXxmptgOTb7cAzv/8/lVdUnv7ZLyg467Uvqq2t1bJlyxrd9uWXX9b/ffTo0V6dvzlBTjr9wWfYsGFatWqVqqurlZubq0suuaTRc+bl5Xl1Fy0ujPU++jVTdna2YmNjdejQIfXq1Ut9+vTRxRdfrMGDByslJUWjRo2S1HC+HAD/l5qaqg8++ECpqalmlwJ4xe12Kz8/X9LppUgSExM9Pkdzg1ydjIyM+r/XPS0CvsNvw1xycrLWr1+v6667TmFhYTpw4IBiYmL00ksvacWKFcrLy5NEmAMCjcPhUPv27ek9gGWVlJTo+PHjkqRu3bp5PFXI0yBXd506dUESvsOvW7OMjAwtX778rPcrKip04MABBQUFqXfv3iZUBsAsBQUF+t3vfqeHHnrIZ+9iBM6ltLS0/u8JCQkeHetNkJNOz+ey2Wxyu90Nrg/f4Ndhrik7d+6U2+1WWlpao5M433zzTUnSrl27Grzu2rWrBg4c2HqFGmBEh446NW7iOfc533bAn1RUVGj9+vW66667zC6lVdAG+J+YmBhNnDhRp06dqp8P3hynTp3S7373O4+DnHR62a4bb7xRdrtdsbGxXteOlhGQYe6rr76S1PQQ66233tro62nTpukvf/lLi9YGAMC5dOjQQTfffLPHx4WEhCgrK0tz585Venq6x89anTRpksfXROsgzDXC7Xa3ZjkAALSKjIwMPf3000pKSuJZq36EMAcAQABp6YXy0foCMszVPbcVQOCJi4tTVlaW4uLizC4FAAwRkGEOQOCKjY3V5MmTzS4DAAzjt+vMAUBjysvLtWrVKpWXl5tdCgAYgjAHIKAUFhbqscceU2FhodmlAIAhCHMAAAAWRpgDAACwMMIcAACAhRHmAASU0NBQpaenKzQ01OxSAMAQLE0CIKB069ZNS5YsMbsMADAMPXMAAAAWRpgDEFByc3M1bNgw5ebmml0KABiCMAcgoLjdbtXU1MjtdptdCgAYgjlzvio0VI7XXzO7iuZjMjlgLKu1ARLtgMHsdrsmTJhg2PkWvLRUxysrFRUZqYd/dttZr41gt9sNOQ88Q5jzUTabTQoLM7sMACahDYDNZpPDYdw/025JLvfpPx0Ox1mvYV0MswIAAFgYURxAQOnatatycnKUlJRkdikAYAjCHICAEhYWpu7du5tdBgAYhmFWAAGlqKhIs2fPVlFRkdmlAIAhCHMAAkpZWZneeecdlZWVmV0KABiCMAcAAGBhhDkAAAALI8wBAABYGGEOQEAJCgrSJZdcoqAgmj8A/oHWDEBAcblc2rZtm1wul9mlAIAhCHMAAAAWRpgDAACwMMIcAACAhRHmAASUqKgojR07VlFRUWaXAgCG4NmsAAJKUlKSZs2aZXYZAGAYeuYABJTq6modOnRI1dXVZpcCAIYgzAEIKPn5+ZowYYLy8/PNLgUADEGYAwAAsDDmzPkot9stWWkYKDRUNpvN7CoAv2G5NkCiHYCh3G63nE6n2WV4xG63m/I7QJjzVdXVqp04zewqms3x+mtSWJjZZQD+w2JtgEQ7AGM5nU4tW7bM7DI8MmHCBDkcrR+tGGYFAACwMHrmAASUHj166IsvvjC7DAAwDD1zAAAAFkaYAxBQDh48qDvuuEMHDx40uxQAMARhDkBAqaqq0o4dO1RVVWV2KQBgCMIcAACAhRHmAAAALIwwBwAAYGGEOQABJSEhQTNnzlRCQoLZpQCAIVhnDkBAadu2rTIzM80uAwAMQ88cgIBSWlqqN954Q6WlpWaXAqCVVVRU6OjRoyouLtaxY8fkcrk8Ov6TTz5RUVFRC1XnPXrmAASUI0eOaMGCBerTp4/at29vdjkAWlBpaanWr1+vvLw87d+/X8eOHWuwPTw8XF27dlVKSoqGDh2q7t27y2azNXquDz74QH/+858VExOjGTNm+NRUDcIcAADwK19//bWWL1+uTZs2yel0NrlfVVWVdu/erd27d2vFihVKSUnR1VdfreHDhyso6L+Dl3VBTpKOHTumzZs3a9y4cS3+dTRXQAyzlpSUKDs7W6mpqQoLC1OnTp2UlZWlyspK3XnnnbLZbHrxxRfNLrNFrC05qpB3X9ez+/Y0uU/Iu6/rpo3rW7EqAK2FNgCBpLq6WosXL9aMGTP0+eefNwhy4eHhysjI0OWXX65hw4bp0ksvVYcOHRocv3//fv3pT3/SzJkz64dTzwxykjR+/Hhdf/31rfMFNZPf98xt375dmZmZKi4uVmRkpHr27KnCwkI9//zz2rdvX32Xa//+/c0tFAAAeO3QoUP6n//5HxUXF9e/17ZtW40cOVJXXHGFEhISGvS21SkvL9fmzZv10UcfKT8/X5KUm5ur7OxsDR48WBs2bKjfd/z48Zo4cWKTQ7Fm8eswV1JSonHjxqm4uFjTp0/XU089paioKEnS/Pnz9cgjj8jhcMhms6lv374mVwugNURERGjIkCGKiIgwuxQABsnPz9dvf/tbVVRUSJKCg4M1ceJEZWZmyuE4d9SJjo7WqFGjNHLkSO3cuVMvv/yyjh49qpqaGksEOcnPh1kfeOABFRQU6P7779fChQvrg5wkZWdnq1+/fqqtrVXXrl0VHR1tYqUAWkvnzp31wgsvqHPnzmaXAsAARUVFeuaZZ+qDXNeuXTV37lyNGzfuvEHuTDabTb1799b8+fOVnp7eYNsll1zis0FO8uMwt3v3bi1dulQdOnTQnDlzGt1nwIABkqR+/frVv/fmm29qwoQJ6tKliyIiItSjRw89/vjj9T8kVnXC6VRJdXWj/wGBxOl0qqKi4pyTov0RbQD8kdPp1Isvvqjjx49LktLT0/Xkk08qKSnJ63OuXbtWubm5Dd776quvVFhYeEG1tiS/HWbNycmRy+XS5MmT1aZNm0b3CQ8Pl9QwzC1cuFCdO3fWM888o+TkZG3fvl0zZ87U2rVrtW7dukbH261gVu5OzcrdaXYZgOn27t2rqVOnavHixerRo4fZ5bQa2gD4oxUrVmjfvn2STj/dJTs7+4KmUHz/Zodu3bopPz9ftbW19TdG+GIO8Nswt3r1aknSyJEjm9ynoKBAUsMw9+677youLq7+9YgRIxQXF6fJkyfr008/1fDhw1uo4pb1084pmpDYqdFtmZ+vbeVqALQ22gD4m2PHjumNN96QdHqI9Oc//7kiIyO9Pl9jd63eeOONevTRR1VcXKy9e/fqk08+0VVXXXXBtRvNb8PcwYMHJUldunRpdHttbW39xMYzw9yZQa7OwIEDJUmHDx/2qpaBAwc2uLumOcKDgrSr/1CvrteY1DZtdFXcRYad7/vS0tJU5eFK2mh9Re1+KQW1VVFxkZKTk80uxxC33HKLR/sfPXpUkrRy5Upt2bKlWceMHz/e47oulNXaAMm324Hxtz+oyDbR9T/7338dCKz2PQgJCWlympR0utOmpqZGkjR27FilpaV5fa3GglzdHLl77rlHTz/9dP1+o0aNanLuXFpamk6dOuVVDfHx8dq8ebNXx/ptmKusrJR0ekHAxixdulQlJSWKiopSt27dznmuTz75RJKUkZHhVS3FxcUeB8EIu13q79XlTFFYWKgTATYHyZKinFKQ5HI6vf5w4mvqftebq65NqKqqavaxZnyvrNYGSL7dDri+q6vuZ//7rwOB1b4HoaGhTW6rra3Vxx9/LEkKCgq6oHXfzhXkJKlHjx5KS0tTXl6e/v3vf2vPnj1N5oHCwkJVmzAP1W/DXHx8vEpLS7V161YNHdrw021RUZEefvhhSVLfvn3PeXfK4cOHNWPGDI0dO9brteji4+M9PibcB8fkzyUxMdFnP5Hjv4rsdrkkBdntSriACcK+xNNhlboAFx4e3uxjL2Qytbes1gZIvt0OBNnt9X8mJSWd9ToQWO17EBIS0uS23bt31z9fecCAAYqNjfXqGucLcnWuvvpq5eXlSZI2bNjQZJhLTEy8oJ45b/ltmBs9erR2796tefPmacyYMfXdr5s2bdKUKVNUUlIi6dyLBVdUVOjGG29USEiIXn31Va9r8abb1H3ypGonTvP6mq0tLy9PtrAws8vAeSSPztHhoyeUEJ+ggh0FZpdjiE2bNnm0f21trX7yk58oKiqq2csWPPfcc15UdmGs1gZIvt0OPPP7/1N5ReXpn/2CgrNeBwKrfQ9qa2u1bNmyRrft37+//u91U6E81dwgJ0mXXnppo9f+vry8PI+WQzGK9T76NVN2drZiY2N16NAh9erVS3369NHFF1+swYMHKyUlRaNGjZLUcL7cmaqqqjRu3Djl5+frww8/9KkH6gLwnsPhUPv27U1pcAEYo+5JDZKUkpLi8fGeBDnp9GLjiYmJkqR///vfqq2t9fiaLclvw1xycrLWr1+v6667TmFhYTpw4IBiYmL00ksvacWKFfXdpY2FuZqaGt1yyy3avHmzVq5cqZ49e7Z2+QBaSEFBgaZPn+6TPREAmqduzTeHw+HxELGnQa5O3Q2VtbW19TdS+Qq//miakZGh5cuXn/V+RUWFDhw4oKCgIPXu3bvBtrq16T7++GO99957Gjx4cGuV2yJGdOioU+MmnnOf820H/ElFRYXWr1+vu+66y+xSWgVtAPxRdHS0YmJiFBoa6tG6bx999JFXQU6SYmJi1L59ewUHB8vtdntVd0vx6zDXlJ07d8rtdistLe2sxQXvu+8+vfHGG3r00UcVERGhzz//vH5b9+7dG126BAAAtJ4nnnjCq+OSk5MVGhqq6upqj5+1OmXKFE2ZMsWr67a0gAxzX331laTGh1hXrlwpSZo7d67mzp3bYNuf//xn/eQnP2nx+gAAgPEyMjL06KOPateuXbr55pt99lmrniLMfc+BAwdauRoAANBaMjIyvF431lf57Q0Q53KuMAfAv8XFxSkrK4spEwD8RkD2zNU9txVA4ImNjdXkyZPNLgMADBOQPXMAAld5eblWrVql8vJys0sBAEMQ5gAElMLCQj322GP161QBgNUR5gAAACyMMAcAAGBhhDkAAAALI8wBCCihoaFKT09XaGio2aUAgCECcmkSAIGrW7duWrJkidllAIBh6JkDAACwMMIcgICSm5urYcOGKTc31+xSAMAQhDkAAcXtdqumpkZut9vsUgDAEIQ5AAAAC+MGCF8VGirH66+ZXUXzcWcgYCyrtQES7QAMZbfbNWHCBMPOt+ClpTpeWamoyEg9/LPbznptBLvdbsh5PEWY81E2m00KCzO7DAAmoQ1AoLPZbHI4jIspbkku9+k/HQ7HWa+tzNrVA4CHunbtqpycHCUlJZldCgAYgjAHIKCEhYWpe/fuZpcBAIbhBggAAaWoqEizZ89WUVGR2aUAgCEIcwACSllZmd555x2VlZWZXQoAGIIwBwAAYGGEOQAAAAsjzAEAAFgYYQ5AQImJidG0adMUExNjdikAYAjCHICAEhQUpODgYAUF0fwB8A+0ZgACSklJiV555RWVlJSYXQoAGIIwBwAAYGGEOQAAAAsjzAEAAFgYYQ5AQImKitLYsWMVFRVldikAYAiH2QUAQGtKSkrSrFmzzC4DAAxDzxyAgFJdXa1Dhw6purra7FIAwBCEOQABJT8/XxMmTFB+fr7ZpQCAIRhm9VFut1snqmrNLqPZIsIdstlshp3P7XZLVus5CQ019HsAAEBzEOZ81ImqWrW5bLHZZTRbxedTFRkRbNwJq6tVO3GacedrBY7XX5PCwswuAwAQYBhmBQAAsDDCHAAAgIUxzAogoPTo0UNffPGF2WUAgGHomQMAALAwwhwQINxu9+m7hL/7e6A6ePCg7rjjDh08eNDsUgDAEAyzAn7qVI1T73zyb63fWqwtu7/R9j3fqPK75W4K/1OlbmOXamCvDhrQs4PGj+qi9G7tzC24lVRVVWnHjh2qqqoyuxQAMARhDvAzhUcr9fu/79Yrb+Xq6LGTTe53oLBCBwor9OZHB/Tr/2+zrhqSqPsmZeimUV1YLw8ALIQwB/gJt9utRW/l6ZcLN+p4ZY3Hx3+8sVAfbyzUVUMStWjmD9QlkQfRA4AVMGcO8APHyqp17b0f6q6Zn3oV5M708cZC9b75H/rr8q8Nqg4A0JLomQMs7sg3VRp910rt+LrUsHNWnKjRlMfWqqT0pB6c0tuw8/qChIQEzZw5UwkJCWaXAgCGIMwBFlZ2/JSuued9Q4PcmR5asFGR4Q7ddUuPFjm/Gdq2bavMzEyzywAAwzDMCljYA3M/05e5x1r0Gvc985m+ymvZa7Sm0tJSvfHGGyotbZkADACtjTAHWNS7a/6txe96Nq9tU84NOvTRJG3KuaHZx9TUuvSTGetUU+PytESfdOTIES1YsEBHjhwxuxQAMERAhLmSkhJlZ2crNTVVYWFh6tSpk7KyslRZWak777xTNptNL774otllAs1Wfcqpe2Zv8Pi4+A4RSr4oUvEdIjw6buvub/Ti33d5fD0AQMvz+zC3fft29enTRwsWLFBxcbF69uypmpoaPf/887rtttu0e/duSVL//v3NLbSF/PaBAXL/607dftPFjW7/ZNG1Orn5J+qV2r6VK2sda0uOKuTd1/Xsvj1N7hPy7uu6aeP6Vqzqwr35Ub4Kj55o1Wu+8Lddcjr9o3cOAPyJX4e5kpISjRs3TsXFxZo+fbqKioq0detWFRcXa968eVqxYoU2bdokm82mvn37ml1ui3j6D9v01d5jevZXQ5R0UcPemAd/3EtXDkrQU3/Yqp0tNIEeLeP3f9/d6tfMP3xc728oaPXrAgDOza/D3AMPPKCCggLdf//9WrhwoaKi/rsIanZ2tvr166fa2lp17dpV0dHRJlbacmpqXZr2xDpFhgdr0dNX1L+f1rWtfvuLgfr8X0e14C9fmVghPLXvULk++/KoKdf2dI6eL4qIiNCQIUMUEeHZUDMA+Cq/DXO7d+/W0qVL1aFDB82ZM6fRfQYMGCBJ6tevX/1769ev1+jRo5WQkKDQ0FAlJyc3GI61om27v9GcRV/qmmHJumtCuoKCbFr82+Gy2aRpT6yTyxW4D123oi+++o9p1960o8S0axulc+fOeuGFF9S5c2ezSwEAQ/jtOnM5OTlyuVyaPHmy2rRp0+g+4eHhkhqGudLSUvXp00c/+9nP1LFjRxUUFGjOnDkaOnSoduzYoeTk5Fap32i/eXmbbriysxZOH6z+PWI1pE9H/XLBRuUdKDO7tFZxwulUSXW12WUYYvMu8wJV/uHj+ubbk4ptF2ZaDRfK6XSqqqpK4eHhstvtZpcDABfMb8Pc6tWrJUkjR45scp+CgtPzf84MczfccINuuKHhsg2DBg1Senq6li1bpqysrBaotuXV1ro17Yl12pRzg+69LUPrtxbrub/uMLusVjMrd6dm5e40uwxDmD2/cde+b3XFgHhTa7gQe/fu1dSpU7V48WL16OE/iyEDCFx+G+YOHjwoSerSpUuj22tra7Vhw+mlHc4Mc42JjY2VJDkc3n27Bg4cqOLiYo+OcSlYinnCq+s1pazilKpPORUSbNd76w/JbeDo6sVpaQrShT0T9EzhQUHa1X+oYef7aecUTUjs1Oi2zM/XGnKNtLQ0Vbla/m7P/0TdIQU3/nO9KeeGcy47Et8hvP7PQx9NOud1iktOaNAP3znr/fG3TFJYje/Mnbvllls82v/o0dPzDVeuXKktW7Y065jx48d7XBd8y/jbH1Rkm2gVFRcpOTn5rNeBINC/B77+9cfHx2vz5s1eHeu3Ya6yslKSVFVV1ej2pUuXqqSkRFFRUerWrdtZ251Op1wulw4ePKhf//rXio+P18SJE72qpbi4WIcPH/bsIFuIFOPV5Zr051lXKCTYrl37SvXE3f31+gf52l9w3JBzFxUWSu5ThpxLkiLsdqm/YadTaps2uiruIuNO2IjCwkKdcDpb9BqSpJRqKbjxTXXryJ2Pwx7UrP0a801JiVTh4c9zC6r7XW+uujahqqqq2cd6/PsLn+P67nfT5XTq8OHDZ70OBIH+PfDnr99vw1x8fLxKS0u1detWDR3asIenqKhIDz/8sCSpb9++stlsZx0/YsSI+p671NRUrV69WnFxcV7X4imXglXk1dUa94sf9dTIwYl67PnN+n+fHNTWpTfp1VlX6Mo73jPk/AmJiYb3zFlNYmJiq/TMlQTb1NTsv+KSc689F98hXA57kGqdLhWXNP5B53zn6hAbrdC2Sc0ptVVERnoWSusCXHh4eLOPTUryna8X3gn6bn5kkN2upKSks14HgkD/Hvj61+9NVqjjt2Fu9OjR2r17t+bNm6cxY8YoLS1NkrRp0yZNmTJFJSWnJ5E3tVjwokWL9O233yo/P18LFizQ1VdfrQ0bNnh1B5w33aaVJ2rU5rLFHh/XmNTO0ZqTNVBffPUfzXv1X3K53Hr6j1s1J2uQfvGjnnrhbxe+sv/evDxFRjTRXeQF98mTqp04zbDztYa8vDzZwlr+xoBfLdyo/1nc+HzHxoZFz3Too0lKvihSxSVV6jTm715dP/fLTxTTNtSrY1vCpk2bPNp/z549ysnJUWZmZrPnzD333HNeVAZf8szv/0/lFZVKiE9QQUHBWa8DQaB/D/z567de90czZWdnKzY2VocOHVKvXr3Up08fXXzxxRo8eLBSUlI0atQoSU3Pl0tPT9eQIUM0adIkffzxxzp+/Ljmz5/fml+CIWw26S+/GS57kE3TnlhbvwzJ/D9/pU07/qM5WQOVkhx1nrPAlwzo2cG0a3dLivKpIOeN1NRUffDBB0pNTTW7FAAwhN+GueTkZK1fv17XXXedwsLCdODAAcXExOill17SihUrlJeXJ+n8Nz9IUrt27ZSamqqvv/adSd/NNX1aHw275CI9+Yet2pP/32VIXC63fjJjnRz2IL0664pznAG+Zkhf74b7jTC4j3lB0igOh0Pt27f3+oYmAPA1fhvmJCkjI0PLly/X8ePHdfz4cW3cuFF33323KisrdeDAAQUFBal3797nPc/Ro0eVm5ur7t27t0LVxunRra1+c9+l+uzLo/qf184eltu171s9/cetGjEwQb/4UU8TKoQ3UpKjNeySlr2ZoynTxjX+jF8rKSgo0PTp0y0/rAIAdQLyo+nOnTvldruVlpZ21iN9fvzjHys1NVX9+/dXu3bttHfvXv3ud7+Tw+HQQw89ZFLF3tmTX6bwQa+dc5+5i/6luYv+1UoVtb4RHTrq1Lhz34V8vu2+6N6JGdqw7UirXjMlOUrXDDP/9v0LVVFRofXr1+uuu+4yuxQAMIRf98w15auvTj+LtLEh1ssuu0zvvfeebr/9dmVmZmrBggW64oortH37dubYwGdMGNPV66VFvPXAj3oqKOjsO78BAOYKyJ65c4W5+++/X/fff39rlwR4JDTErpefHKZr7/uwVa43qHcH3TeJoXgA8EX0zAEWlXlFJ91+k2dz2IpLTqjgSOV516M7U0hwkP7ym+FyOAKyuQAAnxeQPXN1z20FrO657Mv0Ze4xbd39TbP2P986dI3504xh6tm9vcfH+aq4uDhlZWV5vQg4APgaPmoDFhbdJkTv//Ea9Us3+Nlv33nh10N1+01pLXJus8TGxmry5Mn1z1wGAKsjzAEWFxcTrjWLrtX1wzsZds7oNsHKmXel7v+h/82TKy8v16pVq1ReXm52KQBgCMIc4AfaRYfqnRfG6LXZw9UuKuSCzjV2WLJ2vjVBkzKtta5icxUWFuqxxx5TYWGh2aUAgCECcs4c4I9sNpum3nCxrhmWrD+9vlsvL8tV4dHm3ehgs50OcffelqHrhneSzcYSJABgFYQ5wM9cFBuup35+qR77aX+99+khfbr1iLbsKtG2Pd/o2+OnJEl2u03dk6M1oGesBvTsoJtGdVH3TtEmVw4A8AZhDvBTwcFBunFkF904skv9ey6XW06nW8HBzLAAAH9BmAMCSFCQLeCf4hAaGqr09HSFhoaaXQoAGIIwByCgdOvWTUuWLDG7DAAwDGMtAAAAFkaYAxBQcnNzNWzYMOXm5ppdCgAYgjAHIKC43W7V1NTI7XabXQoAGII5cz4qItyhis+nml1Gs0WEG/yjFBoqx+uvGXvOlsaEegCACQhzPspmsykyItjsMkxjs9mksDCzywAAwOcxzAoAAGBh9MwBCChdu3ZVTk6OkpKSzC4FAAxBmAMQUMLCwtS9e3ezywAAwzDMCiCgFBUVafbs2SoqKjK7FAAwBGEOQEApKyvTO++8o7KyMrNLAQBDEOYAAAAsjDAHAABgYYQ5AAAAC+NuVgCWNmjQII/2T05O1lNPPaXRo0crISGhhaoCgNZDmAMQUBISEvT000+bXQYAGIZhVgAAAAsjzAEAAFgYYQ4AAMDCCHMAAAAWRpgDAACwMMIcAACAhRHmAAAALIwwBwAAYGGEOQAAAAsjzAEAAFgYYQ4AAMDCCHMAAAAWRpjzAUuWLNGAAQPUvn17hYeHKyMjQ88++6zcbrfZpQEAmvDee++pf//+Cg0NVdeuXfXss8+aXVKrWrdunW688UZ16dJFNptNs2fPNrukVrVgwQINHTpU7du3V7t27fSDH/xA77//vim1OEy5Khro2LGjZsyYofT0dIWGhmr9+vW69957ZbfblZWVZXZ5AIDv2bx5s2688Ub96le/Uk5OjjZu3Kh77rlHERERuueee8wur1VUVFSoZ8+e+tGPfqQHH3zQ7HJa3erVq3XHHXdo0KBBioiI0CuvvKLrr79ea9eu1bBhw1q1FsKcD7jmmmsavE5JSdHbb7+tNWvWEOYAwAc9++yzGjRokObMmSNJysjI0M6dOzV37tyACXPXXnutrr32WknSI488YnI1rW/lypUNXs+fP1/vv/++3nrrLcJcoHO73dq0aZM2bNigJ554wuxyAMBy8g8VqabW2eC9Wqez/s+8/IKzXp+pTUSYEi/qcM5rbNiwQXfeeWeD98aOHauFCxeqoKBAycnJF/pleO2b0nJ98235We978j3o3jlRdrs1Z2LV1NYq/1DxWe978vXHxbRV+7ZRHl3X5XKpvLxckZGRXlbuPcKcjygrK1NSUpJOnToll8ulp556Sg888IDZZQGA5Rw+UqLlH3/W6LYTVSf16uvvNfnaJumuH15/3msUFRUpPj6+wXt1r4uKikwNc3Z7kP72/1bpZPWpRref73swoE+a0rqZV/+Fctjt+mL7bu3Iy290+/m+/siIMD10x60eX/eZZ57Rt99+q7vvvtvzoi+QNWO3H4qKitL27du1efNmvfjii3r22We1aNEis8sCAMu5fEBvpXZJ8urYKwb3VUrnRIMral3totvoxjHeDfO1bxulcVddbnBFrctms2n8NVeoTWS4V8dPGDvc42P/8Ic/6JlnntGbb75pSpAnzPmIoKAgpaamqm/fvrrnnnuUnZ2txx9/3OyyAMBygmw23XLtCIWFhnh0XHxcjK6+YlCz9k1ISFBxccOhvCNHjtRvM1v/nqnqk57i0TE2SROvu9Lj75sviowI0y2ZIzw+bmDfdPW8uKtHxyxcuFAPP/yw3nnnHY0ePdrjaxqBMOejXC6XTp48aXYZAGBJ7aLb6Karf9Ds/e1BQZp4/Ug5HPZm7T9s2DB98MEHDd57//331aVLF1OHWOvYbDbddM0PFNUmotnHDB/ST906mR9EjdKje2cN6Z/R7P1j2kZp3KihHl3jySef1MyZM/Xee++ZFuQkwpxPeOqpp7Rq1Srt379fubm5+t///V/NmzdP06ZNM7s0ALCsfhnd1bdH83qnrh4+UIkdY5t97oceekhffPGFHn/8ce3Zs0evvfaaXnjhBT366KPelmu4yPDm907Fx8VozA8GenT+iooKbd++Xdu3b9epU6dUXFys7du36+uvv/am3BZx7cjLFNs++rz72SRNvH6kQj3olXzwwQe1YMECLVmyROnp6SouLlZxcbHKysouoGLv2NysTGu6hx56SO+++64OHz6ssLAwpaSk6I477tA999wju715nxIBAGc7UXVSv3v1TR2vONHkPl2T43X3D69XUJBn/RsrVqzQY489pj179ig+Pl5ZWVn65S9/eaElG+7tDz/V59t2Nbndbg/S/VPHK8GDMCtJa9as0ciRI896f8SIEVqzZo2nZbaYfx8+oj/+3zvnXIh/xJB+yrxyiEfntdlsjb4/bdo0/eUvf/HoXBeKMGcxh4qOKrZ9W0WEhZpdCgBYQt7+Q3r1jZWNbgsJCdaDt09QTLvz995Y1alTNXr+L2+ppLTxHqPMK4doxJB+rVxV6/pw3Sat/mxbo9sSOsbqvik3NXuI3RcxzGohtU6n/vqPjzTvj3/Tvw8fMbscALCEtJROGnppz0a3jbtqqF8HOel0YJ14/UgFNdKT1K1Tgq4Y1MeEqlrXVcMGKKmRtQPt9iDd5sFcSV9FmLOQLV/lqux4pUJCgj3uDgeAQJZ55WXqENO2wXs9L+6igX3STaqodXVO7KiRQy9p8F5oSLBuve5Kj4eXrchub/wGl2uGD1Z8XIxJVRnH//8PesjpdGrJkiW6+uqrFRcXp9DQUHXu3Fljx47VK6+8IqfTef6TtIBap1Or/3m6i/jKIf0VHMx6zwDQXCHBDt123X97p9pEhOvma4Y3Oe/JH426/FIlx8fVvx43+nLFePiUAyu7qEN7jR0xuP51t04J+oGf9EoS5s5QXl6uMWPGaOrUqfroo48UEhKifv36yeVy6cMPP9Rdd92l48ePm1JbXa9cVJsIDe7Xw5QaAMDKOiV21MjLT/dO3TzW+0VlrerM3qmeF3fVgN5pZpfU6uoWlA4NCdbE665sdOjZirgB4gy33npr/erNixcvbnCXzpEjR7Ro0SJlZWV5/Ny1F157S8crqi6gMreOV1bJ7XYrLDREIcHBF3AuAAhcbrdbNTW1CgkJ3Hb0VE2tHA673wQZT7lcLjldLgU7fGuEK6pNuH4x7WavjiXMfWfLli0aOHCgHA6Htm3bpt69ext27md+/38qr6g07HwAAMC/RLeJ1GP3TfbqWN+KpSZ6++23JUnXXXedoUFOOp22vUevHAAA/u5CsgJh7ju7dp1eUHHoUM8e5dEc3nabStLG7bv1jw/WK6pNhLLvnsSNDwAAoAGSwXfKy8slSW3btj3Pnp7zfs7c6V45SaqpqdWCl5caWxgAAPAJFzJnjjD3nejo04tGtsQz1Y5XVF3wnLmT1ad0svqUQRUBAAB/QZj7Tq9evfTWW2/ps88+M/zc3o2DM1cOAIBAcSFz5rib9Tvbtm3TpZdequDgYG3fvl09ezb+6JfWwlw5AADQHCwa/J1LLrlEEydOVE1NjTIzM7V27doG248cOaI5c+aosrLllxipdTr1yWc87QEAAJwfPXNnKC8v14033qg1a9ZIkpKSkpSYmKiioiIdPnxYbrdbpaWlateuXYvWQa8cAABoLnrmzhAdHa1Vq1Zp0aJFuvLKK3XixAl9+eWXCgoK0jXXXKNFixYpKqrln2MXEuxQdJtIeuUAAMB50TPno2pqa2WTTQ6H3exSAACADyPMAQAAWBjDrAAAABZGmAMAALAwwhwAAICFEeYAAAAsjDAHAABgYYQ5AAAACyPMAQAAWBhhDgAAwMIIcwAAABZGmAMAALAwwhwAAICFEeYAAAAsjDAHAABgYYQ5AAAACyPMAQAAWBhhDgAAwMIIcwAAABZGmAMAALAwwhwAAICFEeYAAAAsjDAHAABgYYQ5AAAACyPMAQAAWBhhDgAAwMIIcwAAABZGmAMAALAwwhwAAICFEeYAAAAsjDAHAABgYYQ5AAAACyPMAQAAWBhhDgAAwMIIcwAAABZGmAMAALAwwhwAAICFEeYAAAAsjDAHAABgYYQ5AAAACyPMAQAAWNj/D6g9vdtg7AbsAAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "qc.measure(range(3), range(3))\n",
        "display(qc.draw(output=\"mpl\"))"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "cc23d50c-3b3a-4d1f-9fcb-2f991de384ed",
      "metadata": {
        "id": "cc23d50c-3b3a-4d1f-9fcb-2f991de384ed"
      },
      "source": [
        "The circuit is ready to run on the simulator. You can check the result by running the cell below."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "8edb2cbb-fa51-434d-aeff-08a9e3cdf1c9",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8edb2cbb-fa51-434d-aeff-08a9e3cdf1c9",
        "outputId": "7c51feb6-435b-41be-f235-e1244d5de898"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'001': 1024}"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ],
      "source": [
        "# Use local simulator\n",
        "from qiskit_aer import QasmSimulator\n",
        "\n",
        "shots = 1024\n",
        "qasm_backend = QasmSimulator()\n",
        "results = qasm_backend.run(circuits= qc, shots = shots).result()\n",
        "results.get_counts()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "f0e29324-ae44-4bdb-8a9d-8e7a123a061c",
      "metadata": {
        "id": "f0e29324-ae44-4bdb-8a9d-8e7a123a061c"
      },
      "source": [
        "If you see the result, you can see the hidden string \"001\" which we set at very first."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "6ca08509-d58a-4f86-9ac7-a74e2df1d5b1",
      "metadata": {
        "id": "6ca08509-d58a-4f86-9ac7-a74e2df1d5b1"
      },
      "source": [
        "<a id=\"exercise1\"></a>\n",
        "<div class=\"alert alert-block alert-success\">\n",
        "    \n",
        "<b> Exercise 1:</b>\n",
        "    \n",
        "Let us build the Bernstein Vazirani function.\n",
        "Note that there is only one parameter which will be a hidden string.\n",
        "This string consists of \"0\" and \"1\".\n",
        "In the below code block, you should build a function which works well in all general strings\n",
        "to pass the grader.\n",
        "    \n",
        "</div>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "a7709c81-9b7a-4b86-adf3-7d4e55cc3714",
      "metadata": {
        "id": "a7709c81-9b7a-4b86-adf3-7d4e55cc3714"
      },
      "outputs": [],
      "source": [
        "def bernstein_vazirani(string):\n",
        "    #Write your code here!\n",
        "    # Save the length of string\n",
        "\n",
        "\n",
        "    return qc"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "93d96139",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 384
        },
        "id": "93d96139",
        "outputId": "48da12d9-f08a-48f9-bcab-bed61ecb4b9a"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 789.163x451.5 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {},
          "execution_count": 16
        }
      ],
      "source": [
        "bernstein_vazirani('001').draw('mpl')"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "11db2886",
      "metadata": {
        "id": "11db2886"
      },
      "source": [
        "Now, we shall call the function above to construct a Bernstein-Vazirani circuit as defined:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "9b375a0e",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 384
        },
        "id": "9b375a0e",
        "outputId": "caaeaf35-874c-469f-bf9a-1d0c18493c80"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 789.163x451.5 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {},
          "execution_count": 17
        }
      ],
      "source": [
        "# Submit your answer using following code\n",
        "hidden_string = '1011'\n",
        "qc_bz  =bernstein_vazirani(hidden_string)\n",
        "qc_bz.draw('mpl')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "f2db275d",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "f2db275d",
        "outputId": "685ca5cb-8bf6-4b5e-d300-1aa534565bfc"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'001': 1024}"
            ]
          },
          "metadata": {},
          "execution_count": 18
        }
      ],
      "source": [
        "sim_result = qasm_backend.run(qc_bz).result()\n",
        "sim_result.get_counts()"
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "krLFZaCJd4YT"
      },
      "id": "krLFZaCJd4YT",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "e9de4f5e",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "e9de4f5e",
        "outputId": "d689b198-3d9b-4dee-de11-8826297e12bd"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The hidden key is: 001\n"
          ]
        }
      ],
      "source": [
        "print('The hidden key is:',list(sim_result.get_counts().keys())[0])"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "5fa79c90",
      "metadata": {
        "id": "5fa79c90"
      },
      "source": [
        "# Deutsch-Jozsa Algorithm\n",
        "\n",
        "- To implement the Deutsch-Jozsa algorithm in Qiskit, we'll start by generating a quantum circuit.\n",
        "- That implements a query operation for a randomly selected function that satisfies the promise: with 50% chance the function is constant, and with 50% change the function is balanced.\n",
        "- For each possibility, the function is selected uniformly from the possibilities.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "e2afd303",
      "metadata": {
        "id": "e2afd303"
      },
      "outputs": [],
      "source": [
        "from qiskit import QuantumCircuit\n",
        "import numpy as np\n",
        "\n",
        "def dj_function(num_qubits):\n",
        "    \"\"\"\n",
        "    Create a random Deutsch-Jozsa function.\n",
        "    \"\"\"\n",
        "\n",
        "    qc = QuantumCircuit(num_qubits + 1)\n",
        "    if np.random.randint(0, 2):\n",
        "        # Flip output qubit with 50% chance\n",
        "        qc.x(num_qubits)\n",
        "    if np.random.randint(0, 2):\n",
        "        # return constant circuit with 50% chance\n",
        "        return qc\n",
        "\n",
        "    # next, choose half the possible input states\n",
        "    on_states = np.random.choice(\n",
        "        range(2**num_qubits),  # numbers to sample from\n",
        "        2**num_qubits // 2,  # number of samples\n",
        "        replace=False,  # makes sure states are only sampled once\n",
        "    )\n",
        "\n",
        "    def add_cx(qc, bit_string):\n",
        "        for qubit, bit in enumerate(reversed(bit_string)):\n",
        "            if bit == \"1\":\n",
        "                qc.x(qubit)\n",
        "        return qc\n",
        "\n",
        "    for state in on_states:\n",
        "        qc.barrier()  # Barriers are added to help visualize how the functions are created. They can safely be removed.\n",
        "        qc = add_cx(qc, f\"{state:0b}\")\n",
        "        qc.mcx(list(range(num_qubits)), num_qubits)\n",
        "        qc = add_cx(qc, f\"{state:0b}\")\n",
        "\n",
        "    qc.barrier()\n",
        "\n",
        "    return qc"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "2582a4ec",
      "metadata": {
        "id": "2582a4ec"
      },
      "source": [
        "We can show the quantum circuit implementation of the query gate using the draw method."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "99b23e6b",
      "metadata": {
        "id": "99b23e6b",
        "outputId": "9fd88fd5-f1f2-458f-8bbd-5e1fca18565c"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">      ░ ┌───┐     ┌───┐ ░                 ░                 ░       ░ \n",
              "q_0: ─░─┤ X ├──■──┤ X ├─░────────■────────░────────■────────░───■───░─\n",
              "      ░ ├───┤  │  ├───┤ ░ ┌───┐  │  ┌───┐ ░        │        ░   │   ░ \n",
              "q_1: ─░─┤ X ├──■──┤ X ├─░─┤ X ├──■──┤ X ├─░────────■────────░───■───░─\n",
              "      ░ └───┘  │  └───┘ ░ ├───┤  │  ├───┤ ░ ┌───┐  │  ┌───┐ ░   │   ░ \n",
              "q_2: ─░────────■────────░─┤ X ├──■──┤ X ├─░─┤ X ├──■──┤ X ├─░───■───░─\n",
              "      ░      ┌─┴─┐      ░ └───┘┌─┴─┐└───┘ ░ └───┘┌─┴─┐└───┘ ░ ┌─┴─┐ ░ \n",
              "q_3: ─░──────┤ X ├──────░──────┤ X ├──────░──────┤ X ├──────░─┤ X ├─░─\n",
              "      ░      └───┘      ░      └───┘      ░      └───┘      ░ └───┘ ░ </pre>"
            ],
            "text/plain": [
              "      ░ ┌───┐     ┌───┐ ░                 ░                 ░       ░ \n",
              "q_0: ─░─┤ X ├──■──┤ X ├─░────────■────────░────────■────────░───■───░─\n",
              "      ░ ├───┤  │  ├───┤ ░ ┌───┐  │  ┌───┐ ░        │        ░   │   ░ \n",
              "q_1: ─░─┤ X ├──■──┤ X ├─░─┤ X ├──■──┤ X ├─░────────■────────░───■───░─\n",
              "      ░ └───┘  │  └───┘ ░ ├───┤  │  ├───┤ ░ ┌───┐  │  ┌───┐ ░   │   ░ \n",
              "q_2: ─░────────■────────░─┤ X ├──■──┤ X ├─░─┤ X ├──■──┤ X ├─░───■───░─\n",
              "      ░      ┌─┴─┐      ░ └───┘┌─┴─┐└───┘ ░ └───┘┌─┴─┐└───┘ ░ ┌─┴─┐ ░ \n",
              "q_3: ─░──────┤ X ├──────░──────┤ X ├──────░──────┤ X ├──────░─┤ X ├─░─\n",
              "      ░      └───┘      ░      └───┘      ░      └───┘      ░ └───┘ ░ "
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "display(dj_function(3).draw())"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "820f3667",
      "metadata": {
        "id": "820f3667"
      },
      "outputs": [],
      "source": [
        "def compile_circuit(function: QuantumCircuit):\n",
        "    \"\"\"\n",
        "    Compiles a circuit for use in the Deutsch-Jozsa algorithm.\n",
        "    \"\"\"\n",
        "    n = function.num_qubits - 1\n",
        "    qc = QuantumCircuit(n + 1, n)\n",
        "    qc.x(n)\n",
        "    qc.h(range(n + 1))\n",
        "    qc.compose(function, inplace=True)\n",
        "    qc.h(range(n))\n",
        "    qc.measure(range(n), range(n))\n",
        "    return qc"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "6999a27b",
      "metadata": {
        "id": "6999a27b"
      },
      "source": [
        "Finally, a function that runs the Deutsch-Jozsa circuit once is defined.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "ff0c5e9e",
      "metadata": {
        "id": "ff0c5e9e"
      },
      "outputs": [],
      "source": [
        "from qiskit_aer import AerSimulator\n",
        "\n",
        "def dj_algorithm(function: QuantumCircuit):\n",
        "    \"\"\"\n",
        "    Determine if a Deutsch-Jozsa function is constant or balanced.\n",
        "    \"\"\"\n",
        "    qc = compile_circuit(function)\n",
        "\n",
        "    result = AerSimulator().run(qc, shots=1, memory=True).result()\n",
        "    measurements = result.get_memory()\n",
        "    if \"1\" in measurements[0]:\n",
        "        return \"balanced\"\n",
        "    return \"constant\""
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "bd23e892",
      "metadata": {
        "id": "bd23e892",
        "outputId": "e45870da-879b-440f-d230-5a46783606a7"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">           ░                 ░ ┌───┐     ┌───┐ ░                 ░ ┌───┐     »\n",
              "q_0: ──────░────────■────────░─┤ X ├──■──┤ X ├─░────────■────────░─┤ X ├──■──»\n",
              "           ░ ┌───┐  │  ┌───┐ ░ ├───┤  │  ├───┤ ░ ┌───┐  │  ┌───┐ ░ ├───┤  │  »\n",
              "q_1: ──────░─┤ X ├──■──┤ X ├─░─┤ X ├──■──┤ X ├─░─┤ X ├──■──┤ X ├─░─┤ X ├──■──»\n",
              "           ░ ├───┤  │  ├───┤ ░ └───┘  │  └───┘ ░ └───┘  │  └───┘ ░ ├───┤  │  »\n",
              "q_2: ──────░─┤ X ├──■──┤ X ├─░────────■────────░────────■────────░─┤ X ├──■──»\n",
              "     ┌───┐ ░ └───┘┌─┴─┐└───┘ ░      ┌─┴─┐      ░      ┌─┴─┐      ░ └───┘┌─┴─┐»\n",
              "q_3: ┤ X ├─░──────┤ X ├──────░──────┤ X ├──────░──────┤ X ├──────░──────┤ X ├»\n",
              "     └───┘ ░      └───┘      ░      └───┘      ░      └───┘      ░      └───┘»\n",
              "«     ┌───┐ ░ \n",
              "«q_0: ┤ X ├─░─\n",
              "«     ├───┤ ░ \n",
              "«q_1: ┤ X ├─░─\n",
              "«     ├───┤ ░ \n",
              "«q_2: ┤ X ├─░─\n",
              "«     └───┘ ░ \n",
              "«q_3: ──────░─\n",
              "«           ░ </pre>"
            ],
            "text/plain": [
              "           ░                 ░ ┌───┐     ┌───┐ ░                 ░ ┌───┐     »\n",
              "q_0: ──────░────────■────────░─┤ X ├──■──┤ X ├─░────────■────────░─┤ X ├──■──»\n",
              "           ░ ┌───┐  │  ┌───┐ ░ ├───┤  │  ├───┤ ░ ┌───┐  │  ┌───┐ ░ ├───┤  │  »\n",
              "q_1: ──────░─┤ X ├──■──┤ X ├─░─┤ X ├──■──┤ X ├─░─┤ X ├──■──┤ X ├─░─┤ X ├──■──»\n",
              "           ░ ├───┤  │  ├───┤ ░ └───┘  │  └───┘ ░ └───┘  │  └───┘ ░ ├───┤  │  »\n",
              "q_2: ──────░─┤ X ├──■──┤ X ├─░────────■────────░────────■────────░─┤ X ├──■──»\n",
              "     ┌───┐ ░ └───┘┌─┴─┐└───┘ ░      ┌─┴─┐      ░      ┌─┴─┐      ░ └───┘┌─┴─┐»\n",
              "q_3: ┤ X ├─░──────┤ X ├──────░──────┤ X ├──────░──────┤ X ├──────░──────┤ X ├»\n",
              "     └───┘ ░      └───┘      ░      └───┘      ░      └───┘      ░      └───┘»\n",
              "«     ┌───┐ ░ \n",
              "«q_0: ┤ X ├─░─\n",
              "«     ├───┤ ░ \n",
              "«q_1: ┤ X ├─░─\n",
              "«     ├───┤ ░ \n",
              "«q_2: ┤ X ├─░─\n",
              "«     └───┘ ░ \n",
              "«q_3: ──────░─\n",
              "«           ░ "
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "text/plain": [
              "'balanced'"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "f = dj_function(3)\n",
        "display(f.draw())\n",
        "display(dj_algorithm(f))"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "95055945",
      "metadata": {
        "id": "95055945"
      },
      "source": [
        "# Additional information\n",
        "\n",
        "<b>Created by:</b> Dayeong Kang, Yuri Kobayashi, Vishal Bajpe, Kifumi Numata\n",
        "\n",
        "\n",
        "<b>Advisor:</b> Ikko Hanamura\n",
        "<b>Presented by:</b> Sumit\n",
        "<b>Creative assets by:</b> Radha Pyari Sandhir\n",
        "\n",
        "Version: 1.0"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "cacb1fac",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 36
        },
        "id": "cacb1fac",
        "outputId": "88fae03c-ea86-4624-b4bb-52a6d275cd66"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "'1.1.1'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {},
          "execution_count": 21
        }
      ],
      "source": [
        "import qiskit\n",
        "qiskit.__version__"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "785a7732",
      "metadata": {
        "id": "785a7732"
      },
      "outputs": [],
      "source": [
        "def bernstein_vazirani(string):\n",
        "\n",
        "  stringlen = len(string)\n",
        "  qc = QuantumCircuit(stringlen+1, stringlen)\n",
        "  qc.x(stringlen)\n",
        "  qc.h(range(stringlen+1))\n",
        "  for i in range(stringlen):\n",
        "    if string[i] == '1':\n",
        "      qc.cx(i,stringlen)\n",
        "\n",
        "      qc.barrier()\n",
        "\n",
        "  qc.h(range(stringlen))\n",
        "  qc.barrier()\n",
        "\n",
        "  qc.measure(range(stringlen), range(stringlen))\n",
        "  return qc"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "bernstein_vazirani('001').draw('mpl')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 384
        },
        "id": "eThufqb2ebM7",
        "outputId": "49846880-c5a7-4ae9-869e-c77c4a01ba6a"
      },
      "id": "eThufqb2ebM7",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 872.774x451.5 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {},
          "execution_count": 23
        }
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.10.14"
    },
    "vscode": {
      "interpreter": {
        "hash": "9650cb4e16cdd4a8e8e2d128bf38d875813998db22a3c986335f89e0cb4d7bb2"
      }
    },
    "colab": {
      "provenance": [],
      "include_colab_link": true
    }
  },
  "nbformat": 4,
  "nbformat_minor": 5
}