intro_quantum_walks_qkd.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uM4ahwrsPXIZ"
      },
      "source": [
        "### 1W-QKD using QWs on circles & hypercubes: introduction\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2WhbQR5oY1e7"
      },
      "source": [
        "The first code cells are a quicker way to avoid downloading all the necessary modules every time the code is rerun from start to finish. ⚡"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 70
        },
        "id": "_skQXCgjH6qD",
        "outputId": "f3251a8c-543d-4bee-dd98-73d09e54c755"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "\"\\nfrom google.colab import drive\\nimport sys\\ndrive.mount('/content/drive')\\n!pip install qiskit qiskit_aer networkx pylatexenc pygraphviz --target /content/drive/MyDrive/qkd_qw_packages --upgrade\\nsys.path.append('/content/drive/MyDrive/qkd_qw_packages')\\n\""
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {},
          "execution_count": 1
        }
      ],
      "source": [
        "# Import qiskit, qiskit-aer, networkx, pylatexenc && pygraphviz from Google Drive\n",
        "'''\n",
        "from google.colab import drive\n",
        "import sys\n",
        "drive.mount('/content/drive')\n",
        "!pip install qiskit qiskit_aer networkx pylatexenc pygraphviz --target /content/drive/MyDrive/qkd_qw_packages --upgrade\n",
        "sys.path.append('/content/drive/MyDrive/qkd_qw_packages')\n",
        "'''"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "lz4P9n1urkYt",
        "outputId": "aa41a8a6-23e3-4f62-f211-c1724e5be398"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Reading package lists... Done\n",
            "Building dependency tree... Done\n",
            "Reading state information... Done\n",
            "Note, selecting 'libgraphviz-dev' instead of 'graphviz-dev'\n",
            "graphviz is already the newest version (2.42.2-6ubuntu0.1).\n",
            "The following additional packages will be installed:\n",
            "  libgail-common libgail18 libgtk2.0-0 libgtk2.0-bin libgtk2.0-common libgvc6-plugins-gtk\n",
            "  librsvg2-common libxdot4\n",
            "Suggested packages:\n",
            "  gvfs\n",
            "The following NEW packages will be installed:\n",
            "  libgail-common libgail18 libgraphviz-dev libgtk2.0-0 libgtk2.0-bin libgtk2.0-common\n",
            "  libgvc6-plugins-gtk librsvg2-common libxdot4\n",
            "0 upgraded, 9 newly installed, 0 to remove and 49 not upgraded.\n",
            "Need to get 2,434 kB of archives.\n",
            "After this operation, 7,681 kB of additional disk space will be used.\n",
            "Get:1 http://archive.ubuntu.com/ubuntu jammy-updates/main amd64 libgtk2.0-common all 2.24.33-2ubuntu2.1 [125 kB]\n",
            "Get:2 http://archive.ubuntu.com/ubuntu jammy-updates/main amd64 libgtk2.0-0 amd64 2.24.33-2ubuntu2.1 [2,038 kB]\n",
            "Get:3 http://archive.ubuntu.com/ubuntu jammy-updates/main amd64 libgail18 amd64 2.24.33-2ubuntu2.1 [15.9 kB]\n",
            "Get:4 http://archive.ubuntu.com/ubuntu jammy-updates/main amd64 libgail-common amd64 2.24.33-2ubuntu2.1 [132 kB]\n",
            "Get:5 http://archive.ubuntu.com/ubuntu jammy-updates/universe amd64 libxdot4 amd64 2.42.2-6ubuntu0.1 [16.4 kB]\n",
            "Get:6 http://archive.ubuntu.com/ubuntu jammy-updates/universe amd64 libgvc6-plugins-gtk amd64 2.42.2-6ubuntu0.1 [22.5 kB]\n",
            "Get:7 http://archive.ubuntu.com/ubuntu jammy-updates/universe amd64 libgraphviz-dev amd64 2.42.2-6ubuntu0.1 [58.5 kB]\n",
            "Get:8 http://archive.ubuntu.com/ubuntu jammy-updates/main amd64 libgtk2.0-bin amd64 2.24.33-2ubuntu2.1 [7,936 B]\n",
            "Get:9 http://archive.ubuntu.com/ubuntu jammy-updates/main amd64 librsvg2-common amd64 2.52.5+dfsg-3ubuntu0.2 [17.7 kB]\n",
            "Fetched 2,434 kB in 3s (931 kB/s)\n",
            "Selecting previously unselected package libgtk2.0-common.\n",
            "(Reading database ... 123634 files and directories currently installed.)\n",
            "Preparing to unpack .../0-libgtk2.0-common_2.24.33-2ubuntu2.1_all.deb ...\n",
            "Unpacking libgtk2.0-common (2.24.33-2ubuntu2.1) ...\n",
            "Selecting previously unselected package libgtk2.0-0:amd64.\n",
            "Preparing to unpack .../1-libgtk2.0-0_2.24.33-2ubuntu2.1_amd64.deb ...\n",
            "Unpacking libgtk2.0-0:amd64 (2.24.33-2ubuntu2.1) ...\n",
            "Selecting previously unselected package libgail18:amd64.\n",
            "Preparing to unpack .../2-libgail18_2.24.33-2ubuntu2.1_amd64.deb ...\n",
            "Unpacking libgail18:amd64 (2.24.33-2ubuntu2.1) ...\n",
            "Selecting previously unselected package libgail-common:amd64.\n",
            "Preparing to unpack .../3-libgail-common_2.24.33-2ubuntu2.1_amd64.deb ...\n",
            "Unpacking libgail-common:amd64 (2.24.33-2ubuntu2.1) ...\n",
            "Selecting previously unselected package libxdot4:amd64.\n",
            "Preparing to unpack .../4-libxdot4_2.42.2-6ubuntu0.1_amd64.deb ...\n",
            "Unpacking libxdot4:amd64 (2.42.2-6ubuntu0.1) ...\n",
            "Selecting previously unselected package libgvc6-plugins-gtk.\n",
            "Preparing to unpack .../5-libgvc6-plugins-gtk_2.42.2-6ubuntu0.1_amd64.deb ...\n",
            "Unpacking libgvc6-plugins-gtk (2.42.2-6ubuntu0.1) ...\n",
            "Selecting previously unselected package libgraphviz-dev:amd64.\n",
            "Preparing to unpack .../6-libgraphviz-dev_2.42.2-6ubuntu0.1_amd64.deb ...\n",
            "Unpacking libgraphviz-dev:amd64 (2.42.2-6ubuntu0.1) ...\n",
            "Selecting previously unselected package libgtk2.0-bin.\n",
            "Preparing to unpack .../7-libgtk2.0-bin_2.24.33-2ubuntu2.1_amd64.deb ...\n",
            "Unpacking libgtk2.0-bin (2.24.33-2ubuntu2.1) ...\n",
            "Selecting previously unselected package librsvg2-common:amd64.\n",
            "Preparing to unpack .../8-librsvg2-common_2.52.5+dfsg-3ubuntu0.2_amd64.deb ...\n",
            "Unpacking librsvg2-common:amd64 (2.52.5+dfsg-3ubuntu0.2) ...\n",
            "Setting up libxdot4:amd64 (2.42.2-6ubuntu0.1) ...\n",
            "Setting up librsvg2-common:amd64 (2.52.5+dfsg-3ubuntu0.2) ...\n",
            "Setting up libgtk2.0-common (2.24.33-2ubuntu2.1) ...\n",
            "Setting up libgtk2.0-0:amd64 (2.24.33-2ubuntu2.1) ...\n",
            "Setting up libgvc6-plugins-gtk (2.42.2-6ubuntu0.1) ...\n",
            "Setting up libgail18:amd64 (2.24.33-2ubuntu2.1) ...\n",
            "Setting up libgtk2.0-bin (2.24.33-2ubuntu2.1) ...\n",
            "Setting up libgail-common:amd64 (2.24.33-2ubuntu2.1) ...\n",
            "Setting up libgraphviz-dev:amd64 (2.42.2-6ubuntu0.1) ...\n",
            "Processing triggers for libc-bin (2.35-0ubuntu3.4) ...\n",
            "/sbin/ldconfig.real: /usr/local/lib/libtcm_debug.so.1 is not a symbolic link\n",
            "\n",
            "/sbin/ldconfig.real: /usr/local/lib/libtbbbind_2_0.so.3 is not a symbolic link\n",
            "\n",
            "/sbin/ldconfig.real: /usr/local/lib/libumf.so.0 is not a symbolic link\n",
            "\n",
            "/sbin/ldconfig.real: /usr/local/lib/libtcm.so.1 is not a symbolic link\n",
            "\n",
            "/sbin/ldconfig.real: /usr/local/lib/libtbbbind_2_5.so.3 is not a symbolic link\n",
            "\n",
            "/sbin/ldconfig.real: /usr/local/lib/libhwloc.so.15 is not a symbolic link\n",
            "\n",
            "/sbin/ldconfig.real: /usr/local/lib/libur_adapter_level_zero.so.0 is not a symbolic link\n",
            "\n",
            "/sbin/ldconfig.real: /usr/local/lib/libur_adapter_opencl.so.0 is not a symbolic link\n",
            "\n",
            "/sbin/ldconfig.real: /usr/local/lib/libtbb.so.12 is not a symbolic link\n",
            "\n",
            "/sbin/ldconfig.real: /usr/local/lib/libtbbmalloc.so.2 is not a symbolic link\n",
            "\n",
            "/sbin/ldconfig.real: /usr/local/lib/libtbbmalloc_proxy.so.2 is not a symbolic link\n",
            "\n",
            "/sbin/ldconfig.real: /usr/local/lib/libtbbbind.so.3 is not a symbolic link\n",
            "\n",
            "/sbin/ldconfig.real: /usr/local/lib/libur_loader.so.0 is not a symbolic link\n",
            "\n",
            "Processing triggers for man-db (2.10.2-1) ...\n",
            "Processing triggers for libgdk-pixbuf-2.0-0:amd64 (2.42.8+dfsg-1ubuntu0.3) ...\n"
          ]
        }
      ],
      "source": [
        "# Alternatively... (1)\n",
        "!apt-get install -y graphviz graphviz-dev"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "O9WV7aQYdMrR",
        "outputId": "8851b4ab-e35d-4b27-be98-9f1b55f430fc"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Collecting qiskit\n",
            "  Downloading qiskit-1.3.1-cp39-abi3-manylinux_2_17_x86_64.manylinux2014_x86_64.whl.metadata (12 kB)\n",
            "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",
            "Requirement already satisfied: networkx in /usr/local/lib/python3.10/dist-packages (3.4.2)\n",
            "Collecting pylatexenc\n",
            "  Downloading pylatexenc-2.10.tar.gz (162 kB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m162.6/162.6 kB\u001b[0m \u001b[31m15.1 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25h  Preparing metadata (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "Collecting pygraphviz\n",
            "  Downloading pygraphviz-1.14.tar.gz (106 kB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m106.0/106.0 kB\u001b[0m \u001b[31m10.7 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25h  Installing build dependencies ... \u001b[?25l\u001b[?25hdone\n",
            "  Getting requirements to build wheel ... \u001b[?25l\u001b[?25hdone\n",
            "  Preparing metadata (pyproject.toml) ... \u001b[?25l\u001b[?25hdone\n",
            "Collecting rustworkx>=0.15.0 (from qiskit)\n",
            "  Downloading rustworkx-0.15.1-cp38-abi3-manylinux_2_17_x86_64.manylinux2014_x86_64.whl.metadata (9.9 kB)\n",
            "Requirement already satisfied: numpy<3,>=1.17 in /usr/local/lib/python3.10/dist-packages (from qiskit) (1.26.4)\n",
            "Requirement already satisfied: scipy>=1.5 in /usr/local/lib/python3.10/dist-packages (from qiskit) (1.13.1)\n",
            "Requirement already satisfied: sympy>=1.3 in /usr/local/lib/python3.10/dist-packages (from qiskit) (1.13.1)\n",
            "Collecting dill>=0.3 (from qiskit)\n",
            "  Downloading dill-0.3.9-py3-none-any.whl.metadata (10 kB)\n",
            "Requirement already satisfied: python-dateutil>=2.8.0 in /usr/local/lib/python3.10/dist-packages (from qiskit) (2.8.2)\n",
            "Collecting stevedore>=3.0.0 (from qiskit)\n",
            "  Downloading stevedore-5.4.0-py3-none-any.whl.metadata (2.3 kB)\n",
            "Requirement already satisfied: typing-extensions in /usr/local/lib/python3.10/dist-packages (from qiskit) (4.12.2)\n",
            "Collecting symengine<0.14,>=0.11 (from qiskit)\n",
            "  Downloading symengine-0.13.0-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl.metadata (1.2 kB)\n",
            "Requirement already satisfied: psutil>=5 in /usr/local/lib/python3.10/dist-packages (from qiskit_aer) (5.9.5)\n",
            "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.10/dist-packages (from python-dateutil>=2.8.0->qiskit) (1.17.0)\n",
            "Collecting pbr>=2.0.0 (from stevedore>=3.0.0->qiskit)\n",
            "  Downloading pbr-6.1.0-py2.py3-none-any.whl.metadata (3.4 kB)\n",
            "Requirement already satisfied: mpmath<1.4,>=1.1.0 in /usr/local/lib/python3.10/dist-packages (from sympy>=1.3->qiskit) (1.3.0)\n",
            "Downloading qiskit-1.3.1-cp39-abi3-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (6.7 MB)\n",
            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m6.7/6.7 MB\u001b[0m \u001b[31m63.0 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hDownloading qiskit_aer-0.15.1-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (12.3 MB)\n",
            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m12.3/12.3 MB\u001b[0m \u001b[31m106.6 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hDownloading dill-0.3.9-py3-none-any.whl (119 kB)\n",
            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m119.4/119.4 kB\u001b[0m \u001b[31m11.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hDownloading rustworkx-0.15.1-cp38-abi3-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (2.0 MB)\n",
            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m2.0/2.0 MB\u001b[0m \u001b[31m85.8 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hDownloading stevedore-5.4.0-py3-none-any.whl (49 kB)\n",
            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m49.5/49.5 kB\u001b[0m \u001b[31m4.9 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hDownloading symengine-0.13.0-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (49.7 MB)\n",
            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m49.7/49.7 MB\u001b[0m \u001b[31m43.9 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hDownloading pbr-6.1.0-py2.py3-none-any.whl (108 kB)\n",
            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m108.5/108.5 kB\u001b[0m \u001b[31m10.6 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hBuilding wheels for collected packages: pylatexenc, pygraphviz\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=136816 sha256=0b585542349b47a0746d7106cf03c2a19d645ab80397028e4c58d5664e903c0d\n",
            "  Stored in directory: /root/.cache/pip/wheels/d3/31/8b/e09b0386afd80cfc556c00408c9aeea5c35c4d484a9c762fd5\n",
            "  Building wheel for pygraphviz (pyproject.toml) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for pygraphviz: filename=pygraphviz-1.14-cp310-cp310-linux_x86_64.whl size=168634 sha256=36d49119dbfaaa72b0da1c582e56f25fe2283be74e707ac44480c4c43e33381a\n",
            "  Stored in directory: /root/.cache/pip/wheels/61/ab/cd/e24a22c32830b8b4948c8887d8714d399f0f806f206a034698\n",
            "Successfully built pylatexenc pygraphviz\n",
            "Installing collected packages: pylatexenc, symengine, rustworkx, pygraphviz, pbr, dill, stevedore, qiskit, qiskit_aer\n",
            "Successfully installed dill-0.3.9 pbr-6.1.0 pygraphviz-1.14 pylatexenc-2.10 qiskit-1.3.1 qiskit_aer-0.15.1 rustworkx-0.15.1 stevedore-5.4.0 symengine-0.13.0\n"
          ]
        }
      ],
      "source": [
        "# Alternatively... (2)\n",
        "!pip install qiskit qiskit_aer networkx pylatexenc pygraphviz --upgrade"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "1QjAwaerGOsa"
      },
      "outputs": [],
      "source": [
        "# Useful imports\n",
        "import numpy as np\n",
        "import networkx as nx\n",
        "from networkx import hypercube_graph\n",
        "import json\n",
        "import warnings\n",
        "from typing import Callable\n",
        "\n",
        "# Qiskit components\n",
        "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister, transpile\n",
        "from qiskit.quantum_info import Operator\n",
        "from qiskit_aer import AerSimulator\n",
        "\n",
        "# Visualization\n",
        "import matplotlib.pyplot as plt\n",
        "from qiskit.visualization import plot_histogram, plot_bloch_vector\n",
        "from networkx.drawing.nx_agraph import graphviz_layout\n",
        "\n",
        "# Filter all warnings from now on\n",
        "warnings.filterwarnings(\"ignore\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3Qgc4cVLby82"
      },
      "source": [
        "### Quantum computing concepts\n",
        "\n",
        "Quantum computing is an exciting field that leverages the principles of quantum mechanics to perform computations. By exploiting quantum phenomena such as superposition, it has the potential to solve certain problems much more efficiently than classical methods. This discussion delves into the foundational concepts that support quantum computing, starting with quantum bits (qubits), the basic units of quantum information. We will also explore the concept of superposition, a key quantum property that allows qubits to exist in multiple states simultaneously, and quantum gates, which are the building blocks of quantum circuits. Quantum gates manipulate qubits by performing operations that take advantage of quantum principles, allowing the construction of complex quantum algorithms. By examining these foundational elements, we aim to provide a clear and comprehensive understanding of the principles and potential of quantum computing, setting the stage for further exploration into this field."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "W_wK_Jm5blO_"
      },
      "source": [
        "#### Hilbert space\n",
        "\n",
        "The state of a quantum system is mathematically represented within a Hilbert space, a complete vector space equipped with an inner product that allows for the definition of angles and lengths between vectors. This representation forms the mathematical framework for describing quantum states and their evolution. The inner product between two vectors $\\ket{\\psi}$ and $\\ket{\\phi}$ in the Hilbert space is defined as:\n",
        "\n",
        "$$\n",
        "\\langle\\psi\\ket{\\phi} = \\sum_{i=1}^n \\bar{\\psi_i} \\phi_i\n",
        "$$\n",
        "\n",
        "where $\\psi_i$ and $\\phi_i$ are the components of the vectors $\\ket{\\psi}$ and $\\ket{\\phi}$, respectively, in a chosen basis, and $\\bar{\\psi_i}$ denotes the complex conjugate of $\\psi_i$.\n",
        "\n",
        "In the context of quantum mechanics, it is essential to ensure that quantum state vectors are normalized, meaning their magnitude equals one. The norm of a vector, which measures its magnitude, is defined using the inner product as follows:\n",
        "\n",
        "$$\n",
        "\\|\\psi\\| = \\sqrt{\\langle{\\psi}\\ket{\\psi}}\n",
        "$$\n",
        "\n",
        "Normalization ensures that the probability interpretation of quantum mechanics holds, where the square of the magnitude of a state's component represents its likelihood (probability) of being observed in a particular basis."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LBZv1w4odjq3"
      },
      "source": [
        "#### Superposition\n",
        "\n",
        "One of the most remarkable features of quantum systems is superposition. Unlike classical bits, which are limited to being in one of two definite states (i.e., $0$ or $1$) quantum bits, or qubits, have the ability to exist in a combination of both states simultaneously. Mathematically, superposition is described as a linear combination of basis states, where the coefficients associated with these states are complex numbers. If $\\ket{\\psi_1}$ and $\\ket{\\psi_2}$ are two basis states in a Hilbert space $\\mathcal{H}$, the qubit state $\\ket{\\psi}$ can be expressed as:\n",
        "\n",
        "$$\n",
        "\\ket{\\psi} = \\alpha \\ket{\\psi_1} + \\beta \\ket{\\psi_2},  \\: \\ket{\\psi} \\in \\mathcal{H}, \\: \\alpha, \\beta \\in \\mathbb{C}\n",
        "$$\n",
        "\n",
        "Here, $\\alpha$ and $\\beta$ are complex probability amplitudes that determine the contribution of each basis state to the superposition. These amplitudes encode the probabilities of measuring the qubit in the corresponding basis state. A crucial requirement for a valid quantum state is the normalization condition, which ensures that the total probability of all possible measurement outcomes equals one. This condition is expressed as:\n",
        "\n",
        "$$\n",
        "\\|\\alpha\\|^{2} + \\|\\beta\\|^{2} = 1\n",
        "$$\n",
        "\n",
        "where $\\|\\alpha\\|^{2}$ and $\\|\\beta\\|^{2}$ represent the probabilities of finding the system in the states $\\ket{\\psi_1}$ and $\\ket{\\psi_2}$, respectively. The normalization ensures that the qubit state $\\ket{\\psi}$ is physically meaningful and adheres to the probabilistic nature of quantum mechanics."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "h56iwCZ-gZAN"
      },
      "source": [
        "#### Linear operators\n",
        "\n",
        "Operating on the state of a quantum system involves applying a linear operator to the quantum state vector, which represents the system's current state in a $d$-dimensional Hilbert space $\\mathcal{H}$. The quantum state vector is an element of this space, and the action of the operator transforms the state according to the rules of linear algebra. Linear operators acting on a $d$-dimensional Hilbert space can be expressed as $d \\times d$ matrices, where the entries of the matrix encode the operator's effect on the basis states of the Hilbert space. These operators follow the familiar mathematical rules of matrix operations, such as addition, scalar multiplication, and matrix multiplication. For instance, combining two operators corresponds to adding or multiplying their respective matrices, depending on the desired operation. A key property of linear operators is their adherence to the linearity condition. Specifically, for an operator $A$ acting on the Hilbert space, this condition states that for any two state vectors $\\ket{\\psi_1}$, $\\ket{\\psi_2}$ and any complex scalars $\\alpha$ and $\\beta$, the operator satisfies:\n",
        "\n",
        "$$\n",
        "A(\\alpha \\ket{\\psi_1} + \\beta \\ket{\\psi_2}) = \\alpha A(\\ket{\\psi_1}) + \\beta A(\\ket{\\psi_2})\n",
        "$$\n",
        "\n",
        "This property ensures that the operator $A$ preserves the linear structure of the Hilbert space, making it a fundamental tool for describing transformations and dynamics in quantum systems."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "akN4koHegnr2"
      },
      "source": [
        "#### Unitary operators\n",
        "\n",
        "A unitary operator is a special class of linear operators that plays a fundamental role in quantum mechanics and quantum computing due to its important mathematical properties. A linear operator $A$ is said to be unitary if it satisfies the following conditions:\n",
        "\n",
        "$$\n",
        "A^\\dagger A = I, \\: AA^\\dagger = I \\\\\n",
        "$$\n",
        "\n",
        "where $A^\\dagger$ denotes the complex conjugate transpose (or adjoint) of $A$, and $I$ is the identity matrix. These conditions essentially ensure that the operator $A$ preserves the inner product between vectors, which is a critical feature in quantum mechanics where the evolution of quantum states must preserve their physical properties.\n",
        "\n",
        "The significance of unitary operators can be understood through the following key aspects:\n",
        "\n",
        "- **Orthonormality of rows and columns**: rows and columns of a unitary matrix are orthonormal vectors. This means that each row and each column of the matrix is a vector that is orthogonal to the others and has a unit norm. This property is particularly important in quantum mechanics, where unitary operators represent transformations that maintain the structure of quantum states;\n",
        "- **Preservation of inner product and norm**: unitary operators preserve the inner product between two quantum states. More formally, for any two quantum states $\\ket{\\psi_1}$, $\\ket{\\psi_2}$, a unitary operator $A$ satisfies the following: $\\langle\\psi_1 A\\ket{A \\, \\psi_2} = \\bra{\\psi_1} A^\\dagger A \\ket{\\psi_2} = \\langle\\psi_1\\ket{\\psi_2}$\n",
        "\n",
        "This means that the application of a unitary operator does not change the inner product between two vectors, and by extension, it also preserves the norm of quantum states. This property guarantees that the evolution of quantum systems, governed by unitary operators (such as the time evolution in quantum mechanics), is physically meaningful and consistent with the probabilistic interpretation of quantum theory."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wTwCIM7fg6hK"
      },
      "source": [
        "#### Tensor product\n",
        "\n",
        "The tensor product is a fundamental mathematical operation used to combine two quantum systems into a single, larger system. It allows for the construction of composite quantum states from individual ones. This operation is central to many aspects of quantum mechanics, especially when dealing with multi-partite quantum systems, such as entangled states in quantum information theory. Given two matrices $A$ and $B$, their tensor product, denoted $A \\otimes B$, is defined as a block matrix in which each element of matrix $A$ is multiplied by the entire matrix $B$. Specifically, if $A$ is an $m \\times n$ matrix and $B$ is a $p \\times q$ matrix, their tensor product is an $mp \\times nq$ matrix:\n",
        "\n",
        "$$\n",
        "A \\otimes B = \\begin{bmatrix} a_{11} B & a_{12} B & \\dots & a_{1n} B \\\\ a_{21} B & a_{22} B & \\dots & a_{2n} B \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ a_{m1} B & a_{m2} B & \\dots & a_{mn} B \\end{bmatrix}\n",
        "$$\n",
        "\n",
        "In this construction, each element $a_{ij}$ of matrix $A$ is multiplied by the entire matrix $B$, resulting in a block of the larger matrix. Similarly, when taking the tensor product of two vectors $\\ket{\\psi}$ and $\\ket{\\phi}$, where $\\ket{\\psi}$ has components $\\psi_1, \\psi_2, \\dots, \\psi_n$ and $\\ket{\\phi}$ has components $\\phi_1, \\phi_2, \\dots, \\phi_m$ their tensor product is defined as:\n",
        "\n",
        "$$\n",
        "\\ket{\\psi} \\otimes \\ket{\\phi} = \\begin{bmatrix} \\psi_1 \\\\ \\psi_2 \\\\ \\vdots \\\\ \\psi_n \\end{bmatrix} \\otimes \\begin{bmatrix} \\phi_1 \\\\ \\phi_2 \\\\ \\vdots \\\\ \\phi_m \\end{bmatrix} = \\begin{bmatrix} \\psi_1 \\phi_1 \\\\ \\psi_1 \\phi_2 \\\\ \\vdots \\\\ \\psi_1 \\phi_m \\\\ \\psi_2 \\phi_1 \\\\ \\psi_2 \\phi_2 \\\\ \\vdots \\\\ \\psi_2 \\phi_m \\\\ \\vdots \\\\ \\psi_n \\phi_1 \\\\ \\psi_n \\phi_2 \\\\ \\vdots \\\\ \\psi_n \\phi_m \\end{bmatrix}\n",
        "$$\n",
        "\n",
        "This operation produces a new vector whose size is the product of the dimensions of the original vectors, i.e., the resulting vector has $n \\times m$ components. Each component is the product of a corresponding component from $\\ket{\\psi}$ and $\\ket{\\phi}$.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VyQy13Ntg_ZR"
      },
      "source": [
        "#### Common operators\n",
        "\n",
        "In quantum computing, certain operators are used frequently due to their fundamental role in quantum state transformations. These operators manipulate qubits and are crucial for performing quantum computations. Some of the most commonly encountered operators include the Pauli operators, the Hadamard operator, and the phase operator.\n",
        "\n",
        "The **Pauli** operators are a set of three matrices (plus the identity operator) that play a central role in quantum mechanics and quantum computing. These operators act on a single qubit and are used in many quantum algorithms. The four Pauli operators are:\n",
        "\n",
        "- **Identity operator** $I$: this operator leaves the state of the qubit unchanged, acting as the \"do-nothing\" operator in quantum computing;\n",
        "- **Pauli-X operator** $X$: often referred to as the quantum NOT gate, the Pauli-X operator flips the state of the qubit. It changes the state $\\ket{0}$ to $\\ket{1}$ and vice versa;\n",
        "- **Pauli-Y operator** $Y$: this operator applies a rotation to the qubit's state by $\\pi/2$ around the y-axis of the Bloch sphere. It not only flips the state but also introduces a phase factor;\n",
        "- **Pauli-Z operator** $Z$: the Pauli-Z operator flips the sign of the state, introducing a phase of $-1$ for the $\\ket{1}$ state while leaving the $\\ket{0}$ state unchanged.\n",
        "\n",
        "These operators are represented as matrices:\n",
        "\n",
        "$$\n",
        "I = \\begin{bmatrix} 1 & 0 \\\\ 0 & 1 \\end{bmatrix}, \\:\n",
        "X = \\begin{bmatrix} 0 & 1 \\\\ 1 & 0 \\end{bmatrix}, \\:\n",
        "Y = \\begin{bmatrix} 0 & -i \\\\ i & 0 \\end{bmatrix}, \\:\n",
        "Z = \\begin{bmatrix} 1 & 0 \\\\ 0 & -1 \\end{bmatrix}\n",
        "$$\n",
        "\n",
        "They form the foundation for more complex quantum gates, and they are used in a wide variety of quantum algorithms and protocols, including error correction, quantum cryptography, and entanglement creation.\n",
        "\n",
        "Another important operator is the **Hadamard** operator, which is a unitary transformation that converts the basis states $\\ket{0}$ and $\\ket{1}$ to two new states, $\\ket{+}$ and $\\ket{-}$, often referred to as the Hadamard basis. This operator is particularly important in quantum computing as it creates superpositions of states, enabling the parallelism that is a feature of quantum computation. From a mathematical perspective, it operates as follows:\n",
        "\n",
        "$$\n",
        "H\\ket{0} = \\ket{+} = \\frac{1}{\\sqrt{2}} \\begin{bmatrix} 1 \\\\ 1 \\end{bmatrix}, \\:\n",
        "H\\ket{1} = \\ket{-} = \\frac{1}{\\sqrt{2}} \\begin{bmatrix} 1 \\\\ -1 \\end{bmatrix}\n",
        "$$\n",
        "\n",
        "The Hadamard matrix is given by:\n",
        "\n",
        "$$\n",
        "H = \\frac{1}{\\sqrt{2}} \\begin{bmatrix} 1 & 1 \\\\ 1 & -1 \\end{bmatrix}\n",
        "$$\n",
        "\n",
        "The Hadamard gate is extremely useful because it transforms a computational basis state into an equal superposition of both basis states. For example, applying the Hadamard gate to the state $\\ket{0}$ creates a state that has an equal probability of being measured as $\\ket{0}$ or $\\ket{1}$, each with a probability of 50%.\n",
        "\n",
        "Finally, the **phase operator** is used to introduce a phase shift to the qubit's state, rotating it by $\\pi/2$ around the z-axis of the Bloch sphere. This operator is important for adjusting the relative phases of quantum states, which plays a critical role in quantum interference and algorithms such as quantum phase estimation. The phase operator, often denoted by $S$, is represented as:\n",
        "\n",
        "\n",
        "$$\n",
        "S = \\begin{bmatrix} 1 & 0 \\\\ 0 & i \\end{bmatrix} \\\\\n",
        "$$\n",
        "\n",
        "The action of the phase operator is to multiply the $\\ket{1}$ state by a factor of $i$, leaving the $\\ket{0}$ state unchanged. This phase shift does not affect the probability of measuring a qubit in the computational basis, but it is essential for creating interference effects in quantum algorithms. Typically, it is used in combination with other operators to manipulate quantum states in more complex ways.\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UIqXeRF4h1fy"
      },
      "source": [
        "### Qubit\n",
        "\n",
        "The qubit is the fundamental unit of quantum computation and serves as the quantum counterpart to the classical bit. However, unlike a classical bit, which can only exist in one of two states ($0$ or $1$) at a time, a qubit exhibits a unique property known as superposition. This allows a qubit to exist simultaneously in both states, $0$ and $1$, with specific complex coefficients that determine the probability amplitudes of each state when measured. Mathematically, a qubit $\\ket{\\psi}$ is represented as a superposition of the basis states $\\ket{0}$ and $\\ket{1}$, which are the computational basis states of the qubit:\n",
        "\n",
        "$$\n",
        "\\ket{0} = \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix}, \\:\n",
        "\\ket{1} = \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix} \\\\\n",
        "\\ket{\\psi} = \\alpha \\ket{0} + \\beta \\ket{1}, \\:\n",
        "\\alpha, \\beta \\in \\mathbb{C}\n",
        "$$\n",
        "\n",
        "An alternative and visual representation of a qubit is the Bloch sphere. The Bloch sphere provides a geometric model for the state of a qubit as a point on the surface of a unit sphere in three-dimensional space. In this representation, any pure state of a qubit can be described by two angles, $\\theta$ and $\\phi$, which are defined relative to the computational basis state $\\ket{0}$ and the x-axis of the sphere, respectively. The state of the qubit is then written as:\n",
        "\n",
        "$$\n",
        "\\ket{\\psi} = \\cos \\frac{\\theta}{2} \\ket{0} + e^{i \\phi} \\sin \\frac{\\theta}{2} \\ket{1}\n",
        "$$\n",
        "\n",
        "In this expression, $\\theta$ is the angle between the state vector and the z-axis, and $\\phi$ is the angle in the xy-plane. As with the previous representation, this vector must also satisfy the normalization condition, ensuring the qubit remains a unit vector:\n",
        "\n",
        "$$\n",
        "\\cos^2{\\frac{\\theta}{2}} + \\sin^2 {\\frac{\\theta}{2}} = 1\n",
        "$$\n",
        "\n",
        "The Bloch sphere provides an intuitive way to visualize quantum operations such as rotations, which are represented by operators like the Pauli-X, Pauli-Y, and Pauli-Z gates. These gates correspond to rotations of the qubit around the axes of the Bloch sphere, allowing for transformations between different quantum states."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kY0y2NqCjAnN"
      },
      "source": [
        "Let's examine the representation of $\\ket{+}$  state on the Bloch sphere."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 536
        },
        "id": "8a6gFaRHi_pY",
        "outputId": "02aee67c-bc33-4077-a7ad-dba585744157"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {},
          "execution_count": 5
        }
      ],
      "source": [
        "coords = [1, np.pi / 2, 0] # [radius, theta, phi]\n",
        "# Plot Block sphere representation\n",
        "plot_bloch_vector(coords, coord_type=\"spherical\")"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "As shown above, on the Bloch sphere, $\\ket{+}$ state corresponds to a point on the equator with $\\theta = \\pi/2$ and $\\phi = 0$, making it a balanced superposition of $\\ket{0}$ and $\\ket{1}$ states."
      ],
      "metadata": {
        "id": "1SHdI_cs3rFc"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p2UUb_bfjiql"
      },
      "source": [
        "### Quantum gates\n",
        "\n",
        "In quantum computing, the operators discussed earlier are referred to as quantum gates. These gates are the building blocks of quantum circuits and are used to manipulate qubits by applying specific transformations. Each quantum gate is typically represented by a labeled square in circuit diagrams, where the label corresponds to the operator being applied. To understand the practical implementation of quantum gates, we can design and simulate quantum circuits using tools like **Qiskit**, an open-source quantum computing framework. Qiskit allows us to define circuits, apply quantum gates, and simulate their behavior."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 191
        },
        "id": "h-vaBlkbj0BA",
        "outputId": "e5885794-c2f4-4e31-c771-f1c3a3e43533"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 423.588x200.667 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {},
          "execution_count": 6
        }
      ],
      "source": [
        "# Qiskit circuit example\n",
        "q_circuit = QuantumCircuit(2)\n",
        "q_circuit.h(0)\n",
        "q_circuit.x(1)\n",
        "q_circuit.x(0)\n",
        "q_circuit.y(1)\n",
        "q_circuit.h(0)\n",
        "q_circuit.draw(\"mpl\", initial_state=True)"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "In the experiment we are conducting, we begin with an initial quantum state $\\ket{\\psi_0}$, which is a two-qubit state:\n",
        "\n",
        "$$\n",
        "\\ket{\\psi_0} = \\ket{0} \\otimes \\ket{0}\n",
        "$$\n",
        "\n",
        "This represents both qubits initialized to the computational basis state $\\ket{0}$. Next, we design a quantum circuit by applying a sequence of gate operations to the qubits in a defined order. For this specific circuit, the resulting state of the system is:\n",
        "\n",
        "$$\n",
        "\\ket{\\psi_f} = (H \\otimes I)(X \\otimes Y)(H \\otimes X)\\ket{\\psi_0}\n",
        "$$"
      ],
      "metadata": {
        "id": "56lyjRpUXNRb"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SmD07-oxkCf0"
      },
      "source": [
        "#### Controlled gates\n",
        "\n",
        "Controlled gates are a fundamental component of quantum circuits. These gates operate conditionally, applying their effect to a target qubit only when one or more designated control qubits are in a specific state, typically $\\ket{1}$. This conditional behavior enables the implementation of more complex operations and logical constructs, making controlled gates essential for quantum computation. One of the most widely used controlled gates is the **Controlled-NOT** (CNOT) gate. The CNOT gate flips the state of the target qubit (applies the Pauli-X operation) if and only if the control qubit is in the state $\\ket{1}$. When expressed in matrix form, the CNOT operation is represented as:\n",
        "\n",
        "$$\n",
        "CNOT = \\begin{bmatrix} 1 & 0 & 0 & 0 \\\\ 0 & 1 & 0 & 0 \\\\ 0 & 0 & 0 & 1 \\\\ 0 & 0 & 1 & 0 \\end{bmatrix}\n",
        "$$\n",
        "\n",
        "Below there is an example of a quantum circuit in Qiskit that shows the use of controlled gates."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 191
        },
        "id": "dchQxyeyj-4o",
        "outputId": "9687fe02-1d50-4bec-a9d8-ad837eba7e1a"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 423.588x200.667 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {},
          "execution_count": 7
        }
      ],
      "source": [
        "# Qiskit CNOT circuit\n",
        "q_circuit = QuantumCircuit(2)\n",
        "q_circuit.x(0)\n",
        "q_circuit.cx(0, 1)\n",
        "q_circuit.x(0)\n",
        "q_circuit.draw(\"mpl\", initial_state=True)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DpLD_iwblC7v"
      },
      "source": [
        "#### Quantum algorithms\n",
        "\n",
        "In quantum computing, we utilize unitary operators to manipulate the state of qubits, transforming the quantum system in controlled ways. A quantum algorithm is essentially a structured sequence of such unitary operations, designed to evolve an initial quantum state into a final state that encodes the solution to a specific problem. Mathematically, the process can be expressed as:\n",
        "\n",
        "$$\n",
        "\\ket{\\psi_n} = U_n U_{n-1} \\dots U_1 \\ket{\\psi_0}\n",
        "$$\n",
        "\n",
        "where:\n",
        "- $\\ket{\\psi_0}$ represents the initial state of the quantum system;\n",
        "- $U_1 U_2 \\dots U_n$ are the sequence of unitary operators (quantum gates) that define the algorithm;\n",
        "- $\\ket{\\psi_n}$ is the final state of the quantum system after the application of all operations.\n",
        "\n",
        "Once the unitary operations have been applied, the result of the algorithm is obtained through a **measurement** process, collapsing the final quantum state into one of its basis states according to the associated probabilities. This measurement reveals information about the solution to the problem the algorithm was designed to solve."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "25wHCovZlROR"
      },
      "source": [
        "### Classical Markov chains\n",
        "\n",
        "A Markov chain can be visualized as a set of nodes connected by directed links, each associated with a probability. The transition from one node to another is stochastic and governed solely by the probability distribution of the outgoing links from the current node, a feature known as the **Markovian property**. Markov chains can be categorized as discrete or continuous, depending on whether transitions occur at distinct time steps or continuously over time. For our discussion, we will focus exclusively on discrete Markov chains. The behavior of a discrete Markov chain is encapsulated in its **transition matrix**, a square matrix where the rows and columns correspond to the nodes in the chain. Each entry in the matrix specifies the probability of transitioning from one node to another. In addition, it is fundamental in determining the probability distribution of the system after $t$ steps, achieved by raising the transition matrix to the power $t$, denoted as $P^{t}$. This iterative multiplication allows us to track how probabilities evolve over time. For example, a transition matrix for a four-node Markov chain might look like this:\n",
        "\n",
        "$$\n",
        "P = \\begin{pmatrix}\n",
        "0.1 & 0.4 & 0.4 & 0.1 \\\\\n",
        "0.2 & 0.3 & 0.2 & 0.0 \\\\\n",
        "0.6 & 0.2 & 0.1 & 0.1 \\\\\n",
        "0.1 & 0.1 & 0.3 & 0.8 \\\\\n",
        "\\end{pmatrix}\n",
        "$$\n",
        "\n",
        "Each row in this matrix represents the probabilities of transitioning from the corresponding node to all other nodes. The sum of the probabilities in each row equals $1$, reflecting the fact that the system must pass trought to one of the available states.\n",
        "\n",
        "Below there is an example of a classical Markov chain implemented using the NetworkX library."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 516
        },
        "id": "r6OBp35pn2ta",
        "outputId": "3aeed905-94fc-424c-a3bb-b13f319f70d8"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# Define the positions of the nodes in the graph\n",
        "pos = {1: [0.75, 1.0], 2: [0.75, 0.15], 3: [0.5, -0.5], 4: [1.0, -0.5]}\n",
        "# Define the transition matrix U for the directed graph\n",
        "U = [[0.1, 0.2, 0.6, 0.1],\n",
        "     [0.4, 0.3, 0.2, 0.1],\n",
        "     [0.4, 0.2, 0.1, 0.3],\n",
        "     [0.1, 0.0, 0.1, 0.8],]\n",
        "# Create a directed graph using NetworkX\n",
        "G = nx.DiGraph(directed=True)\n",
        "for i in range(1, 5):\n",
        "    G.add_node(i)\n",
        "    for j in range(1, 5):\n",
        "        G.add_edge(i, j, weight=U[i - 1][j - 1])\n",
        "# Draw the graph\n",
        "nx.draw(G, pos=pos, with_labels=True)\n",
        "nx.draw_networkx_edge_labels(G, pos=pos, edge_labels=nx.get_edge_attributes(G, \"weight\"))\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The following code provides a simulation of a classical random walk, where a walker takes a series of steps along a one-dimensional line. The direction of each step is determined by flipping a weighted coin with a specified probability of stepping to the right (`p`). The `random_walk` function calculates the final position of the walker after a defined number of steps (`n_steps`) starting from an initial position. Additionally, the `plot_rw_distribution` function visualizes the distribution of outcomes over multiple runs of the random walk, providing insight into the behavior of the random walk over time."
      ],
      "metadata": {
        "id": "waAYehgAk_Q1"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "id": "uzPncVvSsOUi"
      },
      "outputs": [],
      "source": [
        "# Random walk definition\n",
        "def random_walk(p, n_steps, initial_pos):\n",
        "    \"\"\"\n",
        "    Run a random walk with N steps and a probability of stepping to the right of p\n",
        "    Args:\n",
        "    p (float): probability of stepping to the right\n",
        "    N (int): number of steps\n",
        "    i (int): initial position\n",
        "    Returns:\n",
        "    final position of the walker\n",
        "    \"\"\"\n",
        "    position = initial_pos\n",
        "    for _ in range(n_steps):\n",
        "        coin_flip = list(np.random.choice(2, 1, p=[1 - p, p])) # flips our weighted coin\n",
        "        position += 2 * coin_flip[0] - 1 # moves the walker according to the coin flip\n",
        "    return position"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RRsVzsLos2Dm",
        "outputId": "09316496-ac7b-486a-b56d-30e3000d6667"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The walker is located at: x = -6\n"
          ]
        }
      ],
      "source": [
        "p = 0.5 # probability of the walker stepping to the right\n",
        "n_steps = 50 # number of steps the walker will take\n",
        "initial_position = 0 # initial position of the walker\n",
        "print(f\"The walker is located at: x = {random_walk(p, n_steps, initial_position)}\")"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Plot distribution of the random walk\n",
        "def plot_rw_distribution(n_runs, n_steps):\n",
        "    \"\"\"\n",
        "    Plot the distribution of the random walk\n",
        "    Args:\n",
        "    n_runs (int): number of runs\n",
        "    n_steps (int): number of steps\n",
        "    \"\"\"\n",
        "    positions = range(-1 * n_steps, n_steps + 1)\n",
        "    instances = [0 for _ in range(-1 * n_steps, n_steps + 1)]\n",
        "    for _ in range(n_runs):\n",
        "        result = random_walk(p, n_steps, initial_position)\n",
        "        instances[positions.index(result)] += 1\n",
        "    # Normalize the distribution\n",
        "    probabilities = [n / n_runs for n in instances]\n",
        "    plt.bar(positions, probabilities)\n",
        "    # Add plot styling\n",
        "    plt.title(\"Random walk distribution\", fontsize=12)\n",
        "    plt.xlabel(\"Position\", fontsize=10)\n",
        "    plt.ylabel(\"Probability\", fontsize=10)\n",
        "    plt.xticks(fontsize=8)\n",
        "    plt.yticks(fontsize=8)\n",
        "    # Show the plot\n",
        "    plt.tight_layout()\n",
        "    plt.show()"
      ],
      "metadata": {
        "id": "BGIj2IOKgH0L"
      },
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zvwEljmYtGhd"
      },
      "source": [
        "When visualized, the random walk generates the following probability distribution."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 486
        },
        "id": "4ILeRvUstNN-",
        "outputId": "195cd1de-9156-48d8-e41c-4ea867e19225"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# Plot random walk distribution\n",
        "plot_rw_distribution(n_runs=50000, n_steps=n_steps)"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "As seen in the plot above, the distribution follows a Gaussian shape because the random walk results from many independent steps, each contributing a small, random displacement. According to the central limit theorem, as the number of steps increases, the sum of these independent random steps leads to a normal distribution of positions."
      ],
      "metadata": {
        "id": "JFQtfs0blw8M"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OZXtpMDkrzrf"
      },
      "source": [
        "### Quantum walk\n",
        "\n",
        "Quantum walks serve as the quantum analog of classical Markov chains. In a classical random walk, the system takes discrete steps based on a probabilistic rule, where the future state depends only on the current state. In contrast, quantum walks exploit the principles of superposition and interference. This means that a quantum walk can explore all possible paths simultaneously, as the system exists in a superposition of all possible states. It is only upon measurement that the system collapses into one of these possible states. For instance, in a coined quantum walk, the walker's position is represented as an integer, and a \"coin\" determines whether the walker moves left or right.\n",
        "\n",
        "The quantum coin walk algorithm is essentially a quantum version of the classical coin flip walk, directly adapted to utilize quantum principles. The position of the walker is encoded in an $n$-dimensional space, which has $2^{n}$ possible positions. This space is represented by the Hilbert space $\\mathcal{H}_p = \\{\\ket{j}: j = 0, \\dots, n - 1\\}$, where each state corresponds to a specific position. In addition, to simulate the quantum flip of the coin (deciding whether to move left or right), we define an additional 2-dimensional Hilbert space $\\mathcal{H}_c = \\{\\ket{i} : i = 0, 1\\}$, where the two states $\\ket{0}$ and $\\ket{1}$ represent the two possible coin flips. The total Hilbert space of the system is the tensor product of these two spaces, $\\mathcal{H} = \\mathcal{H_c} \\otimes \\mathcal{H_p}$, where the walker's position and the coin's state are entangled. This entanglement enables the walker to be in a superposition of different positions, with the direction of movement (left or right) determined by the coin state.\n",
        "\n",
        "Regarding the coin operator, there are various ways to represent the coin, but the most commonly used operators are:\n",
        "\n",
        "$$\n",
        "\\ \\\\\n",
        "H = \\frac{1}{\\sqrt{2}} \\begin{bmatrix}\n",
        "1 & 1 \\\\\n",
        "1 & -1 \\\\\n",
        "\\end{bmatrix}\n",
        "\\\\\n",
        "\\ \\\\\n",
        "\\ \\\\\n",
        "G = \\begin{bmatrix}\n",
        "\\frac{2}{n} - 1 & \\frac{2}{n} & \\dots & \\frac{2}{n} \\\\\n",
        "\\frac{2}{n} & \\frac{2}{n} - 1 & \\dots & \\frac{2}{n} \\\\\n",
        "\\vdots & \\vdots & \\ddots & \\vdots \\\\\n",
        "\\frac{2}{n} & \\frac{2}{n} & \\dots & \\frac{2}{n} - 1 \\\\\n",
        "\\end{bmatrix}\n",
        "\\ \\\\\n",
        "$$\n",
        "\n",
        "The Hadamard gate ($H$) creates a uniform distribution over the possible outcomes of the coin flip, meaning the walker has equal probabilities to move in either direction. On the other hand, the Grover gate ($G$) is designed to produce a skewed distribution, favoring certain directions more than others.\n",
        "\n",
        "For what concerns the shift operator in a quantum coin walk, it is responsible for moving the walker to its next position based on the state of the quantum coin. Depending on whether the coin is in the $\\ket{\\downarrow}$ state (corresponding to $\\ket{0}$) or the $\\ket{\\uparrow}$ state (corresponding to $\\ket{1}$), the walker moves to the left or right, respectively. The action of the shift operator on a position and coin state can be defined as follows:\n",
        "\n",
        "$$\n",
        "S(\\ket{0} \\otimes \\ket{j}) = \\ket{0} \\otimes \\ket{j-1}, \\:\n",
        "S(\\ket{1} \\otimes \\ket{j}) = \\ket{1} \\otimes \\ket{j+1}\n",
        "$$\n",
        "\n",
        "Notice that the shift operator does not alter the state of the coin. It only acts on the position state, shifting it left or right based on the coin's state. This property can be formalized in the following operator construction:\n",
        "\n",
        "$$\n",
        "S = \\ket{1}\\bra{1} \\otimes \\sum_j \\ket{j + 1}\\bra{j} + \\ket{0}\\bra{0} \\otimes \\sum_j \\ket{j - 1}\\bra{j} \\\\\n",
        "$$\n",
        "\n",
        "This expression shows that the shift operator consists of two parts: one that shifts the position to the right when the coin is in the $\\ket{1}$ state and another that shifts the position to the left when the coin is in the $\\ket{0}$ state.\n",
        "\n",
        "To summarize, the quantum walk operator is constructed by combining the coin operator and the shift operator as follows:\n",
        "\n",
        "$$\n",
        "U = S \\cdot (C \\otimes I)\n",
        "$$\n",
        "\n",
        "where, $S$ is the shift operator, $C$ is the chosen coin operator, and the identity operator $I$ is included to preserve the walker's state during the coin operation.\n",
        "\n",
        "The principles underlying classical Markov chains can be directly extended to quantum walks. In a quantum walk, the evolution of the system over multiple steps is determined by repeatedly applying the quantum walk operator $U$. Specifically, to compute the state of the system after $t$ steps, the operator $U$ is applied $t$ times, resulting in $U^{t}$, which is the $t$-th power of the operator. If the initial state of the system is represented as $\\ket{\\psi_0}$, the state of the system after $t$ steps is expressed as:\n",
        "\n",
        "$$\n",
        "\\ket{\\psi(t)} = U^t\\ket{\\psi(0)}\n",
        "$$\n",
        "\n",
        "Now, let us consider an example of a coined quantum walk. Suppose the walker's initial position is $\\ket{0}$, and a Hadamard gate is used as the coin operator, starting with the coin in the $\\ket{0}$ state. The state evolution after the first step can be calculated as follows:\n",
        "\n",
        "$$\n",
        "\\begin{array}{ll}\n",
        "\\ket{\\psi(1)} &= U\\ket{\\psi(0)} = S \\cdot (C \\otimes I)\\ket{\\psi(0)} = S \\cdot (H \\otimes I)(\\ket{0} \\otimes \\ket{0}) = S \\cdot (\\frac{1}{\\sqrt{2}}(\\ket{0} + \\ket{1}) \\otimes \\ket{0}) \\\\\n",
        "&= (\\ket{1}\\bra{1} \\otimes \\sum_j \\ket{j + 1}\\bra{j})(\\frac{1}{\\sqrt{2}}(\\ket{0} + \\ket{1}) \\otimes \\ket{0}) + (\\ket{0}\\bra{0} \\otimes \\sum_j \\ket{j - 1}\\bra{j}) (\\frac{1}{\\sqrt{2}}(\\ket{0} + \\ket{1}) \\otimes \\ket{0}) \\\\\n",
        "&= \\frac{1}{\\sqrt{2}}\\ket{1} \\otimes \\ket{1} + \\frac{1}{\\sqrt{2}}\\ket{0} \\otimes \\ket{-1} = \\frac{1}{\\sqrt{2}}(\\ket{1} \\otimes \\ket{1} + \\ket{0} \\otimes \\ket{-1}) \\\\\n",
        "\\end{array}\n",
        "$$\n",
        "\n",
        "As demonstrated above, the Hadamard gate functions as the coin operator, generating a superposition of the coin states. Following this, the shift operator moves the walker to the corresponding positions determined by the state of the coin. The final state is a superposition of the walker located at positions $\\ket{1}$ and $\\ket{-1}$, weighted equally by the coefficients $1/\\sqrt{2}$."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bWChrBikDena"
      },
      "source": [
        "### Quantum coined walk: Qiskit implementation\n",
        "\n",
        "To implement a quantum coined walk in a circuit, the following components are required:\n",
        "\n",
        "- a single qubit to represent the coin: the coin states are encoded as $\\ket{0}$ and $\\ket{1}$, corresponding to $\\downarrow$ (move left) and $\\uparrow$ (move right), respectively;\n",
        "- $n$ qubits to represent the walker position: with $n$ qubits, the walker can occupy $2^{n}$ distinct positions which are encoded in binary format. In this representation, the most significant bit (MSB) is positioned at the top of the qubit register. For example, a 3-qubit system could represent positions ranging from $\\ket{000}$(position 0) to $\\ket{111}$ (position 7);\n",
        "- $n$ classical bits to store the measurement results of the walker's position: after the quantum operations are completed, measurements collapse the walker's position into a classical state, which is then stored using $n$ classical bits."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "id": "8IYFT6QcDy4R"
      },
      "outputs": [],
      "source": [
        "def coined_walk_circuit(n_qubits):\n",
        "    \"\"\"\n",
        "    Create a quantum circuit for the quantum walk\n",
        "    Args:\n",
        "    n_qubits (int): number of qubits used to represent the position of the walker\n",
        "    Returns:\n",
        "    circuit, walker qubits, coin qubits and classical register to store the output\n",
        "    \"\"\"\n",
        "    walker_r = QuantumRegister(n_qubits, name=\"q\")\n",
        "    coin_r = QuantumRegister(1, name=\"c\") # coin requires only one qubit\n",
        "    classic_r = ClassicalRegister(n_qubits, name=\"r\")\n",
        "    q_circuit = QuantumCircuit(walker_r, coin_r, classic_r)\n",
        "    return q_circuit, walker_r, coin_r, classic_r"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Q665dHkZyyIR"
      },
      "source": [
        "The initial state of the circuit is flexible and can be set arbitrarily. The coin state can be initialized as either $\\ket{0}$ or $\\ket{1}$, while the walker's position can be any value between $0$ and $2^{n} - 1$. However, for convenience, it is often practical to start with the walker positioned near the center of the range, at $2^{n - 1}$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "id": "cvOVZfLw6X47"
      },
      "outputs": [],
      "source": [
        "n_qubits = 4 # number of qubits used to represent the position of the walker\n",
        "n_steps = 3 # number of steps of the quantum walk\n",
        "initial_position = 2 ** (n_qubits - 1) # initial position of the walker is the middle of all possible positions\n",
        "initial_coin_value = 0 # initial value of the coin is 0\n",
        "n_runs = 50000 # number of runs of the quantum circuit"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "id": "AqfTag0cy4wo"
      },
      "outputs": [],
      "source": [
        "def initialize_coined_walk(q_circuit, n_qubits, walker_r, coin_r, initial_position, initial_coin_value):\n",
        "    \"\"\"\n",
        "    Initialize the circuit with the initial position of the walker and the initial value of the coin\n",
        "    Args:\n",
        "    q_circuit (QuantumCircuit): quantum circuit\n",
        "    n_qubits (int): number of qubits used to represent the position of the walker\n",
        "    walker_r (QuantumRegister): quantum register containing the walker's position qubits\n",
        "    coin_r (QuantumRegister): quantum register containing the coin qubit\n",
        "    initial_position (int): initial position of the walker\n",
        "    initial_coin_value (int): initial value of the coin\n",
        "    Returns:\n",
        "    Initialized quantum circuit\n",
        "    \"\"\"\n",
        "    if initial_coin_value == 1:\n",
        "        q_circuit.x(coin_r)\n",
        "    for i in range(n_qubits):\n",
        "        if initial_position & (1 << i):\n",
        "            q_circuit.x(walker_r[n_qubits - i - 1])\n",
        "    q_circuit.barrier()\n",
        "    return q_circuit"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TI-YH0Ll0EXh"
      },
      "source": [
        "For the coin operator, the Hadamard gate is the best choice when the initial state of the coin is unknown or cannot be inferred. It creates a superposition of states, ensuring an equal probability of moving in either direction. However, if the initial state of the coin is known, the circuit can be directly initialized to that state using $X$ gates or other appropriate operations, eliminating the need for the Hadamard gate in those cases. To complement the coin operation, the shift operator moves the walker to the appropriate position based on the state of the coin. Specifically, the shift operator must increment or decrement the walker's position depending on whether the coin is in state $\\ket{1}$ or $\\ket{0}$, respectively. This behavior can be implemented using an addition operator $A$, which increments the walker's position, controlled by the coin's state. Since quantum operations are unitary, constructing a corresponding subtraction operator $A^\\dagger$ is straightforward once the addition operator $A$ is defined. The properties of $A$ and its adjoint $A^\\dagger$ are as follows:\n",
        "\n",
        "- $A: \\mathcal{H} \\to \\mathcal{H}: A\\ket{j} = \\ket{j + 1}$ (increments the position);\n",
        "- $A^\\dagger$ satisfies $A^\\dagger A = I$, making it unitary;\n",
        "- From $A^\\dagger A \\ket{j} = A^\\dagger \\ket{j + 1}$, it follows that $A^\\dagger \\ket{k} = \\ket{k - 1}$ (decrements the position).\n",
        "\n",
        "These components combine to define the quantum walk operator $U$, which integrates the coin and shift operations. The quantum walk operator is expressed as:\n",
        "\n",
        "$$\n",
        "U = S \\cdot (C \\otimes I)\n",
        "$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {
        "id": "_Eo7FjT30XGl"
      },
      "outputs": [],
      "source": [
        "def coined_walk_step(q_circuit, walker_r, coin_r):\n",
        "    \"\"\"\n",
        "    Single step of the quantum walk\n",
        "    Args:\n",
        "    q_circuit (QuantumCircuit): quantum circuit\n",
        "    walker_r (QuantumRegister): quantum register containing the walker's position qubits\n",
        "    coin_r (QuantumRegister): quantum register containing the coin qubit\n",
        "    Returns:\n",
        "    Quantum circuit with an added walk step\n",
        "    \"\"\"\n",
        "    # Flip the coin vector\n",
        "    q_circuit.h(coin_r)\n",
        "    # Implement the addition operator\n",
        "    for i in reversed(range(len(walker_r))):\n",
        "        # Qubits with less significant bits than the current one\n",
        "        controls = [walker_r[v] for v in range(len(walker_r) - 1, i, -1)]\n",
        "        controls.append(coin_r) # coin qubit is also used as a control\n",
        "        q_circuit.mcx(controls, walker_r[i]) # multi-controlled X gate\n",
        "        if i != 0:\n",
        "            q_circuit.x(walker_r[i]) # flip the qubit\n",
        "    # Switch the coin vector\n",
        "    q_circuit.x(coin_r)\n",
        "    # Implement the subtraction operator\n",
        "    for i in range(len(walker_r)):\n",
        "        if i != 0:\n",
        "            q_circuit.x(walker_r[i]) # reverse the flip\n",
        "        # Qubits with less significant bits than the current one\n",
        "        controls = [walker_r[v] for v in range(len(walker_r) - 1, i, -1)]\n",
        "        controls.append(coin_r) # coin qubit is also used as a control\n",
        "        q_circuit.mcx(controls, walker_r[i]) # multi-controlled X gate\n",
        "    # Revert the switch of the coin vector\n",
        "    q_circuit.x(coin_r)\n",
        "    return q_circuit"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 328
        },
        "id": "9OSr37sv6gci",
        "outputId": "4d0a7d18-0a6a-47ff-e8ec-c1c42a823554"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 1594.35x535.111 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {},
          "execution_count": 17
        }
      ],
      "source": [
        "# Define coined walk step\n",
        "q_circuit, walker_r, coin_r, _ = coined_walk_circuit(n_qubits)\n",
        "q_circuit = coined_walk_step(q_circuit, walker_r, coin_r)\n",
        "# Draw coined walk step\n",
        "q_circuit.draw(output=\"mpl\", initial_state=True)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "C88O8vuO19Un"
      },
      "source": [
        "With all the necessary operators defined, the circuit is constructed by repeatedly applying the single-step operator for the desired number of iterations. After completing the iterations, the walker's position is measured, and the outcome is stored in the classical bits. It is important to note that measuring the circuit after each step, collapsing its state, would reduce the process to a classical random walk.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "id": "38W0CQ9614xd"
      },
      "outputs": [],
      "source": [
        "def coined_walk(n_qubits, n_steps, initial_position, initial_coin_value, init_func):\n",
        "    \"\"\"\n",
        "    Create a quantum circuit for the quantum walk\n",
        "    Args:\n",
        "    n_qubits (int): number of qubits used to represent the position of the walker\n",
        "    n_steps (int): number of steps of the quantum walk\n",
        "    initial_position (int): initial position of the walker\n",
        "    initial_coin_value (int): initial value of the coin\n",
        "    init_func (Callable): function used to initialize the circuit\n",
        "    Returns:\n",
        "    Quantum circuit for the quantum walk\n",
        "    \"\"\"\n",
        "    q_circuit, walker_r, coin_r, classic_r = coined_walk_circuit(n_qubits)\n",
        "    q_circuit = init_func(q_circuit, n_qubits, walker_r, coin_r, initial_position, initial_coin_value)\n",
        "    for i in range(n_steps):\n",
        "        step_gate = coined_walk_step(QuantumCircuit(walker_r, coin_r), walker_r, coin_r)\n",
        "        q_circuit.append(step_gate.to_gate(label=f\"Step #{i + 1}\"), walker_r[:] + coin_r[:])\n",
        "    q_circuit.barrier()\n",
        "    q_circuit.measure(walker_r, reversed(classic_r))\n",
        "    return q_circuit"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 409
        },
        "id": "mK7V58vi5tx0",
        "outputId": "d5f271e2-c27e-41f2-dc52-2a02e33831bd"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 1259.9x535.111 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {},
          "execution_count": 19
        }
      ],
      "source": [
        "# Define QW circuit\n",
        "q_circuit = coined_walk(n_qubits, n_steps, initial_position,\n",
        "                        initial_coin_value, initialize_coined_walk)\n",
        "# Draw QW circuit\n",
        "q_circuit.draw(output=\"mpl\", initial_state=True)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EH5ttB1Ys95b"
      },
      "source": [
        "Unlike a classical random walk, the results of this quantum circuit exhibit a clear bias toward one side of the graph. If the initial state of the coin is inverted, the resulting distribution will also flip, reflecting the opposite bias. This behavior arises from the repeated application of the Hadamard gate, which introduces interference patterns. Depending on whether the coin begins in the state $\\ket{0}$ or $\\ket{1}$, these interference effects create a bias in the walker's movement, skewing the results accordingly."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {
        "id": "lt7BALphtf17"
      },
      "outputs": [],
      "source": [
        "def plot_results(q_circuit, n_runs, title):\n",
        "    \"\"\"\n",
        "    Plot the results of the quantum walk\n",
        "    Args:\n",
        "    q_circuit: quantum circuit for the quantum walk\n",
        "    n_runs: number of runs of the quantum circuit\n",
        "    Returns:\n",
        "    histogram of the results of the quantum walk\n",
        "    \"\"\"\n",
        "    # Aer simulation\n",
        "    simulator = AerSimulator()\n",
        "    # Transpile before execute\n",
        "    transpiled_qc = transpile(q_circuit, simulator, optimization_level=3)\n",
        "    # Run and get counts\n",
        "    results = simulator.run(transpiled_qc, shots=n_runs).result()\n",
        "    counts = results.get_counts(transpiled_qc)\n",
        "    counts = {int(k, 2): v for k, v in counts.items()}\n",
        "    return plot_histogram(counts, title=title)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {
        "id": "5Wbt1J3Yw3Eh"
      },
      "outputs": [],
      "source": [
        "# Augmented number of steps for our simulation\n",
        "n_steps = 5000\n",
        "# Define QW circuit\n",
        "q_circuit = coined_walk(n_qubits, n_steps, initial_position,\n",
        "                        initial_coin_value, initialize_coined_walk)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 460
        },
        "id": "J_3Pqp9KuCrY",
        "outputId": "6b65d456-9701-4272-d6e0-8a537bb390cc"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {},
          "execution_count": 22
        }
      ],
      "source": [
        "# Plot simulation results\n",
        "plot_results(q_circuit, n_runs, \"Quantum coined walk\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7J4rd58wxx5a"
      },
      "source": [
        "The above plot clearly illustrates the previously stated behavior. To provide a clearer understanding of the observed bias, let us perform some calculations to analyze it in detail. In fact, starting from the initial state $\\ket{\\psi(0)} = \\ket{0} \\otimes \\ket{0}$, the first iteration of the operator will result in the state $\\ket{\\psi(1)} = \\frac{1}{\\sqrt{2}}(\\ket{1} \\otimes \\ket{1} + \\ket{0} \\otimes \\ket{-1})$. Going through the same process, the state after $t$ iterations will be:\n",
        "\n",
        "$$\n",
        "\\begin{array}{ll}\n",
        "\\ket{\\psi(0)} &= \\ket{0} \\otimes \\ket{0} \\\\\n",
        "\\ket{\\psi(1)} &= \\frac{1}{\\sqrt{2}}(\\ket{1} \\otimes \\ket{1} + \\ket{0} \\otimes \\ket{-1}) \\\\\n",
        "\\ket{\\psi(2)} &= \\frac{1}{2}(-\\ket{1} \\otimes \\ket{-2} + (\\ket{0} + \\ket{1})\\ket{0} + \\ket{0} \\otimes \\ket{2}) \\\\\n",
        "\\ket{\\psi(3)} &= \\frac{1}{2\\sqrt{2}}(\\ket{1}\\ket{-3} - \\ket{0}\\ket{-1} + (2\\ket{0} + \\ket{1})\\ket{1} - \\ket{0}\\ket{3}) \\\\\n",
        "\\end{array}\n",
        "$$\n",
        "\n",
        "This few iterations are enough to see that the state is not balanced: the probability of finding the walker in the position $\\ket{1}$ is $\\left(\\frac{2 + 1}{2\\sqrt{2}}\\right)^2 = \\frac{5}{8}$, significantly higher compared to the probability of $\\frac{1}{8}$ for all other positions."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cowk6KsdygrY"
      },
      "source": [
        "#### Balanced coin\n",
        "\n",
        "To eliminate this bias, we can either use a different coin operator or ensure that the initial state of the coin is set to $\\frac{1}{\\sqrt{2}}(\\ket{0} + i \\ket{1})$. In fact, it ensures balance because the relative phase $i$ between $\\ket{0}$ and $\\ket{1}$ offsets the interference effects caused by the Hadamard gate. When the Hadamard gate acts on this state:\n",
        "\n",
        "$$\n",
        "H(\\frac{1}{\\sqrt{2}}(\\ket{0} + i \\ket{1})) = \\frac{1}{\\sqrt{2}} (H \\ket{0} + iH \\ket{1}) = \\frac{1}{2} ((\\ket{0} + \\ket{1}) + i(\\ket{0} - \\ket{1})) = \\frac{1}{\\sqrt{2}}(\\ket{0} + i \\ket{1})\n",
        "$$\n",
        "\n",
        "showing that the state remains unchanged. This balanced state prevents the skew caused by interference in the walk. To prepare it, applying a Hadamard gate followed by an $S$ gate achieves the desired $\\frac{1}{\\sqrt{2}}(\\ket{0} + i \\ket{1})$. This approach removes the bias introduced by starting with $\\ket{0}$ or $\\ket{1}$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {
        "id": "rjLersO9yzxC"
      },
      "outputs": [],
      "source": [
        "def initialize_balanced_coined_walk(q_circuit, n_qubits, walker_r, coin_r, initial_position, initial_coin_value):\n",
        "    \"\"\"\n",
        "    Initialize the circuit with the initial position of the walker and the initial value of the coin\n",
        "    Set the coin qubit to \\ket{+} and apply the S gate to it to make sure that the coin operator keeps being balanced\n",
        "    Args:\n",
        "    q_circuit (QuantumCircuit): quantum circuit\n",
        "    walker_r (QuantumRegister): quantum register containing the walker's position qubits\n",
        "    coin_r (QuantumRegister): quantum register containing the coin qubit\n",
        "    initial_position (int): initial position of the walker\n",
        "    initial_coin_value (int): initial value of the coin\n",
        "    Returns:\n",
        "    Initialized quantum circuit\n",
        "    \"\"\"\n",
        "    if initial_coin_value == 1:\n",
        "        q_circuit.x(coin_r)\n",
        "    q_circuit.h(coin_r)\n",
        "    q_circuit.s(coin_r)\n",
        "    for i in range(n_qubits):\n",
        "        if initial_position & (1 << i):\n",
        "            q_circuit.x(walker_r[n_qubits - i - 1])\n",
        "    q_circuit.barrier()\n",
        "    return q_circuit"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {
        "id": "U5GbuYiy0p0v"
      },
      "outputs": [],
      "source": [
        "n_qubits = 4 # number of qubits used to represent the position of the walker\n",
        "n_steps = 3 # number of steps of the quantum walk\n",
        "initial_position = 2 ** (n_qubits - 1) # initial position of the walker is the middle of all possible positions\n",
        "initial_coin_value = 0 # initial value of the coin is 0\n",
        "n_runs = 50000 # number of runs of the quantum circuit"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 385
        },
        "id": "CYO5EAY00LGz",
        "outputId": "e67ffbae-4f1d-4e42-a2de-72f045e1a710"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 1343.51x535.111 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {},
          "execution_count": 25
        }
      ],
      "source": [
        "# Balanced QW circuit\n",
        "q_circuit_b = coined_walk(n_qubits, n_steps, initial_position,\n",
        "                          initial_coin_value, initialize_balanced_coined_walk)\n",
        "# Draw balanced QW circuit\n",
        "q_circuit_b.draw(output=\"mpl\", initial_state=True)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 460
        },
        "id": "BNKRm0Mz0x40",
        "outputId": "ddf521b0-b413-4a03-931c-e04f01a93bbe"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {},
          "execution_count": 26
        }
      ],
      "source": [
        "# Augmented number of steps for our simulation\n",
        "n_steps = 1000\n",
        "# Define balanced QW circuit\n",
        "q_circuit_b = coined_walk(n_qubits, n_steps, initial_position,\n",
        "                          initial_coin_value, initialize_balanced_coined_walk)\n",
        "plot_results(q_circuit_b, n_runs, \"Balanced quantum coined walk\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ojfu8Tno3QMu"
      },
      "source": [
        "Using a balanced coin, leads to a less skewed distribution with reduced bias. However, achieving a distribution that is more uniform across all states requires significantly more steps $t$, as the walk needs additional time to fully explore the space and reduce the influence of initial conditions. When compared to the classical random walk, the quantum coined walk exhibits significant differences in its results, notably lacking the Gaussian properties of its classical counterpart. This divergence makes the statistical analysis of its behavior more complex. However, it can be proven that the standard deviation of the quantum walk's distribution, representing its width, grows linearly with the number of steps $t$, while the classical random walk only achieves a standard deviation of $\\sqrt{t}$."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5ylc2xjE3YNw"
      },
      "source": [
        "### Quantum walk on a hypercube: Qiskit implementation\n",
        "\n",
        "The quantum random walk can be applied to explore the vertices of a hypercube, which is a highly structured graph. A hypercube of degree $n$ consists of $2^{n}$ vertices, with each vertex representing a distinct binary string of length $n$. Each vertex is connected to others that differ by exactly one bit, meaning that each vertex has $n$ neighbors. These connections form a regular graph, where the edges correspond to flipping a single bit in the binary representation of the vertices.\n",
        "\n",
        "> _Example_\n",
        ">\n",
        "> A 4-dimensional hypercube consists of $2^{4} = 16$ vertices. The neighbors of the vertex $\\ket{0101}$ are the vertices that differ from it by exactly one bit. These neighboring vertices are $\\ket{1101}$, $\\ket{0001}$, $\\ket{0111}$, and $\\ket{0110}$. Each of these vertices is adjacent to $\\ket{0101}$ in the hypercube structure, as they can be obtained by flipping a single bit in the binary representation of $\\ket{0101}$.\n",
        "\n",
        "In the context of a quantum walk on a hypercube, the walker can move between these vertices by applying quantum operations, such as a coin operator and shift operator. The movement is governed by the superposition principle, where the walker can be in a superposition of multiple vertices at once, and measurement collapses the superposition to one of the possible vertices. The walk progresses by applying these quantum operations iteratively, exploring the vertices of the hypercube in a manner that exploits quantum interference and coherence.\n",
        "\n",
        "Below is a hypercube graph visualized using the NetworkX tool, which helps in better understanding its structure and formation.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 27,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 516
        },
        "id": "Cd3aoDyqD4P4",
        "outputId": "c8229467-5f7a-4479-f451-402db6fc83fd"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAApQAAAHzCAYAAACe1o1DAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy81sbWrAAAACXBIWXMAAA9hAAAPYQGoP6dpAABJOklEQVR4nO3de3DU9b3/8dduliRNsktIiFCqqCfKRUFE58iM2qJUp+ioHWihcrHQeuVUPW3pGa2lWqw/j1Y7ta2Cl1qlAnKsl+qpxXY4gqVUawsFBUQuKoIKxFzckJDE3f3+/qC77C0he/1+vvt9PmYyo5vNdz9Zsu88893d79djWZYlAAAAIEteuxcAAAAAZyMoAQAAkBOCEgAAADkhKAEAAJATghIAAAA5ISgBAACQE4ISAAAAOSEoAQAAkBOCEgAAADkhKAEAAJATghIAAAA5ISgBAACQE4ISAAAAOSEoAQAAkBOCEgAAADnx2b0AALCbZVkKh8Pq7u6OfYRCIVmWFfvweDyxD5/Pp4qKithHWVmZPB6P3d8GANjGY1mWZfciAKDYenp6dPDgwVhARiKRrLfl9XpjcVlTU6Py8vI8rhQAzEdQAnANy7LU0dGhYDCorq6ugt1OZWWlAoGAqqur2XMJwBUISgAlLxQKKRgMKhgM5rQnMlNer1eBQECBQEA+H68wAlC6CEoAJSsSiai5uVnt7e12L0V+v1/19fXyenkvJIDSQ1ACKEmdnZ1qampSOBy2eykxZWVlamhoUFVVld1LAYC8IigBlBST9kr2hr2VAEoNQQmgZJi4V7I37K0EUEoISgAloa2tTS0tLXYvI2N1dXWqra21exkAkBOCEoCjWZal1tZWtbW12b2UrNXW1mrQoEEcYgiAYxGUABzLsiw1NzcrGAzavZScBQIB1dfXE5UAHIlXhANwrNbW1pKISUkKBoNqbW21exkAkBWCEoAjtbW1Ofpp7nRK8XsC4A4EJQDH6ezsdOQbcPqjpaVFnZ2ddi8DADJCUAJwlEgkoqamJruXUVBNTU1FPUUkAOSKoATgKM3NzY44zmQuwuGwmpub7V4GAPQbQQnAMTo7O40+A04+tbe389Q3AMcgKAE4ghue6k7GU98AnIKgBOAIbniqOxlPfQNwCoISgPFCoZBrnupO1t7erlAoZPcyAKBPBCUA45XKwcuz5fbvH4D5CEoARrMsy/VBFQwGxVlyAZiMoARgtI6ODte/MSUSiaijo8PuZQBArwhKAEZz+97JKO4HACYjKAEYq6enR11dXXYvwwhdXV3q6emxexkAkBZBCcBYBw8etHsJRuH+AGAqghKAsbq7u+1eglG4PwCYiqAEYCTLslIC6qGHHtKFF15Y0m/SeeWVVzR27Ni0BzQnKAGYiqAEYKRwOJwQju3t7Xr44Yd17bXXyutNHF2rVq3SZZddptGjR+vcc8/Vfffdl/PBwNevX6/p06fr1FNP1YQJE7Rw4cKc32m9c+dOzZ07V2PHjtUZZ5yh+fPnp4TjxIkTdfzxx+vBBx9M+fpIJMJBzgEYiaAEYKTkvXFPP/20QqGQLr300oTL16xZo+uuu05+v1+33XabLrzwQj3wwANauHBh1re9detWXXHFFerq6tIPfvADTZ8+XStWrND111+f9TY/+ugjzZgxQ7t379b8+fN11VVXafXq1ZozZ07Km21mzJihJ598Mu1rJtlLCcBEPrsXAADppAvKCy64QBUVFQmX33XXXRo1apSWLFkin+/wSKupqdHixYs1d+5cNTY2Znzb9957rwYOHKhly5bJ7/dLko499ljdcsstWrt2rT7/+c9nvM3Fixers7NTzz//vIYNGyZJGjdunL7+9a/rmWee0YwZM2LX/dKXvqSFCxdq5cqVmjZtWsJ2uru7VV1dnfHtA0AhsYcSgJHig3LPnj3atm2bzj777ITr7NixQzt27NDll18ei0lJmj17tizL0sqVKzO+3fb2dq1bt05f/vKXYzEpSVOmTFF1dbX+8Ic/ZPHdSC+99JImTZoUi0lJOuecc3TiiSembHPw4MEaNWqUVq1albId9lACMBFBCcBI8a8V3LBhgyRpzJgxCdfZunWrJGns2LEJlw8ZMkRDhw6NfT4Tb7/9tkKhUMo2y8vLNXr0aG3ZsiXjbe7bt0/Nzc0p65cO76VMt85TTz019n3H4zWUAExEUAIwUvy5q3ft2iXp8NPO8Q4cOCBJamhoSPn6Y445Jvb5TDQ1NcW+Pl/bjH5Num02NDSora0tZc/j8OHD1dLSoo8//jjhcs7pDcBEBCUAI8WHU1tbm3w+X8prB6Nn0SkvL0/5+oqKiqzOstPXNsvLy7PaZjQWe1tn/HWiBg4cKElqbW1NuJygBGAighKAkfoTTpWVlZKU9pSE3d3dsc9noq9t9vT0ZLXNaDT2ts7460RFv3+Px5P2cgAwCUEJwEjxIVVbW6tQKJRyGJ3oU8jRp6njHThwIO1TzEcTffo83VPb2W4z+jXpttnU1KTa2tqUoPzkk08kSYMGDUq4PDkwAcAEBCUAI8WHU/TQP3v37k24zujRoyVJb775ZsLl+/fv1759+2Kfz8TIkSPl8/lSttnT06O33npLp5xySsbbHDp0qOrq6rR58+aUz23atCntOvfs2aO6ujrV19cnXE5QAjARQQnASPHhNH78eEmp4ThixAg1NjZqxYoVCofDscuXLVsmj8ejiy66KOPb9fv9Ovvss/X8888n7BH93e9+p46Ojqy2KUmTJ0/Wyy+/rA8//DB22bp16/Tuu+/q4osvTrn+li1bYt93PIISgIkISgBGij+u5PDhwzVixAitW7cu5Xo333yztm3bpjlz5mjFihW6/fbbtXjxYk2fPl0nnXRS7Hp79+5VY2Oj/uu//uuotz1//ny1tbVp5syZWr58uX7605/qRz/6kT7/+c9r4sSJCddtbGzUzJkzj7rNefPm6TOf+YxmzZqlJUuWaPHixbrhhhs0cuRIfeUrX0m47scff6xt27bpggsu6PN+AQBTEJQAjJT8msJp06bp5ZdfTnmX9aRJk7Ro0SJ98sknWrhwof74xz9q3rx5KadejJ6Huz+vgRwzZoyeeOIJVVRU6I477tCKFSs0ffp03X///Wm3me6wRcmGDRum5cuX6/jjj9c999yjhx9+WOedd55+85vfpHyvf/rTn1ReXp52z2XydQHABB6LtwwCMFBHR4f2798f+//29nadd955uummmzR9+vSMt7d06VLdfffdWr16tQYPHpyXNa5evVpXX321XnzxRY0cOTIv25SkSy+9VBMmTNCCBQtSPjdkyBBOvQjAOOyhBGCk5D1xfr9f11xzjR555BFFIpGMt/faa69pzpw5eYvJ6DYvueSSvMbkK6+8ovfee0/XXXdd2s+zhxKAidhDCcBIlmVp9+7dWcVjqfJ6vTrhhBPsXgYApGAPJQAjeTwe9sYl4f4AYCqCEoCxCKhE3B8ATEVQAjBWTU2N3UswCvcHAFMRlACMVV5entW5s0tRZWWlysvL7V4GAKRFUAIwWiAQsHsJRuB+AGAyghKA0SoqKtTT02P3Mmzl9Xo59iQAoxGUAIwUCoX0+OOPa/To0XrwwQdde/igcDisJUuWaMmSJQqFQnYvBwDSIigBGCUakqNGjdI3vvENnXbaafrGN74hr9ed48rr9eq9997TN77xDY0aNUqPP/44YQnAOO6c0ACMky4k//nPf+rZZ5/VuHHj5Pf77V6iLQKBgB577DFt3LhR48aNIywBGImgBGCrvkLy9NNPj12vvr5eZWVl9i3UBmVlZaqvr5ckjRs3Ts888wxhCcBIBCUAW/Q3JKO8Xq8aGhqKv1AbNTQ0pDzVT1gCMBFBCaCoMg3JeFVVVa556tvv96uqqqrXzxOWAExCUAIoilxCMp4bnvqOf6r7aAhLACYgKAEUVL5CMsoNT32ne6r7aAhLAHYiKAEURL5DMl5VVZXq6urys1DD1NXV9flU99EQlgDsQFACyKtChmS82tpa1dbW5m17Jsjn90RYAigmghJAXhQrJOMNGjSoZM5xHQgENGjQoLxvl7AEUAwEJYCc2BGSUR6PR/X19Y7fU1lbW6v6+np5PJ6C3QZhCaCQCEoAWbEzJON5PB7V1dU59jWV0bUXMibjEZYACoGgBJARU0IyWW1trYYOHeqYQwqVlZVp6NChtu1dJSwB5BNBCaBfTA3JeFVVVTruuOOMP/i53+/Xcccdl9O7ufOFsASQDwQlgD45ISTjRY9TaeLeyuheyWyOM1lohCWAXJg10QAYw2khmcy0vZUm7ZXsC2EJIBsEJYAETg/JeNG9lcOHD1dtbW3R9wp6vV7V1tZq+PDhRu6V7AthCSATHsuyLLsXAcB+oVBIS5cu1R133KFdu3ZpypQpuvXWWx0XkX2xLEsdHR0KBoPq6uoq2O1UVlYqEAiourq6aO/eLrRNmzbp9ttv17PPPqvGxkYtWLBAs2fPls/ns3tpAAxAUAIu54aQTKenp0cHDx5Ud3e3uru7FYlEst6W1+tVRUWFKioqVFNTo/Ly8jyu1CyEJYB0CErApdwakulYlqVwOByLy+7uboVCIVmWpZ6eHgWDQQUCAZWXl8vj8cjn88UCsqKiwpUxRVgCiEdQAi5DSGZmw4YNOvPMM7V+/XqdccYZdi/HOIQlAIk35QCuUUpvtoE5ePMOAImgBEoeIYliICwBdyMogRJFSMIOhCXgTgQlUGIISZiAsATchaAESgQhCRMRloA7EJSAwxGScALCEihtBCXgUIQknIiwBEoTQQk4DCGJUkBYAqWFoAQcgpBEKSIsgdJAUAKGIyThBoQl4GwEJWAoQhJuRFgCzkRQAoYhJAHCEnAaghIwBCEJpCIsAWcgKAGbEZLA0RGWgNkISsAmhCSQOcISMBNBCRQZIQnkjrAEzEJQAkVCSAL5R1gCZiAogQIjJIHCIywBexGUQIEQkkDxEZaAPQhKIM8IScB+hCVQXAQlkCeEJGAewhIoDoISyBEhCZiPsAQKi6AEskRIAs5DWAKFQVACGSIkAecjLIH8IiiBfiIkgdJDWAL5QVACR0FIAqWPsARyQ1ACvSAkAfchLIHsEJRAEkISAGEJZIagBP6FkASQjLAE+oeghOslh+S4ceO0ceNGQhJADGEJ9I2ghGv1FpLPPPOMxo0bZ/fyABiIsATSIyjhOoQkgFwRlkAighKuQUgCyDfCEjiMoETJIyQBFBphCbcjKFGyCEkAxUZYwq0ISpQcQhKA3QhLuA1BiZJBSAIwDWEJtyAo4XiEJADTEZYodQQlHIuQBOA0hCVKFUEJxyEkATgdYYlSQ1DCMQhJAKWGsESpIChhPEISQKkjLOF0BCWMRUgCcBvCEk5FUMI4hCQAtyMs4TQEJYxBSAJAIsISTkFQwnaEJAD0jbCE6QhK2IaQBIDMEJYwFUGJoiMkASA3hCVMQ1CiaAhJAMgvwhKmIChRcIQkABQWYQm7EZQoGEISAIqLsIRdCErkHSEJAPYiLFFsBCXyhpAEALMQligWghI5IyQBwGyEJQqNoETWCEkAcBbCEoVCUCJjhCQAOBthiXwjKNFvhCQAlBbCEvlCUOKoCEkAKG2EJXJFUKJXhCQAuAthiWwRlEhBSAKAuxGWyJTHsizL7kUUg2VZCofD6u7ujn2EQiFZlhX78Hg8sQ+fz6eKiorYR1lZmTwej93fRkGFQiEtXbpUd9xxh3bt2qWpU6fq1ltvJSJR8vqaDz09PQoGgwoEAiovL3ftfIC7bdq0SbfffrueffZZNTY2asGCBZo9e7Z8Pp/dSys4+qF/Sjooe3p6dPDgwdgPQCQSyXpbXq839sNRU1Oj8vLyPK7UXoQk3Ij5AGTOLWHJfMhcyQWlZVnq6OhQMBhUV1dXwW6nsrJSgUBA1dXVjv3Lg5CE2zAfgPwoxbBkPuSmZIIyFAopGAwqGAzm9JdEprxerwKBgAKBgGMeSIQk3Ib5ABRGKYQl8yE/HB+UkUhEzc3Nam9vt3sp8vv9qq+vl9dr5nudCEm4DfMBKA4nhiXzIb8cHZSdnZ1qampSOBy2eykxZWVlamhoUFVVld1LiSEk4UbMB6D4nBKWzIf8c2QKRyIRNTU1ad++fUb9MEhSOBzWvn371NTUVNRd5+lw+B+4EfMBsI/phxtiPhSO4/ZQmvhXRW/s+muDPZJwK+YDYBaT9lgyHwrLUXso29rajPyrojfRvzba2tqKcnvskYSbMR8A85iyx5L5UHiOCErLstTS0qKWlha7l5KV6NoLtTOYkISbMR8A89kVlsyH4jE+KC3LUnNzs6MqPZ22tjY1Nzfn9YeCkITbMR8AZylmWDIfisv4oGxtbVUwGLR7GXkRDAbV2tqa83YISeAw5gPgTMUIS+ZDcRkdlG1tbY7/yyJZLt8TIQkcwXwAnK9QYVmKjyXTvydjg7Kzs9Oxr3k4mpaWFnV2dvb7+oQkkIj5AJSWfIYl88EeRgZl9DhRpaw/x5kiJIFUzAegdOUalswH+xgZlM3NzY55a3+2wuGwmpub036OkAR65/b5ALhBtmHJfLCPcUHZ2dlpxHk1i6G9vT1h1zUhCfTNzfMBcKNMwpL5YC+jgtINu6qTNTU1qaenh5AEjsKt88HEp7aAYjtaWDIf7GdUULphV3WyUCikBx98kJAEjsKN88HUp7YAu/QWln/961+ZDzYz5lzeoVBI77//vt3LsEUkElFnZ6dOO+00u5cCGMnN80GShg8fbsu5jwHTbdq0ST//+c/1/e9/X2VlZXYvxxamzAdjgrKlpcXo4ysVWm1trerq6uxeBmAk5gPzAehNS0uLWltb5fF47F6KLUyZD0Y85W1ZVskczT5bwWDQ+NMqAXZgPjAfgN5E54NbY1IyZz4YEZQdHR1GvbDUDpFIRB0dHXYvAzAO84H5APSG+WDOfDAiKN2+9yGK+wFIxePiMO4HIBWPi8NMuB9sD8qenh51dXXZvQwjdHV1qaenx+5lAMZgPhzBfAASMR+OMGE+2B6UBw8etHsJRuH+AI7g8ZCI+wM4gsdDIrvvD9uDsru72+4lGIX7AziCx0Mi7g/gCB4Piey+P2wNSsuyUu6Ahx56SBdeeGFJv8h2x44dGjFihN5+++2Uz9n9AwGYgvnAfAB6k24+SO6eEXbPB1uDMhwOJ/yjt7e36+GHH9a1114rrzdxaatWrdJll12m0aNH69xzz9V9993X5wni+2P9+vWaPn26Tj31VE2YMEELFy7M6Z1SmzZt0q233qrLLrtMI0eOVGNjY9rrnXzyyTr//PN13333pXwuEonk/H0BpcDO+bB27VrdfPPNmjx5sk4++WR94QtfyHpb8fbt26cbbrhBp59+usaNG6drr7025YDtzAfg6JLng9T7jPj973+v7373u5o0aZIaGxs1c+bMvKxh586dmjt3rsaOHaszzjhD8+fPz/nMNbnMCLvng61BmVzTTz/9tEKhkC699NKEy9esWaPrrrtOfr9ft912my688EI98MADWrhwYda3vXXrVl1xxRXq6urSD37wA02fPl0rVqzQ9ddfn/U216xZo6eeekoej0fHHXdcn9edMWOG/vSnP2n37t0pn7P7rwzABHbOhxdeeEEvvPCC/H6/jjnmmKy3E6+jo0OzZs3S3/72N82bN0//+Z//qS1btmjGjBlqbW1NuC7zAehbusdBbzNi+fLlWrVqlT772c9q4MCBebn9jz76SDNmzNDu3bs1f/58XXXVVVq9erXmzJmT9Ztj8jEj7JwPtp6rJ90vjAsuuEAVFRUJl991110aNWqUlixZEju9UE1NjRYvXqy5c+f2uiewL/fee68GDhyoZcuWye/3S5KOPfZY3XLLLVq7dq0+//nPZ7zNWbNm6dprr1VlZaV+9KMf6d133+31uuecc44GDhyoZ599Vt/5zncSPtfd3a3q6uqMbx8oJXbOh+9973u68847NWDAAF111VXavn179t/IvyxdulTvvfeennvuudhpVidOnKiLLrpIjz76qL73ve/Frst8APrWW1CmmxH33nuvhg4dKq/Xq8mTJ+fl9hcvXqzOzk49//zzGjZsmKTD5xn/+te/rmeeeUYzZszIeJv5mBF2zgdj9lDu2bNH27Zt09lnn51wnR07dmjHjh26/PLLE85VOXv2bFmWpZUrV2Z8u+3t7Vq3bp2+/OUvx2JSkqZMmaLq6mr94Q9/yOK7kQYPHqzKysp+XXfAgAGaMGGCVq1alfI59kAA9s0HSRoyZIgGDBiQ3cJ78dJLL+m0006L/aKQpMbGRp199tl68cUXE67LfAD6lvw46G1GSNKwYcNSXiaTq5deekmTJk2KxaR0OPJOPPHErBsiHzPCzvlga1DGP9e/YcMGSdKYMWMSrrN161ZJ0tixYxMuHzJkiIYOHRr7fCbefvtthUKhlG2Wl5dr9OjR2rJlS8bbzMaYMWO0fft2tbe3J1zOa6QA++ZDIUQiEW3bti1lnZJ02mmn6f3330855AfzAehd8uOgtxlRCPv27VNzc3Pa2xo3blxWcydfM8K1r6GMP/fkrl27JB1+2jnegQMHJEkNDQ0pX3/MMcfEPp+Jpqam2Nfna5vZOO644xSJRPTOO+8kXG7COTkBu9k1Hwqhra1NPT09va5TUspamQ9A75IfB73NiEKIPlbTNURDQ4Pa2toy3lOYrxlh53wwJijb2trk8/lSnvuPHgW/vLw85esrKiqyOkp+X9ssLy8v2pH3oy8ObmlpSbicXxiAffOhEI62zvjrRDEfgN4lPw56mxGFEI3Fvh7PmQZlvmYEQdmH6GsS071rqru7u9+vWezvNnt6erLaZjai37/H40l7OeBmds2HQjjaOuOvE8V8AHpn5+MgGnh9PZ6T3xh0NPmaEa4Nyvg7oba2VqFQKOU1AtFdvdGnqeMdOHAgq0N6RHcpp3s6LNttZiN6Mve6urqEy5N/gQBuZNd8KITa2lqVl5f3uk4p9ekz5gPQu+THQW8zohB6ewpaOjyLamtrMw7KfM0IO+eDMUEZPbTH3r17E64zevRoSdKbb76ZcPn+/fu1b9++2OczMXLkSPl8vpRt9vT06K233tIpp5yS8TazsWfPHnm9Xp144okJl/MLA7BvPhSC1+vVyJEjU9YpHT4hwvDhw1VTU5NwOfMB6F3y46C3GVEIQ4cOVV1dnTZv3pzyuU2bNmU1d/I1IwhKSePHj5eU+othxIgRamxs1IoVKxQOh2OXL1u2TB6PRxdddFHGt+v3+3X22Wfr+eefT/hr5ne/+506Ojqy2mY2Nm/erJNPPjnh0EUSvzAAyb75UCgXXXSR3njjDb3xxhuxy9555x29+uqradfJfAB6l/w46G1GFMrkyZP18ssv68MPP4xdtm7dOr377ru6+OKLs9pmPmaEnfPB1gOb+3w+ffrpp5Kk4cOHa8SIEVq3bp2mTZuWcL2bb75Z11xzjebMmaNLLrlE27dv1xNPPKHp06frpJNOil1v7969mjhxoqZOnap77rmnz9ueP3++pk2bppkzZ+ryyy/XRx99pEcffVSf//znNXHixITrNjY2asKECVq+fHmf2/zggw/03HPPSTryQ33//fdLkj73uc9pypQpset++umnev311zVr1qy09wvgdnbOh23btsWO77Z79261t7fHHsujR4/WF7/4xdh1o6dl/POf/9znNmfNmqUVK1boqquu0lVXXaUBAwbo0Ucf1eDBg3XllVcmXJf5APQtfj5Ifc+I119/Xa+//rqkw29gOXToUOzxfNZZZ+mss86KXbe/v+/nzZunlStXatasWZo7d646Ozv1yCOPaOTIkfrKV76ScN1izgg754Otk6miokKHDh2K/f+0adN03333qaurK+HFp5MmTdKiRYv0y1/+UgsXLlRdXZ3mzZunG264IWF70fNw9+d1U2PGjNETTzyhu+++W3fccYeqq6s1ffr0hCPRx28z3Vv5k+3Zs0c/+9nPEi6L/v+ECRMSgvKvf/2r2traNHXq1JTtZPraC6AU2TkfNm/e3OtjeerUqQlBeejQIR1//PFH3WZNTY2WL1+u//f//p8eeOABWZalCRMm6Ac/+IHq6+sTrst8APqWPB+k3mfEq6++ql/84hcJ140+nm+88cZYUGby+37YsGFavny57rzzTt1zzz0aMGCAzj//fN1yyy0pj9Fizgg754PHsvEtQR0dHdq/f3/s/9vb23Xeeefppptu0vTp0zPe3tKlS3X33Xdr9erVGjx4cF7WuHr1al199dV68cUXNXLkyLxsU5KuvfZaeTwePfjggymfGzJkCKdWg+s5YT7s2LFDkydP1q9+9Sudf/75edmmxHwAjiZ5Pki5z4hC/L4v9oywcz7Y+hrK5JL2+/265ppr9MgjjygSiWS8vddee01z5szJ2y+L6DYvueSSvMbkzp07tXr16pRz9EaxBwJwznwYP358Xn9RMB+Ao0v3OMjHjMj37/tizwjX7qG0LEu7d+/O6h++VHm9Xp1wwgl2LwOwHfMhFfMBOIz5kMru+WD7u7z5azsR9wdwGPMhFfcHcBjzIZXd94etQSnZfweYhvsDOILHQyLuD+AIHg+J7L4/bA/K5AN1uh33B3AEj4dE3B/AETweEtl9f9gelOXl5cacb9dulZWVaU8MD7gV8+EI5gOQiPlwhAnzwfaglKRAIGD3EozA/QCk4nFxGPcDkIrHxWEm3A9GBGV1dbW8XiOWYhuv18ux5YA0qqurZePBKIzAfADSox/MmQ9G/Ct4PB4j6tou4XBY27dvV09Pj91LAYyybds2XXHFFbr//vsTztXtJuFwWKtWrdLbb79t91IAo3R3d2vx4sX69a9/7dr5IB3eO2nnObyjjAhKyYzdtXbxeDyaO3euTjrpJC1atEjd3d12Lwmw1bZt2zR79mydeuqpeuWVVzR27FiVlZXZvSxbeL1eLVq0SKeccopmzZqlbdu22b0kwFbd3d1atGiRTjrpJN1www36+OOPXb2X0pR+MuZfwOfzye/3270MWwwcOFAvv/yyJk6cqBtuuIGwhGslh+T999+vnTt36pvf/KZr50MgENCrr76qRYsWae3atYQlXCs5JCdOnKgtW7Zo0aJFxkRVsfn9fvl8PruXIcmgoJSk+vp61+2FKCsrU319vUaNGqWlS5dqy5YthCVcp7eQnDdvXuzYam6eDxUVFbruuuu0Y8cOwhKu01tILl26VKNGjZLk7vlgCqOC0uv1qqGhwe5lFFVDQ0PCrnrCEm7Sn5CMYj6IsISr9Ccko5gP9jNnJf9SVVXlmqe2/H6/qqqq0n6OsEQpyyQk4zEfDiMsUcoyCcl4zAd7GReUkjt2Xfd3VzVhiVKSbUjGYz4cQViilGQbkvGYD/YxMijdsOs6013VhCWcLB8hGcV8SEVYwsnyEZJRzAf7mLeif6mqqlJdXZ3dyyiIurq6rHdVE5ZwknyGZDzmQ3qEJZwknyEZj/lgD2ODUpJqa2tVW1tr9zLyKl/fE2EJkxUqJOMxH3pHWMJkhQrJeMyH4jM6KCVp0KBBJXN8qUAgoEGDBuV1m4QlTFKMkIzHfOgbYQmTFCMk4zEfisv4oPR4PKqvrze6yvujtrZW9fX1BTs9EmEJOxU7JKOYD/1DWMJOxQ7JKOZDcRkflNLhH4q6ujrHviYiuvZi/DAQligmu0IyHvOh/whLFJNdIRmP+VA8HsuyLLsXkYnOzk41NTU54kTwZWVlamhosPUFtNu2bdMdd9yhJ598UsOGDdP3v/99XXnllUX7ZY/SlPxzdcstt+ib3/ym7T9XzIfMdHd367HHHtOdd96pvXv3asaMGfrhD39YtF/2KE3d3d169NFH9d///d/68MMPNWPGDC1YsMD2nyvmQ2E5LiglKRKJqLm5We3t7XYvpVd+v1/19fXGvLWfsEQ+mBqS8ZgPmSMskQ+mhmQ85kPhODIoo0z8a8P0vyoIS2TDCSGZjPmQOcIS2XBCSCZjPuSfo4NSMuuvDSf9VUFYoj+cGJLxmA/ZISzRH04MyXjMh/xyfFBGhUIhBYNBBYNBRSKRot2u1+tVIBBQIBCQz+cr2u3mC2GJdJweksmYD9khLJGO00MyGfMhP0omKKMsy1JHR4eCwaC6uroKdjuVlZUKBAKqrq52xLuvjoawhFR6IZmM+ZAdwhJS6YVkMuZDbkouKOP19PTo4MGD6u7uVnd3d05/eXi9XlVUVKiiokI1NTUqLy/P40rNQVi6U6mHZDrMh8wRlu5U6iGZDvMhcyUdlPEsy1I4HI79cHR3dysUCsmyLPX09CgYDCoQCKi8vFwej0c+ny/2A1BRUVESu6MzQVi6gxtDMp2+5kP0w+PxxD7cPh8IS3dwY0imQz/0kwVr/fr1liRr/fr1di/FOG+99ZY1a9Ysy+v1Wscee6z1wAMPWF1dXXYvCzlK/nddtGgR/67IWFdXl7V48WLruOOOszwejzVz5kzrrbfesntZyFFXV5f1wAMPWMcee6zl9XqtWbNm8e/aC/rhCOe+nQhFwZl3SosJZ7ZB6eDMO6XFhDPbwLkISvQLYelshCQKibB0NkIS+UBQIiOEpbMQkigmwtJZCEnkE0GJrBCWZiMkYSfC0myEJAqBoEROCEuzEJIwCWFpFkIShURQIi8IS3sRkjAZYWkvQhLFQFAirwjL4iIk4SSEZXERkigmghIFQVgWFiEJJ0sOyz//+c+EZR51d3dr8eLFhCSKiqBEQRGW+UVIopREw3Lnzp164IEHCMscxYfk9ddfT0iiqAhKFAVhmRtCEqWsoqJC8+bNIyyzREjCBAQlioqwzAwhCTchLDNDSMIkBCVsQVj2jZCEmxGWfSMkYSKCErYiLBMRksARhGUiQhImIyhhBLeHJSEJ9M7tYUlIwgkIShjFbWFJSAL957awJCThJAQljFTqYUlIAtkr9bAkJOFEBCWMVmphSUgC+VNqYUlIwskISjiC08OSkAQKx+lhSUiiFBCUcBSnhSUhCRSP08KSkEQpISjhSKaHJSEJ2Mf0sCQkUYoISjiaaWFJSALmMC0sCUmUMoISJcHusCQkAXPZHZaEJNyAoERJKXZYEpKAcxQ7LAlJuAlBiZJU6LAkJAHnKnRYEpJwI4ISJS3fYUlIAqUj32FJSMLNCEq4Qq5hSUgCpSvXsCQkAYISLpNpWBKSgHtkGpaEJHAEQQlXOlpYEpKAex0tLAlJIBVBCVdLDsvrr79edXV1OuWUU7RmzRpCEnCx5LB85ZVXNHr0aNXV1RGSQBKCEojj8XgS/t+yLJtWAsBE0RkRiUSYD0AcghKulu6p7ZaWFm3dulXnnXee7WfeAWCf5Ke2zzvvPG3dulUtLS1atGiR7WfeAUxCUMKVjvYaSbvPvAPAPkd7jaTdZ94BTERQwlUyfbMNYQm4R6ZvtiEsgSMISrhCru/aJiyB0pXru7YJS4CgRInL9+F/CEugdOT78D+EJdyMoERJKvRxJAlLwLkKfRxJwhJuRFCipBT7gOSEJeAcxT4gOWEJNyEoURLsPrMNYQmYy+4z2xCWcAOCEo5md0gmIywBc9gdkskIS5QyghKOZFpIJiMsAfuYFpLJCEuUIoISjmJ6SCYjLIHiMT0kkxGWKCUEJRzBaSGZjLAECsdpIZmMsEQpIChhNKeHZDLCEsgfp4dkMsISTkZQwkilFpLJCEsge6UWkskISzgRQQmjlHpIJiMsgf4r9ZBMRljCSQhKGMFtIZmMsAR657aQTEZYwgkIStjK7SGZjLAEjnB7SCYjLGEyghK2ICT7RljCzQjJvhGWMBFBiaIiJDNDWMJNCMnMEJYwCUGJoiAkc0NYopQRkrkhLGECghIFRUjmF2GJUkJI5hdhCTsRlCgIQrKwCEs4WXxIfutb3yIk8yxdWJ566qmaPXs2YYmCISiRV4RkcRGWcJLkkPzCF76grVu3EpIFEh+W999/v1555RXCEgVDUCIvCEl7EZYwWW8huWzZMkKyCAhLFANBiZwQkmYhLGESQtIshCUKiaBEVghJsxGWsBMhaTbCEoVAUCIjhKSzEJYoJkLSWQhL5BNBiX4hJJ2NsEQhEZLORlgiHwhK9ImQLC2EJfKJkCwthCVyQVAiLUKytBGWyAUhWdoIS2TDY1mWZfciisGyLIXDYXV3d8c+QqGQLMtST0+PgsGgAoGAysvL5fF45PP5VFFREfsoKyuTx+Ox+9souG3btumOO+7Qk08+qWHDhumWW27RN7/5TSKyxCX/u3//+9/XlVde6Zp/977mQ/TD4/HEPtw6H7q7u/XrX/9ad955pz744APNmDFDP/zhD4nIEhf/7/7hhx9qxowZWrBggWv+3emH/inpoOzp6dHBgwdjPwCRSCTrbXm93tgPR01NjcrLy/O4UvsRkpDcFZbMh/4jJCG5KyyZD5kruaC0LEsdHR0KBoPq6uoq2O1UVlYqEAiourra0X95EJJIp1TDkvmQGUIS6ZRqWDIfclMyQRkKhRQMBhUMBnP6SyJTXq9XgUBAgUBAPp+vaLebK0IS/VEqYcl8yAwhif4olbBkPuSH44MyEomoublZ7e3tdi9Ffr9f9fX18nrNfa8TIYlsODUsmQ+ZISSRDaeGJfMhvxwdlJ2dnWpqalI4HLZ7KTFlZWVqaGhQVVWV3UtJQEgiH5wUlsyH/iMkkQ9OCkvmQ/45MihN+quiN6b8tUFIohBMDkvmQ/8RkigEk8OS+VA4jgtKE/+q6I2df20QkigG08KS+dA/hCSKwbSwZD4UlqOCsq2tTS0tLXYvI2N1dXWqra0tym0RkrCDCWHJfDg6QhJ2MCEsmQ+F54j9qZZlqaWlxZE/DJJiay9ku3NmG9jJzjPvMB+OjjPbwE52nnmH+VA8xgelZVlqbm5WW1ub3UvJSVtbm5qbm/P+Q0FIwiTFDkvmQ98ISZik2GHJfCgu44OytbVVwWDQ7mXkRTAYVGtra162RUjCZMUKS+ZDeoQkTFassGQ+FJfRQdnW1ub4vyyS5fo9EZJwkkKGJfMhFSEJJylkWDIfis/YoOzs7HTsax6OpqWlRZ2dnRl9DSEJJ8t3WDIfEhGScLJ8hyXzwR5GBmUkElFTU5Pdyyiopqamfp3iiZBEKclHWDIfjiAkUUryEZbMB/sYGZTNzc2OOE5ULsLhsJqbm3v9PCGJUpZLWDIfCEmUtlzCkvlgH+OCsrOz0+gj2OdTe3t7yq5rQhJukmlYun0+EJJwk0zD0u3zwW5GBaUbdlUni+66JiThZv0JSzfPB0ISbtafsHTzfDCFUWfKaWpqcs1fF1GWZekf//iHZs6cyZltgH9Jd+adqVOnGvcXeTHs2bNHs2fP5sw2wL+kO/PObbfdprKyMruXVnR+v18NDQ12L0OSQUEZCoX0/vvv270MW4TDYa1du1azZs0iJIE40bBcvXq11qxZ48pfGOFwWD/96U/17W9/m5AE4kTD8pFHHtH//M//uHI+SNLw4cPl8/nsXoY5QdnS0mL08ZUKrba2VnV1dXYvAzDSjh075PF45PUa9SqdorAsS4MGDWI+AL1oampSMBiUx+Oxeym2MKUfjJjOlmWVzNHssxUMBo0/rRJgB8uyNGDAAFfGpCR5PB7mA9ALy7LU0dHh2piUzOkHIyZ0R0eHUS8stUMkElFHR4fdywCMw3xgPgC9YT6YMx+MCEq3752M4n4AUvG4OIz7AUjF4+IwE+4H24Oyp6dHXV1ddi/DCF1dXerp6bF7GYAxmA9HMB+ARMyHI0yYD7YH5cGDB+1eglG4P4AjeDwk4v4AjuDxkMju+8P2oOzv+XvdgvsDOILHQyLuD+AIHg+J7L4/bA1Ky7JS7oCHHnpIF154YUm/yLa1tVVjxozR6tWrUz5n9w8EYArmA/MB6E26+SC5e0bYPR9sDcpwOJzwj97e3q6HH35Y1157bcohQlatWqXLLrtMo0eP1rnnnqv77rtPoVAo69teu3atbr75Zk2ePFknn3yyvvCFL2S9rah33nlHd9xxh7761a9q9OjRamxs1N69e1OuN2jQIE2fPl0/+9nPUj4XiURy+r6AUtHf+fD73/9e3/3udzVp0iQ1NjZq5syZebn9nTt3au7cuRo7dqzOOOMMzZ8/X83NzVlvj/kA5E/yfJCKOyM2bdqkW2+9VZdddplGjhypxsbGnLcpHX5zzS233KJ///d/15gxYzRz5kxt3rw54Tq9zQi754OtQZlc008//bRCoZAuvfTShMvXrFmj6667Tn6/X7fddpsuvPBCPfDAA1q4cGHWt/3CCy/ohRdekN/v1zHHHJP1duJt2LBBS5YsUUdHh0466aQ+rztz5kxt2bJFf/3rX1M+Z/dfGYAJ+jsfli9frlWrVumzn/2sBg4cmJfb/uijjzRjxgzt3r1b8+fP11VXXaXVq1drzpw5Wb/wnfkA5E+6x0ExZ8SaNWv01FNPyePx6LjjjsvLNiORiK688kr97//+r6644grddNNNamlp0axZs/Tuu+8mXLe3GWHnfDAuKC+44IKU0w/eddddGjVqlJYsWaLLL79ct912m6677jo9+eST2rVrV1a3/b3vfU+bNm3Sb3/7W40ePTrr7yHeBRdcoH/+859auXKlLrvssj6ve9JJJ2nEiBF65plnUj7HLwyg//Ph3nvv1caNG7Vs2bK8/XG4ePFidXZ2atmyZZo7d67+4z/+Q7/85S/11ltvpX3M9gfzAcif3oKyWDNi1qxZ2rhxo55//nmde+65ednmypUrtWHDBv3kJz/RjTfeqCuuuELLli2T1+vVz3/+84Tr9jYjCEpJe/bs0bZt23T22WcnXGfHjh3asWOHLr/88oRzVc6ePVuWZWnlypVZ3faQIUM0YMCA7Bbei9raWtXU1PT7+ueee65efvnllCPc8wsD6N98kKRhw4bl/Sw6L730kiZNmqRhw4bFLjvnnHN04okn6g9/+ENW22Q+APmT/Dgo9owYPHiwKisr87rNl156SYMHD9aXvvSl2GX19fW6+OKLtWrVqpTvOd2McG1Qxj/Xv2HDBknSmDFjEq6zdetWSdLYsWMTLh8yZIiGDh0a+7wTjRkzRsFgUNu3b0+4nNdIAf2bD4Wwb98+NTc3p72tcePGFW3mMB+A3iU/Doo5Iwply5YtOvXUU1Pid9y4cTp06JDee++9hMvTzQjXvoYyvqqjT10fe+yxCdc5cOCAJKmhoSHl64855pjY550o+rqLnTt3Jlxuwjk5Abv1Zz4UQnSmpHtqrKGhQW1tbUXZC8B8AHqX/Dgo5owolKampl7njiTt378/4fJ0M8LO+WBMULa1tcnn86m6ujrhOtGj4JeXl6d8fUVFhaOPkh99cXBra2vC5fzCAPo3HwohGou9zZz46xQS8wHoXfLjoJgzolC6urr6nDvJvZNuRhCUfYi+RiHdOyu7u7vz/hqGYop+/x6PJ+3lgJvZ9TiIDu/eZk78dQqJ+QD0rhQfB5WVlX3OneTeSTcjXBuU8XdCbW2tQqFQyqmDort/m5qaUr7+wIEDeXvHlh0++eQTSYePKRUv+RcI4Eb9mQ+FEJ0p6V5O09TUpNra2qIEJfMB6F3y46CYM6JQGhoaep070uH3jsRLNyPsnA/GBGX0oKDJB/qNHtLnzTffTLh8//792rdvX94O+WOH6PeafEBUfmEA/ZsPhTB06FDV1dWlHExYOnww42LNHOYD0Lvkx0ExZ0ShnHLKKdqyZUvKAds3btyoz3zmMzrhhBMSLk83IwhKSePHj5eUGo4jRoxQY2OjVqxYoXA4HLt82bJl8ng8uuiii4qz2ALYvHmz/H6/RowYkXA5vzCA/s2HQpk8ebJefvllffjhh7HL1q1bp3fffVcXX3xxUdbAfAB6l/w4KPaMKITJkyfr448/1h//+MfYZS0tLVq5cqUmTZqU8sxIuhlh53zwHf0qBbxxn0+ffvqpJGn48OEaMWKE1q1bp2nTpiVc7+abb9Y111yjOXPm6JJLLtH27dv1xBNPaPr06QlnnNi7d68mTpyoqVOn6p577unztrdt26ZVq1ZJknbv3q329nbdf//9kg7vFf3iF78Yu270tIx//vOf+9xme3u7lixZIklav369JOk3v/mNAoGAAoGAvv71rydc/y9/+Yu++MUvpvwAxB9vE3Cr/s6H119/Xa+//rqkw8P30KFDscfyWWedpbPOOit23cbGRk2YMEHLly/v87bnzZunlStXatasWZo7d646Ozv1yCOPaOTIkfrKV76ScF3mA1B88fNBKv6M+OCDD/Tcc89JOhKx0W1+7nOf05QpU2LXnTlzpv72t78d9UQsF110kR5//HHddNNN2rlzpwYNGqSlS5cqEono29/+dsr1080IO+eDrZOpoqJChw4div3/tGnTdN9996mrqyvhxaeTJk3SokWL9Mtf/lILFy5UXV2d5s2bpxtuuCFhex0dHZLSH+4j2ebNm1POgxn9/6lTpyYE5aFDh3T88ccfdZuffPJJyjYfffRRSYd/wOJ/YezatUvbt2/XggULUrZTjNdnAabr73x49dVX9Ytf/CLha6OPwxtvvDH2yyI6H9IdgizZsGHDtHz5ct1555265557NGDAAJ1//vm65ZZbUh6fzAeg+JLng1TcGbFnz55eG2LChAkJQdnR0dGvbZaVlenRRx/VXXfdpSVLlqirq0unnXaafvKTn+jf/u3fEq7b24ywcz54LBvfEtTR0ZFwXKX29nadd955uummmzR9+vSMt7d06VLdfffdWr16tQYPHpyXNe7YsUOTJ0/Wr371K51//vl52aYk/fjHP9bf//53Pf/88yl7IIYMGeLoQx8A+ZDv+bB69WpdffXVevHFFzVy5Mi8rJH5ANgjeT5IZs6IgwcP6swzz9SCBQt0xRVX5GWbUu8zws75YOtrKJNL2u/365prrtEjjzyS8qLU/njttdc0Z86cvMVkdJvjx4/P6y+L1tZWPfXUU/rOd76T9vUO7IEACjMfLrnkkrz9oohuk/kAFF+6x4GJM+Lvf/+7hgwZoq997Wt522ZfM8K1eygty9Lu3buz+ocvVV6vN+WdXIAbMR9SMR+Aw5gPqeyeD7a/y5u/thNxfwCHMR9ScX8AhzEfUtl9f9galJL9d4BpuD+AI3g8JOL+AI7g8ZDI7vvD9qCsqamxewlG4f4AjuDxkIj7AziCx0Miu+8P24OyvLzc0efjzqfKysq0J4YH3Ir5cATzAUjEfDjChPlge1BKUiAQsHsJRuB+AFLxuDiM+wFIxePiMBPuByOCsrq6Wl6vEUuxjdfr5dhyQBrMB+YD0BvmgznzwYh/BY/HY0Rd2yUSiejQoUOcoxdIw+3zQTq894H5AKTatGmTXnrpJYXDYbuXYhtT5oMRQSmZsbvWTueff76mTp2qjRs32r0UwDhunw9u//6BZBs3btTUqVM1fvx4Pf74467eS2nKfDDmX8Dn88nv99u9DFv4/X7dddddeuONNzR+/HjCEkji9vng8/nsXgZghPiQfOONN/TYY4/pL3/5izFRVWwmzQdjglKS6uvrVVZWZvcyiqqsrEwNDQ2aO3eutm3bpscee4ywBNJw63yor6+3exmA7dKF5LZt2zR37lz5fD7mgwGMCkqv16uGhga7l1FUDQ0NsV31Pp+PsAR64fb5ALjR0UIyivlgP3NW8i9VVVWueWrL7/erqqoq5XLCEkiP+QC4Q39DMh7zwV7GBaXkjqe2+rOrmrAEUjEfgNKVTUjGYz7Yx8igdMOu60x2VROWwBHMB6D05BqSUcwH+5i3on+pqqpSXV2d3csoiLq6uqx2VROWwGHMB6A05Csk4zEf7GFsUEpSbW2tamtr7V5GXuXjeyIsAeYD4GSFCMl4pfhYMv17MjooJWnQoEElc3ypQCCgQYMG5W17hCXcjvkAOEuhQzIe86G4jA9Kj8ej+vp6o6u8P2pra1VfX1+Q0yMRlnAr5gPgDMUMySjmQ3EZH5TS4R+Kuro6x74mIrr2Qv8wEJZwI+YDYC47QjIe86F4HBGUUbW1tRo6dKhjDglQVlamoUOHFv2vI8ISbsR8AMxhd0gmYz4UnseyLMvuRWQqEomoublZ7e3tdi+lV36/X/X19Ua8tT8UCmnp0qW64447tGvXLk2ZMkW33nqrTj/9dLuXBuQd8wGwz8aNG3X77bfrueeeU2NjoxYsWKDZs2cbc75p5kPhOGu1/xI9zpSJf21E/6ow6ThR7LGEmzAfgOIzbY9kb5gPhePIPZTxTPprwyl/VbDHEm7BfAAKy/Q9kn1hPuSX44MyKhQKKRgMKhgMKhKJFO12vV6vAoGAAoGAIx5A8QhLuAXzAcgvJ4dkMuZDfpRMUEZZlqWOjg4Fg0F1dXUV7HYqKysVCARUXV3tiHdf9YWwhFswH4DclFJIJmM+5KbkgjJeT0+PDh48qO7ubnV3d+f0l4fX61VFRYUqKipUU1Oj8vLyPK7UDIQl3IT5APRfKYdkOsyHzJV0UMazLEvhcDj2w9Hd3a1QKCTLsmIfHo8n9uHz+WI/ABUVFSX7oEmHsITb9DUfenp6FAwGFQgEVF5e7vr5AHdxW0imQz/0j2uCEpkjLAFpw4YNOvPMM7V+/XqdccYZdi8HKApCEply7tuJUHAcbggA3MUph/+BeQhKHBVhCQCljZBErghK9BthCQClhZBEvhCUyBhhCQDORkgi3whKZI2wBABnISRRKAQlckZYAoDZCEkUGkGJvCEsAcAshCSKhaBE3hGWAGAvQhLFRlCiYAhLACguQhJ2IShRcIQlABQWIQm7EZQoGsISAPKLkIQpCEoUHWEJALkhJGEaghK2ISwBIDOEJExFUMJ2hCUA9I2QhOkIShiDsASARIQknIKghHEISwBuR0jCaQhKGIuwBOA2hCSciqCE8QhLAKWOkITTEZRwDMISQKkhJFEqCEo4DmEJwOkISZQaghKORVgCcBpCEqWKoITjEZYATEdIotQRlCgZhCUA0xCScAuCEiWHsARgN0ISbkNQomQRlgCKjZCEWxGUKHmEJYBCIyThdgQlXIOwBJBvhCRwGEEJ1yEsAeSKkAQSEZRwLcISQKYISSA9ghKuFx+Wjz/+OGEJIAUhCfSNoAT+xefzac6cOYQlgBhCEugfghJIQlgCICSBzBCUQC8IS8B9CEkgOwQlcBSEJVD6CEkgNwQl0E+EJVB6CEkgPwhKIEOEJeB8hCSQXwQlkCXCEnAeQhIoDIISyBFhCZiPkAQKi6AE8oSwBMxDSALFQVACeUZYAvYjJIHiIiiBAiEsgeIjJAF7EJRAgRGWQOERkoC9CEqgSAhLIP8IScAMBCVQZIQlkDtCEjALQQnYhLAEMkdIAmYiKAGbEZbA0RGSgNkISsAQhCWQipAEnIGgBAxDWAKEJOA0BCVgKMISbkRIAs5EUAKGIyzhBoQk4GwEJeAQhCVKESEJlAaCEnAYwhKlgJAESgtBCTgUYQknIiSB0kRQAg5HWMIJCEmgtBGUQIkgLGEiQhJwB4ISKDGEJUxASALuQlACJYqwhB0IScCdCEqgxBGWKAZCEnA3ghJwCcIShUBIApAISsB1CEvkAyEJIJ7HsizL7kUAsE8oFNKyZcv04x//WLt27dKUKVN066236vTTT7d7aUVjWZbC4bC6u7tjH6FQSJZlqaenR8FgUIFAQOXl5fJ4PPL5fKqoqIh9lJWVyePx2P1tFMXGjRt1++2367nnnlNjY6MWLFig2bNnE5GAyxGUACS5Lyx7enp08ODBWEBGIpGst+X1emNxWVNTo/Ly8jyu1AyEJIC+EJQAEpRyWFqWpY6ODgWDQXV1dRXsdiorKxUIBFRdXe34PZeEJID+4DWUABKU4mssQ6GQWlpatHv3bh04cKCgMSlJXV1dOnDggHbv3q2WlhaFQqGC3l4h8BpJAJkgKAGkVQphGYlE1NTUpPfff19tbW05Pa2d7e23tbXp/fffV1NTU9FvPxuEJIBsEJQA+uTUsOzs7NSePXvU3t5u91IkSe3t7dqzZ486OzvtXkpahCSAXBCUAPrFKWEZ3Su5b98+hcNhu5eTIBwOa9++fUbtrSQkAeQDQQkgIyaHpWl7JXtjwt5KQhJAPhGUALJiWli2tbUZuVeyN9G9lW1tbUW9XUISQCEQlAByYndYWpallpYWtbS0FPy2CiG69kIfwY2QBFBIBCWAvLAjLC3LUnNzc9H38uVbW1ubmpubCxKVhCSAYiAoAeRVMcOytbVVwWAwr9u0SzAYVGtra962R0gCKCaCEkBBFDos29raHL9nMlk+vidCEoAdCEoABVWIsOzs7HTsayaPpqWlJat3fxOSAOxEUAIoinyFZfQ4k6Usk+NUEpIATEBQAiiqXMOyubnZMYcGylY4HFZzc3Of1yEkAZiEoARgi2zCsrOz0/iDludLe3t72qe+CUkAJiIoAdiqv2Hphqe6k8U/9U1IAjAZQQnACEcLSzc81Z0sHA5r+/bthCQA43msQp+eAQCyEAqFtGzZMv34xz9WR0eH1q5dK6/XfX8Dh8NhzZ49W/PmzdPs2bOJSABGIigBGC0UCmnt2rU69thjVVZWZvdyis6yLA0cOFCDBw+2eykA0Cv3/bkPwFHKysp04oknujImJcnj8ejgwYMFP9c3AOSCoARgtI6Ojn4fk7FURSIRdXR02L0MAOgVQQnAaKVyru5ccT8AMBlBCcBYPT096urqsnsZRujq6lJPT4/dywCAtAhKAMY6ePCg3UswCvcHAFMRlACM1d3dbfcSjML9AcBUBCUAI1mWlRJQDz30kC688MKSfpPOp59+qnPOOUdLly5N+RxBCcBUBCUAI4XD4YRwbG9v18MPP6xrr7024QDnv//97/Xd735XkyZNUmNjo2bOnJnzbW/atEm33nqrLrvsMo0cOVKNjY05b/PAgQP6yU9+opkzZ+q0005TY2OjXnvttZTrDRgwQFdeeaUWLVqUEpCRSEShUCjntQBAvhGUAIyUHFNPP/20QqGQLr300oTLly9frlWrVumzn/2sBg4cmJfbXrNmjZ566il5PB4dd9xxednmO++8o4ceekj79+/XiBEj+rzuV7/6VbW2tuqFF15I+Rx7KQGYiKAEYKR0QXnBBReooqIi4fJ7771XGzdu1LJly3TMMcfk5bZnzZqljRs36vnnn9e5556bl22OGTNG69ev1//93//pyiuv7PO6gUBA5557rp555pmUzxGUAExEUAIwUnw47dmzR9u2bdPZZ5+dcr1hw4bl/RzfgwcPVmVlZV63WVNTo9ra2n5f/5xzztE//vEPtbW1JVxOUAIwEUEJwEjxrxXcsGGDpMN7+dxizJgxsiwr9r1H8RpKACYiKAEYKf7c1bt27ZIkHXvssXYtp+iGDx8uSdqxY0fC5ZzTG4CJCEoARooPp7a2Nvl8PlVXV9u4ouKKvsGotbU14XKCEoCJCEoARnJ7OEW/f4/Hk/ZyADAJQQnASPEhVVtbq1Ao5KpTD37yySeSpEGDBiVcnhyYAGACghKAkeLDKXpg8b1799q1nKLbs2ePJOmkk05KuJygBGAighKAkeLDafz48ZKkN998067lFN3mzZvl8Xhi33sUQQnARD67FwAA6fh8Pn366aeSDr/jecSIEVq3bp2mTZuWcL3XX39dr7/+uiSppaVFhw4d0v333y9JOuuss3TWWWfFrtvY2KgJEyZo+fLlfd72Bx98oOeee07SkYiNbvNzn/ucpkyZErvuzJkz9be//S32TvS+RLcRfef27373O/3jH/+QJF1//fUJ1123bp3OPPPMlKe8fT7GNgDzMJkAGKmiokKHDh2K/f+0adN03333qaurK+Gg46+++qp+8YtfJHztz372M0nSjTfeGAvKjo4OSVJDQ8NRb3vPnj2xbSRvc8KECQlB2dHR0a9txm8j6re//W3sv+ODsr29XX/5y1+0cOHClG0knykIAEzgsXjLIAADdXR0aP/+/bH/b29v13nnnaebbrpJ06dPz3h7q1ev1tVXX60XX3xRI0eOzMsaDx48qDPPPFMLFizQFVdckZdtStJjjz2mhx9+WKtXr045Y8+QIUNcdfgkAM7AaygBGCl5T5zf79c111yjRx55RJFIJOPtvfbaa7rkkkvyFpOS9Pe//11DhgzR1772tbxt89NPP9Wjjz6qb33rW2lP/8geSgAmYg8lACNZlqXdu3dnFY+lyuv16oQTTrB7GQCQgj2UAIzk8XjYG5eE+wOAqQhKAMYioBJxfwAwFUEJwFg1NTV2L8Eo3B8ATEVQAjBWeXl52jemuFFlZaXKy8vtXgYApEVQAjBaIBCwewlG4H4AYDKCEoDRqqur5fW6e1R5vV6OPQnAaO6e0gCM5/F4XL93LhAIcA5vAEYjKAEYj6B09/cPwHwEJQDj+Xw++f1+u5dhC7/fL5/PZ/cyAKBPBCUAR6ivr1dZWZndyyiqsrIy1dfX270MADgqghKAI3i9XjU0NNi9jKJqaGhw/RuSADgDkwqAY1RVVbnmqW+/36+qqiq7lwEA/UJQAnAUNzz1zVPdAJyGoATgKG546punugE4DRMLgONUVVWprq7O7mUURF1dHU91A3AcghKAI9XW1qq2ttbuZeRVKX5PANyBoATgWIMGDSqZg34HAgENGjTI7mUAQFY8lmVZdi8CALJlWZZaW1vV1tZm91KyVltbq0GDBnF6RQCORVACKAltbW1qaWmxexkZq6ur42luAI5HUAIoGZ2dnWpqalI4HLZ7KUdVVlamhoYG3oADoCQQlABKSiQSUXNzs9rb2+1eSq/8fr/q6+s5NBCAkkFQAihJJu6tZK8kgFJFUAIoWSbtrWSvJIBSRlACKHmhUEjBYFDBYFCRSKRot+v1ehUIBBQIBOTz+Yp2uwBQbAQlANewLEsdHR0KBoPq6uoq2O1UVlYqEAiourqaQwEBcAWCEoAr9fT06ODBg+ru7lZ3d3dOey69Xq8qKipUUVGhmpoalZeX53GlAGA+ghKA61mWpXA4HIvL7u5uhUIhWZYV+/B4PLEPn88XC8iKigqezgbgegQlAAAAcsLbDQEAAJATghIAAAA5ISgBAACQE4ISAAAAOSEoAQAAkBOCEgAAADkhKAEAAJATghIAAAA5ISgBAACQE4ISAAAAOSEoAQAAkBOCEgAAADkhKAEAAJATghIAAAA5ISgBAACQk/8PGnzKnFQCVY8AAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "n = 3 # number of qubits\n",
        "G = hypercube_graph(n) # create hypercube graph\n",
        "# Draw graph\n",
        "nx.draw(G, with_labels=True, pos=graphviz_layout(G, prog=\"dot\"),\n",
        "        node_color=\"#dddddd\", node_size=2500)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PNi2Bz7qEJfu"
      },
      "source": [
        "The state of the system in a quantum random walk involves two distinct spaces: the coin space and the walker space. The coin space, denoted as $\\mathcal{H_c} = \\mathcal{H}^{n}$, corresponds to the state of the quantum coin, which can be in a superposition of $n$ possible states. The walker space, denoted as $\\mathcal{H_p} = \\mathcal{H}^{2^{n}}$, represents the possible positions of the walker, with each position corresponding to a binary string of length $n$, leading to $2^{n}$ distinct positions. The total state of the system is the tensor product of these two spaces: $\\mathcal{H} = \\mathcal{H_c} \\otimes \\mathcal{H_p}$. This combined space can be defined as the set of all possible states:\n",
        "\n",
        "$$\n",
        "\\mathcal{H} = \\{\\ket{a} \\otimes \\ket{v}: 0 \\le a \\lt n, v \\in \\{(00 \\dots 00)_2, (00\\dots 01)_2, \\dots, (11 \\dots 11)_2\\}\\}\n",
        "$$\n",
        "\n",
        "where $\\ket{a}$ corresponds to the coin state and $\\ket{v}$ corresponds to the binary representation of the walker's position. The value of $a$ determines the position in the walker space where the next move occurs. Specifically, the value of $a$ identifies which bit in the position vector $\\ket{v}$ has to be flipped. When the coin state is $\\ket{a}$, the shift operator will flip the $a$-th bit of the walker's current position $\\ket{v}$, thereby determining the walker's next position.\n",
        "\n",
        "> _Example_\n",
        ">\n",
        "> Considering the state $\\ket{a} \\otimes \\ket{v} = \\ket{2} \\otimes \\ket{0101}$, the walker will transition to the node $\\ket{0111}$, as the bit at position 2 is flipped.\n",
        "\n",
        "A circuit implementing a quantum coined walk for hypercubes requires:\n",
        "\n",
        "- $n$ qubits to represent the coin: it will generate one of the $2^n$ possible outcomes, determining which qubit to invert;\n",
        "- $n$ qubits to represent the walker position: positions are encoded in binary form, with the most significant bit at the top;\n",
        "- $n$ classical bits to store the measurement of the walker's position."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 28,
      "metadata": {
        "id": "KfJnz-OpOVqm"
      },
      "outputs": [],
      "source": [
        "n_qubits = 2 # dimension of the hypercube\n",
        "n_steps = 2 # number of steps of the quantum walk"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "metadata": {
        "id": "fiNbChhrOTjN"
      },
      "outputs": [],
      "source": [
        "def hypercube_walk_circuit(n_qubits):\n",
        "    \"\"\"\n",
        "    Create a quantum circuit for hypercube topology\n",
        "    Args:\n",
        "    n_qubits (int): number of qubits used to represent the position of the walker\n",
        "    Returns:\n",
        "    quantum circuit for graph walk, walker register, coin register and output register\n",
        "    \"\"\"\n",
        "    walker_r = QuantumRegister(n_qubits, name=\"q\")\n",
        "    coin_r = QuantumRegister(n_qubits, name=\"c\")\n",
        "    classic_r = ClassicalRegister(n_qubits, name=\"r\")\n",
        "    q_circuit = QuantumCircuit(walker_r, coin_r, classic_r)\n",
        "    return q_circuit, walker_r, coin_r, classic_r"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BTnDEnC1O5IH"
      },
      "source": [
        "The theoretically optimal choice for a quantum walk on hypercubes is the Grover coin operator, $C$. It is defined as:\n",
        "\n",
        "$$\n",
        "C = \\begin{bmatrix}\n",
        "\\frac{2}{n} - 1& \\frac{2}{n} & \\dots & \\frac{2}{n} \\\\\n",
        "\\frac{2}{n} & \\frac{2}{n} - 1& \\dots &  \\frac{2}{n} \\\\\n",
        "\\vdots & \\vdots & \\ddots & \\vdots \\\\\n",
        "\\frac{2}{n} & \\frac{2}{n} & \\dots & \\frac{2}{n} - 1\n",
        "\\end{bmatrix}\n",
        "$$\n",
        "\n",
        "However, in our case, we will observe that using a generic rotation coin is more efficient. This alternative approach will be explored later in the notebook.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 30,
      "metadata": {
        "id": "018S-HQ1O7rU"
      },
      "outputs": [],
      "source": [
        "def grover_coin(coin_r):\n",
        "    \"\"\"\n",
        "    Create the Grover coin operator\n",
        "    Args:\n",
        "    coin_r (QuantumRegister): quantum register containing the coin qubit\n",
        "    Returns:\n",
        "    Grover coin operator\n",
        "    \"\"\"\n",
        "    matrix_size = 2 ** len(coin_r)\n",
        "    grover_matrix = np.full((matrix_size, matrix_size), 2 / matrix_size) - np.eye(matrix_size)\n",
        "    return Operator(grover_matrix)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "M1GQc5kvPQpS"
      },
      "source": [
        "The shift operator $S$ determines how the walker moves across the hypercube based on the coin state. To formalize this, let $e_a$ represent a vector with a single $1$ in the $a$-th position and $0$ everywhere else. The shift operator $S$ is then defined as:\n",
        "\n",
        "$$\n",
        "S(\\ket{a} \\otimes \\ket{v}) = \\ket{a} \\otimes \\ket{v \\oplus e_a}\n",
        "$$\n",
        "\n",
        "The system's state consists of two parts:\n",
        "- $\\ket{a}$: coin state, which determines the bit to modify. It specifies the position $a$ in the binary representation of the walker's position $\\ket{v}$;\n",
        "- $\\ket{v}$: walker's current position, represented as a binary string corresponding to a node on the hypercube.\n",
        "\n",
        "The walker's position is updated by flipping the bit at position $a$. This is done using the binary XOR operation ($\\oplus$) between the walker's position $v$ and a vector $e_a$. As a consequence, after applying $S$, the coin state $\\ket{a}$ remains unchanged, while the walker's position is updated to reflect the movement imposed by the coin."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 31,
      "metadata": {
        "id": "IeSY0eX6PJ5F"
      },
      "outputs": [],
      "source": [
        "def shift_operator(walker_r, coin_r):\n",
        "    \"\"\"\n",
        "    Create a quantum circuit for the shift operator\n",
        "    Args:\n",
        "    walker_r (QuantumRegister): quantum register containing the walker's position qubits\n",
        "    coin_r (QuantumRegister): quantum register containing the coin qubit\n",
        "    Returns:\n",
        "    Quantum circuit for the shift operator\n",
        "    \"\"\"\n",
        "    q_circuit = QuantumCircuit(walker_r, coin_r)\n",
        "    for i in reversed(range(len(walker_r))):\n",
        "        q_circuit.mcx(coin_r, walker_r[i])\n",
        "        q_circuit.x(coin_r[-1])\n",
        "        for j in range(1, len(coin_r)):\n",
        "            if i & ((1 << j) - 1) == 0:\n",
        "                q_circuit.x(coin_r[-(j + 1)])\n",
        "    return q_circuit"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BygMLRPuP2Qc"
      },
      "source": [
        "Finally, the quantum walk operator is constructed by combining the coin operator and the shift operator, as follows:\n",
        "\n",
        "$$\n",
        "U = S \\cdot (C \\otimes I)\n",
        "$$\n",
        "\n",
        "This composition integrates the coin operation, which determines the walker's direction, with the shift operation, which updates the walker's position based on the coin state.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 32,
      "metadata": {
        "id": "g8ugOXPVPygJ"
      },
      "outputs": [],
      "source": [
        "def hypercube_walk_step(walker_r, coin_r):\n",
        "    \"\"\"\n",
        "    Create a quantum circuit for one step of the hypercube walk\n",
        "    Args:\n",
        "    walker_r (QuantumRegister): quantum register containing the walker's position qubits\n",
        "    coin_r (QuantumRegister): quantum register containing the coin qubit\n",
        "    Returns:\n",
        "    Quantum circuit for one step of the graph walk\n",
        "    \"\"\"\n",
        "    shift = shift_operator(walker_r, coin_r)\n",
        "    grover_c = grover_coin(coin_r)\n",
        "    walk_step = QuantumCircuit(walker_r, coin_r)\n",
        "    walk_step.unitary(grover_c, coin_r, label=\"G\")\n",
        "    walk_step.compose(shift, inplace=True)\n",
        "    return walk_step"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 33,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 449
        },
        "id": "ZJ5vKlvBQYh-",
        "outputId": "56e4986f-9c96-43c7-8f97-e47d4d997747"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 925.456x535.111 with 1 Axes>"
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtwAAAGwCAYAAACad7LVAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy81sbWrAAAACXBIWXMAAA9hAAAPYQGoP6dpAABTdUlEQVR4nO3de1iUdf7/8ddwPpoHUlRMFMRTeFhR1MwzauGpLTdb29TM3G0td9eVVtd2a8vUsv118JvfMlPbLZfWahMopfKsmRJongilUFGQ8ICIyHF+f/iFjRiQwblnRng+rqvLy7k/n/vzvprb4cU97/u+TWaz2SwAAAAAhnBxdAEAAABAQ0bgBgAAAAxE4AYAAAAMROAGAAAADETgBgAAAAxE4AYAAAAMROAGAAAADETgBgAAAAxE4AYAAAAMROAGAAAADETgBgAAAAxE4AYAAAAMROAGAAAADETgBgAAAAxE4AYAAAAMROAGAAAADETgBgAAAAxE4AYAAAAMROAGAAAADETgBgAAAAxE4AYAAAAMROAGAAAADETgBgAAAAxE4AYAAAAMROAGAAAADETgBgAAAAxE4AYAAAAMROAGAAAADETgBgAAAAxE4AYAAAAMROAGAAAADETgBgAAAAxE4AYAAAAMROAGAAAADETgBgAAAAxE4AYAAAAMROAGAAAADETgBgAAAAxE4AYAAAAMROAGAAAADETgBgAAAAxE4AYAAAAMROAGAAAADETgBgAAAAzk5ugCAAAAGrPikjIdOnZBXx/JVXpmvoqKy+Tm6qJmTTzUu0sL9ekWoJYtvB1dJm4AgRsAAMDOzGaztuzN0uuxRxW37aSKS8prHR/W/hY9el9nTZ8Ypua3eNqpStiKyWw2mx1dBAAAQGPx2Zen9cSSL5X6fZ7Vc708XfXrSV303Ow+8vVxN6A6GIHADQAAYAeXLhdr3t/36s31397wvkLa+evtZ+7U4IjWNqgMRiNwAwAAGOz02QJFzdqoo99dtNk+TSbp9T8P1K9/0dVm+4QxuEuJHWRkZMhkMmno0KE222d+fr6WLVum2NhYm+0TAADYXtYPVzR4eoJNw7Ykmc3Sb57brf/51xGb7he2R+B2EomJiRozZoxatGghHx8fhYeHa/HixSouLrY43s/PTy+//LJmzpxZ4xgAAOBYxSVluvu3m/RdZr5ha8x+/kvFbztp2P5x4wjcTuCll17S6NGjtWnTJvn7+6tz585KTU3VggULNGzYMBUWFlabYzKZNHbsWOXn52vz5s0OqBoAAFzPc2/u1/7U81bN2bduvE59Nln71o2v85yZz+zU+bwia8uDnRC4HWzv3r2aN2+eTCaT1qxZo4yMDKWkpCg1NVWhoaHavXu35s+fb3HuuHHjJEkbNmywZ8kAAKAOko/k6vm3Dlg9LzDAR0GtfBUY4FPnOdm5hfrd0j1WrwX7IHA72LPPPiuz2azp06dr6tSpla+HhIRo1apVkqQVK1YoJyen2twRI0bI19dXcXFxdqsXAADUzTP/m6KyMvvdm+If8ceV+v1Fu62HumtUgTs3N1cxMTEKDQ2Vl5eX2rVrpzlz5qigoEAzZsyQyWTS8uXL7VZPfn6+EhMTJUkzZ86stn3w4MEKCwtTcXGxxbPYXl5eioqKUmZmppKTkw2vFwAA1M2JM/mK337K7uv+7/updl8T19doAvf+/fsVHh6uF198UdnZ2erWrZtKSkr06quv6v7779fRo0clSb169bJbTSkpKSouLpanp6ciIiIsjhk0aJAkac8ey18TjR9/rb+LthIAAJzHyg++VXm5/e+8vGbDMV0pLLX7uqhdowjcubm5GjdunLKzszV37lxlZWUpOTlZ2dnZWrp0qRISErRv3z6ZTCb16NHDbnWlpaVJktq3by83NzeLY0JCQqqM/ano6Gi5uLgQuAEAcCKffXnGIevm5Rcr6fAPDlkbNWsUgfuJJ55QZmamZs+erWXLlsnf379yW0xMjHr27KnS0lIFBwerSZMmdqvrwoULkqRmzZrVOKZiW8XYn2rZsqUiIyOVkpKizMxM2xcJAACsUlJSrgNp1t2ZxJa+PnrOYWvDsgYfuI8eParY2FgFBARo8eLFFsf06dNHktSzZ88qr3///fcaP368/P391axZMz300EM6d852B/HVq1clSR4eHjWO8fT0lCSLtwasQFsJAADO48h3F1RUXOaw9b8+kuuwtWGZ5T6GBmTdunUqLy/XlClT5OfnZ3GMt7e3pKqBOz8/X8OGDVPz5s21bt06FRYWKiYmRmPHjtWuXbvk4nLjv6t4eXlJUq0PrikqKqpSoyXR0dGaP3++EhIS9Nhjj1ldR0REhLKzs62eBwAAqrvqHiL5P2Rx27514697u7/AAO/KP099NrnGcdm5V9T3geon29b/J1Fb//GgFRWjLgIDA5WUlFSvuQ0+cFc8FGbYsGE1jqloxfhx4H7zzTd1+vRpbd++XbfddpskKSgoSAMHDtSGDRs0ceLEG67teu0iP95WW9vJiRMnJEnt2rWrVx3Z2dk6ffp0veYCAICf8A+Q/C1vqrjHdl24ubrUeeyPFRWX8XPdyTT4wF0RRtu3b29xe2lpqXbt2iWpauCOj4/XoEGDKsO2JA0YMEAdO3ZUXFycTQJ3WFhYZY2lpaUWL5xMT0+vMtaSilaSitYSawUGBtZrHgAAqO6q2y2qqQE1O/fKdecHBnjLzdVFpWXlys6tuaW0pn15ergqoG3bupQKK9xIXmrwgbugoEBSzT3QsbGxys3Nlb+/vzp06FD5+pEjRzRp0qRq47t3764jR47YpLbevXvLw8NDRUVFSkpKUv/+/auN2blzpyQpMjLS4j7MZrPi4+Pl6+urESNG1KuO+n49AgAAqjt07LzC7/3I4jZLLSA/deqzyQpq5avs3EK1i/qX1evf//PRWrvoeavnwTgN/qLJit9GLD0YJisrS/PmzZMk9ejRQyaTqXLbhQsX1LRp02pzmjdvrvPnbXPlsb+/v6KioiRJK1eurLZ9+/btSktLk4eHhyZMmGBxH0lJScrKytKoUaMqL7AEAACO06VDU3l7uTps/T7dAhy2Nixr8IF75MiRkqSlS5dWuZf1vn37NGzYMOXmXruS154PvPmxhQsXymQyafXq1Vq7dm3l6+np6ZoxY4YkadasWWrZsqXF+TfaTgIAAGzLzc1FvTq3cNj6BG7n0+ADd0xMjFq0aKFTp06pe/fuCg8PV6dOndSvXz917NhRw4cPl1T9loDNmjXTxYsXq+3v/Pnzat68uc3q69+/v5YsWSKz2axp06YpODhYvXv3VpcuXXT8+HFFRkZqyZIlNc6Pi4uTi4uLxo4da7OaAADAjRlzR5BD1m3R1FN9ujku7MOyBh+4g4KCtGPHDkVHR8vLy0sZGRlq3ry53njjDSUkJFSe9f5p4O7atavFXu0jR46oa9euNq0xJiZGGzduVFRUlPLy8pSamqqwsDAtWrRI27Ztk4+P5dsHnTx5UgcOHNDAgQMVEMBvswAAOItHfh4mNzfT9Qfa2Ix7wuTl2eAv0bvpNIp3pGvXroqPj6/2+uXLl5WRkSEXFxfdfvvtVbaNHTtWCxYsUGZmpoKCrv2W+tVXXyk9PV0vvviizWscPXq0Ro8ebdUc2kkAAHBObVr66p7hwfp34vd2W9NkkmZN6mK39VB3Df4Md20OHz4ss9msTp06VTuL/Oijj6p169aaMGGC4uPjtX79ej3wwAPq169fjRcw2ltcXJwkAjcAAM7o6d/0loe7/aLWo/d1UcegJnZbD3XXqAP3wYMHJVVvJ5GkJk2aaPPmzWrdurUmT56sRx55RAMHDlR8fLxNnjJ5o/Lz87V161aFhYWpc+fOji4HAAD8RLeQZnrmsZ/ZZa32bfz04h/62mUtWK9RtJTUpLbALUkhISEWW1GcgZ+fn/Ly8uTq6rjbDgEAgNr9cWq44rad1O79OXWeU/FAm7o8JEeSXF1NevuZO+Xv61GvGmE8ArdqDtzOzGQyycvLy9FlAACAWri5uWjDq1Ea+vAnOnT8Qp3m1OXhOBVMJuntZ+7U8Mg29S0RdmAym81mRxcBAADQkOVeuKq7HtukpMO5Ntunm5tJ7zw3RA/cHWKzfcIYBG4AAAA7uFpUqr++nqxlaw+pvPzG4lePsOZa8+yd6t2V2wLfDAjcAAAAdvTVNzn63Qt7tOebH6ye29TfQ7//1e3604we8nDnOq6bBYEbAADAAZKP5GrF+0f1wecZunCpuMZxrq4mRXQL0KP3ddHkMR3l492oL8G7KRG4AQAAHMhsNivj9GV9fSRX6ZmXtGjlAeUXlOgWP3dtXDFGPcKaE7JvcgRuAAAAJxI0cp1O51xR25Y+yvz8AUeXAxtw/BNcAAAAgAaMwA0AAAAYiMANAAAAGIjADQAAABiIwA0AAAAYiMANAAAAGIjADQAAABiIwA0AAAAYiMANAAAAGIjADQAAABiIwA0AAAAYiMANAAAAGIjADQAAABiIwA0AAAAYiMANAAAAGIjADQAAABiIwA0AAAAYiMANAAAAGIjADQAAABiIwA0AAAAYiMANAAAAGIjADQAAABiIwA0AAAAYiMANAAAAGIjADQAAABiIwA0AAAAYiMANAAAAGIjADQAAABiIwA0AAAAYiMANAAAAGMjN0QUAAACprKxcJ7MKdPlKiUwmyc/HXbe19pOLi8nRpQG4QQRuAAAcJPlIrv6ZcFx7D+Vqf+o5FRSWVtnu7+uun3VtocjwW/XQuE7qHtrMQZUCuBEms9lsdnQRAAA0FmazWf/69Du98u5hfXXwB6vmDu4TqN//qrsmDGsvk4kz3w1V0Mh1Op1zRW1b+ijz8wccXQ5sgDPcAADYycmsy5r5zE4l7j5dr/nbv87W9q+zdc+I9lqx8A61auFt4woBGIGLJgEAsIOPvsjQ7T//sN5hu+q+TqjbxA+UuDvTBpUBMBqB2w4yMjJkMpk0dOhQm+0zPz9fy5YtU2xsrM32CQAwxj/jj+u+uZuVX1Bis32ezyvS2Nmf6eMtJ2y2TwDGIHA7icTERI0ZM0YtWrSQj4+PwsPDtXjxYhUXF1sc7+fnp5dfflkzZ86scQwAwPHitp7U1IXbVV5u+0umSkrL9Ys/btaWvWdsvm8AtkPgdgIvvfSSRo8erU2bNsnf31+dO3dWamqqFixYoGHDhqmwsLDaHJPJpLFjxyo/P1+bN292QNUAgOvJzr2iaU9ZF7b3rRuvU59N1r514+s0vrikXL9asE0XLxXVt0wABiNwO9jevXs1b948mUwmrVmzRhkZGUpJSVFqaqpCQ0O1e/duzZ8/3+LccePGSZI2bNhgz5IBAHVgNpv1m+d263yedUE4MMBHQa18FRjgU+c5p3Ou6A/LvrK2RAB2QuB2sGeffVZms1nTp0/X1KlTK18PCQnRqlWrJEkrVqxQTk5OtbkjRoyQr6+v4uLi7FYvAKBuNu7M1H8226+/evV/junLA2ftth6AumtUgTs3N1cxMTEKDQ2Vl5eX2rVrpzlz5qigoEAzZsyQyWTS8uXL7VZPfn6+EhMTJUkzZ86stn3w4MEKCwtTcXGxxbPYXl5eioqKUmZmppKTkw2vFwBQd6+tO2L3NZevO2r3NQFcX6MJ3Pv371d4eLhefPFFZWdnq1u3biopKdGrr76q+++/X0ePXvuQ6tWrl91qSklJUXFxsTw9PRUREWFxzKBBgyRJe/bssbh9/PhrPX60lQCA80g/dUkbd9n/ln3/TvxeOeeqX/cDwLEaReDOzc3VuHHjlJ2drblz5yorK0vJycnKzs7W0qVLlZCQoH379slkMqlHjx52qystLU2S1L59e7m5WX4GUUhISJWxPxUdHS0XFxcCNwA4kX8nfi9HPMe5pLRcH9mxjQVA3TSKwP3EE08oMzNTs2fP1rJly+Tv71+5LSYmRj179lRpaamCg4PVpEkTu9V14cIFSVKzZs1qHFOxrWLsT7Vs2VKRkZFKSUlRZiYPQAAAZ5B0ONdha399xHFrA7CswQfuo0ePKjY2VgEBAVq8eLHFMX369JEk9ezZs/K1ioDer18/eXp6ymQy2by2q1evSpI8PDxqHOPp6SlJFm8NWIG2EgBwLo4MvQRuwPk0+MC9bt06lZeXa8qUKfLz87M4xtvbW1LVwH38+HF98MEHCgwMVN++fQ2pzcvLS5JqfXBNUVFRlRotiY6OliQlJCTYsDoAQH0Ul5Qp48xlh63/bUaew9YGYJnlxuEGpOKhMMOGDatxTEUrxo8D9+DBg5WVlSVJevrpp7Vr1y6b13a9dpEfb6ut7eTEiWv9eu3atatXHREREcrOzq7XXABAVeUmT6nZghq371s3vtZ7bAcGeFf+eeqzyTWOy869or4PVP9ms+BKsdoGBcn238vCXrKa/kFyuUVZ2VkKCgpydDn4P4GBgUpKSqrX3AYfuCvCaPv27S1uLy0trQzTPw7cLi7Gn/wPCwuTdK3G0tJSixdOpqenVxlrSUUrSUVribWys7N1+vTpes0FAPyEi6dU8zmSygfbXI+bq0udxlVXrjN8pt/c/MskF6m8rIyfzw1Egw/cBQUFkmrugY6NjVVubq78/f3VoUMHe5am3r17y8PDQ0VFRUpKSlL//v2rjdm5c6ckKTIy0uI+zGaz4uPj5evrqxEjRtSrjsDAwHrNAwBUZ5ZJZ8xlksnV4vbs3Cu1zg8M8Jabq4tKy8qVnVvz9Ts17cdkLlabtm3rXjCcTparq8olubi6qjXvpdO4kbzU4AN3YGCgLly4oOTkZA0YMKDKtqysLM2bN0+S1KNHD0MujKyNv7+/oqKilJCQoJUrV1YL3Nu3b1daWpo8PDw0YcIEi/tISkpSVlaW7rnnnsoLLK1V369HAACW9Zr0kQ58e97iNkttID926rPJCmrlq+zcQrWL+pfVaw+NDNHmVdy16mYWNHKdTudcUevA1so8xHvZEDT4iyZHjhwpSVq6dGmVe1nv27dPw4YNU27utau57fnAmx9buHChTCaTVq9erbVr11a+np6erhkzZkiSZs2apZYtW1qcf6PtJAAA24voFuCwtfs4cG0AljX4wB0TE6MWLVro1KlT6t69u8LDw9WpUyf169dPHTt21PDhwyVV7d+2p/79+2vJkiUym82aNm2agoOD1bt3b3Xp0kXHjx9XZGSklixZUuP8uLg4ubi4aOzYsXasGgBQmwE9LZ8kaehrA7CswQfuoKAg7dixQ9HR0fLy8lJGRoaaN2+uN954QwkJCZVnvR0VuKVrvxRs3LhRUVFRysvLU2pqqsLCwrRo0SJt27ZNPj6Wr2Y/efKkDhw4oIEDByoggDMaAOAsJo3qID8fd7uv27K5l6IH1++OVQCM0+B7uCWpa9euio+Pr/b65cuXlZGRIRcXF91+++0OqOy/Ro8erdGjR1s1h3YSAHBOTfw89KuxIVrxfqpd133k553l6WH5Yk0AjtMoAndNDh8+LLPZrLCwMItnkdevXy9JOnLkSJW/BwcHKyIiwn6F1iAuLk4SgRsAnNGcKd311odpKiktt8t6vt5u+s0vutplLQDWadSB++DBg5JqbieZNGmSxb9PnTpVa9asMbS268nPz9fWrVsVFhamzp07O7QWAEB1nTs01V9+3UtPLU+2y3pLf99XQYH1uW83AKMRuFVz4DabzfYsxyp+fn7Ky8uTqytfHQKAs3pyek999MUJJR89V+c5FffXvt79un9saN/WnN0GnBiBW469YLK+TCaTvLy8HF0GAKAW7u4u+uDvIzRoarxO59QtQF/vPt0/FdLOX+uWDpWLCw9zB5yVyezMp3EBAGgAvv3+okY+ulGZZwtsut/Q25ro8zfHqH0bf5vuF45V8eCbti19lPn5A44uBzbQ4G8LCACAo3Xu0FS7/zFWQ/u2ttk+774zSDvXjiVsAzcBAjcAAHbQLtBPX6y8S6/NHyAfr/p3dN7i76HVz96p+OWj1KqFtw0rBGCURt3DDQCAPbm4mDT7gW6aNKqDVn34rd5Yn6qTWXVrMwm9rYl+PamLpk3opBZNuYYHuJnQww0AgIOUlZVrR/JZ7T34g74+mqvDxy8o9fs8lZWb5eZq0qRRHRTRPUD9br9VA3u14sLIRoIe7oaHM9wAADiIq6uLhvZtXaW3uyJstWrhrfeWDnNgdQBshR5uAAAAwEAEbgAAAMBABG4AAADAQARuAAAAwEAEbgAAAMBABG4AAADAQARuAAAAwEAEbgAAAMBABG4AAADAQARuAAAAwEAEbgAAAMBABG4AAADAQARuAAAAwEAEbgAAAMBABG4AAADAQARuAAAAwEAEbgAAAMBABG4AAADAQARuAAAAwEAEbgAAAMBABG4AAADAQARuAAAAwEAEbgAAAMBABG4AAADAQARuAAAAwEAEbgAAAMBABG4AAADAQARuAAAAwEAEbgAAAMBABG4AAADAQARuAAAAwEBuji4AABqzU9mX9eWBHCUdztWBtPO6eKlYZeVmeXm6qtNtTdSnW4AiugWo7+0BcnXlHAkA3IwI3ABgZ2Vl5fpkR6Zejz2qjbsyaxy3K+Ws1nx8TJLUvo2ffj2pix6eGKaWLbztVSoAwAY4XQIAdvT1kVz1mvQfjX/is1rD9k+dOHNZ819J0m2jY/XC29+orKzcwCoBALZE4AYAOygtLdfC15IUOWWDDh2/UO/9FBWX6cmX9+mOh+KVlpFnwwoBAEYhcAOAwa4Wleq+uV9o0coDKisz22SfXx38QQN+Fad9h36wyf4AAMYhcNtBRkaGTCaThg4darN95ufna9myZYqNjbXZPgHYXklJue6ft0Ufbzlp832fzytS1KyNOvDtOZvvGwBgOwRuJ5GYmKgxY8aoRYsW8vHxUXh4uBYvXqzi4mKL4/38/PTyyy9r5syZNY4B4Hh/ef1rbdhq+7BdIS+/WOMe/0x5+XwOAICzInA7gZdeekmjR4/Wpk2b5O/vr86dOys1NVULFizQsGHDVFhYWG2OyWTS2LFjlZ+fr82bNzugagDXs+/QD3ph9UHr5qwbr1OfTda+dePrPOdUdoHm/X2vteUBAOyEwO1ge/fu1bx582QymbRmzRplZGQoJSVFqampCg0N1e7duzV//nyLc8eNGydJ2rBhgz1LBlAHpaXlmvbUdpWXW9ezHRjgo6BWvgoM8LFq3soPvtXmr85YNQcAYB8Ebgd79tlnZTabNX36dE2dOrXy9ZCQEK1atUqStGLFCuXk5FSbO2LECPn6+iouLs5u9QKom/jtJ3Uk/aJd11y6+hu7rgcAqJtGFbhzc3MVExOj0NBQeXl5qV27dpozZ44KCgo0Y8YMmUwmLV++3G715OfnKzExUZI0c+bMatsHDx6ssLAwFRcXWzyL7eXlpaioKGVmZio5OdnwegHU3euxR+2+ZuLu0zp2glsFAoCzaTSBe//+/QoPD9eLL76o7OxsdevWTSUlJXr11Vd1//336+jRaz8ce/XqZbeaUlJSVFxcLE9PT0VERFgcM2jQIEnSnj17LG4fP/5anydtJYDzyDidr8++dEx7x1sffuuQdQEANWsUgTs3N1fjxo1Tdna25s6dq6ysLCUnJys7O1tLly5VQkKC9u3bJ5PJpB49etitrrS0NElS+/bt5ebmZnFMSEhIlbE/FR0dLRcXFwI34ER27T/rwLWrt58BAByrUQTuJ554QpmZmZo9e7aWLVsmf3//ym0xMTHq2bOnSktLFRwcrCZNmtitrgsXrj1trlmzZjWOqdhWMfanWrZsqcjISKWkpCgzs+6PiQZgnK+P5Dps7ZSj53jsOwA4mQYfuI8eParY2FgFBARo8eLFFsf06dNHktSzZ8/K19avX697771X7du3l4+Pj7p06aI///nPunz5ss1qu3r1qiTJw8OjxjGenp6SZPHWgBVoKwGcy/7U8w5b+8rVUh07eclh6wMAqrPcx9CArFu3TuXl5ZoyZYr8/PwsjvH29pZUNXAvW7ZMt912m55//nkFBQVp//79euaZZ7Rt2zZt375dLi43/ruKl5eXJNX64JqioqIqNVoSHR2t+fPnKyEhQY899pjVdURERCg7O9vqeQAsy2kyS3JrY3HbvnXja73lX2CAd+Wfpz6bXOs62blX1PeB6r9oDx46Rh5lfON1s8pq+gfJ5RZlZWcpKCjI0eXAATgGnFNgYKCSkpLqNbfBB+6Kh8IMGzasxjEVrRg/DtxxcXG69dZbK/8+ZMgQ3XrrrZoyZYp27typwYMH33Bt12sX+fG22tpOTpw4IUlq165dverIzs7W6dOn6zUXgAXe5TV+ulbcZ/t63Fxd6jTOkh9yz0lX+Dd90/Ivk1yk8rIyPpsbK46BBqfBB+6KMNq+fXuL20tLS7Vr1y5JVQP3j8N2hYo7idjq4A8LC6ussbS01OKFk+np6VXGWlLRSlLRWmKtwMDAes0DYFmOu1RSw7bs3Cu1zg0M8Jabq4tKy8qVnVtzK1lt+7o1oKk8ytrWpVQ4oSxXV5VLcnF1Veu2vI+NEceAc7qRvNTgA3dBQYGkmnugY2NjlZubK39/f3Xo0KHWfW3ZskWS1LVrV5vU1rt3b3l4eKioqEhJSUnq379/tTE7d+6UJEVGRlrch9lsVnx8vHx9fTVixIh61VHfr0cAWPbLJ7do3affWdxmqQXkx059NllBrXyVnVuodlH/qtf6aQd3qmkTz3rNheMFjVyn0zlX1DqwtTIP0RrUGHEMNDwN/qLJit9GLD0YJisrS/PmzZMk9ejRQyaTqcb9nD59Wk899ZTGjBljs3t1+/v7KyoqSpK0cuXKatu3b9+utLQ0eXh4aMKECRb3kZSUpKysLI0aNaryAksAjtWnW4DD1g5p50/YBgAn0+AD98iRIyVJS5curXIv63379mnYsGHKzb12+67aQvTly5c1YcIEeXh46O2337ZpfQsXLpTJZNLq1au1du3aytfT09M1Y8YMSdKsWbPUsmVLi/NvtJ0EgO1FdHdc4HZk2AcAWNbgA3dMTIxatGihU6dOqXv37goPD1enTp3Ur18/dezYUcOHD5dUtX/7xwoLCzVu3Dh9//33SkxMVOvWrW1aX//+/bVkyRKZzWZNmzZNwcHB6t27t7p06aLjx48rMjJSS5YsqXF+XFycXFxcNHbsWJvWBaD+BvZsVXm3EXubFFV7axwAwP4afOAOCgrSjh07FB0dLS8vL2VkZKh58+Z64403lJCQUHnW21LgLikp0X333aekpCR9+umn6tatmyE1xsTEaOPGjYqKilJeXp5SU1MVFhamRYsWadu2bfLxsXwLsZMnT+rAgQMaOHCgAgI4qwU4C3d3Fz16bxe7r9v6Vh9NGGb5AnEAgOM0+IsmpWsXOcbHx1d7/fLly8rIyJCLi4tuv/32Ktsq7t39xRdf6JNPPlG/fv0MrXH06NEaPXq0VXNoJwGc16P3ddbzq/artNRstzVn3ddZ7u4N/jwKANx0GvUn8+HDh2U2m9WpU6dqZ5F/+9vf6t///rd+//vfy8fHR3v27Kn874cffnBQxVXFxcVJInADzqhtK18tnNnLbut1DPLXH6eG2209AEDdNerAffDgQUmW20k+/fRTSdKSJUs0YMCAKv8lJCTYtU5L8vPztXXrVoWFhalz586OLgeABfMf6amenZvbZa1Vz9wpXx93u6wFALBOo2gpqUltgTsjI8PO1VjHz89PeXl5cnV1dXQpAGrg4e6qfywaokHT4nXpck2Pwqmq4mE213tAzo/9aUYPDe1r2wu6AQC2Q+BWzXcocWYmk0leXl6OLgPAdYSHNVf8a6N012ObVFBYet3x13swzk89el9nPf9ERH3LAwDYQaMO3Js3b7bLOsHBwTKb7XfhFADncmefQH2x8i5NmPO5zp6r/XHt1njy4R5aPCei1od2AQAcr1H3cAOAvUT2aKkj/7lXU6JDbnhfwW389MXKu7Tkd30J2wBwEyBwA4CdNL/FU/9cPFTxy6N0589aWT2/VQtvPTWrlw5++HMNj2xjQIUAACM06pYSAHCE6MG3KXrwbTqYdl5vffitdh/I0Tdp51VcUl5tbPs2furTNUCTRgXr5yOD5eHOhdIAcLMhcAOAg4SHNdcrfxogSSouKVPq93ka8cgnyr1YpFubeerIf+5TQDMujgaAmx0tJQDgBDzcXdUjrLk8PVwr/07YBoCGgcANAAAAGIjADQAAABiIwA0AAAAYiMANAAAAGIjADQAAABiIwA0AAAAYiMANAAAAGIjADQAAABiIwA0AAAAYiMANAAAAGIjADQAAABiIwA0AAAAYiMANAAAAGIjADQAAABiIwA0AAAAYiMANAAAAGIjADQAAABiIwA0AAAAYiMANAAAAGIjADQAAABiIwA0AAAAYiMANAAAAGIjADQAAABiIwA0AAAAYiMANAAAAGIjADQAAABiIwA0AAAAYiMANAAAAGIjADQAAABiIwA0AAAAYyM3RBQCNndls1umzV5R8NFfZ5wpVXFIuT3cXBbXyVZ9uAWrZwtvRJQIAgBtA4AYcwGw2a2fyWa14/6i++OqMcs5frXFsUCtfjbmjrR67v6t6dw2wY5UAAMAWCNyAnX285YSeWv61Dh67UKfxmWcL9NaHaXrrwzT173Grlvyur4ZEtDa4SgAAYCv0cAN2cu7iVU3501ZNnPN5ncP2T+355gcNffgTPb74SxVcKbFxhQAAwAgEbsAODqadV4/7PtJ7n6TbZH/L1x1Rn8kf62TWZZvsDwAAGIfAbQcZGRkymUwaOnSozfaZn5+vZcuWKTY21mb7hDG+STuvIQ8n6EzOFZvu99uMPN05LZ7QDQCAkyNwO4nExESNGTNGLVq0kI+Pj8LDw7V48WIVFxdbHO/n56eXX35ZM2fOrHEMHO9MToFGzdqoC5eMeY9OZhUo6tGNyi/gGAAAwFkRuJ3ASy+9pNGjR2vTpk3y9/dX586dlZqaqgULFmjYsGEqLCysNsdkMmns2LHKz8/X5s2bHVA1rsdsNmvW33bp7Lnq719N9q0br1OfTda+dePrPCftRJ5i/r6vPiUCAAA7IHA72N69ezVv3jyZTCatWbNGGRkZSklJUWpqqkJDQ7V7927Nnz/f4txx48ZJkjZs2GDPklFH/4g7rvjtp6yaExjgo6BWvgoM8LFq3v/+O1Vf7Dlj1RwAAGAfBG4He/bZZ2U2mzV9+nRNnTq18vWQkBCtWrVKkrRixQrl5ORUmztixAj5+voqLi7ObvWibkpKyvWnV5LsuuYf//6VzGazXdcEAADX16gCd25urmJiYhQaGiovLy+1a9dOc+bMUUFBgWbMmCGTyaTly5fbrZ78/HwlJiZKkmbOnFlt++DBgxUWFqbi4mKLZ7G9vLwUFRWlzMxMJScnG14v6u4/W04o6wfbXiR5PftTz+urb36w65oAAOD6Gk3g3r9/v8LDw/Xiiy8qOztb3bp1U0lJiV599VXdf//9Onr0qCSpV69edqspJSVFxcXF8vT0VEREhMUxgwYNkiTt2bPH4vbx46/1+tJW4lxejz3qkHX/J/aIQ9YFAAA1axSBOzc3V+PGjVN2drbmzp2rrKwsJScnKzs7W0uXLlVCQoL27dsnk8mkHj162K2utLQ0SVL79u3l5mb5oZ8hISFVxv5UdHS0XFxcCNxOJL+gWNuSshyydsL2U7SVAADgZBpF4H7iiSeUmZmp2bNna9myZfL396/cFhMTo549e6q0tFTBwcFq0qSJ3eq6cOHa0wabNWtW45iKbRVjf6ply5aKjIxUSkqKMjMzbV8krJZy9JwclXkvXCpWxmnuyw0AgDNp8IH76NGjio2NVUBAgBYvXmxxTJ8+fSRJPXv2rHxtx44dGjlypFq3bi1PT08FBQVVaT2xhatXr0qSPDw8ahzj6ekpSRZvDViBthLnknz0nEPX//pIrkPXBwAAVTX4wL1u3TqVl5drypQp8vPzszjG29tbUtXAfeHCBYWHh+vVV19VYmKili5dqsOHD2vAgAE2O5Ps5eUlSbU+uKaoqKhKjZZER0dLkhISEmxSF27MyWzHnmF29PoAAKAqy43DDUjFQ2GGDRtW45iKAP3jwD1+/PjKM8cV+vbtq86dO+uDDz7QnDlzbri267WL/HhbbW0nJ06ckCS1a9euXnVEREQoOzu7XnNR3UWfaMmrn8Vt+9aNr/Ue24EB3pV/nvpscq3rZOdeUd8Hqn+r8czfntffF+ywomI4k6ymf5BcblFWdpaCgoIcXQ4cgGMAHAPOKTAwUElJ9bvlb4MP3BVhtH379ha3l5aWateuXZKqBm5LWrRoIUk1XuBorbCwsMoaS0tLLe43PT29ylhLKlpJfvoLQl1lZ2fr9OnT9ZoLC1rnSV6WN1U82OZ63Fxd6jTOkkt553Upl/fzpuVfJrlI5WVl/LtsrDgGwDHQ4DT4wF1QUCCp5h7o2NhY5ebmyt/fXx06dKi2vaysTOXl5Tpx4oTmz5+vwMBA/eIXv7BJbb1795aHh4eKioqUlJSk/v37Vxuzc+dOSVJkZKTFfZjNZsXHx8vX11cjRoyoVx2BgYH1mgfL8r1cdKmGbdm5td+bOzDAW26uLiotK1d2bu2PhK9pX0393eTr2bYupcIJZbm6qlySi6urWrflfWyMOAbAMeCcbiQvNfjAHRgYqAsXLig5OVkDBgyosi0rK0vz5s2TJPXo0UMmk6na/CFDhlSeAQ8NDdXmzZt166232qQ2f39/RUVFKSEhQStXrqwWuLdv3660tDR5eHhowoQJFveRlJSkrKws3XPPPZUXWFqrvl+PwLJPd5zS3b9NtLjNUgvIj536bLKCWvkqO7dQ7aL+Va/1d2z6h27v1Lxec+F4QSPX6XTOFbUObK3MQ9x5qDHiGADHQMPT4C+aHDlypCRp6dKlVe5lvW/fPg0bNky5udfu6FDTA29WrVqlPXv2aN26dWrSpIlGjRqlkydP2qy+hQsXymQyafXq1Vq7dm3l6+np6ZoxY4YkadasWWrZsqXF+TfaTgLb69MtwGFre3u5qkuHpg5bHwAAVNfgA3dMTIxatGihU6dOqXv37goPD1enTp3Ur18/dezYUcOHD5dUc/92586dFRkZqcmTJ+uLL75Qfn6+XnjhBZvV179/fy1ZskRms1nTpk1TcHCwevfurS5duuj48eOKjIzUkiVLapwfFxcnFxcXjR071mY14ca0bOGtbiFNHbL24J8Fys2twf+zBgDgptLgfzIHBQVpx44dio6OlpeXlzIyMtS8eXO98cYbSkhIqDzrfb0LJiWpadOmCg0N1fHjx21aY0xMjDZu3KioqCjl5eUpNTVVYWFhWrRokbZt2yYfH8t3tTh58qQOHDiggQMHKiDAcWdVUd2vJ3VxzLq/cMy6AACgZg2+h1uSunbtqvj4+GqvX758WRkZGXJxcdHtt99+3f3k5OTo22+/rfECxhsxevRojR492qo5tJM4r4fGddL8V5JUUFhqtzWDWvlq7ODb7LYeAACom0YRuGty+PBhmc1mhYWFVTuL/OCDDyo0NFS9evVS06ZNdezYMf2///f/5Obmpt///vcOqriquLg4SQRuZ3SLv4f+8NDtevaN/XZbc+GjvWgnAQDACTXqn84HDx6UZLmdpH///vrkk080ffp03XXXXXrxxRd15513av/+/QoNDbV3qdXk5+dr69atCgsLU+fOnR1dDiz488xeuj205gcW2dKIyDZ69D6OAwAAnFGjPsNdW+CePXu2Zs+ebe+S6szPz095eXlydXV1dCmogaeHq9Y8N1gDHoxTSWl5neZU3Fv7evfr/rEmfu5a9cwgi7e1BAAAjkfgVt0umHQ2JpNJXl41PM4QTqNPtwC9u2SoJsdsUXm5+brjr3ef7p/y8nRV3KtRat/Gv74lAgAAgzXqwL1582a7rBMcHCyz+fphCw3TpFHXnmA65U9b63ymuy78fNwV91qUBke0ttk+AQCA7TXqHm7AXiaN6qCda8eqa8emNtlfZPit2rduvIb2JWwDAODsCNyAnfQLv1XJsRP05MM95OlRv957Px93Lf1dX+16ZyxPlAQA4CbRqFtKAHvz8nTTkt/11bxp4Vr9n2Na8f5RfZeZf9154Z2a6bH7u2pKdIj8fT3sUCkAALAVAjfgAC2aeumP08I1d+rtOnHmspIO5+rro7l69d3DunK1TD5ervrj1B7q062F+nQLUJuWPtyFBACAmxSBG3Agk8mk4Lb+Cm7rr/tGddA/4o7rytUratbEU8/89meOLg8AANgAPdwAAACAgQjcAAAAgIEI3AAAAICBCNwAAACAgQjcAAAAgIEI3AAAAICBCNwAAACAgQjcAAAAgIEI3AAAAICBCNwAAACAgQjcAAAAgIEI3AAAAICBCNwAAACAgQjcAAAAgIEI3AAAAICBCNwAAACAgQjcAAAAgIEI3AAAAICBCNwAAACAgQjcAAAAgIEI3AAAAICBCNwAAACAgQjcAAAAgIEI3AAAAICB3BxdAG5OZrNZpYVFji7DKm7enjKZTI4uA2gwzGazrhSWOroMq/h4u/E5ANgInwF1R+BGvZQWFundkAcdXYZVpqT/U+4+Xo4uA2gwrhSWyq//O44uwyqX9zwkXx93R5cBNAh8BtQdLSUAAACAgQjcAAAAgIEI3AAAAICBCNwAAACAgQjcAAAAgIEI3AAAAICBCNwAAACAgQjcAAAAgIEI3AAAAICBCNwAAACAgQjcdpCRkSGTyaShQ4fabJ/5+flatmyZYmNjbbZPAAAA2B6B20kkJiZqzJgxatGihXx8fBQeHq7FixeruLjY4ng/Pz+9/PLLmjlzZo1jAAAA4HgEbifw0ksvafTo0dq0aZP8/f3VuXNnpaamasGCBRo2bJgKCwurzTGZTBo7dqzy8/O1efNmB1QNAACAuiBwO9jevXs1b948mUwmrVmzRhkZGUpJSVFqaqpCQ0O1e/duzZ8/3+LccePGSZI2bNhgz5LrzmRSt0fH6p4dr+hX37+nSUn/q4i/PiQ3b09HV+aUzl28qqvFZZKkq8Vlyi/gm4vG5rvMS7padO0YKCopU2lpuYMrso9FT/SR+ZsZmj6xk8XtW1bdratJ09Q9tJmdK7Mvs9mslKO5KiwqlSSVlJbLbDY7uCrYU3FJmXZ8nV15DJSW8RkgNYzPAAK3gz377LMym82aPn26pk6dWvl6SEiIVq1aJUlasWKFcnJyqs0dMWKEfH19FRcXZ7d6rdHvb9PU75lpupiWqT0L31ZG/JfqNuNujXjnT5LJ5OjynEbykVxNW7hdbUf+S+cuFkmSzl0sUtuR/9JvF+3Wt99fdGyBMJTZbNbHW05o1KxPFXL3v3Uu79oxkHuhSB3uel/PvZmi3AtXHVylsZ5+PUUHj53X3/8YqbatfKps+92D3TW0b2v99fVkHT5+wUEVGqvwaqlWxB5Vj3s/0s/u/1jn8679sp1z/qr6PrBBb3+UpuKSMgdXCSNl517RU8u/VvvRsRo8PaHyGDh77qrGzU7Upl2ZDq7QWI3hM6BRBu7y8nKtX79eEydOVJs2beTp6ak2bdpo+PDheuWVV+zWE52fn6/ExERJ0syZM6ttHzx4sMLCwlRcXGzxLLaXl5eioqKUmZmp5ORkw+u1RtOwIHV9+C5lJOzRlhkv6ti7n2vf02u19+m1aj0oXB0m3uHoEp3CWx98q35TNmjthmMqKq76AzW/oESvxx5V71/8Rxu2nHBQhTBSWVm5Zv1tlybO+VyffXmm2vbMswV6anmy+j7wcYP+xauktFxTF26Xr7e7Vj19Z+XrYcG3aNHjEdrzTY5eXHPQgRUa59zFqxr+yCd6bNFuHbIQJr4+kqsZf92hux9L1KXLfOvVEO1PPafev/iPnntzv7Jzq7eQxm8/pTG/2aR5L+1tsN94NIbPgEYXuHNycjR8+HBNmjRJH3/8sdzd3dWrVy+5u7try5Ytmj9/vlxdXe1SS0pKioqLi+Xp6amIiAiLYwYNGiRJ2rNnj8Xt48ePl+R8bSUd7hkkk4uLjqxMqPL6sXc/V8mVqwq5d7CDKnMesRu/08xndqqsrPYP0MKiMt03d7O27K0eyHBz+/2LX2nlB99ed1zGmcuKmrVRZ3IK7FCVY6QcPafFqw5o9B1BmnlvZ7m4mPTOosEymaSpC7ervLzhBY3Cq6UaOztRe7754bpjv/jqjO6b+4VKShpHi0FjkX7qkqJmbbQYtH9q2dqD+uvrznVyzZYa+mdAowrcBQUFuvvuu7Vt2zYNGTJEBw4c0IkTJ/TVV1/pxIkTOnTokP70pz/ZLXCnpaVJktq3by83NzeLY0JCQqqM/ano6Gi5uLg4XeAO6BWq8rIy5aYcq/J6WVGJzh/KUECvEAdV5hyuFpVq9uIv6zy+pLRcv33+ywZ7dqMx2p96Tq+9d6TO409lF+hvb+w3riAn8OybKdqfek7L5vbTa/MHKDK8pf782tdKy8hzdGmGWPVRWp3CdoXPvjyj9xO/M7Ai2Nv8V5Ksahl77s39+j4z38CKHKshfwY0qsA9d+5cff311xo0aJASExPVo0ePKtu7d++uv/zlL3ar58KFa18fNmtW80UAFdsqxv5Uy5YtFRkZqZSUFGVmOk+Pl0+rZio6n6/y4tJq265kn5dXi1vk4m75l4zGYP1nGVb35R797qK2JWUbVBHsbcX7R62e88/448rLb7htBaWlZk1duF1enq567P6u2pGcrZf/ecjRZRnCbDbr9Vjrj4H6zIFzyvrhij76IsOqOWaz9Mb6VGMKcgIN+TOg0QTu1NRUvfXWW/L09NS7774rDw+P6875/vvvNX78ePn7+6tZs2Z66KGHdO7cOZvVdPXqtcBVWy2entfu6GHp1oAVnLGtxNXbU2XFJRa3lRVde93N+/rvQUO15uNj1x9kwdoN9ZsH51JSUq5/xqdbPa+gsFQffJ5h+4KcSN7l4srrGT7ZcUoN9UudfYdydfS7i1bP270/p0Gc7YP03ifpKr1OS6El9f35cbNoqJ8BjeYU43vvvaeysjI99NBDuu222647Pj8/X8OGDVPz5s21bt06FRYWKiYmRmPHjtWuXbvk4nLjv6t4eXlJUq0XaRYVXbtjgbe3d41joqOjNX/+fCUkJOixxx6zuo6IiAhlZ1t35tTd7KK/ql+N28sKi+Tue4vFba6e7pKk0kL7nqkL6xSmEpNz9D+eveVxyTXA6nnr1m/UZ6t/aUBFsKcyk6+uNIup19zfzfub/vL4VtsWVE/lcpeaL7TpPlf/7U55uLvqSPoFLXy0l97f9L2+s+FX6J3CwuQiyycD7KnQvavkP7lec+8YOlaepd/buCLY20WfMZLXAKvnnT1XqLZB7WWS4+9c09g+AwIDA5WUlFSvuY0mcH/++eeSpLvvvrtO4998802dPn1a27dvrwzoQUFBGjhwoDZs2KCJEyfecE3Xaxf58bba2k5OnLh2B4t27drVq47s7GydPn3aqjkeJlepVc3br5y9oFvCguTi4VatrcQnsLmunstTeUn1dhMjnck6o2Kz4z+gJEk+JVI9LhUoulpk9XsFJ+TqJ9XzdrL5+XnKz3GSY8DkITW33e4e/2U3DevXRgteTdLHW04oOXai3v7bnRr68Cc2WyPrzBnJ7ARtOU1aSf71m5qb+4NU4CTHAOqv9WXJq35Tz5w+LTlB4OYzoO4aTeA+deqUJKljx451Gh8fH69BgwZVORs+YMAAdezYUXFxcTYJ3GFhYZKuBebS0lKLF06mp6dXGWtJRStJRWuJtQIDA62e4252kWo5WZy7/7jaDu2lgN6dlPPVf3sOXT3d1fz2YJ3dY/8+xDat2zjNGe5c1ysqqsc8H4+rata2rc3rgX2Z5aIsc5HMJusfAtXU1yxfJzkGyuWuLBvtK/S2Jlo8J0J7D/6gpW9/o/Jys55ekazFc/rq8V92s+oC09q0btPGKc5wF7u66gfpWlNuXZ9L8H9jWzX3kFtT5zgGUH/5XmW6VI95LuX5at3W+p/bRmhsnwH1yUsVGk3gLii4djut2nqhf+zIkSOaNGlStde7d++uI0ds86b37t1bHh4eKioqUlJSkvr3719tzM6dOyVJkZGRFvdhNpsVHx8vX19fjRgxol511OfrkZIrV/VuyIM1bv/+493q8cTP1W1mdJXA3WnKSLn7eOm7D7fXq9YbkXYsTe4+9TydYGPvJaRryvytVs/79N2FGhzxP7YvCHb3m2d36X//bd3FT34+bjqx+0M18XOO6x8KrpTIr/87N7wfk0la8+xgubqYNHXhtsrbf72w+qB+PiJYi+dEKGH7KZt8rXwsLU2+Pu43vJ8bZTabFf7zD3U4/WLdJ5lMGtS7lXas/cawumA/2blX1C7qX1b3cT85c5Cen/M7Y4qyEp8BdddoLpqsaLfYvXt3ncZfuHBBTZs2rfZ68+bNdf78eZvU5O/vr6ioKEnSypUrq23fvn270tLS5OHhoQkTJljcR1JSkrKysjRq1KjKCyydwcXUk0pdvVHB0f01bNU8dfrlCEX89SH1e3qqsncf1ncf7nR0iQ51b1Swbm1mXfjvHtJUd/ZxjrMauHG/ub+r1XN+NTbUacK2Lc2dGq47erfSX15PVur3/70gsLzcrGlPbZebq4ve/tudtezh5mMymfRYPY6B+syBcwoM8NG9UcFWzTGZpFmTOhtTkAM1hs+ARhO477nnHknSokWLKp/uWOH06dN6/vnndeyY/a/8XbhwoUwmk1avXq21a9dWvp6enq4ZM2ZIkmbNmqWWLVtanH+j7SRG2vuXNdr39Fo1DQtS/+cfUYcJd+jo25/q818tVoO57LiePD1ctWLhwDp/k+zh7qIVC++Qqa4T4PR6hDXX73/Vvc7j27fx019+3dvAihyjS4db9Oxvf6YvD+TopbXVb/91JP2inl6RrCERrfX4L7s5oELjPHxPmAb1ruVimJ8Yc0eQJo3qYGBFsLfFT/RVqxY13xThp57+zc/Uvk09m/+dVGP5DDCZG8mTNC5fvqwhQ4ZUPgI9MDBQ7dq10/nz5/Xdd9/JZDLp0qVL8vX1lSS1atVKkyZN0vLly6vsZ/z48frhhx/05Zd1f2hJRkaGOnTooCFDhmjr1q3Vtr/wwgt68sknJV17CE6zZs106NAhlZaWKjIyUps3b5aPj4/Ffffq1UsHDx7U2bNnFRBg/V0v6ut6LSXOaEr6P52mpaTC2o+P6ZGnd9T6laKvt5veXzZcd99Zv4ti4bzKy816fPGX1723ckg7f21cMUahtzWxU2V1Y6uvk+3p8p6HnKKlpMKFS0Ua//hn2plyttZxY+4I0r9fGi4/J6odtnEw7bzuemyTTudcqXXc/Bk9teiJPk514oXPgLprNGe4/fz8tGPHDj333HPq2bOn8vLydOjQIZWXl2vixIlau3ZtZdiWpK5du1rs1T5y5Ii6drXtV3oxMTHauHGjoqKilJeXp9TUVIWFhWnRokXatm1bjWH75MmTOnDggAYOHGjXsA3bmTqhk76OnahHfh4mb6+qty25xd9Dv3uwu/b/+x7CdgPl4mLS8gUD9Mn/jFL04HbVvvEIbuOnpb/rq33rJjhd2IZtNGviqc9X3qW3nh6k3l1aVNvev8etemfRYG14NYqw3UCFhzVXcuxE/e23P1PbltV/3v98RLA2v3WXnp8T4VRhG9ZpNGe4rbVs2TItWLBA3333nYKCgiRJX331lfr3768PP/ywskWlLq53hru+li9frscff1wvvPCC5s2bZ7P91gVnuG3vwqUihY39t3IvFimgqacyNt7vVGfiYLyTWZf1s/v/o3MXi3RrM09lbf6lXF2d97wIZ7dsy2w269CxCxo24xOdyytSy+ZeOrt1iqPLgh2VlpZr3+EfNG72ZzqXV6TAFl7K2uK8xwCfAXXnvJ/kDvboo4+qdevWmjBhguLj47V+/Xo98MAD6tevX40XMNpbXFycJOfs34b1mjXxlKfHtbPcnh6uThsKYJzbWvvJ6/+OAQ93V6cO27A9k8mk8LDm8vK8dgy4u/H+NzZubi4a0LNV5THAZ0DDwTtZgyZNmmjz5s1q3bq1Jk+erEceeUQDBw5UfHy8TZ4yeaPy8/O1detWhYWFqXPnhnfFMgAAQEPRaO7DXR8hISGKj493dBkW+fn5KS8vT66u9XhcIQAAAOyGwH2TMplM8vJy3n5kAAAAXEPgtoPg4GBxbSoAAEDj5PhmZAAAAKABI3ADAAAABiJwAwAAAAYicAMAAAAGInADAAAABiJwAwAAAAYicAMAAAAGInADAAAABiJwAwAAAAbiSZMAgHrx8XbT5T0POboMq/h482MPsBU+A+qOTx4AQL2YTCb5+rg7ugwADsJnQN0RuOHUXD3dFTp5uILH9lezrrfJo4mvSq8U6dL3WcraeUjHYzcr7/gZR5cJAABQIwI3nJbfbS018h/z1TSsnbJ3H9bhNxNUePaC3Hy91Lx7sDo9MEzdfzNO6yN+oyvZ5x1dLgAAgEUEbjglVy8PjfznAvm3b6XND7+gk5/urTbmqwXu6vboWJnNZgdUCAAAUDcEbjilTr8coaadgnTglQ8shm1JKisq0cHXPrJzZQAAANbhtoBwSsFj+0uSjr37hYMrAQAAuDGc4YZTatr5NhVfKtDlUzlVXje5uMijqW+V10qvFKnsarE9ywMAAKgzAjeckoe/twpzLlZ7/ZZObTVx6/+r8tq+Z97R4f/dYKfKAAAArEPghlMqzi+Uu793tdcvn8zRpl88I0lq3i1YfZ+eau/SAAAArELghlO6+O1JBQ7oLr92Lau0lZQWFilrx0FJkrm03FHlAQAA1BkXTcIpZcTvkSR1mjLCwZUAAADcGAI3nNKx977QxWOZuv0343XbXf0sDzLZtyYAAID6oKUETqnsarE+f/B5jfzHfA1/O0ZZuw7pzLYDKsy5KHd/b90S2lYdxg9UeWmZCs7kOrpcAACAGhG44bQun8xR3Ogn1WnycLUf21/dfz1OHv4+Kr1SpEsZ2Up77wsdW7dZl9LPOLpUAACAGhG44dTKrhYrdc1Gpa7Z6OhSAAAA6oUebgAAAMBABG4AAADAQARuAAAAwED0cAOoF7PZrCuFpY4uwyo+3m4ymbifpK1wDDRuvP/gGKg7AjeAerlSWCq//u84ugyrXN7zkHx93B1dRoPBMdC48f6DY6DuaCkBAAAADETgBgAAAAxE4AYAAAAMROAGAAAADETgBgAAAAxE4AYAAAAMROAGAAAADETgBgAAAAxE4AYAAAAMROAGAAAADETgtoOMjAyZTCYNHTrUZvvMz8/XsmXLFBsba7N9AgAAwPYI3E4iMTFRY8aMUYsWLeTj46Pw8HAtXrxYxcXFFsf7+fnp5Zdf1syZM2scAwAAAMcjcDuBl156SaNHj9amTZvk7++vzp07KzU1VQsWLNCwYcNUWFhYbY7JZNLYsWOVn5+vzZs3O6BqAAAA1AWB28H27t2refPmyWQyac2aNcrIyFBKSopSU1MVGhqq3bt3a/78+Rbnjhs3TpK0YcMGe5ZcZ+GP36Ohb87VvXv+R9Oy1uu+va87uiQ4oUVP9JH5mxmaPrGTxe1bVt2tq0nT1D20mZ0rg71wDIBjoHFrDO8/gdvBnn32WZnNZk2fPl1Tp06tfD0kJESrVq2SJK1YsUI5OTnV5o4YMUK+vr6Ki4uzW73W6LNgigLvuF35GdkqupDv6HKcltls1rakLN0/b7Oycq99m5GdW6iH/7JdXx/JdXB1xnv69RQdPHZef/9jpNq28qmy7XcPdtfQvq3119eTdfj4BQdVaLzikjL969N0DZvxibJyr0iSzp4r1MLXknQy67KDqzMex4B0Pq9If3/noHpN+khZP1w7BnLOX9X//OuILl1u+G2DHANS+qlLmvfSXoVGv68z/3cM5F64qg8/z1BpabmDqzNWY3j/G2XgLi8v1/r16zVx4kS1adNGnp6eatOmjYYPH65XXnnFbj3R+fn5SkxMlCTNnDmz2vbBgwcrLCxMxcXFFs9ie3l5KSoqSpmZmUpOTja8Xmutj3xM/+o+XYmTn9WVszfvPxIjncq+rL4PbNDQhz/R+5u+V3m5WZJUVm7W6v8cU8TkjxX16Kc6n1fk4EqNU1JarqkLt8vX212rnr6z8vWw4Fu06PEI7fkmRy+uOejACo21LSlL7UfH6oEnt2rrviyV/9/P1dIysxatPKAOd72vOUu+VFlZw/2B29iPgeXrjqjtyHWau2yvDnx7Xv/3MaCS0nLNfv5LtR25Tms/PubYIg3WmI+B4pIyPfLXHQqN/reWrT2o9FP5Mv/fMVBUUq57//CFQqLfV9LhHxxbqIEaw/vf6AJ3Tk6Ohg8frkmTJunjjz+Wu7u7evXqJXd3d23ZskXz58+Xq6urXWpJSUlRcXGxPD09FRERYXHMoEGDJEl79uyxuH38+PGSnLOt5PLJ6mfl8V+Z2QUa+Kv4657F/nzPGQ2eFq+Llxpu6E45ek6LVx3Q6DuCNPPeznJxMemdRYNlMklTF26v/EWkoflizxmNmrVR2bnVr9OoUF5u1qvvHdFDf264/x+kxnsMLH7rgB5f/KWuFpXVOObylVJNe2q7VsQetWNl9tcYj4HS0nLd+/svtOqjtFrHncwq0JDpn+irbxruz9WG/v43qsBdUFCgu+++W9u2bdOQIUN04MABnThxQl999ZVOnDihQ4cO6U9/+pPdAnda2rV/YO3bt5ebm5vFMSEhIVXG/lR0dLRcXFycMnCjdpOf3KLMswV1Gns4/aJ+/dwugytyrGffTNH+1HNaNrefXps/QJHhLfXn175WWkaeo0szxIVLRbr3D1+ouKRuZ67f+yRdK95v2IGrsR0D25KytODVpDqPn734S6UcbdhtZo3tGFjy9gHFbz9Vp7FXrpZqwpzPVXi11OCqHKchv/+NKnDPnTtXX3/9tQYNGqTExET16NGjyvbu3bvrL3/5i93quXDhWptFs2Y1XwRQsa1i7E+1bNlSkZGRSklJUWZmpu2LhCH2HfpBu1LOWjVn/WcZysyuW0C/GZWWmjV14XZ5ebrqsfu7akdytl7+5yFHl2WYNR8fU56VvbmvvHv4pj/LU5vGdgy88u5hq8aXl5u1/F8N+5euxnQMlJSU63+sfD/PnitU7KbvDKrI8Rry+99oAndqaqreeusteXp66t1335WHh0et4zMzMzV79mz169dPnp6eMplMNq/p6tWrklRrLZ6enpJk8daAFZy5rQSW1edMZVmZWSs/+NaAapxH3uViFRVf+2r9kx2nKvsYGxqz2VyvY+DYiUvavPeMARU5j8ZyDGRmF+jjLSetnvfeJ+m60IDby6TGcwz8Z8uJWtvJavJ6A28taqjvv+U+hgbovffeU1lZmR566CHddttt1x1//PhxffDBB+rbt688PDy0a5ftv8738vKSpFov0iwquvbB6u3tXeOY6OhozZ8/XwkJCXrsscesriMiIkLZ2dlWzXE3u+iv6mf1Wo4U1ilMJSbnuPDsbJPfSG6BVs9b+lqsVi0eb0BF1iuXu9R8oU33ufpvd8rD3VVH0i9o4aO99P6m7/Vdpu3ucNMpLEwuKrHZ/uqr3OSprGYL6jX33gfnyv/qThtXVD8cA/VX6B6mcv8pVs+7WlSmsB5D5VlatzYEIxnx/kvGHgPO8v5LUp53lOQ9yOp5+w7mqG1QO5nk+CTa2D4DAgMDlZRU9zawH2s0gfvzzz+XJN199911Gj948GBlZWVJkp5++mlDAvf12kV+vK22tpMTJ05Iktq1a1evOrKzs3X69Gmr5niYXKVW9VrOYc5knVGxueYLk+zK16Ve//qKis1Wv1eGMXlIzW23u8d/2U3D+rXRgleT9PGWE0qOnai3/3anhj78ic3WyDpzRjI7wS3W3G6R6nk72UuXr+rSWY6B+nKaY+CW1pJ//abmnrskXXaCY8DG779k/DHgNO+/JLUukmo+l1Yzk4vOnDkrmZ3gFwc+A+qs0QTuU6eunQ3o2LFjnca7uBjfbRMWFibpWmAuLS21eOFkenp6lbGWVLSSVLSWWCsw0Pozre5mF8k5ThbXWZvWbZzmDHeOa2m9fr/28ihXi7ZtbV5PfZTLXVk22lfobU20eE6E9h78QUvf/kbl5WY9vSJZi+f01eO/7KbX3jtik3Vat2njFGe3buT/XRM/D/m7cQzUl7McA1fdfXSunnNvbe4nj1scfwzY8v2X7HMMOMv7L0mXvN1Ur/O25lK1adNStm90tV5j+wyoT16q0GgCd0HBtYvNauuFtrfevXvLw8NDRUVFSkpKUv/+/auN2bnz2lfHkZGRFvdhNpsVHx8vX19fjRgxol511OfrkZIrV/VuyIP1Ws9R0o6lyd3Hy9FlSJKeWv61nntzv9XzXnnuET163zLbF1QPBVdK5Nf/nRvej8kkrXl2sFxdTJq6cFvlRYEvrD6on48I1uI5EUrYfsomXykeS0uTr4/7De/HFoY+nKBtSda1cknSl5veULcQ53jaGsdA/V2+UqI2I9Ypv8C6H/yBAd468fVuebjb525atbHV+y/Z7xhwlvdfknbvP6s7Hoq3et7EESH66GXnuEkCnwF112gumqxot9i9e7eDK/kvf39/RUVFSZJWrlxZbfv27duVlpYmDw8PTZgwweI+kpKSlJWVpVGjRlVeYOksOt43WD1+d696/O5eebVoInd/n8q/d7xvsKPLc6hH77t2j1FrNPFz1y/vDjGoIseZOzVcd/Rupb+8nqzU7/9766fycrOmPbVdbq4uevtvd9ayh5vTY/d3tXrO0L6tnSZs21JjPAb8fNw1dbzlx1jXZua9nZ0ibNtaYzwGBvRsqZ6dre/HqM9nh7NrDO9/ownc99xzjyRp0aJFlU93rHD69Gk9//zzOnbM/k/yWrhwoUwmk1avXq21a9dWvp6enq4ZM2ZIkmbNmqWWLVtanH+j7SRGCntghH725AP62ZMPyPvWpvJs6lf597AH6nc2vqFoF+in6ROs+2H7+wdvl5+TnJmxlS4dbtGzv/2ZvjyQo5fWVr/105H0i3p6RbKGRLTW47/s5oAKjXPP8GB1D2la5/Emk7TgkZ7GFeQgjfkYmDOlu/x96/5vukVTT/16UhcDK3KMxnoMmEwmLZzZy6o5/XvcqhGRbYwpyEEay/tvMpsbyg1Xanf58mUNGTKk8hHogYGBateunc6fP6/vvvtOJpNJly5dkq+vb7W5Tz/9tJ555hnV939VRkaGOnTooCFDhmjr1q3Vtr/wwgt68sknJV17CE6zZs106NAhlZaWKjIyUps3b5aPj4/Ffffq1UsHDx7U2bNnFRAQUK/66uNmbCmZkv5Pp2kpkaSi4jKNf+IzJe6+/sVPvxobqjXPDbb6rLiRbPl1sr1c3vOQ03ydLEknsy5ryPQEZZy5fN2xKxYO1K9/4VxntjgGbtzne05r/OOfqbCWJ01K177h2rRijPr3tHzyxRF4/21j6dsH9KeXr9/a2bVjU21ddbdatqjPlZbG4Biou0ZzhtvPz087duzQc889p549eyovL0+HDh1SeXm5Jk6cqLVr11oM2/YQExOjjRs3KioqSnl5eUpNTVVYWJgWLVqkbdu21Ri2T548qQMHDmjgwIF2DduwDU8PV8W9FqU/Tg2v8SxXQDMvPf9EhNOFbdjGba39tOfd8bovKliurpbf387Bt+jD/zfC6cI2bGNk/7ba+na0BvaqOUgP69taO9eMdaqwDdt58uGe+sfzQ9ShreXb1ri7uejBsSHa9c5YpwrbsE6juWhSknx8fPTnP/9Zf/7znx1dSjWjR4/W6NGjrZrjzO0kqBsPd1e9OLef/vqb3no3IV2795/V5SulauLnrpH92+i+qA7y9Gh4/Zr4r1YtvPXvl0bo9NkCvf2fNKV+n6ei4jLd2sxLk0Z10LB+rQ158BacR7/wW7XrnXHan3pO78Qd0+mcKzKZpNsC/TRtQqcG2bePqh4cG6pf3h2iTbsy9dHmEzqfVyQvT1fdHtpMD08MI2g3AI0qcFtr/fr1kqQjR45U+XtwcLAiIiIcVleFuLg4SQTuhsDPx12zJnXRrAbYn4m6advKV0/N6u3oMuBAvbq0UK8uLRxdBhzExcWku+5sp7vurN8zNeDcCNy1mDRpksW/T506VWvWrHFARf+Vn5+vrVu3KiwsTJ07d3ZoLQAAAKgZgbsWznw9qZ+fn/Ly8uTqSrsBAACAMyNw36RMJpO8vJznjhsAAACwjMBtB8HBwU59thwAAADGaTS3BQQAAAAcgcANAAAAGIjADQAAABiIwA0AAAAYiMANAAAAGIjADQAAABiIwA0AAAAYiMANAAAAGIjADQAAABjIZOYRiKgHs9ms0sIiR5dhFTdvT5lMJkeX0WCYzWZdKSx1dBlW8fF24xiwIY6Bxo33HxwDdUfgBgAAAAxESwkAAABgIAI3AAAAYCACNwAAAGAgAjcAAABgIAI3AAAAYCACNwAAAGAgAjcAAABgIAI3AAAAYCACNwAAAGAgAjcAAABgIAI3AAAAYCACNwAAAGAgAjcAAABgIAI3AAAAYCACNwAAAGAgAjcAAABgIAI3AAAAYCACNwAAAGAgAjcAAABgIAI3AAAAYCACNwAAAGAgAjcAAABgIAI3AAAAYCACNwAAAGAgAjcAAABgoP8PlmlpLpKfffcAAAAASUVORK5CYII=\n"
          },
          "metadata": {},
          "execution_count": 33
        }
      ],
      "source": [
        "coin_r = QuantumRegister(n_qubits, name=\"c\")\n",
        "h_walk_step = hypercube_walk_step(walker_r, coin_r)\n",
        "h_walk_step.draw(output=\"mpl\", initial_state=True)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "metadata": {
        "id": "FN0vCsfLR4pO"
      },
      "outputs": [],
      "source": [
        "def hypercube_walk(n_qubits, n_steps):\n",
        "    \"\"\"\n",
        "    Create a quantum circuit for the quantum walk over a hypercube\n",
        "    Args:\n",
        "    n_qubits (int): dimension of the hypercube\n",
        "    n_steps (int): number of steps of the quantum walk\n",
        "    Returns:\n",
        "    Quantum circuit for the quantum walk over a hypercube\n",
        "    \"\"\"\n",
        "    q_circuit, walker_r, coin_r, classic_r = hypercube_walk_circuit(n_qubits)\n",
        "    for i in range(n_steps):\n",
        "        step_gate = hypercube_walk_step(walker_r, coin_r).to_gate(label=f\"Step #{i + 1}\")\n",
        "        q_circuit.append(step_gate, walker_r[:] + coin_r[:])\n",
        "    q_circuit.barrier()\n",
        "    q_circuit.measure(walker_r, reversed(classic_r))\n",
        "    return q_circuit"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 384
        },
        "id": "4mcC37wqStln",
        "outputId": "8bf52937-3f54-42a5-c102-24620e13e2ad"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 758.032x451.5 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {},
          "execution_count": 35
        }
      ],
      "source": [
        "q_circuit = hypercube_walk(n_qubits, n_steps)\n",
        "q_circuit.draw(output=\"mpl\", initial_state=True)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 36,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 451
        },
        "id": "QCysOKLdUXsD",
        "outputId": "80d1fcaf-d9e0-40ea-8b73-4e8a5e0db516"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlIAAAGyCAYAAAAvcypsAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy81sbWrAAAACXBIWXMAAA9hAAAPYQGoP6dpAABHwElEQVR4nO3deXwNZ///8ffJyUYkESQiFZJw11JLLEXUUqSCUFrd7dwtqgtpbW1t3WzV0hVtbcW3i+6oWkJtKUpD6a1FEXdJ7AlCtjO/P/wytyOJxgiJeD0fjzwezjXXmflcc50478zMmWMzDMMQAAAArppLYRcAAABwsyJIAQAAWESQAgAAsIggBQAAYBFBCgAAwCKCFAAAgEUEKQAAAIsIUgAAABYRpAAAACwiSAG4pdhsNo0dO9Z8PHbsWNlsNh0/frzwirqO1qxZI5vNpkWLFhV2KUWCzWbTU089VdhloBghSAEFaNeuXerevbtuu+02eXh4KCgoSN27d9fvv/9e2KU5+f333zV27FgdOHCgsEsBgJsaQQooIF999ZXq16+vVatWqU+fPnr//ffVr18/xcbGqn79+vr2228Lu0TT77//rnHjxhGkAOAauRZ2AUBxsG/fPvXo0UNhYWFau3at/P39zWXPPvusmjdvru7du2vHjh0KDQ0txEqBm0NmZqYcDofc3d0LuxTgijgiBRSAyZMnKzU1VTNnznQKUZJUrlw5zZgxQ2fPntXkyZPN9t69eyskJCTHurKv2bnU7Nmz1bp1awUEBMjDw0M1a9bUBx98kOO5ISEh6tixo9avX69GjRrJ09NTYWFhmjdvntlnzpw5evDBByVJrVq1ks1mk81m05o1ayTlvIbo0nX37t3baT02m03r16/XM888I39/f5UuXVr9+/dXenq6Tp8+rZ49e8rPz09+fn4aNmyYDMO44n6MiYlR2bJlnfo9/fTTstlsevvtt822pKQk2Ww2cx+kp6dr9OjRatCggXx9feXl5aXmzZtr9erVV9xeXg4ePKiqVauqVq1aSkpKumLfX3/9Ve3bt5ePj49KlSqlNm3a6Oeff3bqk72vNmzYoJiYGPn7+8vLy0v33Xefjh079o/17NixQ71791ZYWJg8PT0VGBiovn376sSJE/kek8Ph0GuvvaaKFSvK09NTbdq00d69e83lY8aMkZubW671PPHEEypdurQuXLgg6X+vs+XLlys8PFyenp6qWbOmvvrqqxzPPX36tAYPHqzg4GB5eHioatWqmjhxohwOh9nnwIEDstlseuONNzR16lRVqVJFHh4e5inx3bt366GHHpK/v79KlCihatWq6cUXXzSffzW/S9kWLFigatWqydPTUw0aNNDatWtz9Pn777/Vt29flS9fXh4eHrrjjjs0a9asPPYwblUEKaAAfP/99woJCVHz5s1zXd6iRQuFhITo+++/t7T+Dz74QJUrV9YLL7ygKVOmKDg4WE8++aTee++9HH337t2rBx54QPfcc4+mTJkiPz8/9e7dW7t27TJreeaZZyRJL7zwgj755BN98sknqlGjhqXann76ae3Zs0fjxo3Tvffeq5kzZ2rUqFHq1KmTsrKy9Prrr6tZs2aaPHmyPvnkkyuuq3nz5jp58qRZqyStW7dOLi4uWrdunVNb9lgkKSUlRR999JHuvvtuTZw4UWPHjtWxY8cUFRWl+Pj4qxrPvn371KJFC3l7e2vNmjUqX758nn137dql5s2ba/v27Ro2bJhGjRql/fv36+6779amTZty9H/66ae1fft2jRkzRgMHDtT333+frwufV6xYob/++kt9+vTRO++8o0ceeUSffvqpOnTo8I/hNNuECRP09ddf6/nnn9fIkSP1888/q1u3bubyHj16KDMzU5999pnT89LT07Vo0SJ17dpVnp6eZvuePXv08MMPq3379ho/frxcXV314IMPasWKFWaf1NRUtWzZUvPnz1fPnj319ttv66677tLIkSMVExOTo8bZs2frnXfe0RNPPKEpU6aoTJky2rFjhxo3bqzY2Fg9/vjjmjZtmrp06WL5d0mSfvrpJw0ePFjdu3fXyy+/rBMnTqhdu3bauXOn2ScpKUlNmjTRypUr9dRTT2natGmqWrWq+vXrp6lTp1reNoohA8A1OX36tCHJ6Ny58xX73XvvvYYkIyUlxTAMw+jVq5dRuXLlHP3GjBljXP6rmZqamqNfVFSUERYW5tRWuXJlQ5Kxdu1as+3o0aOGh4eH8dxzz5ltX3zxhSHJWL16dY71SjLGjBmTo71y5cpGr169zMezZ882JBlRUVGGw+Ew2yMiIgybzWYMGDDAbMvMzDQqVqxotGzZMsd6L3X06FFDkvH+++8bhnFx37q4uBgPPvigUb58ebPfM888Y5QpU8bcbmZmppGWlua0rlOnThnly5c3+vbte8XxZe/vY8eOGf/5z3+MoKAg48477zROnjx5xVoNwzC6dOliuLu7G/v27TPbDh8+bHh7exstWrQw27L3VWRkpNO+GjJkiGG3243Tp09fcTu5zf///d//5Zjr3KxevdqQZNSoUcNpH02bNs2QZPz2229mW0REhNG4cWOn53/11Vc5XivZr7Mvv/zSbEtOTjYqVKhg1KtXz2x75ZVXDC8vL+PPP/90WueIESMMu91uJCQkGIZhGPv37zckGT4+PsbRo0ed+rZo0cLw9vY2Dh486NR+6X68mt8lSYYk45dffjHbDh48aHh6ehr33Xef2davXz+jQoUKxvHjx52e/8gjjxi+vr65zgluTRyRAq7RmTNnJEne3t5X7Je9PLv/1ShRooT57+TkZB0/flwtW7bUX3/9peTkZKe+NWvWdDoy5u/vr2rVqumvv/666u3mR79+/ZxOnzRu3FiGYahfv35mm91uV8OGDf+xBn9/f1WvXt08zbJhwwbZ7XYNHTpUSUlJ2rNnj6SLR6SaNWtmbtdut5vX0jgcDp08eVKZmZlq2LChtm3blq9x7Ny5Uy1btlRISIhWrlwpPz+/K/bPysrS8uXL1aVLF4WFhZntFSpU0GOPPab169crJSXF6TlPPPGE075q3ry5srKydPDgwStu69L5v3Dhgo4fP64mTZpIUr7H16dPH6frjbJfI5fOSc+ePbVp0ybt27fPbFuwYIGCg4PVsmVLp/UFBQXpvvvuMx/7+PioZ8+e+vXXX5WYmChJ+uKLL9S8eXP5+fnp+PHj5k9kZKSysrJynE7r2rWr06nxY8eOae3aterbt68qVark1DevU3b5ERERoQYNGpiPK1WqpM6dO+vHH39UVlaWDMPQl19+qU6dOskwDKfao6KilJycnO/9juKPIAVco/wGpDNnzshms6lcuXJXvY0NGzYoMjJSXl5eKl26tPz9/fXCCy9IUo4gdfkbjiT5+fnp1KlTV73d/Lh8e76+vpKk4ODgHO35qaF58+bmqbt169apYcOGatiwocqUKaN169YpJSVF27dvz3Eade7cuapTp448PT1VtmxZ+fv7a8mSJTn2T146deokb29v/fjjj/Lx8fnH/seOHVNqaqqqVauWY1mNGjXkcDh06NAhp/bL91V2WPun/XLy5Ek9++yzKl++vEqUKCF/f3/zQwv5HV9+tv3www/Lw8NDCxYsMNe9ePFidevWLUdwqVq1ao6222+/XZLMT4Pu2bNHy5Ytk7+/v9NPZGSkJOno0aNOz7/8gxjZIa9WrVr5GmN+/etf/8rRdvvttys1NVXHjh3TsWPHdPr0afOax0t/+vTpk2vtuHXxqT3gGvn6+iooKEg7duy4Yr8dO3aoYsWK5lGBvP6izsrKcnq8b98+tWnTRtWrV9ebb76p4OBgubu7a+nSpXrrrbecLtqVLh6dyY2Rz2tp8nJ5Xf+0vdza81NDs2bN9OGHH+qvv/7SunXr1Lx5c9lsNjVr1kzr1q1TUFCQHA6HU5CaP3++evfurS5dumjo0KEKCAiQ3W7X+PHjnY6uXEnXrl01d+5cLViwQP3798/Xc66W1bl56KGHtHHjRg0dOlTh4eEqVaqUHA6H2rVrl2P+r2Xbfn5+6tixoxYsWKDRo0dr0aJFSktLU/fu3fO1jcs5HA7dc889GjZsWK7Ls4NXtkuPvF2N/P4u5Vf2Pu3evbt69eqVa586depYWjeKH4IUUAA6deqkGTNmaP369WrWrFmO5evWrdOBAwecLrD18/PT6dOnc/S9/DTP999/r7S0NH333XdORxWsfiJNuvJpkdzqSk9P15EjRyxv72pkB6QVK1Zoy5YtGjFihKSLF5Z/8MEHCgoKkpeXl9OpmUWLFiksLExfffWV09jGjBmT7+1OnjxZrq6uevLJJ+Xt7a3HHnvsiv39/f1VsmRJ/fHHHzmW7d69Wy4uLjmOyllx6tQprVq1SuPGjdPo0aPN9uzTnAWtZ8+e6ty5s7Zs2aIFCxaoXr16uuOOO3L027t3rwzDcNrff/75pySZn6CrUqWKzp49ax6BulrZp0wvvQg8N/n9XcqW2777888/VbJkSfPUore3t7KysizXjlsHp/aAAvD888+rZMmS6t+/f46PpJ88eVIDBgyQj4+P0ye0qlSpouTkZKcjWUeOHNHXX3/t9PzsIwmXHjlITk7W7NmzLdfr5eUlSbm++VSpUiXHtSszZ860/Nf91QoNDdVtt92mt956SxkZGbrrrrskXQxY+/bt06JFi9SkSRO5uv7v78Dc9tGmTZsUFxeX7+3abDbNnDlTDzzwgHr16qXvvvvuiv3tdrvatm2rb7/91unGpklJSVq4cKGaNWuWr1OE/yS3sUm6bp8ca9++vcqVK6eJEyfqp59+yvNo1OHDh51eqykpKZo3b57Cw8MVGBgo6eKRtLi4OP344485nn/69GllZmZesRZ/f3+1aNFCs2bNUkJCgtOyS/dHfn+XssXFxTld43To0CF9++23atu2rex2u+x2u7p27aovv/wy1xCXn1tW4NbBESmgAFStWlXz5s3To48+qtq1a6tfv34KDQ3VgQMH9PHHH+vUqVP69NNPna4BeeSRRzR8+HDdd999euaZZ5SamqoPPvhAt99+u9N/8m3btpW7u7s6deqk/v376+zZs/rwww8VEBBg+ShReHi47Ha7Jk6cqOTkZHl4eJj3qfr3v/+tAQMGqGvXrrrnnnu0fft2/fjjj5au7bKqefPm+vTTT1W7dm3zWp769evLy8tLf/75Z46jRR07dtRXX32l++67T9HR0dq/f7+mT5+umjVr6uzZs/nerouLi+bPn68uXbrooYce0tKlS9W6des8+7/66qtasWKFmjVrpieffFKurq6aMWOG0tLSNGnSJGuDv4yPj49atGihSZMmKSMjQ7fddpuWL1+u/fv3F8j6L+fm5qZHHnlE7777rux2ux599NFc+91+++3q16+ftmzZovLly2vWrFlKSkpyCvhDhw7Vd999p44dO6p3795q0KCBzp07p99++02LFi3SgQMH/vF19fbbb6tZs2aqX7++nnjiCfP3asmSJeatLfL7u5StVq1aioqK0jPPPCMPDw+9//77kqRx48aZfSZMmKDVq1ercePGevzxx1WzZk2dPHlS27Zt08qVK3Xy5Mmr3bUorgrnw4JA8fTbb78Zjz32mBEYGGi4uLgYkgxPT09j165dufZfvny5UatWLcPd3d2oVq2aMX/+/Fw/sv3dd98ZderUMTw9PY2QkBBj4sSJxqxZswxJxv79+81+lStXNqKjo3Nsp2XLljluPfDhhx8aYWFhht1ud/p4e1ZWljF8+HCjXLlyRsmSJY2oqChj7969ed7+YMuWLU7rvfR2Apfq1auX4eXl9Q978KL33nvPkGQMHDjQqT0yMtKQZKxatcqp3eFwGK+//rpRuXJlw8PDw6hXr56xePHiXD8Wryvc/iBbamqq0bJlS6NUqVLGzz//fMVat23bZkRFRRmlSpUySpYsabRq1crYuHGjU5+89lX2rQlyuw3Fpf773/8a9913n1G6dGnD19fXePDBB43Dhw/neauK3LbxxRdfOLVn33Jg9uzZOZ6zefNmQ5LRtm3bXNeZ/Tr78ccfjTp16hgeHh5G9erVc2zDMAzjzJkzxsiRI42qVasa7u7uRrly5YymTZsab7zxhpGenu5Uy+TJk3Pd3s6dO83xe3p6GtWqVTNGjRrl1Ce/v0uSjEGDBhnz5883/vWvf5mvl9zmICkpyRg0aJARHBxsuLm5GYGBgUabNm2MmTNn5lonbk02w7jGK1AB5GnevHnq3bu3unfv7nR3caAo2759u8LDwzVv3jz16NEjx/KQkBDVqlVLixcvLoTqgKKFU3vAddSzZ08dOXJEI0aMUMWKFfX6668XdknAP/rwww9VqlQp3X///YVdClDkEaSA62z48OEaPnx4YZcB/KPvv/9ev//+u2bOnKmnnnrK/FACgLwRpAAAki5+F2BSUpI6dOjgdOE1gLxxjRQAAIBF3EcKAADAIoIUAACARVwjdR05HA4dPnxY3t7e1/RN5QAA4MYxDENnzpxRUFCQXFyufMyJIHUdHT58uEC+awsAANx4hw4dUsWKFa/YhyB1HXl7e0u6OBEF8Z1bAADg+ktJSVFwcLD5Pn4lBKnrKPt0no+PD0EKAICbTH4uy+FicwAAAIsIUsXUhAkTZLPZNHjwYKf2uLg4tW7dWl5eXua3yp8/f95c/ueff6pz584qV66cfHx81KxZM61evdpcfuLECbVr105BQUHy8PBQcHCwnnrqKaWkpJh91qxZI5vNluMnMTHxuo8bAIAbiSBVDG3ZskUzZsxQnTp1nNrj4uLUrl07tW3bVps3b9aWLVv01FNPOX0ioWPHjsrMzFRsbKy2bt2qunXrqmPHjmYIcnFxUefOnfXdd9/pzz//1Jw5c7Ry5UoNGDAgRx1//PGHjhw5Yv4EBARc34EDAHCDcWfz6yglJUW+vr5KTk6+YddInT17VvXr19f777+vV199VeHh4Zo6daokqUmTJrrnnnv0yiuv5Prc48ePy9/fX2vXrlXz5s0lSWfOnJGPj49WrFihyMjIXJ/39ttva/LkyTp06JCki0ekWrVqpVOnTql06dIFPkYAAK6nq3n/5ohUMTNo0CBFR0fnCD1Hjx7Vpk2bFBAQoKZNm6p8+fJq2bKl1q9fb/YpW7asqlWrpnnz5uncuXPKzMzUjBkzFBAQoAYNGuS6vcOHD+urr75Sy5YtcywLDw9XhQoVdM8992jDhg0FO1AAAIoAglQx8umnn2rbtm0aP358jmV//fWXJGns2LF6/PHHtWzZMtWvX19t2rTRnj17JF38dMLKlSv166+/ytvbW56ennrzzTe1bNky+fn5Oa3v0UcfVcmSJXXbbbfJx8dHH330kbmsQoUKmj59ur788kt9+eWXCg4O1t13361t27Zdx9EDAHDjEaSKiUOHDunZZ5/VggUL5OnpmWO5w+GQJPXv3199+vRRvXr19NZbb6latWqaNWuWpIt3ch00aJACAgK0bt06bd68WV26dFGnTp105MgRp/W99dZb2rZtm7799lvt27dPMTEx5rJq1aqpf//+atCggZo2bapZs2apadOmeuutt67jHgAA4MbjPlLFxNatW3X06FHVr1/fbMvKytLatWv17rvv6o8//pAk1axZ0+l5NWrUUEJCgiQpNjZWixcv1qlTp8xzwu+//75WrFihuXPnasSIEebzAgMDFRgYqOrVq6tMmTJq3ry5Ro0apQoVKuRaX6NGjZxOIwIAUBwQpIqJNm3a6LfffnNq69Onj6pXr67hw4crLCxMQUFBZqDK9ueff6p9+/aSpNTUVEnK8b1CLi4u5hGt3GQvS0tLy7NPfHx8niELAICbFUGqmPD29latWrWc2ry8vFS2bFmzfejQoRozZozq1q2r8PBwzZ07V7t379aiRYskSREREfLz81OvXr00evRolShRQh9++KH279+v6OhoSdLSpUuVlJSkO++8U6VKldKuXbs0dOhQ3XXXXQoJCZEkTZ06VaGhobrjjjt04cIFffTRR4qNjdXy5ctv3A4BAOAGIEjdQgYPHqwLFy5oyJAhOnnypOrWrasVK1aoSpUqkqRy5cpp2bJlevHFF9W6dWtlZGTojjvu0Lfffqu6detKkhmuhgwZorS0NAUHB+v+++93Ou2Xnp6u5557Tn///bdKliypOnXqaOXKlWrVqlWhjBsAgOuF+0hdR4VxHykAAHBtuI8UAADADUCQAgAAsIggBQAAYBFBCgAAwCKCFAAAgEUEKQAAAIsIUgAAABYRpAAAACwiSAEAAFhEkAIAALCIIAUAAGARQQoAAMAighQAAIBFBCkAAACLCFIAAAAWEaQAAAAsIkgBAABYRJACAACwyLWwC4B1ISOWFHYJBeLAhOjCLgEAAEs4IgUAAGARQQoAAMAighQAAIBFBCkAAACLCFIAAAAWEaQAAAAsIkgBAABYRJACAACwiCAFAABgUZEOUhMmTJDNZtPgwYPNtrvvvls2m83pZ8CAAU7PS0hIUHR0tEqWLKmAgAANHTpUmZmZTn3WrFmj+vXry8PDQ1WrVtWcOXNybP+9995TSEiIPD091bhxY23evPl6DBMAANykimyQ2rJli2bMmKE6derkWPb444/ryJEj5s+kSZPMZVlZWYqOjlZ6ero2btyouXPnas6cORo9erTZZ//+/YqOjlarVq0UHx+vwYMH69///rd+/PFHs89nn32mmJgYjRkzRtu2bVPdunUVFRWlo0ePXt+BAwCAm0aR/K69s2fPqlu3bvrwww/16quv5lhesmRJBQYG5vrc5cuX6/fff9fKlStVvnx5hYeH65VXXtHw4cM1duxYubu7a/r06QoNDdWUKVMkSTVq1ND69ev11ltvKSoqSpL05ptv6vHHH1efPn0kSdOnT9eSJUs0a9YsjRgxItdtp6WlKS0tzXyckpIiScrIyFBGRoYkycXFRXa7XVlZWXI4HGbf7PbMzEwZhmG22+12ubi45NpeXGTvm+yxZj/O5up68WV6+VHFvNrd3NzkcDiUlZVlttlsNrm6uubZntd8FMQ8MSbGxJgYE2O6+caUX0UySA0aNEjR0dGKjIzMNUgtWLBA8+fPV2BgoDp16qRRo0apZMmSkqS4uDjVrl1b5cuXN/tHRUVp4MCB2rVrl+rVq6e4uDhFRkY6rTMqKso8hZienq6tW7dq5MiR5nIXFxdFRkYqLi4uz7rHjx+vcePG5Whfvny5WV+lSpVUr1497dixQwkJCWafatWqqXr16tq8ebOOHTtmtoeHh6ty5cpau3atzpw5Y7ZHRETkWcfNZunSpZIujikgIEDLly93ehG3atVKJUqUMPtl69Chg86fP6/Vq1ebba6uroqOjtbx48ed5srb21utW7fWoUOHFB8fb7b7+/uradOm2rNnj/744w+zvSDniTExJsbEmBjTzTWmDRs2KL9sxqVRrAj49NNP9dprr2nLli3y9PTU3XffrfDwcE2dOlWSNHPmTFWuXFlBQUHasWOHhg8frkaNGumrr76SJD3xxBM6ePCg02m61NRUeXl5aenSpWrfvr1uv/129enTxykoLV26VNHR0UpNTdWpU6d02223aePGjU6BZdiwYfrpp5+0adOmXGvP7YhUcHCwjh8/Lh8fH0kFm/jDXvjByi4ucva80lZS8fkrpjj+ZcaYGBNjYky30phOnjypsmXLKjk52Xz/zkuROiJ16NAhPfvss1qxYoU8PT1z7fPEE0+Y/65du7YqVKigNm3aaN++fapSpcqNKjVXHh4e8vDwyNHu5uYmNzc3pza73Z7r6bnsF1R+24uDy/fN5Y+ttLu4uMjFJeclgHm15zUfBTVPjIkxMSbGdKV2xnRzjCk3Repi861bt+ro0aOqX7++XF1d5erqqp9++klvv/22mTQv17hxY0nS3r17JUmBgYFKSkpy6pP9OPu6qrz6+Pj4qESJEipXrpzsdnuuffK6NgsAANx6ilSQatOmjX777TfFx8ebPw0bNlS3bt0UHx+fa5rMPkdaoUIFSRfPzf72229On65bsWKFfHx8VLNmTbPPqlWrnNazYsUK8zSeu7u7GjRo4NTH4XBo1apVxeraJAAAcG2K1Pkib29v1apVy6nNy8tLZcuWVa1atbRv3z4tXLhQHTp0UNmyZbVjxw4NGTJELVq0MG+T0LZtW9WsWVM9evTQpEmTlJiYqJdeekmDBg0yT7sNGDBA7777roYNG6a+ffsqNjZWn3/+uZYsWWJuNyYmRr169VLDhg3VqFEjTZ06VefOnTM/xQcAAFCkgtQ/cXd318qVK81QExwcrK5du+qll14y+9jtdi1evFgDBw5URESEvLy81KtXL7388stmn9DQUC1ZskRDhgzRtGnTVLFiRX300UfmrQ8k6eGHH9axY8c0evRoJSYmKjw8XMuWLXP6NCAAALi1FblP7RUnKSkp8vX1zddV/1aEjFjyz51uAgcmRBd2CQAAmK7m/btIXSMFAABwMyFIAQAAWESQAgAAsIggBQAAYBFBCgAAwCKCFAAAgEUEKQAAAIsIUgAAABYRpAAAACwiSAEAAFhEkAIAALCIIAUAAGARQQoAAMAighQAAIBFBCkAAACLCFIAAAAWEaQAAAAsIkgBAABYRJACAACwiCAFAABgEUEKAADAIoIUAACARQQpAAAAiwhSAAAAFhGkAAAALCJIAQAAWESQAgAAsIggBQAAYBFBCgAAwCKCFAAAgEUEKQAAAIsIUgAAABYRpAAAACwiSAEAAFhEkAIAALCIIAUAAGARQQoAAMAighQAAIBFBCkAAACLCFIAAAAWEaQAAAAsIkgBAABYRJACAACwiCAFAABgEUEKAADAIoIUAACARQQpAAAAiwhSAAAAFhGkAAAALCJIAQAAWESQAgAAsIggBQAAYBFBCgAAwCKCFAAAgEUEKQAAAIsIUgAAABYRpAAAACwiSAEAAFhEkAIAALCIIAUAAGARQQoAAMAighQAAIBFBCkAAACLCFIAAAAWEaQAAAAsIkgBAABYRJACAACwiCAFAABgEUEKAADAIoIUAACARQQpAAAAiwhSAAAAFhGkAAAALCJIAQAAWESQAgAAsIggBQAAYBFBCgAAwCKCFAAAgEUEKQAAAIsIUgAAABYRpAAAACwiSAEAAFhEkAIAALCIIAUAAGARQQoAAMAighQAAIBFBCkAAACLCFIAAAAWEaQAAAAsIkgBAABYRJACAACwiCAFAABgEUEKAADAIoIUAACARQQpAAAAiwhSAAAAFhW5IPXBBx+oTp068vHxkY+PjyIiIvTDDz+Yyy9cuKBBgwapbNmyKlWqlLp27aqkpCSndSQkJCg6OlolS5ZUQECAhg4dqszMTKc+a9asUf369eXh4aGqVatqzpw5OWp57733FBISIk9PTzVu3FibN2++LmMGAAA3pyIXpCpWrKgJEyZo69at+uWXX9S6dWt17txZu3btkiQNGTJE33//vb744gv99NNPOnz4sO6//37z+VlZWYqOjlZ6ero2btyouXPnas6cORo9erTZZ//+/YqOjlarVq0UHx+vwYMH69///rd+/PFHs89nn32mmJgYjRkzRtu2bVPdunUVFRWlo0eP3ridAQAAijSbYRhGYRfxT8qUKaPJkyfrgQcekL+/vxYuXKgHHnhAkrR7927VqFFDcXFxatKkiX744Qd17NhRhw8fVvny5SVJ06dP1/Dhw3Xs2DG5u7tr+PDhWrJkiXbu3Glu45FHHtHp06e1bNkySVLjxo1155136t1335UkORwOBQcH6+mnn9aIESPyVXdKSop8fX2VnJwsHx+fgtwlkqSQEUsKfJ2F4cCE6MIuAQAA09W8f7veoJosycrK0hdffKFz584pIiJCW7duVUZGhiIjI80+1atXV6VKlcwgFRcXp9q1a5shSpKioqI0cOBA7dq1S/Xq1VNcXJzTOrL7DB48WJKUnp6urVu3auTIkeZyFxcXRUZGKi4uLs9609LSlJaWZj5OSUmRJGVkZCgjI8Ncj91uV1ZWlhwOh9P67Xa7MjMzdWm2tdvtcnFxybW9uMjeN9ljzX6czdX14sv08tOzebW7ubnJ4XAoKyvLbLPZbHJ1dc2zPa/5KIh5YkyMiTExJsZ0840pv4pkkPrtt98UERGhCxcuqFSpUvr6669Vs2ZNxcfHy93dXaVLl3bqX758eSUmJkqSEhMTnUJU9vLsZVfqk5KSovPnz+vUqVPKysrKtc/u3bvzrHv8+PEaN25cjvbly5erZMmSkqRKlSqpXr162rFjhxISEsw+1apVU/Xq1bV582YdO3bMbA8PD1flypW1du1anTlzxmyPiIjIs46bzdKlSyVdHFNAQICWL1/u9CJu1aqVSpQoYfbL1qFDB50/f16rV68221xdXRUdHa3jx487hV5vb2+1bt1ahw4dUnx8vNnu7++vpk2bas+ePfrjjz/M9oKcJ8bEmBgTY2JMN9eYNmzYoPwqkqf20tPTlZCQoOTkZC1atEgfffSRfvrpJ8XHx6tPnz5OR30kqVGjRmrVqpUmTpyoJ554QgcPHnS63ik1NVVeXl5aunSp2rdvr9tvv119+vRxOuK0dOlSRUdHKzU1VadOndJtt92mjRs3OgWWYcOG6aefftKmTZtyrTu3I1LBwcE6fvy4eWiwIBN/2Av/uwj/ZrbnlbaSis9fMcXxLzPGxJgYE2O6lcZ08uRJlS1b9uY9tefu7q6qVatKkho0aKAtW7Zo2rRpevjhh5Wenq7Tp087HZVKSkpSYGCgJCkwMDDHp+uyP9V3aZ/LP+mXlJQkHx8flShRQna7XXa7Pdc+2evIjYeHhzw8PHK0u7m5yc3NzaktexuXy35B5be9OLh831z+2Eq7i4uLXFxyfpYir/a85qOg5okxMSbGxJiu1M6Ybo4x5abIfWovNw6HQ2lpaWrQoIHc3Ny0atUqc9kff/yhhIQE88hRRESEfvvtN6dP161YsUI+Pj6qWbOm2efSdWT3yV6Hu7u7GjRo4NTH4XBo1apVxeqUGgAAuDZF7jDHyJEj1b59e1WqVElnzpzRwoULtWbNGv3444/y9fVVv379FBMTozJlysjHx0dPP/20IiIi1KRJE0lS27ZtVbNmTfXo0UOTJk1SYmKiXnrpJQ0aNMg8WjRgwAC9++67GjZsmPr27avY2Fh9/vnnWrLkf5+Ci4mJUa9evdSwYUM1atRIU6dO1blz59SnT59C2S8AAKDosRyk1q5dq5CQEFWqVCnPPocOHdL+/fvVokWLfK/36NGj6tmzp44cOSJfX1/VqVNHP/74o+655x5J0ltvvSUXFxd17dpVaWlpioqK0vvvv28+3263a/HixRo4cKAiIiLk5eWlXr166eWXXzb7hIaGasmSJRoyZIimTZumihUr6qOPPlJUVJTZ5+GHH9axY8c0evRoJSYmKjw8XMuWLctxAToAALh1Wb7Y3G63a8yYMU43urzca6+9ptGjRztdEHYr4T5S+cN9pAAARcnVvH9bvkYqP/nL4XDIZrNZ3QQAAECRdl0vNt+zZ498fX2v5yYAAAAKzVVdI9W3b1+nx998840OHDiQo19WVpYOHTqktWvXqn379tdUIAAAQFF1VUFqzpw55r9tNpvi4+Od7ix6KZvNpjvvvFNvvfXWtdQHAABQZF1VkNq/f7+ki9dHhYWFafDgwXr22Wdz9LPb7fLz85OXl1fBVAkAAFAEXVWQqly5svnv2bNnq169ek5tAAAAtxLL95Hq1atXQdYBAABw07nmO5tv3rxZW7Zs0enTp3O9X5TNZtOoUaOudTMAAABFjuUgdfLkSXXp0kUbNmy44j2lCFIAAKC4shykYmJitH79et19993q1auXKlaseFXflgwAAHCzs5x8Fi9erEaNGmnVqlXcvRwAANySLN/Z/Pz582rRogUhCgAA3LIsB6nw8PBc72oOAABwq7AcpMaMGaPvvvtOP//8c0HWAwAAcNOwfI1UYmKioqOj1bJlS3Xr1k3169eXj49Prn179uxpuUAAAICiymZc6d4FV+Di4iKbzeZ064PLr5cyDEM2my3X+0vdClJSUuTr66vk5OQ8Q+a1CBmxpMDXWRgOTIgu7BIAADBdzfu35SNSs2fPtvpUAACAYoGviAEAALDI8sXmAAAAtzrLR6QSEhLy3bdSpUpWNwMAAFBkWQ5SISEh+boZp81mU2ZmptXNAAAAFFmWg1TPnj1zDVLJycnavn279u/fr5YtWyokJORa6gMAACiyLAepOXPm5LnMMAxNmTJFkyZN0scff2x1EwAAAEXadbnY3Gaz6fnnn9cdd9yhoUOHXo9NAAAAFLrr+qm9hg0bKjY29npuAgAAoNBc1yC1b98+LjQHAADFluVrpPLicDj0999/a86cOfr222/Vpk2bgt4EAABAkWA5SGV/115eDMOQn5+fpkyZYnUTAAAARZrlINWiRYtcg5SLi4v8/Px05513qk+fPgoICLimAgEAAIoqy0FqzZo1BVgGAADAzYfv2gMAALCoQC4237Bhg+Lj45WSkiIfHx+Fh4frrrvuKohVAwAAFFnXFKQ2btyoPn36aO/evZIuXmCefd3Uv/71L82ePVsRERHXXiUAAEARZDlI7dq1S23btlVqaqruuecetWrVShUqVFBiYqJWr16t5cuXKyoqSj///LNq1qxZkDUDAAAUCZaD1Msvv6z09HQtXbpU7dq1c1o2fPhwLVu2TPfee69efvllffrpp9dcKAAAQFFj+WLzNWvW6IEHHsgRorK1a9dODzzwgFavXm25OAAAgKLMcpBKTk5WaGjoFfuEhoYqOTnZ6iYAAACKNMtBKigoSD///PMV+2zatElBQUFWNwEAAFCkWQ5S9957r9asWaNRo0bpwoULTssuXLigMWPGaPXq1ercufM1FwkAAFAU2QzDMKw88cSJE2rcuLH279+vsmXLqlGjRipfvrySkpK0ZcsWHTt2TGFhYdq8ebPKlClT0HXfFFJSUuTr66vk5GT5+PgU+PpDRiwp8HUWhgMTogu7BAAATFfz/m35U3tly5bVzz//rGHDhunTTz/V0qVLzWWenp7q06ePJk6ceMuGKAAAUPxd0w05y5Urp1mzZmnGjBnavXu3eWfz6tWry83NraBqBAAAKJKuOki99tprOnfunMaNG2eGJTc3N9WuXdvsk56erhdffFHe3t4aMWJEwVULAABQhFzVxeYrV67U6NGjVbZs2SsecXJ3d1fZsmX14osvch8pAABQbF1VkJo3b578/Pz01FNP/WPfQYMGqUyZMpo9e7bl4gAAAIqyqwpSGzduVGRkpDw8PP6xr4eHhyIjI7VhwwbLxQEAABRlVxWkDh8+rLCwsHz3Dw0N1ZEjR666KAAAgJvBVQUpFxcXZWRk5Lt/RkaGXFws3/MTAACgSLuqlBMUFKSdO3fmu//OnTt12223XXVRAAAAN4OrClLNmzdXbGysDhw48I99Dxw4oNjYWLVo0cJqbQAAAEXaVQWpQYMGKSMjQw888ICOHz+eZ78TJ07owQcfVGZmpgYOHHjNRQIAABRFV3VDzvr162vw4MGaOnWqatasqQEDBqhVq1aqWLGiJOnvv//WqlWrNHPmTB07dkwxMTGqX7/+dSkcAACgsF31nc2nTJkiT09PTZ48Wa+99ppee+01p+WGYchut2vkyJF69dVXC6xQAACAouaqg5TNZtPrr7+ufv36afbs2dq4caMSExMlSYGBgbrrrrvUu3dvValSpcCLBQAAKEosf2lxlSpVOOIEAABuadzkCQAAwCKCFAAAgEUEKQAAAIsIUgAAABYRpAAAACwiSAEAAFhEkAIAALCIIAUAAGARQQoAAMAighQAAIBFBCkAAACLCFIAAAAWEaQAAAAsIkgBAABYRJACAACwiCAFAABgEUEKAADAIoIUAACARQQpAAAAiwhSAAAAFhGkAAAALCJIAQAAWESQAgAAsIggBQAAYBFBCgAAwCKCFAAAgEUEKQAAAIsIUgAAABYRpAAAACwiSAEAAFhEkAIAALCIIAUAAGARQQoAAMAighQAAIBFBCkAAACLCFIAAAAWEaQAAAAsIkgBAABYRJACAACwiCAFAABgEUEKAADAIoIUAACARUUuSK1du1adOnVSUFCQbDabvvnmG6flvXv3ls1mc/pp166dU5+TJ0+qW7du8vHxUenSpdWvXz+dPXvWqc+OHTvUvHlzeXp6Kjg4WJMmTcpRyxdffKHq1avL09NTtWvX1tKlSwt8vAAA4OZV5ILUuXPnVLduXb333nt59mnXrp2OHDli/vzf//2f0/Ju3bpp165dWrFihRYvXqy1a9fqiSeeMJenpKSobdu2qly5srZu3arJkydr7Nixmjlzptln48aNevTRR9WvXz/9+uuv6tKli7p06aKdO3cW/KABAMBNyWYYhlHYReTFZrPp66+/VpcuXcy23r176/Tp0zmOVGX7z3/+o5o1a2rLli1q2LChJGnZsmXq0KGD/vvf/yooKEgffPCBXnzxRSUmJsrd3V2SNGLECH3zzTfavXu3JOnhhx/WuXPntHjxYnPdTZo0UXh4uKZPn56v+lNSUuTr66vk5GT5+PhY2ANXFjJiSYGvszAcmBBd2CUAAGC6mvdv1xtUU4Fas2aNAgIC5Ofnp9atW+vVV19V2bJlJUlxcXEqXbq0GaIkKTIyUi4uLtq0aZPuu+8+xcXFqUWLFmaIkqSoqChNnDhRp06dkp+fn+Li4hQTE+O03aioqDwDnCSlpaUpLS3NfJySkiJJysjIUEZGhiTJxcVFdrtdWVlZcjgcZt/s9szMTF2abe12u1xcXHJtLy6y9032WLMfZ3N1vfgyzczMzFe7m5ubHA6HsrKyzDabzSZXV9c82/Oaj4KYJ8bEmBgTY2JMN9+Y8uumC1Lt2rXT/fffr9DQUO3bt08vvPCC2rdvr7i4ONntdiUmJiogIMDpOa6uripTpowSExMlSYmJiQoNDXXqU758eXOZn5+fEhMTzbZL+2SvIzfjx4/XuHHjcrQvX75cJUuWlCRVqlRJ9erV044dO5SQkGD2qVatmqpXr67Nmzfr2LFjZnt4eLgqV66stWvX6syZM2Z7RETEFffTzST72rOIiAgFBARo+fLlTi/iVq1aqUSJEjmuUevQoYPOnz+v1atXm22urq6Kjo7W8ePHFRcXZ7Z7e3urdevWOnTokOLj4812f39/NW3aVHv27NEff/xhthfkPDEmxsSYGBNjurnGtGHDBuXXTXdq73J//fWXqlSpopUrV6pNmzZ6/fXXNXfuXKcdKUkBAQEaN26cBg4cqLZt2yo0NFQzZswwl//++++644479Pvvv6tGjRpyd3fX3Llz9eijj5p93n//fY0bN05JSUm51pLbEang4GAdP37cPDRYkIk/7IUf/mEP3hz2vNJWUvH5K6Y4/mXGmBgTY2JMt9KYTp48qbJlyxbfU3uXCgsLU7ly5bR37161adNGgYGBOnr0qFOfzMxMnTx5UoGBgZKkwMDAHGEo+/E/9clenhsPDw95eHjkaHdzc5Obm5tTm91uz/X0XPYLKr/txcHl++byx1baXVxc5OKS87MUebXnNR8FNU+MiTExJsZ0pXbGdHOMKTdF7lN7V+u///2vTpw4oQoVKki6eEjx9OnT2rp1q9knNjZWDodDjRs3NvusXbvWKS2vWLFC1apVk5+fn9ln1apVTttasWJFsTqlBgAArk2RC1Jnz55VfHy8ee5z//79io+PV0JCgs6ePauhQ4fq559/1oEDB7Rq1Sp17txZVatWVVRUlCSpRo0aateunR5//HFt3rxZGzZs0FNPPaVHHnlEQUFBkqTHHntM7u7u6tevn3bt2qXPPvtM06ZNc7q4/Nlnn9WyZcs0ZcoU7d69W2PHjtUvv/yip5566obvEwAAUDQVuSD1yy+/qF69eqpXr54kKSYmRvXq1dPo0aNlt9u1Y8cO3Xvvvbr99tvVr18/NWjQQOvWrXM6pbZgwQJVr15dbdq0UYcOHdSsWTOne0T5+vpq+fLl2r9/vxo0aKDnnntOo0ePdrrXVNOmTbVw4ULNnDlTdevW1aJFi/TNN9+oVq1aN25nAACAIq1IX2x+s+M+UvnDfaQAAEXJ1bx/F7kjUgAAADcLghQAAIBFBCkAAACLCFIAAAAWEaQAAAAsIkgBAABYRJACAACwiCAFAABgEUEKAADAIoIUAACARQQpAAAAiwhSAAAAFhGkAAAALCJIAQAAWESQAgAAsIggBQAAYBFBCgAAwCKCFAAAgEUEKQAAAIsIUgAAABYRpAAAACwiSAEAAFhEkAIAALCIIAUAAGARQQoAAMAighQAAIBFBCkAAACLCFIAAAAWEaQAAAAsIkgBAABYRJACAACwiCAFAABgEUEKAADAIoIUAACARQQpAAAAiwhSAAAAFhGkAAAALCJIAQAAWESQAgAAsIggBQAAYBFBCgAAwCKCFAAAgEUEKQAAAIsIUgAAABYRpAAAACwiSAEAAFhEkAIAALCIIAUAAGARQQoAAMAighQAAIBFBCkAAACLCFIAAAAWEaQAAAAsIkgBAABYRJACAACwiCAFAABgEUEKAADAIoIUAACARQQpAAAAiwhSAAAAFhGkAAAALCJIAQAAWESQAgAAsIggBQAAYBFBCgAAwCKCFAAAgEUEKQAAAIsIUgAAABYRpAAAACwiSAEAAFhEkAIAALCIIAUAAGARQQoAAMAighQAAIBFBCkAAACLCFIAAAAWEaQAAAAsIkgBAABYRJACAACwiCAFAABgEUEKAADAIoIUAACARQQpoBCFhITIZrPl+Bk0aJAkad++fbrvvvvk7+8vHx8fPfTQQ0pKSsqxniVLlqhx48YqUaKE/Pz81KVLlxs8kuKhIOYjt3VMmDChMIZz07vSfBw4cCDXZTabTV988YW5joSEBEVHR6tkyZIKCAjQ0KFDlZmZWYijunllZWVp1KhRCg0NVYkSJVSlShW98sorMgzD7GMYhkaPHq0KFSqoRIkSioyM1J49e3JdX1pamsLDw2Wz2RQfH3+DRlHwCFJAIdqyZYuOHDli/qxYsUKS9OCDD+rcuXNq27atbDabYmNjtWHDBqWnp6tTp05yOBzmOr788kv16NFDffr00fbt27VhwwY99thjhTWkm1pBzIckvfzyy07refrppwtjODe9K81HcHCw07IjR45o3LhxKlWqlNq3by/p4ht/dHS00tPTtXHjRs2dO1dz5szR6NGjC3NYN62JEyfqgw8+0Lvvvqv//Oc/mjhxoiZNmqR33nnH7DNp0iS9/fbbmj59ujZt2iQvLy9FRUXpwoULOdY3bNgwBQUF3cghXBc249IoiQKVkpIiX19fJScny8fHp8DXHzJiSYGvszAcmBBd2CUUGYMHD9bixYu1Z88erVixQu3bt9epU6fM109ycrL8/Py0fPlyRUZGKjMzUyEhIRo3bpz69etXyNUXP1c7H9LFoyiDBw/W4MGDC7Hy4unS+bDZbDmW16tXT/Xr19fHH38sSfrhhx/UsWNHHT58WOXLl5ckTZ8+XcOHD9exY8fk7u5+Q+u/2XXs2FHly5c3968kde3aVSVKlND8+fNlGIaCgoL03HPP6fnnn5d08XekfPnymjNnjh555BHzeT/88INiYmL05Zdf6o477tCvv/6q8PDwGz2kPF3N+zdHpIAiIj09XfPnz1ffvn1ls9mUlpYmm80mDw8Ps4+np6dcXFy0fv16SdK2bdv0999/y8XFRfXq1VOFChXUvn177dy5s7CGUWxYmY9sEyZMUNmyZVWvXj1NnjyZU0kF4PL5uNzWrVsVHx/v9AdFXFycateubYYoSYqKilJKSop27dp1Q+ouTpo2bapVq1bpzz//lCRt375d69evN48A7t+/X4mJieYfFZLk6+urxo0bKy4uzmxLSkrS448/rk8++UQlS5a8sYO4DghSQBHxzTff6PTp0+rdu7ckqUmTJvLy8tLw4cOVmpqqc+fO6fnnn1dWVpaOHDkiSfrrr78kSWPHjtVLL72kxYsXy8/PT3fffbdOnjxZWEMpFqzMhyQ988wz+vTTT7V69Wr1799fr7/+uoYNG1ZIoyg+Lp+Py3388ceqUaOGmjZtarYlJiY6hShJ5uPExMTrVmtxNWLECD3yyCOqXr263NzcVK9ePQ0ePFjdunWT9L99mts+z15mGIZ69+6tAQMGqGHDhjd2ANcJQQooIj7++GO1b9/evGbA399fX3zxhb7//nuVKlVKvr6+On36tOrXry8Xl4u/utnX5rz44ovq2rWrGjRooNmzZ+e44BZXz8p8SFJMTIzuvvtu1alTRwMGDNCUKVP0zjvvKC0trbCGUixcPh+XOn/+vBYuXMjp7evs888/14IFC7Rw4UJt27ZNc+fO1RtvvKG5c+fmex3vvPOOzpw5o5EjR17HSm8s18IuAIB08OBBrVy5Ul999ZVTe9u2bbVv3z4dP35crq6uKl26tAIDAxUWFiZJqlChgiSpZs2a5nM8PDwUFhamhISEGzeAYsbqfOSmcePGyszM1IEDB1StWrXrXXqxlNd8ZFu0aJFSU1PVs2dPp/bAwEBt3rzZqS37U5aBgYHXp9hibOjQoeZRKUmqXbu2Dh48qPHjx6tXr17mPk1KSjL/b8p+nH39U2xsrOLi4pxOkUtSw4YN1a1bt6sKZUUFR6SAImD27NkKCAhQdHTuF96XK1dOpUuXVmxsrI4ePap7771XktSgQQN5eHjojz/+MPtmZGTowIEDqly58g2pvTiyOh+5iY+Pl4uLiwICAq5XucXeP83Hxx9/rHvvvVf+/v5O7REREfrtt9909OhRs23FihXy8fFx+uMD+ZOamup09FWS7Ha7eWQ8NDRUgYGBWrVqlbk8JSVFmzZtUkREhCTp7bff1vbt2xUfH6/4+HgtXbpUkvTZZ5/ptddeu0EjKVgckQIKmcPh0OzZs9WrVy+5ujr/Ss6ePVs1atSQv7+/4uLi9Oyzz2rIkCHmkQ0fHx8NGDBAY8aMUXBwsCpXrqzJkydLuvgRcVy9a5mPuLg4bdq0Sa1atZK3t7fi4uI0ZMgQde/eXX5+foUxnJveleZDkvbu3au1a9eab8iXatu2rWrWrKkePXpo0qRJSkxM1EsvvaRBgwblOCKCf9apUye99tprqlSpkvlJuzfffFN9+/aVJNlsNg0ePFivvvqq/vWvfyk0NFSjRo1SUFCQeW+7SpUqOa2zVKlSkqQqVaqoYsWKN3Q8BYUgBRSylStXKiEhwfzP6FJ//PGHRo4cqZMnTyokJEQvvviihgwZ4tRn8uTJcnV1VY8ePXT+/Hk1btxYsbGxvHFbdC3z4eHhoU8//VRjx45VWlqaQkNDNWTIEMXExNzIIRQrV5oPSZo1a5YqVqyotm3b5lhmt9u1ePFiDRw4UBEREfLy8lKvXr308ssvX++yi6V33nlHo0aN0pNPPqmjR48qKChI/fv3d7ov17Bhw3Tu3Dk98cQTOn36tJo1a6Zly5bJ09OzECu/vriP1HXEfaTyh/tIAQCKEu4jBQAAcANwag8oIBwhLFqYD+DK+B0pGAQpAMB1x5s2iitO7eXDe++9p5CQEHl6eqpx48Y57ksCAABuTQSpf/DZZ58pJiZGY8aM0bZt21S3bl1FRUU53ZcEAADcmghS/+DNN9/U448/rj59+qhmzZqaPn26SpYsqVmzZhV2aQAAoJBxjdQVpKena+vWrU7fCeTi4qLIyEinb7LOlpaW5vR9WsnJyZKkkydPKiMjw3y+3W5XVlaWeTfYS9szMzN16R0p7Ha7XFxccm13pKUW3GAL0YkTJyT9b6zZ+ypb9k34MjMz89Xu5uYmh8OhrKwss81ms8nV1TXP9rzm42rmqbjOR16vyaI+T8VtPqz8H1GU5qm4zkdB/F9eWPNUnOakIP8vd3FxMb/0PT93iCJIXcHx48eVlZWV6zdZ7969O0f/8ePHa9y4cTnaQ0NDr1uNxUG5qYVdAS7FfBQtzEfRwnwUPddzTs6cOSNfX98r9iFIFaCRI0c63cHY4XDo5MmTKlu2rGw2WyFWZk1KSoqCg4N16NCh63JDUVwd5qNoYT6KFuaj6LmZ58QwDJ05c0ZBQUH/2JcgdQXlypWT3W43vy08W1JSUq7fHO7h4ZHj+5tKly59PUu8IXx8fG66X4LijPkoWpiPooX5KHpu1jn5pyNR2bjY/Arc3d3VoEEDp2+ydjgcWrVqlflN1gAA4NbFEal/EBMTo169eqlhw4Zq1KiRpk6dqnPnzqlPnz6FXRoAAChkBKl/8PDDD+vYsWMaPXq0EhMTFR4ermXLluW4AL048vDw0JgxY3KcrkThYD6KFuajaGE+ip5bZU5sRn4+2wcAAIAcuEYKAADAIoIUAACARQQpAAAAiwhSAAAAFhGkAAAALCJIAQCKFT6MjhuJIIV8SUlJcfr2cAAX8aZddKSkpEiS03ebOhyOwioHtwiCFPJ0/PhxvfvuuwoNDVWbNm0UFRWlsWPHau/evbx5ALr4Jm2z2ZSRkWE+RuH45Zdf1K1bN02bNk2bNm3S+fPnJUkuLi5KTk4u5OpuTQ6HQwkJCVq4cKFiY2PlcDiK5XsHN+REnvr27avt27erffv28vHx0fHjx/Wf//xHhw4dUvXq1TV27FhVr169sMu8pZw/f14lSpQo7DIgaffu3Zo6dapiY2PVpEkTjRs3TqGhoTIMw+mICG6MF198UePHj1fr1q2VmZmpGjVqKDIyUidOnFBMTIxSUlLk4sKxgxtpxowZmjZtmtLS0hQYGKh33nlH9evX1/79+1W5cuViMx8EKeTKMAyVKlVKS5Ys0d1332227du3T+vWrdNHH32k5ORkff7556pZs2bhFnsLee6553TXXXepQYMGCgwMzPWrF06cOKGyZcsWQnW3lsaNG6tkyZKKjIzUN998o2PHjmnNmjUKCQkx+6Snp8vd3b3wiryFxMXFqVu3bho8eLDOnDmj5cuXKy0tTf/973/l7e2tiRMnqm7duqpcuXJhl3pLMAxDgYGBeuWVV1S3bl1NmDBBt99+u06dOqVt27YpKSlJzzzzjJ566qmb/49DA8jFzp07jVq1ahlbtmzJdXlqaqpRp04dY8yYMTe2sFvYggULDJvNZri5uRmhoaHGkCFDjNjYWCMpKcnIyMgwDMMwzp49a3Tu3NnYsWNHIVdbvM2ZM8eoVauWceLECcMwLu73u+66y+jfv79hGIbhcDgMwzCMCRMmGIcPHy60Om81H3/8sdG9e3cjMzPTOH/+vPHtt98arq6uRvXq1Y0mTZoYrVu3Nvbt21fYZd4SPvnkE6N69epGVlaWYRiG8fvvvxseHh7GI488YsybN88YO3asERwcbMTFxRVypdeueBxXQ4ELCwtTQECAnnvuOe3fvz/Hee0SJUqoV69eWrx4cSFVeOuJjY3VgAEDtHv3bvXr109ff/212rRpo/bt2+uNN97Qr7/+qs8//1xLlixR7dq1C7vcYu2rr75SdHS0ypQpo4yMDHl5eWnUqFGKjY3VwYMHZbPZtGbNGo0cOVIVKlQo7HJvCQ6HQz179lRWVpbeeOMNeXp6yuFwqEKFClq8eLH+/e9/KyQkRGFhYYVd6i3hr7/+cjpb8dlnn6l27dr65JNP1KNHDz355JOqXr26vvnmm8IrsoAQpJCrEiVK6NVXX1VKSop69OihhQsX6siRI+YFnGlpafr5559VrVq1Qq701pCZmamwsDCVLl1aYWFhevHFF7V//37Fx8erYcOGmjBhglq0aKH+/furR48ehV1usZaWliY3NzeVLl1ahmHIzc1NmZmZioqKUsWKFTV9+nRJ0ocffqiHHnqokKu9dbi4uMjV1VUDBgzQzJkzdfDgQb377ru6//77VaVKFfXr108ff/xxYZd5y2jdurXWrVun0aNH69VXX9Xs2bPVoUMHubq6SpL8/f1Vrlw5XbhwoZArLQCFfUgMRduOHTuMBx980PD09DTKlStndOnSxRgwYIARGhpq3Hnnncb27dsLu8RbxqlTp4zdu3cbhmEYaWlp5umjbPPnzzdsNpsRHx9fGOXdMhwOh7F161ZjypQp5uNs33zzjVGuXDkjISHB8PX1NdavX19YZd7S5s2bZ4SFhRk2m828PCEzM7OQq7q1ZGZmGhMmTDCaNGlitG/f3hg3bpzRsGFD81R3QkKCUa5cuWJxao+LzZEvR48e1eLFi/XNN9+oRIkSqlWrlh544AHVqFGjsEu7pWV/nNhut+vDDz/Us88+q9TU1MIu65ZiXPIpvfT0dHXp0kUJCQlKSUlRQkJCIVd3a8rKytLo0aOVnJysyZMn3/wXM9/Ezp8/b94ipEuXLgoODpafn59++uknVahQQUuWLCnsEq8ZQQpXzeFwFJuPrRYnb775prKysjR06NDCLuWWlB2oFi5cqO7du2vs2LEaPXp0YZd1y8rKylJqaqq8vb0LuxT8f3///bcmTZqkDRs26N5779Vjjz2mqlWrFnZZ14wgBRQTGRkZstvthNxCZhiGfvnlF4WFhXEbCiAXRjG71xpBCgAAwCL+dAUAALCIIAUAAGARQQoAAMAighQAAIBFBCkAAACLCFIAAAAWEaQAAAAsIkgBAABY9P8AcCnRgoi6xHsAAAAASUVORK5CYII=\n"
          },
          "metadata": {},
          "execution_count": 36
        }
      ],
      "source": [
        "n_qubits = 4 # dimension of the hypercube\n",
        "n_steps = 1 # number of steps of the quantum walk\n",
        "n_runs = 50000 # number of runs of the quantum circuit\n",
        "q_circuit = hypercube_walk(n_qubits, n_steps)\n",
        "plot_results(q_circuit, n_runs, \"Quantum walk on a hypercube\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mEfvYUAgZH2o"
      },
      "source": [
        "As illustrated in the plot above, the probability distribution across all states is noticeably biased, a result heavily influenced by the specific initial state of the hypercube. This bias primarily derives from the properties of the Grover coin. In fact, it amplifies certain probabilities based on the structure of the graph and the initial state, leading to uneven distributions. In the context of our QW on the hypercube for constructing a secure QKD protocol, this characteristic poses a significant problem. A highly biased distribution makes the system more predictable and, consequently, more vulnerable to eavesdroppers. The greater the bias, the easier it is for an adversary to infer critical information about the system, compromising its security. For this reason, we will explore alternative coin operators in our QW hypercube construction. By choosing a coin operator that ensures a more uniform and balanced distribution, we can enhance the security of the protocol and mitigate potential vulnerabilities."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RkmjTYr1Z1RD"
      },
      "source": [
        "### QW on a circle with a predefined number of positions $2P$\n",
        "\n",
        "In the circle scenario, the walker moves along discrete positions on a circle. The Hilbert space $H$, which describes the QW, is the tensor product of the position Hilbert space $H_p$ and the coin Hilbert space $H_c$, i.e., $H = H_p \\otimes H_c$. The position Hilbert space $H_p$ is spanned by points on a circle, denoted as $\\{\\ket{x}: \\, x \\in \\{0, \\dots, P - 1\\} \\}$, where $P$ is the total number of discrete positions. The coin Hilbert space $H_c$ is spanned by the two possible coin states $\\{\\ket{R}, \\: \\ket{L}\\}$, representing heads and tails, respectively. The evolution of the QW for one step is governed by the unitary operator:\n",
        "\n",
        "$$\n",
        "U = S \\cdot (R_c \\otimes I_p)\n",
        "$$\n",
        "\n",
        "where $I_p$ is the identity operator in $H_p$, and $R_c \\in SU(2)$ is a rotation in $H_c$. In its generical matrix form, $R_c$ can be written as:\n",
        "\n",
        "$$\n",
        "R_c(\\phi, \\theta) = \\begin{bmatrix} e^{i \\phi} \\cos(\\theta) & e^{i \\phi} \\sin(\\theta) \\\\ -e^{-i \\phi} \\sin(\\theta) & e^{-i \\phi} \\cos(\\theta) \\end{bmatrix}\n",
        "$$\n",
        "\n",
        "where $\\phi$ denotes the phase angle of the rotation, and $\\theta$ represents the actual rotation angle.\n",
        "\n",
        "The shift operator $S$ moves the walker one position to the right or left on the circle, based on its coin state. Explicitly, $S$ is defined as:\n",
        "\n",
        "$$\n",
        "S = \\sum_{x=0}^{P-1} \\left(\\ket{x + 1 \\ (\\text{mod} \\ P)} \\bra{x} \\otimes \\ket{R} \\bra{R} + \\ket{x - 1 \\ (\\text{mod} \\ P)} \\bra{x} \\otimes \\ket{L} \\bra{L}\\right)\n",
        "$$\n",
        "\n",
        "This operator shifts the walker either clockwise or counterclockwise, depending on the coin state. Since the walker is on a circle, position $P$ is identified with position $0$, creating a continuous loop of discrete steps.\n",
        "\n",
        "For the QKD protocol under consideration, we aim to apply an $F$ operator before evolving the walk. This operator functions as a coin flip (i.e., Pauli-X, Pauli-Y, or identity) acting solely on the coin space, with the resulting final state $\\ket{\\psi(t)}$ defined as:\n",
        "\n",
        "$$\n",
        "\\ket{\\psi(t)} = U^{t} \\cdot (F \\otimes I_p) \\ket{\\psi_0}\n",
        "$$\n",
        "\n",
        "where $\\ket{\\psi_0}$ is the initial state of our protocol.\n",
        "\n",
        "As outlined in [B. L. Douglas et al.](https://arxiv.org/abs/0706.0304), we can construct the QW on a circle using the same approach discussed earlier. However, there are critical differences to consider when applying this method to our QKD protocol. Unlike the general QW setup, where states can be initialized in superposition for broader explorations, our protocol requires precise initialization of the states to align with its security objectives. Specifically, the walker states must be initialized using $X$ gates applied in a controlled manner to set them appropriately for the protocol's requirements. Similarly, the coin operator cannot be a generic superposition like a Hadamard gate; instead, it must use the generic coin rotation operator, tailored and parameterized for the desired behavior in the QKD protocol.\n",
        "\n",
        "The following presents the implementation of the QW on a circle, specifically customized to align with the requirements of our QKD protocol."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 37,
      "metadata": {
        "id": "DkMwIrrDGOsn"
      },
      "outputs": [],
      "source": [
        "class QW_Circle:\n",
        "    def __init__(self, P, t, initial_position=0, F='I', phi=0, theta=np.pi/4):\n",
        "        \"\"\"\n",
        "        Quantum walk on a circle with 2P positions\n",
        "        Args:\n",
        "        P (int): base number of positions on the circle (must be odd); the total number of positions is 2P\n",
        "        t (int): number of steps to perform in the walk\n",
        "        initial_position (int): initial position of the walker\n",
        "        F (string): F operator type. Choose 'I', 'X', or 'Y'\n",
        "        phi (float): phase angle for the coin rotation operator\n",
        "        theta (float): rotation angle for the coin rotation operator\n",
        "        \"\"\"\n",
        "        self.P = P\n",
        "        self.t = t\n",
        "        self.initial_position = initial_position\n",
        "        self.F = F\n",
        "        self.phi = phi\n",
        "        self.theta = theta\n",
        "        self.n_walker_qubits = int(np.ceil(np.log2(2 * self.P))) # number of qubits for the walker\n",
        "        # Create quantum and classical registers\n",
        "        self.walker_r = QuantumRegister(self.n_walker_qubits, 'q')\n",
        "        self.coin_r = QuantumRegister(1, 'c')\n",
        "        self.classic_r = ClassicalRegister(self.n_walker_qubits, 'r')\n",
        "        # Initialize the quantum circuit\n",
        "        self.circuit = QuantumCircuit(self.walker_r, self.coin_r, self.classic_r)\n",
        "        # Build the QRW circuit\n",
        "        self._build_circuit()\n",
        "\n",
        "    def _build_circuit(self):\n",
        "        \"\"\"\n",
        "        Build the quantum random walk circuit with the specified parameters\n",
        "        \"\"\"\n",
        "        # Initialize the walker and coin qubits\n",
        "        self._initialize_circuit()\n",
        "        # Apply F operator before evolving the walk\n",
        "        self._apply_F()\n",
        "        # Add a barrier for clarity\n",
        "        self.circuit.barrier()\n",
        "        # Perform the specified number of walk steps\n",
        "        for step in range(self.t):\n",
        "            # Apply the coined walk step\n",
        "            self.circuit = self._coined_walk_step(self.circuit, self.walker_r, self.coin_r)\n",
        "        # Add a barrier for clarity\n",
        "        self.circuit.barrier()\n",
        "        # Add measurement operations\n",
        "        self.circuit.measure(self.walker_r, reversed(self.classic_r))\n",
        "\n",
        "    def _initialize_circuit(self):\n",
        "        \"\"\"\n",
        "        Initialize the circuit with the initial position of the walker\n",
        "        \"\"\"\n",
        "        # Set the walker to the initial position (in the range 0 to 2P - 1)\n",
        "        for i in range(self.n_walker_qubits):\n",
        "            if self.initial_position & (1 << i): # check if bit i is set in initial_position\n",
        "                self.circuit.x(self.walker_r[self.n_walker_qubits - i - 1])\n",
        "        self.circuit.barrier()\n",
        "\n",
        "    def _apply_F(self):\n",
        "        \"\"\"\n",
        "        Apply operator F to the coin qubit at the end of the walk\n",
        "        \"\"\"\n",
        "        if self.F == 'I':\n",
        "            pass # identity operation, do nothing\n",
        "        elif self.F == 'X':\n",
        "            self.circuit.x(self.coin_r)\n",
        "        elif self.F == 'Y':\n",
        "            self.circuit.y(self.coin_r)\n",
        "        else:\n",
        "            raise ValueError(\"Invalid operator type. Choose 'I', 'X', or 'Y'\")\n",
        "\n",
        "    def coin_rotation_operator(self, coin_r):\n",
        "        \"\"\"\n",
        "        Create a quantum circuit for the coin rotation operator\n",
        "        \"\"\"\n",
        "        # Create a quantum circuit for the coin rotation operator\n",
        "        q_circuit = QuantumCircuit(len(coin_r))\n",
        "        # Apply the rotation to each coin qubit\n",
        "        for qubit in range(len(coin_r)):\n",
        "            q_circuit.u(self.theta, self.phi, 0, qubit)\n",
        "        # Convert the circuit to an operator\n",
        "        coin_rotation_operator = Operator(q_circuit)\n",
        "        return coin_rotation_operator\n",
        "\n",
        "    def _coined_walk_step(self, q_circuit, walker_r, coin_r):\n",
        "        \"\"\"\n",
        "        Single step of the quantum walk\n",
        "        Args:\n",
        "        q_circuit (QuantumCircuit): quantum circuit\n",
        "        walker_r (QuantumRegister): quantum register containing the walker's position qubits\n",
        "        coin_r (QuantumRegister): quantum register containing the coin qubit\n",
        "        Returns:\n",
        "        Quantum circuit with an added walk step\n",
        "        \"\"\"\n",
        "        # Apply the coin rotation (U3 gate)\n",
        "        coin_operator = self.coin_rotation_operator(coin_r)\n",
        "        q_circuit.unitary(coin_operator, coin_r, label=\"R\")\n",
        "        # Shift operations\n",
        "        # Right shift (coin is \\ket{1}) or left shift (coin is \\ket{0})\n",
        "        for i in reversed(range(len(walker_r))):\n",
        "            controls = [walker_r[v] for v in range(len(walker_r) - 1, i, -1)] # controls are higher bits\n",
        "            controls.append(coin_r) # coin qubit as control\n",
        "            q_circuit.mcx(controls, walker_r[i]) # multi-controlled X gate for shift\n",
        "            if i != 0:\n",
        "                q_circuit.x(walker_r[i]) # flip the qubit if necessary\n",
        "        # Revert the coin state for left shift (subtraction)\n",
        "        q_circuit.x(coin_r)\n",
        "        for i in range(len(walker_r)):\n",
        "            if i != 0:\n",
        "                q_circuit.x(walker_r[i]) # reverse the flip\n",
        "            controls = [walker_r[v] for v in range(len(walker_r) - 1, i, -1)] # controls for the next shift\n",
        "            controls.append(coin_r) # coin qubit as control\n",
        "            q_circuit.mcx(controls, walker_r[i]) # multi-controlled X gate for left move\n",
        "        # Revert the coin qubit flip after the subtraction operation\n",
        "        q_circuit.x(coin_r)\n",
        "        return q_circuit\n",
        "\n",
        "    def draw_circuit(self):\n",
        "        \"\"\"\n",
        "        Draw the quantum circuit\n",
        "        \"\"\"\n",
        "        return self.circuit.draw(\"mpl\")\n",
        "\n",
        "    def plot_states_hist(self, shots=50000, title=None):\n",
        "        \"\"\"\n",
        "        Plot a histogram of measurement results for QW states\n",
        "        Args:\n",
        "        shots (int): number of circuit executions\n",
        "        title (str): title for the histogram\n",
        "        \"\"\"\n",
        "        simulator = AerSimulator(max_parallel_experiments=0, max_memory_mb=None)\n",
        "        self.circuit = transpile(self.circuit, backend=simulator, optimization_level=1)\n",
        "        job = simulator.run(self.circuit, shots=shots)\n",
        "        results = job.result()\n",
        "        counts = results.get_counts()\n",
        "        # Plot histogram\n",
        "        fig, ax = plt.subplots(figsize=(12, 6))\n",
        "        plot_histogram(counts, title=title or f'QW results (P={self.P})', sort='value_desc', ax=ax)\n",
        "        ax.set_xlabel('Measured states')\n",
        "        ax.set_ylabel('Counts')\n",
        "        plt.xticks(rotation=45)\n",
        "        plt.tight_layout()\n",
        "        plt.show()\n",
        "\n",
        "    def execute(self):\n",
        "        \"\"\"\n",
        "        Execute the circuit once and return a result state\n",
        "        \"\"\"\n",
        "        simulator = AerSimulator(max_parallel_experiments=0, max_memory_mb=None)\n",
        "        self.circuit = transpile(self.circuit, backend=simulator, optimization_level=1)\n",
        "        results = simulator.run(self.circuit, shots=1).result()\n",
        "        answer = results.get_counts()\n",
        "        state = list(answer.keys())[0]\n",
        "        return state\n",
        "\n",
        "    def get_probabilities(self, shots=50000):\n",
        "        \"\"\"\n",
        "        Get the probability distribution\n",
        "        Args:\n",
        "        shots (int): number of circuit executions\n",
        "        Returns:\n",
        "        dict: probability distribution of states\n",
        "        \"\"\"\n",
        "        simulator = AerSimulator(max_parallel_experiments=0, max_memory_mb=None)\n",
        "        self.circuit = transpile(self.circuit, backend=simulator, optimization_level=1)\n",
        "        results = simulator.run(self.circuit, shots=shots).result()\n",
        "        counts = results.get_counts()\n",
        "        probabilities = {}\n",
        "        total = sum(counts.values())\n",
        "        for state, count in counts.items():\n",
        "            probabilities[state] = count / total\n",
        "        return probabilities"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Sf_jq8yZ11Mw"
      },
      "source": [
        "Let's explore an example to verify if our concept is implemented correctly. In this context, the probability distribution across the possible states is initially biased with a low number of steps ($t$), resulting in a skewed outcome. However, as $t$ increases, the distribution approaches uniformity, which is crucial for achieving a secure QKD protocol by ensuring that the key exchange is resistant to eavesdropping."
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Simulations parameters\n",
        "shots = 100000"
      ],
      "metadata": {
        "id": "J4Q4Hp916UZs"
      },
      "execution_count": 38,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": 39,
      "metadata": {
        "id": "O4_3HguV1t4Z"
      },
      "outputs": [],
      "source": [
        "# Test QW on a circle with 2P positions\n",
        "qw_c = QW_Circle(P=3, t=1, initial_position=2, F='Y', phi=0, theta=np.pi/4)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 40,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 242
        },
        "id": "JlRB709v1yGI",
        "outputId": "a25f2850-b381-4c69-e0bc-f8dd746e409b"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 1876.11x451.5 with 1 Axes>"
            ],
            "image/png": "iVBORw0KGgoAAAANSUhEUgAABbgAAAFvCAYAAACIKK2mAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy81sbWrAAAACXBIWXMAAA9hAAAPYQGoP6dpAABtdklEQVR4nO3dd3wU1frH8e8mm04IKUBCKKH3Jk1AFBAURARERUVF8YpiQy+KDUWwIIrKFa/+9NobIOBVpAh6UUEUpQjSayghCRAI6QlJdn9/cMk1kkA27O5kZz7v18sX7s6cOU/Iw86cZ8+csTmdTqcAAAAAAAAAAPAxfkYHAAAAAAAAAABAZVDgBgAAAAAAAAD4JArcAAAAAAAAAACfRIEbAAAAAAAAAOCTKHADAAAAAAAAAHwSBW4AAAAAAAAAgE+iwA0AAAAAAAAA8EkUuAEAAAAAAAAAPokCNwAAAAAAAADAJ1HgBgAAAAAAAAD4JArcAAAAAAAAAACfRIEbAAAAAAAAAOCTKHADAAAAAAAAAHwSBW4AAAAAAAAAgE+iwA0AAAAAAAAA8EkUuAEAAAAAAAAAPokCNwAAAAAAAADAJ1HgBgAAAAAAAAD4JArcAAAAAAAAAACfRIEbAAAAAAAAAOCTKHADAAAAAAAAAHwSBW4AAAAAAAAAgE+iwA0AAAAAAAAA8EkUuAEAAAAAAAAAPokCNwAAAAAAAADAJ1HgBgAAAAAAAAD4JArcAAAAAAAAAACfRIEbAAAAAAAAAOCT7EYHAJyPNWvWuLR/WlqavvjiC1199dWKiYmpUJsuXbpUJjR4CTkAAAAAANbljTGhxLgQqMqYwQ1LSUtL0zvvvKO0tDSjQ4FByAEAAAAAsC7GhID5UOAGAAAAAAAAAPgkCtwAAAAAAAAAAJ9EgRsAAAAAAAAA4JMocMNSwsPDNWDAAIWHhxsdCgxCDgAAAACAdTEmBMzH5nQ6nUYHAVSWq09LrgyelFy1kQMAAAAAYF3eGBNKjAuBqowZ3LCUgoICHTx4UAUFBUaHAoOQAwAAAABgXYwJAfOhwA1LSUxM1PDhw5WYmGh0KDAIOQAAAAAA1sWYEDAfu9EBAAAAAAAAAPgfp9Op4uJio8Nwib+/v2w2m9FhwIIocAMAAAAAAABVSHFxsebPn290GC4ZPny47HZKjfA+ligBAAAAAAAAAPgkCtwAAAAAAAAAAJ/EfQOwlBYtWui3334zOgwYiBwAAAAAAOtiTAiYDzO4AQAAAAAAAAA+iQI3LGX//v0aPXq09u/fb3QoMAg5AADWVFTk0N6kTG3aeVybdx3X/uQsORxOo8OCF+XmFWlH4gn9sfO4tu5J15FjeUaHBAAwAGNCwHxYogSWkpeXp82bNysvjwGNVZEDAGANTqdTazan6dNFu7VmS5o27DimvPziUvtEhAfqghbRurBdLY26qomaN6xhTLDwiKIihxatPKgvl+/Xuq1p2rr3hIqLS3+pUadWqDq1jNElnWN1y+AmqhkVYlC0AABvYUwImA8FbgAAAJiGw+HUJwt367XPtmrd1rSz7puRdVLfr0nR92tSNPXdjbq0Wx39/ZY2uqJXPS9FC0/Izi3UjE826625O5R0OOes+yYfyVXykQP6+scDevy1tbru8oaacGs7tW0W5aVoAQAAcL4ocAMAAMAU9iZlavRTK/Xj2tRKtf/Pr8n6z6/Jun5AI818rLtiIoPdHCE87fvfknX7pJ+UeCjL5bYnCx36ZOEezf5mr54c01GP3d5eAQGs6AgAAFDVccUGAAAAnzdr8R61vfrflS5u/9nsb/aq9bD5WrE2xQ2RwRscDqcefvk39f3bkkoVt/+sqMipSW+sV7eRC5SUevYZ4AAAADAeBW5YSlxcnCZPnqy4uDijQ4FByAEAMJ+3523XjY/+oNz8Ircd88jxfF0+dqmWrkpy2zHhGQ6HU7dPWqnpH25y63F/335MF926UIlJ51cwBwBULYwJAfOhwA1LiYiI0MCBAxUREWF0KDAIOQAA5jLnm72665lVHjl2fkGxhj34nX7ZeNgjx4d7PPDian3w1S6PHHt/crb637lER4/zIDIAMAvGhJV39OhRpaWd/RkngBFYgxuWkp6eru+++079+vVTZGSk0eHAAOQAAJjHgZRs3TH5JzmdFW+zZtZVio0JVWparrrcsOCc++flF2vkoz9q0/xhCgsNOI9o4Qlf/3BAMz/b6lIbV3Ngz8Es3f3cz5r78qWVDRMAUIVYbUx46NAhbdmyRYmJiUpMTFRWVpaKi4tlt9tVs2ZNNWrUSA0bNlS7du1UvXr1co9z9OhRTZkyRTabTU899ZRiYmK8+FMAZ0eBG5Zy+PBhvfTSS2rbtq0lTmQ4EzkAAObgdDr1t6dXKiun0KV2sTGhqls7zKU2iYey9Og/1mrmY91dagfPSs8s0J2VmL1fmRyY9+0+fb50r667vJHL/QEAqhYrjAmLior022+/admyZdq+fXu5+6WlpWnbtm2SpICAAF144YW67LLL1LRp01L7nS5uHz16VJL0zjvv6NFHH/XcDwC4yBJLlKSlpWnChAlq0qSJgoODVa9ePY0bN045OTm6/fbbZbPZ9PrrrxsdJgAAACpo/rf79O0vyV7r7/VZW7VxxzGv9Ydze/qN9Uo5muu1/u6b+ovyC9y3zjsAAJ6we/duPfroo3rttdfOKG7bbDZFRkYqJiZG4eHhpbYVFhZq5cqVevLJJzVjxgxlZmZKOrO4HRcXpzvvvNM7PwxQQaafwb1hwwYNHDhQqampCgsLU6tWrZScnKzXXntNe/bs0fHjxyVJHTp0MDZQAAAAVNjMWa4tS+EO/5y9TW9Pusjr/eJMWTkn9b6H1t0uz5Hj+Zq7LFE3D2567p0BAPAyh8OhOXPmaMGCBXL+af22+Ph49enTR82aNVODBg0UFBRUsi0jI0N79+7V5s2b9eOPPyo7O1uStHr1am3dulUjRozQl19+Waq4/dRTT5l25jt8l6kL3GlpaRo8eLBSU1M1fvx4TZo0qeQbqhdffFGPPPKI7Ha7bDab2rVrZ3C0AAAAqIjNu45rxbpUr/f76aI9evHBLqpRPejcO8OjPl20x+XladzhjTnbKHADAKqcoqIivf7661q9enXJew0bNtRNN92kVq1ayWazldkuIiJCHTt2VMeOHTVixAitWLFCs2fPVnZ2tjIzM/Wvf/2rZF+K26jKTL1Eyf3336+kpCTde++9mj59eqnbLyZMmKD27durqKhICQkJZ11IH+YRGhqqbt26KTQ01OhQYBByAAB835yliYb0m5tfpIUrDhrSN0qb/c1eQ/pd/cdR7U/OMqRvAIB7mG1M6HA49MYbb5QUt/39/XXdddfpmWeeUevWrcstbv9VYGCg+vXrp+nTp6tt27alttWoUYPiNqo00xa4t23bpjlz5igmJkZTp04tc59OnTpJktq3b1/q/cTERF111VUKDw9XZGSkbrnlFh07xpqLZlC/fn3NnDlT9evXNzoUGIQcAADft3ZLmmF9r9tqXN84xeFwav02467N121lXAAAvsxsY8LFixfr559/lnTqQZEPPfSQrr76atntlVu0obCwUKmppe+Uy8zMVFYWX/Ci6jJtgXvWrFlyOBwaOXKkqlWrVuY+ISEhkkoXuLOystSnTx8lJSVp1qxZevvtt7Vy5UpdeeWVcjgcXokdnlNcXKzs7GwVFxcbHQoMQg4AgG9zOp2GFpkpcBtv1/4MQ5YnOY0cAADfZqYxYXJysubMmSPp1AMkH3jgAXXs2LHSx/vrAyVPz3J3OBx68803VVTEw5ZRNZm2wL18+XJJUp8+fcrdJykpSVLpAvfbb7+tQ4cO6csvv9SVV16pa6+9Vp999plWr16tBQsWeDZoeNyuXbvUt29f7drl3YcSoeogBwDAt53IOqmj6fmG9b9jX4ZhfeMUo38HRvcPADg/ZhkTOp1Ovf322yosPPWl74ABA0pWKqiMvxa34+LiNG3aNNWtW1fSqdUOFi9efP6BAx5g2odM7t+/X5LUoEGDMrcXFRVp1apVkkoXuBcuXKiLLrqo1K0q3bt3V6NGjfT1119r6NChLsfSuXPnM27vgHtcc801Lu1/5MgRSdKSJUu0bt26CrUZNmyYy3HBe8gBALCWYlu4FPlQudvXzLpKsTHlr6kZGxNS8ufBb68vd7/UtFx1ueHMyQ1Hj2WUDPRgjNzA1lK168rcdq7fv3T+ObBw8TLV/XyUCxEDADzJG2NCyfvjwsDAwHKX3JWkPXv2aPv27ZKk2NhYXX99+ee0cymruH16ze2xY8dq4sSJcjqdWrJkia644opylz9p1qyZTp48Wek4YG2xsbFau3ZtpdqatsCdk5MjScrLyytz+5w5c5SWlqbw8HA1bNiw5P2tW7fq2muvPWP/1q1ba+vWrZWKJTU1VYcOHapUW5zd6d9zRZ3Oh7y8vAq35XdXtZEDAGAx9urSWZ5vFBsTqrq1w859GH+/Cu33V05HMecFo1WPlcpegbDCv3+p8jlQkJ9HDgBAFeKNMaHk/XFhUFDQWbcvW7as5P+HDh16zv3Lc7bitiQ1btxYnTt31po1a5Senq5169apW7duZR4rOTlZBQUFlYoDOB+mLXDHxsYqPT1d69evV/fu3UttS0lJ0cMPPyxJateuXaknyqanp6tGjRpnHC8qKko7duyodCzwjLAw1wYlp09eISEhFW4bHx/vclzwHnIAAKzFoQClnGV7alruWdvHxoTI7u+nomKHUtPKnghxtuP466RiOS8YKt8epvIe83iu3790/jkQEmRTFDkAAFWGN8aEkvfHhYGBgeVuy8/P1y+//CLp1M//17pXRZ2ruH1a//79tWbNGknS999/X26Bu06dOszgRqWdT/3UtAXufv36adu2bZo2bZr69++vZs2aSZLWrFmjm2++WWlppx4O06FDB4/HUtnp9Ti30x+wFbV9+3bNmjVLAwcOVIsWLSrUZsaMGZWIDN5CDgCA9TS9cq52H8gsc1tZS0r82cFvr1fd2mFKTctTvf6zXe57YJ+2+vr1JJfbwX1S03IV13dWmdvO9fuXzj8Hnn7kdk0Y/Q+X2wEAPMMbY0LJ++PCoqIizZ8/v8xt+/btK1l7u0uXLpWavV3R4rYktWnTRhEREcrIyNCuXbvkdDpLTRY9befOneUuXwJ4kmkfMjlhwgRFR0fr4MGDat26tdq2baumTZuqa9euatSokfr27Sup9PrbkhQZGakTJ06ccbzjx48rKirKG6HDg5o0aaKlS5eqSZMmRocCg5ADAOD7OreKMazvTgb2jVNiY0IVX+vs62x7EjkAAL7NDGPCvXv3lvx/ZX4OV4rbkuTn56dGjRpJOjUD/nQ7oKowbYG7bt26WrlypQYNGqTg4GDt27dPUVFReuutt7Ro0SLt3LlT0pkF7pYtW5a51vbWrVvVsmVLr8QOz7Hb7YqMjOQbRQsjBwDA93VvX8uSfeN/jPo9BNj91KlVtCF9AwDcwwxjwgMHDpT8/5+fK1cRrha3Tztd4Jak/fv3u9Qn4GmmLXBLp4rVCxcuVFZWlrKysvTrr79qzJgxysnJ0b59++Tn56c2bdqUanPllVfqp59+UlLS/249/fXXX7Vnzx4NHjzY2z8C3CwpKUnjx48v9fuFtZADAOD7bryisYIC/b3eb/24MPW7sI7X+8WZbh/W3JB+h/dLUI3qlXuIFwCgajDDmPD0gzIlKSIiosLtKlvc/ms/f+4fqApMXeAuz5YtW+R0OtW0aVOFhpa+vXHMmDGKi4vTkCFDtHDhQs2bN0833HCDunbtqiFDhhgUMdwlOztbK1euVHZ2ttGhwCDkAAD4vpjIYI243LXZSu5w5zUt5O9vycvnKueyHvFqXC/c6/3ePYI7OgHA15lhTHjHHXfo9ddf1yuvvKIaNWpUuN3hw4dLluV1pbgtST169NCMGTP0z3/+UxdeeGElogY8x5JX6Js2bZJ05vIkklS9enUtX75ccXFxuv766/W3v/1NPXr00MKFC+XnZ8m/LgAAgCrn77e0kZ/fmQ838pSI8ED97WpjZg3jTH5+No2/pa1X++zWtqYuuqC2V/sEAKAs1apVU0xMjOrUqePSUitt2rTRQw89pAYNGrhU3D7dZ2xsrKKjoxUYGFiZsAGP8d0Fh87D2QrcktS4cWMtXLjQmyEBAADABe2bR2vCbW31wrt/eKW/GRO6qVZ0iFf6QsXceW0LzVqyRyvXH/Z4X4EBfnpvSi/ZbN77UgUAAE9o37692rZtyyROmIols/lcBW4AAABUfU+PvUCtGtdwqU1qWq6SDucoNS23wm0GXVxPo65q6mJ08DQ/P5vem3KxQoJdW4+9Mjkw+e4L1KpxxWe5AQBQlVHchtlYcgb38uXLjQ4BBqlZs6bGjRunmjVrGh0KDEIOAIB5BAX669+v9lOvWxfqyPH8CrXpcsMCl/po1biGPnjmYmbuVlFN6lfXZy/01jXjl6u42FmhNq7mwHWXN9TDt3p3ORQAgOcwJgTMh69sYCnR0dEaOXKkoqOjjQ4FBiEHAMBcmiVE6Lu3B6q2B5YPadW4hr59a4BiIoPdfmy4z9C+Cfp0am/Z7e7/EuKa/gn6+PlLeLgoAJgIY0LAfLhSg6VkZmbqu+++U2ZmptGhwCDkAACYT9tmUfr54yvVvX0ttx1z2KUNtOL9QapTK8xtx4TnjBjQSEvfHKC6td3z+/L3t+nxv7XX7Bf7KDDAtSVQAABVG2NCwHwocMNSkpOT9fjjjys5OdnoUGAQcgAAzKlR3epa+cEgTR/fVcFBlS9IRkUE6bMXemv+K5cqugYzt31J3251tPmLq3X7sGbndZzWjWto9SeD9dz9nZm5DQAmxJgQMB+u2AAAAGAK/v5+Gj+qrfYsulaT775AdWqFVrht84QI/eORC7Vn0bW64YrGrLntoyLCA/XO5F7aOG+Y7rq2hcJCKv7Iod5d4vT59L76/fNh6tyadVkBAAB8hSUfMgkAAADzqlMrTE/d1VGP3d5eK9alas2Wo1q3NU1b957QjsQMFTucstttGnF5I3VuFaNu7Wrqwna1KGqbSLtmUXrzyZ6a9mAX/efXZK3bmqZ1W49pb1KW9hzMVLHDqQC7n24f1kydWsWo1wW11bxhDaPDBgAAQCVQ4AYAAIApBQT46dIL6+jSC+uUvFe33ywdOpKr2lEh+mRqb+OCg1dUrxaoYZcmaNilCSXvnc6BWlHBevPJnsYFBwAAALdgiRJYSlBQkJo3b66goCCjQ4FByAEAAAAAsC7GhID5MIMbltKwYUN9/PHHRocBA5EDAAAAAGBdjAkB82EGNwAAAAAAAADAJ1HghqXs2LFDPXv21I4dO4wOBQYhBwAAAADAuhgTAuZDgRuW4nQ6VVhYKKfTaXQoMAg5AAAAAADWxZgQMB/W4AYAAAAAAACqEH9/fw0fPtxtx3vprTnKyslReFiYHr5zxBmv3cHf398txwFcRYEbAAAAAAAAqEJsNpvsdveV7ZySHM5Tf9rt9jNeA76MJUoAAAAAAAAAAD6Jr2hgKQkJCZo1a5bi4+ONDgUGIQcAAAAAwLoYEwLmQ4EblhIcHKzGjRsbHQYMRA4AAAAAgHUxJgTMhyVKYCkpKSl69tlnlZKSYnQoMAg5AAAAAADWxZgQMB8K3LCUjIwMLViwQBkZGUaHAoOQAwAAAABgXYwJAfOhwA0AAAAAAAAA8EkUuAEAAAAAAAAAPokCNwAAAAAAAADAJ1HghqX4+fmpY8eO8vMj9a2KHAAAAAAA62JMCJgP/5phKQ6HQ7///rscDofRocAg5AAAAAAAWBdjQsB8KHADAAAAAAAAAHwSBW4AAAAAAAAAgE+iwA0AAAAAAAAA8EkUuGEp4eHhGjBggMLDw40OBQYhBwAAAADAuhgTAuZjNzoAwJvi4+M1ZcoUo8OAgcgBAAAAALAuxoSA+TCDG5ZSUFCggwcPqqCgwOhQYBByAAAAAACsizEhYD4UuGEpiYmJGj58uBITE40OBQYhBwAAAADAuhgTAubDEiVVlNPpVG5ekdFhVFhoiF02m83oMAAAMA2uBQBr87XPAInPAQCAezmdThUXFxsdhkv8/f05FxqAAncVlZtXpGoXfmR0GBWWvfoWhYUGGB0GAACmwbUAYG2+9hkg8TkAAHCv4uJizZ8/3+gwXDJ8+HDZ7ZRbvY0lSgAAAAAAAAAAPokCNwAAAAAAAADAJzFnHpbSokUL/fbbb0aHAQORAwAAAABgXYwJAfNhBjcAAAAAAAAAwCdR4Ial7N+/X6NHj9b+/fuNDgUGIQcAAAAAwLoYEwLmwxIlsJS8vDxt3rxZeXl5RocCg5ADgLXsO5SlXzYe0bqtadq487gyswtV7HAqJMhfzRIi1LlVjDq3jlGnVjHy87MZHS4AwM1OZBbo5/+eB9ZtTdPhY3k6WehQUKC/4muFqlOrU+eAHu1rKSw0wOhwAXgBY0LAfChwAwAAUykqcujrHw/ojTnb9N3q5HL3++n3w3rv3zslSY3rheuua1vqtqFNFV0j2FuhAgA8ZN3WNL0xZ5s+W7xH+QXF5e4379t9kqTq1QI06qqmGntdS7VsVMM7QQIAALdgiRIAAGAav2w8rDZXf6GrH/zPWYvbf7XnYJYefuU31b9sjl77dIscDqcHowQAeErK0VwNHfetOl//ld77986zFrf/LDO7UDM/26pWQ+dr9FMrdCKzwMORAgAAd6HADQAAfF7ByWI9/PJvumjUIu3Yl1Hp4+TmF2nctNXqPXqREpOy3BghAMDTZi3eo9bD5uur7w+c13He/3KX2lz9hZauSnJTZAAAwJMocMNS4uLiNHnyZMXFxRkdCgxCDgDmk5NbqKvu/1bTP9zktpnXK9cfVvebv9bGHcfccjwAgGc9/68NuvHRH5SeedItxzt0JFdX3LOsZCkrAObBmBAwHwrcsJSIiAgNHDhQERERRocCg5ADgLkUnCzWsAe/07KfD7n92IeP5anfmG+0be8Jtx8bAOA+L7y7UU/MXOf24zocTt0+aaU+WrDL7ccGYBzGhDgfDofD6BBQBgrcsJT09HTNnTtX6enpRocCg5ADgLk8/Mpv+vaXiq+17aq09Hxddf+3ys0r8lgfAIDKW7zyoB77x1qP9jF60kqt25rm0T4AeA9jQutxOBw6dOiQfvrpJ82fP1+zZ8/W3LlztXjxYm3dulW5ubkVOs6mTZs0YcIEpaVxTqhq7EYHAHjT4cOH9dJLL6lt27aKjIw0OhwYgBwAzOPHtSma+dlWl9qsmXWVYmNClZqWqy43LKhQm90HMvXEzLV6dcKFlQkTAOAhJzILdMfkn1xqU5nzQHGxU7dOXKF1c4YoMMC/MqECqEIYE1qD0+nU7t27tWzZMq1du1Z5eXln3T8hIUF9+/ZVr169FBIScsb2TZs26cUXX1RhYaGmTJmiyZMnkz9ViCVmcKelpWnChAlq0qSJgoODVa9ePY0bN045OTm6/fbbZbPZ9PrrrxsdJgAAqKCCk8Ua/dRKl9vFxoSqbu0wxcaEutTuH59u0S8bD7vcH6oWh8NZsk670+me9drhWwoLHSomB0zj4Vd+U/KRis26O62y54HNu9P1/L82utQGAGCM7du36/HHH9eTTz6plStXnrO4LUn79u3Te++9p7Fjx2r27Nk6efJ/z3T4c3Fbkho0aKDw8HCPxQ/Xmb7AvWHDBrVt21YvvfSSUlNT1apVKxUWFuq1117TiBEjtG3bNklShw4djA3UQ567v5Ocf9yu24Y2LXP79+9eofy1t6p1E751AgD4jnnfJmpvUpbX+nM6pZc+2OS1/tyJawFpw/ZjGjP5J4Vf+JFS0k4NcFLT8jThld+0NynT4OjgaQ6HU0tWHtSV9y5TUOf3lfrfHDh8PF+vfrxZ6ZkFBkfoWWb9DEg5mqsPvLw29mufbWHJKgCowgoKCvThhx9q8uTJSkxMLHk/LCxMXbp00YgRI/TQQw/piSee0GOPPaYxY8aoX79+SkhIKNk3Pz9fX375pR577DHt3r37jOJ2ly5dNG7cONntLIpRlZj6t5GWlqbBgwcrNTVV48eP16RJk0q+YXnxxRf1yCOPyG63y2azqV27dgZH6xlPv/G7Bl9SX6881E3LfjmkQ4f/N8PhgZtaq3eXOD06Y4227GbtKQCA73hjzjav9/nV9weUlJqjurFhXu/7fFj5WqCoyKF7nv9Zb8/bccY2x3+/tJj+4SY9d19nPXp7O9lsNgOihCcdPZ6nq+7/Vqv/OHrGtuJip/7+0q+a9MZ6ff5SXw24qK4BEXqeWT8D3vlih4qKvDsLPz3zpOYs3avbhjbzar8AgHM7ceKEXnjhBe3bt6/kvYSEBA0YMEA9evRQYGBgme369u0r6dQM7mXLlunHH39UcXGxDh06pIkTJ8rf31/FxcWSKG5XZaaewX3//fcrKSlJ9957r6ZPn17q9oEJEyaoffv2KioqUkJCgqpXr25gpJ5TWOTQqIkrFBYSoHef7lXyfrOECD13X2et/uOIz85Iq4zQ0FB169ZNoaGu3ZII8yAHAN+3dU+6ft5wxOv9OhxOvfflTq/3e76sei3gdDp165Mryixul95Pevy1tXrmrQ3eCQxecyKzQH3/tqTM4vafZeUUavB9y7R0VZKXIvMuM34GOJ1OvfPF2f9te8rb87Yb0i8A92FMaD6ZmZmaMmVKSXE7ICBAN910k55//nn17t273OL2nyUkJGjMmDF64YUX1KhRo5L3KW77BtMWuLdt26Y5c+YoJiZGU6dOLXOfTp06SZLat29f8t7pgnjXrl0VFBRkipk8v287pqnvbtTlPevqjuHN5edn00fPXSybTRo1cUXJWpRWUL9+fc2cOVP169c3OhQYhBwAfN9Pvxu3FvaqDb65DrcVrwU+XbRHny7aU+H9J72xXr/+4f0vTuA5E15do80VnJVcVOzUDY98r5zcQg9HZQyzfQYkHc7RgZQcQ/peuzVN+QUsUwL4MsaE5lJUVKRp06YpOTlZkhQdHa2pU6fqyiuvlJ+f62XPevXqacSIEWe07dOnD8XtKsy0Be5Zs2bJ4XBo5MiRqlatWpn7nH4q6p8L3Lt379b8+fMVGxurLl26eCVWb3jm7d+1YfsxTR/fVTMf665ubWvpiZnrtHNfhtGheVVxcbGys7NLvoGD9ZADgO9btzXN0L599cF0VrsWeH3WVpfbGLH0DTzjRGaBPlm026U26ZknNWvJXg9FZDwzfQYYeR4oKnJq0y7fWs4FQGmMCc1lwYIF2rPn1KSGqKgoTZo0SXXrVn7ZsU2bNmn69OlyOByl3n/nnXeUm+vag43hPaYtcC9fvlzSqW9YypOUdOo2xD8XuC+++GKlpKRowYIF6tevn2eD9KKiIqdGTVyh4CB/3T2ipVauT9WMTzYbHZbX7dq1S3379tWuXd59IA2qDnIA8H0bth83rO9jJwqUdNiYWYPny0rXAhu2H9Ovm86+LEVZ5ixNNP0DB63ik0V7lJfveuHi/+aad/kJM30G/L7NuPOAdOozBoDvYkxoHgcOHND8+fMlSX5+fho/frxq1apV6eOV9UDJ1q1bS5KOHz+ujz/++PyDhkeYdm79/v37JUkNGjQoc3tRUZFWrVolqXSBuzK3L5xL586dlZqa6lIbhwKkqIlujSMj+6QKThYrMMBfi1celDsnoDVt1kx+8v4tnddcc41L+x85curW4yVLlmjdunUVajNs2DCX44L3kAOA9RyOuE/yjylz25pZVyk2pvz1FGNjQkr+PPjt9WftJzUtV11uWHDG+527XayAYs8vZcG1QOXlBraVqrl2fpCkgpPFat72IgUWp3ggKnjTidArpWDX78ZcvyX5vGZ9uZOvfQZI3vscOBE6UAq+sMxt3jgPPPToJE1+YJULEQPwJG+MCSXfHxcOu+0BhVWrrpTUFNWtW/eM11VRYGBgucsOS9K8efNKZuIPHjxYjRs3rnRfZRW3x40bp/T0dE2YMEF5eXn6/vvvNWTIEMXGxpZ7nGbNmunkyZOVjsPKYmNjtXbt2kq1NW2BOyfn1OyqvLy8MrfPmTNHaWlpCg8PV8OGDT0aS2pqqg4dOuRaI1ugFOXeON6f0kuBAf7auiddE8d00OdLE7U3Kcstx05JTpac3v8HfPr3XFGn8yEvL6/CbV3+3cGryAHAgsIckn/Zm2JjQlW3dtg5D2H396vQfmU5ciRNyvfC5wLXApUXmSCVvULdOR1NS5dy+dz3efEFUrDrzZyyV53zvo99Bkhe/Byok1vu79cb54HMzGxlHq0ieQLAK2NCyffHhY7/FoIdxcU6dOjQGa+roqCgoHK3HTt2rKQYWqNGDQ0fPrzS/ZRX3Lbb7apZs6aGDh2qWbNmSZK+/fZb3XzzzeUeKzk5WQUF3BHobaYtcMfGxio9PV3r169X9+7dS21LSUnRww8/LElq166dxx8kebZvdsrjUIDcOXfovhtbqU/XOnr8tbX66vv9Wj9nqN6b0ku9Ry92y/Hj6tQxZNZWWJhrF6WnT14hISEVbhsfH+9yXPAecgCwnsP+TpX3eK/UtLOvixcbEyK7v5+Kih1KTSv7S/BzHatWzSgF/GVNPk/gWqDy8gIC5fICBk6nZLOpVnSYAiL53Pd1GSFSdiXa+TlzFVdFzvu+9hkgee9zICMkqNzfrzfOAxHhoaoWWDXyBIB3xoSS748L/fz9S/6Mj48/43VVFBgYWO625cuXl6yTfemll55137M5W3H7tD59+mjevHkqLCzUDz/8oBEjRpTbX506dZjBXUmVqZ+eZtoCd79+/bRt2zZNmzZN/fv3V7NmzSRJa9as0c0336y0tFMPJunQoYPHY6nM9Pqc3EJVu/Ajt/TfpH51TR3XWb9tOqpp7/0hh8Opp99cr6njuui+G1tp5meuP4Tpr3bt3Kmw0AA3ROuaNWvWuLT/9u3bNWvWLA0cOFAtWrSoUJsZM2ZUIjJ4CzkAWM+Q+7/Vgh8OlLmtrFvJ/+zgt9erbu0wpablqV7/2S737e9v076daxUS7PlLKK4FKi83r0jx/WbpRJYLgwubTW2bRmrjvA0en/wAz/tt01F1G3n2z4Oy3HVDF/3ziSQPROQ6X/sMkLz3OfB/n2/T2Gd/LnObp88DkvTxuy9rcO/6lWoLwP28MSaUfH9c+Pw/P1Vmdo7iYuOUlJR0xuuqqKioqGSN7b/6448/Sv6/b9++lTp+RYrbklS9enV16dJFP//8s3JycrR3795yc2fnzp1ntIfnmfYhkxMmTFB0dLQOHjyo1q1bq23btmratKm6du2qRo0alST/n9ffNiObTfrgmYvl72fTqIk/yuE4tdDei+9v0prNRzV1XGc1qhtucJTe06RJEy1dulRNmjQxOhQYhBwAfF+nVmWvv+0NrRtHeqW47U5WvBYIDbHrtqFNXW5394iWFLdNokubmEp9Vtw9oqUHojGWGT8DjDwPnOo/2tD+AZwfxoS+r7i4uOTZe7Vr11Z0tOufyxUtbp/WqlWrkv/fu3dvJaKGJ5m2wF23bl2tXLlSgwYNUnBwsPbt26eoqCi99dZbWrRokXbu3CnJ/AXu8aPaqmfH2nrqjfXanphR8r7D4dStT66Q3d9P703pZWCE3mW32xUZGcm3aRZGDgC+r3Nr4wobvljUsOq1wIM3t1HNyIovwtyqcQ3dfCUDXbOw2Wx69t5O8vOr+BcWN13ZWK2bRHowKmOY8TOgXbMoBdiNGcrGxoSoTq3Krd0NoGpgTOj7kpOTS5YBqcxz9Vwtbv+1HwrcVY9pC9yS1LJlSy1cuFBZWVnKysrSr7/+qjFjxignJ0f79u2Tn5+f2rRpY3SYHtOiYYSeuecC/bLxiF7+cPMZ27fuOaGn31yvSzrH6b4bW5VxBPNJSkrS+PHjq+ztN/A8cgDwfX26xCmyeuXW2Dtf1/b37IOp3c3K1wL1Yqtp8RuXKbpG+Q8nOq1J/epa8sblVWaJFbjHgIvq6p2nL5K//7mL3Ff0qqt3nvatIm9FmPUzICjQX4MvMWaJkGsv863zAIAzMSb0fceP/+9pK3FxcS61rUxxWzq1tvZpJ06ccKlPeJ4lv67asmWLnE6nmjVrptDQ0DO2z5s3T5K0devWUq8TEhLUuXNn7wV6nrYnZiiky4dn3eeFd//QC+/+cdZ9zCQ7O1srV67UHXfcYXQoMAg5APi+kGC7Rg9tppc/OrNY40kN48N1ec+6Xu3zfFn9WqBz65pa/clVmvTGes1dlqjCotIPB60WatfNVzbRlHs6KcaF2d7wHbcNbaYGcdX07Nsb9P2aMx/ZWLd2mO4e0VIP39pWdoNmBHuSmT8D7h7RUl/8Z5/X+x17nfmWsQGshjGh76tdu7auvfZaFRYWllo65Fxyc3M1Y8YMl4vb0qkHXg4ePFiBgYHn9TBEeIYlC9ybNm2SVP7yJNdee22Zr0eNGqUPPvjAo7EBAIBzu+u6lnr1ky0la8l6w90jWrq03AGqhib1q+vTF3rrlYe7ae6yRD32jzXKzi1SjfBAHVg2QuFhxtwNAO/p262O+naro6170vX1jwf07NsblJ1bpKiIQCUuuc6UhW0r6NstTi0aRpRadsXjfXaNU8tGNbzWHwCgbLGxsRo+fLjL7UJDQ3X//fdr+vTp6tChQ4WL25Lk7++vkSNHutwnvMOSV3PnKnA7nc4y/6O4DQBA1dCkfnWNv8V7y4y1bFRD997ArD1fVjs6RPfe0EoR1U4VtMNC7BS3LaZV40g9Mrp9SQ6EBNkpbvswm82m1x/r4bX+Aux+mjHhQq/1BwDwjPbt2+vpp592qbiNqs+SV3TnKnADAICqb/LdF6h5QoTH+/Hzs+mDZy5WcBAXwABQlVx6YR3ddW0Lr/T11F0d1LZZlFf6AgB4VuPGjSlum4wlC9zLly+X0+nUoEGDjA4FXlazZk2NGzdONWvWNDoUGIQcAMwjJNiuT6ZeotDgil+cpqblKulwjlLTcivcZvLdHdW1LZ8ZAFAVvfj3LmrTJLLC+1fmPHBJ51g9chuTowCzYEwImA9fV8BSoqOjWTPJ4sgBwFw6t66pL//RT1fd/63yC4rPuX+XGxa4dPwHbmqtJ+7oUMnoAACeFh4WqGVvDdAloxdp1/7Mc+7v6nmga5uaWvBafwUEWHJuGGBKjAkB8+EsDUvJzMzUd999p8zMc1/8wpzIAcB8+neP19I3L1dMZLDbjmmzSU+P7ahXHu4mm40HSwJAVRZXM1QrP7hSXdrEuPW4l/eI13f/GqDq1VivHzATxoSA+VDghqUkJyfr8ccfV3JystGhwCDkAGBOF3eO05YvrtbwfgnnfaymDaprxfuDNGnsBRS3AcBH1I4O0aoPB+vZezsp4DwfHhoWYtcbT/TQ4jcu52G0gAkxJgTMhwI3AAAwhVrRIZr3yqX64tVL1b19LZfb16kVqin3XKANnw/TRRfEeiBCAIAnBQT46YkxHbR+zhCNGNBQdrtrX1IGB/lr9LBm2jT/ao0d0VJ+fnzJCQCAL2ANbgAAYCrDLk3QsEsT9Pu2NL377536ZeMRbdqVrsIixxn7NowPV6dW0bp+QCNd1bsBa6wCgAm0aRql2S/2VcrRXL377x36z68pWr8tTZnZhWfsGxURpE6tojWgZ13dOqSZoiKCDIgYAACcDwrcAADAlDq2jNHrLU+tx1pwsljbE0+o3x1LlHaiQDUjg7R9wbUUMgDAxOJqhmrimI6aOKajHA6n9hzMVI+bv1baiQLF1AjS2tlDVD+uGstRAQDg4yhww1KCgoLUvHlzBQVR0LAqcgCwpqBAf7VvHq2gQH9JUmCAP8VtALAQPz+bmjaIKDkPBAX6q0GdcIOjAmAExoSA+VDghqU0bNhQH3/8sdFhwEDkAAAAAABYF2NCwHxYaBIAAAAAAAAA4JMocMNSduzYoZ49e2rHjh1GhwKDkAMAAAAAYF2MCQHzocANS3E6nSosLJTT6TQ6FBiEHAAAAAAA62JMCJgPa3BXUaEhdmWvvsXoMCosNIRUAgDAnbgWAKzN1z4DJD4HAADu5e/vr+HDh7vteC+9NUdZOTkKDwvTw3eOOOO1O/j7+7vlOHANVyBVlM1mU1hogNFhAAAAg3AtAFgbnwEAAKuz2Wyy291XunRKcjhP/Wm32894Dd/FEiUAAAAAAAAAAJ/E1xOwlISEBM2aNUvx8fFGhwKDkAMAAAAAYF2MCQHzocANSwkODlbjxo2NDgMGIgcAAAAAwLoYEwLmwxIlsJSUlBQ9++yzSklJMToUGIQcAAAAAADrYkwImA8FblhKRkaGFixYoIyMDKNDgUHIAQAAAACwLsaEgPlQ4AYAAAAAAAAA+CQK3AAAAAAAAAAAn0SBGwAAAAAAAADgkyhww1L8/PzUsWNH+fmR+lZFDgAAAACAdTEmBMyHf82wFIfDod9//10Oh8PoUGAQcgAAAAAArIsxIWA+FLgBAAAAAAAAAD6JAjcAAAAAAAAAwCdR4AYAAAAAAAAA+CQK3LCU8PBwDRgwQOHh4UaHAoOQAwAAAABgXYwJAfOxGx0A4E3x8fGaMmWK0WHAQOQAAAAAAFgXY0LAfJjBDUspKCjQwYMHVVBQYHQoMAg5AAAAAADWxZgQMB8K3LCUxMREDR8+XImJiUaHAoOQAwAAAABgXYwJAfOhwA0AAAAAAAAA8EmswQ0AQBXkdDqVm1dkdBguCQ2xy2azGR0GAACmwLUAAFib0+lUcXGx0WG4xN/f35DzAAVuAACqoNy8IlW78COjw3BJ9upbFBYaYHQYAACYAtcCAGBtxcXFmj9/vtFhuGT48OGy271fbmaJEgAAAAAAAACAT2IGNyylRYsW+u2334wOAwYiBwAAAADAuhgTAubDDG4AAAAAAAAAgE+iwA1L2b9/v0aPHq39+/cbHQoMQg4AAAAAgHUxJgTMhyVKYCl5eXnavHmz8vLyjA4FBiEHrMfpdOpgao7Wb0vTkeP5KixyKCjAX/Viw9SpVYxiIoONDhEAAAAe5HA4tXN/hjbuOK70zAIVO5wKCbKraf3q6tgyWtV4MKalMCYEzIcCNwDAdJxOp35Yk6L/m7tdy39LUVp6frn71o8L06Be9TT2upZq2yzKi1ECAADAU04WFuvL5fv1zhc79MvGo8rOLSxzP5tNap4QoWsva6gxw1uobmyYlyMFAJwvCtwAANNwOp2auyxRk95Yr+2JGRVqcyAlR29+vl1vfr5dvS6orWkPdlH39rU9HCkAAAA8oajIoRmfbNHLH21Satq5Z+g6ndL2xAw989YGPf/ORg3t00Av/b2rGtYN90K0AAB3YA1uAIApHD6Wp2v+vlwjHv6+wsXtv1q5/rAuGrVID7/8m/Lyi9wcIQAAADxpy+509bjlaz38ym8VKm7/VXGxU/O/26e2w7/QG7O3yuFweiBKAIC7UeCGpcTFxWny5MmKi4szOhQYhBwwp3Vb09T26i/0xX/2nfexHA6npn+4Sd1GLlDK0dzzDw4AAAAe9/nSvbpgxJdaszntvI+Vk1eke57/RcMe+E75BUx6MBvGhID5UOCGpURERGjgwIGKiIgwOhQYhBwwnzWbj6rP7Yt19CzrbFfGpl3p6nXrQorcAAAAVdyni3br+gnf62Shw63HXfDDAQ2+71uK3CbDmBAwHwrcsJT09HTNnTtX6enpRocCg5AD5rLvUJYGjF2qrJyyHxp0vvYczNLld33DciUAAABV1H9WJ2vUxBVyemg1ke9WJ+vWJ1fI6akO4HWMCWFlWVlZOnz4sFJTU5Wenu7yZ9uyZcuUlnb+d8q4Gw+ZhKUcPnxYL730ktq2bavIyEijw4EByAHzcDicun3SSh3PKKhwmzWzrlJsTKhS03LV5YYFFWqzaVe6nnx9naY/1K2yoQIAAMADMrJO6ranVqi4uOIFmspcD875JlFXXdJANw5qXNlQUYUwJoSVpKWlaeXKldq1a5cSExPP+GInNDRUDRs2VKNGjdSjRw81bNiw3GN99dVXmjVrlhYuXKinnnpKMTExng6/wihwAwB80ltzt2v5bykutYmNCVXd2mEu9/XKx5t1db8E9ehQ2+W2AAAA8IyHXv5VB1NzXGpT2evB+174RX27xSk2JtTltgDgbdu3b9eiRYu0du3as87Szs3N1ZYtW7RlyxZ9/fXXatq0qQYMGKAePXrIZrOV7He6uC1JR44c0fr163XZZZd5/OeoKEssUZKWlqYJEyaoSZMmCg4OVr169TRu3Djl5OTo9ttvl81m0+uvv250mACACsrLL9LE19d5rT+nU5rw6hqv9edOz93fSc4/btdtQ5uWuf37d69Q/tpb1bqJuWev7E3K1OP/WKtj/53xn55ZoP+sTuZ2Y4twOp36ZeNh3f3sKh07cSoHMrJOausebk22iqIih+Z/m6hRT/xYkgNZOYU6fCzP4MjgLRlZJ/X6rK0ld34dzyjQ+1/utMQyZGa9Fti294Te+WKn1/o7nlGg59/Z6LX+AKAy8vLy9M477+jpp5/WmjVrSo13wsLC1Lp1a/Xo0UM9e/ZUx44dFRUVVar9rl27NHPmTD333HM6evSopNLFbUm64YYbqlRxW7LADO4NGzZo4MCBSk1NVVhYmFq1aqXk5GS99tpr2rNnj44fPy5J6tChg7GBAgAqbM7SvS4tTeIOq34/rD92Hle7ZlHn3rkKefqN3zX4kvp65aFuWvbLIR06/L+HZj5wU2v17hKnR2es0Zbd5iz07U/O0t3P/awlPyWVWpszN79Y/cYsUfOECL34YBdd1aeBcUHCo35cm6IHXlytDduPl3o/O69IrYd9od5d4vTPx7urVWPfKuyg4t6au11T3vpdyUdKPzQ4M6dQ9frP1vUDGum1Ry9UjepBBkUITyo4WaxHZ6zRv+bvUE7e/4rZeQXFGv3USo2f/qseuKmNJo7pID8/21mO5LvMei3wf59v83qfHy7Ypan3d1ZYaIDX+waAc0lMTNTLL79cao3syMhIXXrpperZs6diY2NLzco+7cSJE1q7dq2WLVumAwcOSJI2b96shx9+WBdccIF+/vnnkn1vuOEGDRkyxPM/jItMPYM7LS1NgwcPVmpqqsaPH6+UlBStX79eqampmjZtmhYtWqQ1a9bIZrOpXbt2RocLLwgNDVW3bt0UGsptZVZFDpjDG3O8P6Axst/zUVjk0KiJKxQWEqB3n+5V8n6zhAg9d19nrf7jiF76YJOBEXrOzn0ZuvCmr7V4ZVK5D57asS9DQx/4Tu9+scO7wcErvly+T/3HfHNGcfvPfliTop63LNTaLUe9GBm85bF/rNFdz6w6o7h9WmGRQx8v3K1ety7SsRP5Xo4OnpZfUKQr7l6qGZ9sKVXc/rP0zJOa9MZ6jXz0BxUXO7wcoXeY8VogJ7dQHyzY5fV+M7ML9eniPV7vF+7FmBBmtGPHDk2ZMqWkuB0UFKTbbrtNM2fO1DXXXKO4uLgyi9uSVKNGDfXr10/Tpk3TI488oujoaElSfn6+TxS3JZMXuO+//34lJSXp3nvv1fTp0xUeHl6ybcKECWrfvr2KioqUkJCg6tWrGxgpvKV+/fqaOXOm6tevb3QoMAg54PuOHMvTms3GPLV50YqDhvR7vn7fdkxT392oy3vW1R3Dm8vPz6aPnrtYNps0auIKORzmW6YjN69IA+9eqtS0cy8/4HRKdz6zSivWuramO6q2TTuP64ZHflBh0bkLVieyTmrQPct09DjLVZjJe//eqRfe/aNC+27ena7hf/8PyxaZzN3P/Vzh53XM/mavnn7zdw9HZByzXQv89PthZWYXGtK3r14P4n8YE8JsDhw4oGnTpikv79S1bNOmTfXiiy/q8ssvl91e8cU7bDabOnbsqJdeekkJCQmltvXo0aPKFrclExe4t23bpjlz5igmJkZTp04tc59OnTpJktq3b1/y3rx58zR8+HA1aNBAoaGhatGihZ544gllZ2d7JW54VnFxsbKzs1VcXGx0KDAIOeD71m01prgtSUmHc3TER9drfebt37Vh+zFNH99VMx/rrm5ta+mJmeu0c1+G0aF5xKwle7Q3KavC+xcXO/XCexUrhME3vPzRZuUXVPyz/sjxfK+u5QrPcjicev6dDS61+XFtqlb9ftgzAcHrDqRk68MFu11q849Ptygr56SHIjKema4FjLweNLJvuAdjQphJYWGhZs6cqdzcU3ertW3bVhMnTlTt2rUrfcxvv/1W+/btK/Xe+vXrS9bkropMW+CeNWuWHA6HRo4cqWrVqpW5T0hIiKTSBe7p06fL399fzz//vJYsWaKxY8fqzTff1IABA+RwmPOWNSvZtWuX+vbtq127vH87G6oGcsD3rd92zND+fXVQU1Tk1KiJKxQc5K+7R7TUyvWpmvHJZqPD8gin06l/znZ9OZlvViVpz8FMD0QEbzt2Il+zv9nrcrv/m7vNtEsUWM23vxzSnoMV/5LrNF9cigple3vedpdnJWflFOqTheZdfsJM1wLrthp3PXjoSK5S08pe9gi+gTEhzOSLL77QwYOn7ixp0KCBxo8fr6Cgyj9X5K8PlDw9kzs/P19vv/12lb3bzbQF7uXLl0uS+vTpU+4+SUlJkkoXuL/++mt9/vnnGjlypC655BKNGzdOr7/+ulatWqWffvrJs0EDAM7pQKqxd9QcSM0xtP/zkZF9UgUnT81UWbzyYLnrUvu6tPR8/b7d9YGv0ykt+/mQByKCt/24NrUk111xICVH2/aecH9A8LpvViVVqt2SnyrXDlVPZX+XZs8Bs1wLGH09eNCHrwcBmEdqaqq++uorSZK/v7/uvvtuBQcHV/p4fy1u33DDDXrqqacUFRUlSdq0aZN++eWX8wvaQyq+EIuP2b9/v6RT316UpaioSKtWrZJUusBds2bNM/bt3LmzJOnQocoNejt37qzU1NRKtcXZXXPNNS7tf+TIEUnSkiVLtG7dugq1GTZsmMtxwXvIAetJDxsqBXUsc9uaWVcpNqb8h8XExoSU/Hnw2+vP2k9qWq663LDgjPcfeXSinnlwdcUDriSHAqSoiW495vtTeikwwF9b96Rr4pgO+nxpokvLeJxL02bN5Cdj1sP8syK/KKnGuEq1ffSJyXpuPF9o+7qcwA5Stcp9dvfpP0hBRayv6uvSw4ZIQRe43O5EZr7i69ZV2Y9ggi9Jjbhf8o92ud3S71aobt3bPBCR67gWKN/h6mMle2yZ27xxPXjFlUMUVHTAhYjhSd4YE0q+Py4cdtsDCqtWXSmpKapbt+4Zr63A1/4OAgMDy112WTq1lMjp1SauuuqqcmugFVFWcfv0mtt33HGHpk2bJkn65ptv1KNHj3KP06xZM508WbnlvmJjY7V27dpKtTVtgTsn59Q3qqcXWP+rOXPmKC0tTeHh4WrYsOFZj/X9999Lklq2bFmpWFJTUytdHMfZnf49V9TpfMjLy6twW353VRs5YEHxWVI5d1zFxoSqbu2wcx7C7u9Xof3KknHimDKOeyEnbIFSlPsOd9+NrdSnax09/tpaffX9fq2fM1TvTeml3qMXu62PlORkyVkF1i61Z0s1Ktc088RRZR7j37zPi6gjlb1C3TmlHT4k5ZMDPq/OiXLPFWflOKlkzvvmEJIrhbhe4D6Zn1V1rv24FihfSEG51QxvXA+mHUmV8qpInsArY0LJ98eFjv+uOe4oLtahQ4fOeG0FvvZ3cLalRgoKCvTDDz9IkgICAjRw4MBK93O24rYkdejQQfXq1dPBgwe1c+dO7du374yHUJ6WnJysgoKCSsdSWaYtcMfGxio9PV3r169X9+7dS21LSUnRww8/LElq166dbLby52gcOnRITz75pAYMGKAOHTpUOhZ4RliYaxckp09eISEhFW4bHx/vclzwHnLAejJCpPJuSj3XeoixMSGy+/upqNih1LSzPyyyvGNFVQ9QSIjnc8KhAKW46VhN6lfX1HGd9dumo5r23h9yOJx6+s31mjqui+67sZVmfrbVLf3E1alTJWZwO2XT4eITKvav4UIjp2SzqWZYtgKD+Tfv64r88nRYKvm9VpTNkafYaH/5iRzwdbmBJ5ReiXZBjmTFcN43hXTbEeWqnsvtwu1pql5FcoBrgfKl+Z9UeeUTb1wP1o4Jk91RNfIE3hkTSr4/LvTz9y/5Mz4+/ozXVuBrfweBgYHlbvvjjz9Kcrl79+6qXr16pfo4V3Fbkmw2m/r376/33ntPkrRq1apyC9x16tQ5rxnclWXaAne/fv20bds2TZs2Tf3791ezZs0kSWvWrNHNN9+stLRTDwk7W9E6OztbQ4YMUWBgYMkvsTIqO70e57ZmzRqX9i8qKtKtt96q8PBw2e0VS/8ZM2ZUIjJ4CzlgPfOWJerah5aXua2sW0j/7OC316tu7TClpuWpXv/Zlep/7cr5alg3vFJtXZGTW6hqF3503sex2aQPnrlY/n42jZr4Y8kDt158f5OuvjRBU8d11qIVB91ye/KunTsVFhpw3sdxh+f/tUFPzKz4Laey2XRBy2itnb36rF98w3cMHLvU5XWY77+5s2Y8kuihiOBN+QVFiu83W8czXJtB9Olrf9Pw/s95KCp40/qtaep0/VcutfH3t2nbT28pvpKzet2Na4HyPfHaWj3/zsYyt3n6erBGeKBSNv7B9UIV4o0xoeT748Ln//mpMrNzFBcbp6SkpDNeW4Gv/R0UFRVp/vz5ZW7bs+d/D0U+vbSyqypS3D6tS5cuJbXRvXvLf5j7zp07Xfp35S6mfcjkhAkTFB0drYMHD6p169Zq27atmjZtqq5du6pRo0bq27evpNLrb/9ZXl6eBg8erMTERC1btkxxcXHeDB8eYrfbFRkZacg/NlQN5IDv69QqxrC+I6sHKiG+kuseGGT8qLbq2bG2nnpjvbYnZpS873A4deuTK2T399N7U3oZGKFn3H51c1ULde3f+QM3tWawaiIP3NTapf0D7H4ae10LD0UDbwsOsuuua137fSbUqaareld+7UpULRe0ilGvC2q71Oa6yxpWmeK2O5nxWsDI68FOrWK4XvBxjAlhBomJ/5uU0ahRI5fbu1LclqTIyEhFRkZKkvbt2ydnFXtKsWkL3HXr1tXKlSs1aNAgBQcHa9++fYqKitJbb72lRYsWaefOnZLKLnAXFhbqmmuu0dq1a7VkyRK1atXK2+HDQ5KSkjR+/Pgq+c0cvIMc8H0J8dWUUMeYInOfLnV8akDTomGEnrnnAv2y8Yhe/nDzGdu37jmhp99cr0s6x+m+G811rqsdHaLPX+oru3/Ffl9jr2uhm65s4uGo4E2X96yrSXeV/UDav7LZpPem9FLzhjU8GxS86umxF+jyHhW73TiiWqAWvNZfAQGmHR5Z0uwX+6h+XMUK1u2aRenNiT09HJH3mfVa4KKOtWW3G3NN1qcLk998HWNCmMHpNcPDwsIUHe3aMydcLW6fdvohljk5OTpx4oRLfXqaqa/gWrZsqYULFyorK0tZWVn69ddfNWbMGOXk5Gjfvn3y8/NTmzZtSrVxOBwaOXKk/vOf/+irr75S165dDYoenpCdna2VK1cqO7u8FXxhduSA77PZbLrTxVl57nKXj83u3J6YoZAuH6rHzV+X3I78Vy+8+4ds7d5129qbVcnAXvX0zZsDVDs6pNx9Aux+mjimg15/vIdPfXmBipk0tqNeebibgoP8y90nsnqg5k7vyxccJhQQ4KevXuuvUVc1PetS7M0aROinDwepbTM3Ps0PVUKdWmH6+aPBurBdzbPuN6BnXf3w3hWKCC9/rVNfZdZrgVrRIbr60gSv92u32zR6WDOv9wv3YkwIM4iMjFRUVJRq167t0jjm66+/rlRxW5Kio6MVGRmp2rVrq/i/D+isKix5P8aWLVvkdDrVrFkzhYaGltp2zz33aO7cuXr00UcVGhqq1atXl2xr3LixatY8+8URAMDzbh/WTJPeWK+ThQ6v9dm0QXVd2q2O1/qDe1x6YR0dWDZC//7Pfr09b7t+XJuqYodTdn+bJt99gW6/uvlZC+DwbTabTQ/e3Ea3DmmqD7/apY8X7taGHcfkcEiBAX76vyd76voBjRQSbMlLYksICvTXB89erCfv7KC35m7Xgh8OaNf+DDmcUnCgv778Rz/17x4vPz++4DKr+Nph+vnjwVr9xxH9c/Y2zV6yV8UOp/z9bPrb8OYae10LtW/u2sw3VA13j2ipz5d697kJV1+aoLiaoefeEQA87JlnnqlUu/r16ysgIECFhYUuFbcl6Y477qhUn95g6hnc5dm0aZOkspcnWbJkiSTphRdeUPfu3Uv9t2jRIq/GCQAoW82oEN17g3dvo33qzo4UQHxUYIC/RgxopP+8c4ViY04Vs2tHh+jxOzpQ3LaIyOpBeuDmNlo3Z6jiYk4VJmpGBuu2oc0obltE43rV9eLfu2r7gmtKilPRNYJ0ec+6fLZbgM1mU/f2tfXJ1N4l54HYmBD935M9KW77sIs7xaq3F5cLsdttevxvZT/DCwB8Rfv27fXQQw9p5MiRLhW3qzpLXtGfrcC9b98+L0cDAKiMZ+7ppK9/PKBd+zM93tfgS+pr5KDGHu8HAAAAFWOz2fTu5IvUbvi/lZNX5PH+nvhbB74QAWAK7du3L7Mm6suYwQ1LqVmzpsaNG8dSMxZGDphHaIhd70+5WP4VfIigJKWm5SrpcI5S03Ir3CYqIkhvPdWT9ZkBAACqmEZ1q+ulv7v23KzKXA92bBGtx++gfmAWjAkB87HkDO7ly5cbHQIMEh0drZEjRxodBgxEDphLz4619d7kXho1cUWF9u9ywwKXjh8WYtfif17GWosAAABV1F3XtdCuAxl69eMtFdrf1evBhvHhWvh6fwUGlP/AYvgWxoSA+VhyBjesKzMzU999950yMz2/pAGqJnLAfG65qqk+fNa1mdwVUSM8UN++PUDd2tVy63EBAADgPjabTS8/1E0P39rW7cdunhChH9+/QnVqhbn92DAOY0LAfChww1KSk5P1+OOPKzk52ehQYBBywJxuuaqpfnj3CjWpX90tx+t1QW2tnT1E3dvXdsvxAAAA4Dk2m03THuyiT6ZeosjqgW455s1XNtEvnwxWvdhqbjkeqg7GhID5UOAGAJjCRRfEauPcYXrw5tYKDKjc6S0iPFD/eORC/fDeIDWu555iOQAAADzPZrNp5KAm2vLv4br60oRKH6d+XJgWvNZfHz1/iSKrB7kvQACAx1hyDW4AgDmFhtj1ysMX6tHR7fXelzv1f3O3a39y9jnbdWwRrbtHtNQNAxspLDTAC5ECAADAE+Jqhmr+q5dq1/4M/d/c7Xr/y51Kzzx5znaX9YjX3SNaalCverLbmQsIAL6EAjcAwHRqRYfo0dvb65HR7bQ3KUvrtqZp/bZjmvnZFuXmFys02F8TbmunTq1i1KlVDA+RBAAAMJmmDSL08kPdNO2BLtq294TWbUvThu3H9a/520uuB58ee4E6tYrRBS2jVYPZ2gDgsyhww1KCgoLUvHlzBQVx8WJV5IC12Gw2Na5XXY3rVdd1lzfSJwt3Kzc/V5HVgzRp7AVGhwcAAAAPs9v91LZZlNo2i5KGSPO+TSy5Hnz4tnZGhwcDMCYEzIcCNyylYcOG+vjjj40OAwYiBwAAAADAuhgTAubDwlIAAAAAAAAAAJ9EgRuWsmPHDvXs2VM7duwwOhQYhBwAAAAAAOtiTAiYDwVuWIrT6VRhYaGcTqfRocAg5AAAAAAAWBdjQsB8KHADAAAAAAAAAHwSD5kEAKAKCg2xK3v1LUaH4ZLQEC4rAABwF64FAMDa/P39NXz4cLcd76W35igrJ0fhYWF6+M4RZ7x2B39/f7ccx1WcfQAAqIJsNpvCQgOMDgMAABiEawEAsDabzSa73X2lW6ckh/PUn3a7/YzXvsy3owdclJCQoFmzZik+Pt7oUGAQcgAAAAAArIsxIWA+FLhhKcHBwWrcuLHRYcBA5AAAAAAAWBdjQsB8eMgkLCUlJUXPPvusUlJSjA4FBiEHAAAAAMC6GBMC5kOBG5aSkZGhBQsWKCMjw+hQYBByAAAAAACsizEhYD4UuAEAAAAAAAAAPokCNwAAAAAAAADAJ1HgBgAAAAAAAAD4JArcsJSoqCiNGjVKUVFRRocCg5ADAAAAAGBdjAkB86HADUvx8/NTQECA/PxIfasiBwAAAADAuhgTAubDv2ZYSlpamt555x2lpaUZHQoMQg4AAAAAgHUxJgTMhwI3AAAAAAAAAMAnUeAGAAAAAAAAAPgkCtwAAAAAAAAAAJ9EgRuWEh4ergEDBig8PNzoUGAQcgAAAAAArIsxIWA+dqMDALwpPj5eU6ZMMToMGIgcAAAAAADrYkwImA8zuGEpBQUFOnjwoAoKCowOBQYhBwAAAADAuhgTAuZDgRuWkpiYqOHDhysxMdHoUGAQcgAAAAAArIsxIWA+LFECVEFOp1NFeb71bbI9JEg2m83oMEyDHAAAa3M6ncrNKzI6DJeEhtg5DwCAG3EuAICKocANVEFFeQX6tPFNRofhkpF7PlFAaLDRYZgGOQAA1pabV6RqF35kdBguyV59i8JCA4wOAwBMg3MBAFQMS5QAAAAAAAAAAHwSBW4AAAAAAAAAgE9iiRJYSosWLfTbb78ZHQYMRA4AAAAAgHUxJgTMhxncAAAAAAAAAACfRIEblrJ//36NHj1a+/fvNzoUGIQcAAAAAADrYkwImA8FblhKXl6eNm/erLy8PKNDgUHIAQAAAACwLsaEgPlQ4AYAAAAAAAAA+CQK3AAAAAAAAAAAn0SBGwAAAAAAAADgkyhww1Li4uI0efJkxcXFGR0KDEIOAAAAAIB1MSYEzMdudACAN0VERGjgwIFGhwEDkQMAAAAAYF2MCQHzYQY3LCU9PV1z585Venq60aHAIOQAAAAAAFgXY0LAfChww1IOHz6sl156SYcPHzY6FBiEHAAAAAAA62JMCJgPBW4AgCUcOZan/IJiSVLByWLl5BYaHBG8bdf+jJIcOFlYrOJih8ERwZucTqfWbjmqvIIiSVJhEb9/qyk4Wawf16aU5ACfAdZz7ES+8k+eOg/knyxWVs5JgyOCt+1Nyvzf9WBhsYo4FwCAKVDgBkyu97/G65akOarVtUWZ22t1baFbkuao97/GezkyeEts99a6NWVeqf9G7v5Yg5e9qFZjrpTN39yngl//OKKRj/6guv1n61hGgSQp7USB4vvP1rgXftGeg5kGRwhPcjqdmrcsUX1vX6xmg+eV5MDR9AI1GTRX097bqPTMAoOjhCfl5BbqtU+3qNXQ+epywwIdzzhV0DpyPF8XjlygjxbsMn2B47n7O8n5x+26bWjTMrd//+4Vyl97q1o3ifRyZN6RlJqjx/6xRvX6z1bv0YtLciD1WL6ufvA7ff9bssERwtPWb03TrRNXKL7fbB07ceoz/9iJAtW5dJbuee5n7Ug8YWyA8Cin06mvvt+vy+5cosZXzP3f9WB6gRoO/FzPvv270tLzDY7Ss6x+HgBgfuaualSCw+HQvHnzNHToUNWpU0dBQUGqU6eO+vbtq3/84x86eZJv+eFbfnn0Xyo4nqWLZtwje0hQqW3+IYG6aMY9KjiepV8eedugCOEte79YqRX3/kMr7ntNG16eKz+7v7pOvlUXvnCH0aF5zMzPtqj7zV/rs8V7zpitmZF1Uq99tlUdrv23lv2cZFCE8KTCQodueeJHXfvQcn2/JuWM7fuSs/XojLXqNnKB9ibxRYcZpabl6uLbFmnctNXanphxxvZfNx3VqIkrNPSB75SbV2RAhN7x9Bu/a9Ou43rloW6Krx1aatsDN7VW7y5xmvTGem3Zbb61SH/944g6jvhSL7z7h46WUcD693/2q+/fluipf66T0+k0IEJ42jvzd6jryAX6cMEuFfx39vZp2blFemPONnW87kst+H6/QRHCk4qLHbpzyioNHfedvv3lzC+zkg7n6MnX16vzDV9pu4m/6LDyeQCANVDg/pMjR46ob9++uvbaa/XVV18pICBAHTp0UEBAgL7//ns99thj8vf3NzpMnIfQ0FB169ZNoaGh597ZJAqOZeqXCW+pesM4dXry5lLbOj9xk6o3jNPPD7+lguNZBkXoXVbMgdOObUrU3vkrtXfeCm15c4EWDXpcOYfS1OzGSxUUXd3o8Nzu/S936v4XVutc9Yrs3CINGfedVm884p3A4BVOp1N3PbtKnyzcc859d+3P1GV3fqOjx/O8EBm8JTu3UFfcvUzrtx07576LVhzUDY98b9olKwqLHBo1cYXCQgL07tO9St5vlhCh5+7rrNV/HNFLH2wyMELP2LonXQPGLq3QzMxn3tqgF9//wwtRwZvmfLNXd0z+ScXFZ78YyCso1jXjlzOb34QefOlX/Wv+jnPutz85W/3HfKNDh3O8EJX3WfU8UB4rjwkBs6LA/V85OTm64oor9OOPP+qSSy7Rxo0btX//fv3666/av3+/Nm/erEcffZQCt4+rX7++Zs6cqfr16xsdilcd+GaNds/9US1GXaa4i9pKOrVsRYvbBmj35z/o4NI1BkfoPVbNgbIU5RXo6Ppdsvn5qXqD2kaH41bZuYUaN211hffPLyjWfS/84sGI4G2/bDyi9/69s8L77zmYpRfeo7hlJv+cvVW/bz93cfu0BT8c0Nc/HvBgRMb6fdsxTX13oy7vWVd3DG8uPz+bPnruYtls0qiJK+RwmG/28sOv/KYTWRW/+3LizHVKOZrrwYjgTfkFRbp3asXP7YVFDt3z/C/M5DeRDduPaeZnWyu8f9LhHE1563cPRmQsK54HysOYEDAfCtz/NX78eK1bt04XXXSRli1bpnbt2pXa3rp1az311FMGRQd3KS4uVnZ2toqLi8+9s8n8NvFd5aYcV89X71ZI7Uj1fPVu5aYc168T3zM6NK+ycg6UJTzhVGG74ES2wZG416eL9igrx7WHSK7dkqY1m496KCJ42xtztrnc5v0vd5p6mQorKS526P8+3+5yu8rkjS955u3ftWH7MU0f31UzH+uubm1r6YmZ67Rz35nLt/i6xKQsLfnJteWnioqdeueLc8/0hG+Y9+0+l9dV3rb3hH5cm+qhiOBtb37u+mf6Jwv3KMOFL8Z8jZXOA2fDmBAwHwrckrZv36533nlHQUFB+vTTTxUYGGh0SPCQXbt2qW/fvtq1a5fRoXjdycxcrRr/pqrVrakh/5muavVq6qe/v6HCLGvNVLJyDthDAhUUFa6g6Oqq0aK+uj3/N0W3baSj63cpc++Z6xP7sg++qvjM3T/7cIH18sKMcnILNXdZosvt0jNPmnoGr5WsWJeqfcmuf3H37S/JSko15+3pklRU5NSoiSsUHOSvu0e01Mr1qZrxyWajw/KIjxfuPucSVWX54CvOA2ZR2XM6OWAORUUOfbro3MuU/VVufpHmf7fP/QFVEVY6D5yNlceEgFnZjQ6gKvjss89UXFysW265xSO3qHTu3FmpqcwE8IRrrrnGpf2PHDm1xu6SJUu0bt26CrUZNmyYy3GdrwCnnyapq9uPm/zjRu34eJma33yZdny8TCkr3Hc7frOmzVRo8/7apeRAxXWccL06Tri+1Hv7Fq3Wr4+945bjG5UDZUmp8XfJL8Lldu9+9G99+cZ1HogI3lTkV0MnazxYqbZj7n1U4/N/dnNE8LbcwPZStasr1faCbn0VWHzIzRG5zqEAKWqi24+bkX1SBSeLFRjgr8UrD1aqCFyeps2ayU+u3T3jKemhV0nBnVxut/dguuLr1pXNAzHBuw5H3Cv513S53ez5S/XdBzd6ICJ4U7EtVDmRj1Sq7QMTpuip+35wb0CV5IlzgSfPA5Ix5wJvjAklY8aF7jTstgcUVq26UlJTVLdu3TNeW4HV/w6q+s8fGxurtWvXVqotBW5J3333nSTpiiuu8MjxU1NTdeiQ8QMlM8rJcW2WVV5eXsmfFW1rxO8u0OYveWhJ5KNrd6r5zZfp6NrKzXAtT3JKsk46vX+LFzlQcTs+XqZ9X/8ivwC7IlvUV5t7hiosLlrFBe65DdOoHChTtWKpEjfj5Ofl8XltBgH5Uo3KNc3MyFBmGjng82rUk6pVrunRo0elvCqQA7ZAKcr9h31/Si8FBvhr6550TRzTQZ8vTdTeJPc8aDolOVlyVpFb++OzpeBKtHM6lcx5wBxCi6RKPD6poCCfawEz8K8mRVauaVZmprKOVJEc8MC5wJPnAcmYc4E3xoSSMeNCd3L8d0kWR3GxDh06dMZrK7D634GZf34K3JIOHjwoSWrUqJFHjh8bG+uR40IKCwtzaf/TJ6+QkJAKt42Pj3c5rvMV4PSTqsZE2AqrE1fHkNm75EDFZe5NVcrKU09HP7T8dx3+bbuu+OoZdZ92p34c++p5H9+oHCjLUVu2TlZiNBAWdFI1DPh9w70cClCKs0iyuX6ZExkuhQaRA76uwO6vNFcbOZ2SzabY6CD5O43PAYcC5O7Fo+67sZX6dK2jx19bq6++36/1c4bqvSm91Hv0YrccP65OnSozgzszuFiVKdf4OzMVy3nAFNL8c1RQiXahAQWKJAd8nlN+SnEWyGkLcrltjTCnwqpIDrj7XODp84BkzLnAG2NCyZhxoTv5+fuX/BkfH3/Gayuw+t9BVf/5z6d+SoFb//twO/0tnrtVdno9zm3NmjUu7b99+3bNmjVLAwcOVIsWLSrUZsaMGZWI7PwU5ubr08Y3eb3f87Fz104FhFZmqtT5IQcq7+jaHdozb4WaXNdbW99drKNrz+/BWkblQFn+NW+7xkxZ5XK7H798Xp1ave2BiOBttzz+oz5euNulNlERQUr6bZFCgrk88nUOh1NNBs1V4iEXSpw2my7vEa9v/q9qPGgyJ7dQ1S78yG3Ha1K/uqaO66zfNh3VtPf+kMPh1NNvrtfUcV10342tNPOzrefdx66dOxUWGuCGaM/fvkNZanTF5y7fej953GV6YswEzwQFr/ps0R6NfOwHl9st+fQJXdz5dfcHBK8b+8wq/d9c1x44HBZi1/6f56t6tarxXC53ngu8cR6QjDkXeGNMKBkzLnSn5//5qTKzcxQXG6ekpKQzXluB1f8OzPzz85BJSfXq1ZMk/fwza26aXZMmTbR06VI1adLE6FBgEHKgtI2vzpOjqFgdHx5hdChudeMVjVW9mmsX1l3b1FSnVjEeigjedveIli63GT20GcVtk/Dzs2nsdRUfsJ5WmbzxBTab9MEzF8vfz6ZRE3+Uw3Gq6vvi+5u0ZvNRTR3XWY3qhhscpXslxIdrUK96LrUJsPvp9qubeSgieNvw/gmqGenaF++tG9dQr07cfWsWYyvxmX7zlU2qTHHbnax4HjgbxoSA+VDg1v8eFPDcc89p2bJlpbYdOnRIzz//PE/XNQm73a7IyEjZ7RQwrIocKC1rX6oSv1qlOhe3U61u5inshIUG6PXHuld4/9Bgu15/vOL7o+rr1q6mxlzTvML7N21QXY/e3s6DEcHb7h7RUp1bV/xLq6svTdCgi10riPqK8aPaqmfH2nrqjfXanphR8r7D4dStT66Q3d9P703pZWCEnjF9fFdFRVR8eYKp4zorNibUgxHBm4IC/fXmxB6yVfCJoYEBfnpzYk/ZKtoAVV67ZlF68ObWFd6/QZ1qeuqujh6MyDhWPQ+UhzEhYD4UuCU99NBDuuCCC5SRkaHLL79ccXFx6tq1q5o0aaJ69erpySefVJ06dYwOE26QlJSk8ePH+/ytF6g8cuBMf/xjvhzF5pvFffPgpnpzYg/5+Z19oFq9WoC+ntlfXdrU9FJk8AabzaZ/Pt5Dtw1tes59WzSM0LdvDVB0jaqxxA7cIyw0QIv/eZm6tDl3kXto3wb6ZOol8vc336Vxi4YReuaeC/TLxiN6+cPNZ2zfuueEnn5zvS7pHKf7bmxlQISe07xhDS39v8tVK+rc/7afufcC/f2WNl6ICt40vH9DvT/lYtn9z34tEBZi179n9GP2tglNH9+tQnfnNKobrm/fGqC4mub7ksvK54HyMCYEzIevqyRVq1ZNK1eu1Kuvvqq5c+dq586dysjIUGxsrIYOHaqrr77a5YcWoGrKzs7WypUrdccddxgdimF2f/6Ddn/+g9FhGMaKOZD6yxZ9EHdNudszdh3SR3XNVdw+7a7rWqpLm5qa+dlWzf5mrwpOFpdsi4oI0uihzXTP9S2VEG+dWzKtxG7307uTe2lInwZ6Y842Lfu59JPBm9SvrrHXtdDtw5orItx8tyNDqhkVoh/fG6QPF+zSP2dv0+bd6aW297qgtsZe11LXXd7QlMVtSdqemKGQLh+edZ8X3v1DL7z7h5ci8q7OrWtqw9xhevPzbfrX/B1KTfvfM3fs/jZd3S9B917fisKmiY0a0lQdW0Zr5mdb9OniPcrL/9+1QER4oG69qqnuvaGVmtSvbmCU8BQ/P5tef7y7rry4nv45Z5sWrzxYam3+hDrVNPa6lrrjmuaKrO76Ayl9gdXPA2Wx4pgQMDsK3P8VGhqqJ554Qk888YTRoQAA3KhTqxh98OzFevmhrvpj53Hl5BUpolqgOreOYb1lC7DZbBrSp4GG9GmgxKQs7T6YqcIih2pFBeuCljHnnOEP3xcSbNdd17XUnde20B87jyv5SK78/W1KqBOuZgkRRocHL4irGaop93TSxDEdtHZLmtIzCxQSZFerxjVYksQi2jWL0r+e7qUX/95VG3ccV3ZuoaqHBahTq5gq82BUeI7NZtPAXvU0sFc9HUjJ1s79GSo4WayakSHq1CratF9wAoCVMLIHAFhCdI1g9enKclNW1rBuuBpa6AFKKM1ms6l982i1bx5tdCgwSGCAv3p0qG10GDBQZPUg9e4SZ3QYMFD9uGqqH1fN6DAAAG7GV5UAAAAAAAAAAJ9EgRuWUrNmTY0bN041a/IwOasiBwAAAADAuhgTAubDEiWwlOjoaI0cOdLoMGAgcgAAAAAArIsxIWA+zOCGpWRmZuq7775TZmam0aHAIOQAAAAAAFgXY0LAfChww1KSk5P1+OOPKzk52ehQYBByAAAAAACsizEhYD4UuAEAAAAAAAAAPokCNwAAAAAAAADAJ1HgBgAAAAAAAAD4JArcsJSgoCA1b95cQUFBRocCg5ADAAAAAGBdjAkB87EbHQDgTQ0bNtTHH39sdBgwEDkAAAAAANbFmBAwH2ZwAwAAAAAAAAB8EgVuWMqOHTvUs2dP7dixw+hQYBByAAAAAACsizEhYD4UuGEpTqdThYWFcjqdRocCg5ADAAAAAGBdjAkB82ENbqAKsocEaeSeT4wOwyX2EB7Q4U7kAABYW2iIXdmrbzE6DJeEhjC0AAB34lwAABXDJw9QBdlsNgWEBhsdBgxEDgCAtdlsNoWFBhgdBgDAQJwLAKBiWKIEAAAAAAAAAOCTmMENS0lISNCsWbMUHx9vdCgwCDkAAAAAANbFmBAwHwrcsJTg4GA1btzY6DBgIHIAAAAAAKyLMSFgPixRAktJSUnRs88+q5SUFKNDgUHIAQAAAACwLsaEgPlQ4IalZGRkaMGCBcrIyDA6FBiEHAAAAAAA62JMCJgPBW4AAAAAAAAAgE+iwA0AAAAAAAAA8EkUuAEAAAAAAAAAPsludADA+ejSpYtL+9etW1eTJk1Sv379FBcX56Go4E3kAAAAAABYF2NCABS4YSlxcXF6+umnjQ4DBiIHAAAAAMC6GBMC5sMSJQAAAAAAAAAAn0SBGwAAAAAAAADgkyhwAwAAAAAAAAB8EgVuAAAAAAAAAIBPosANAAAAAAAAAPBJFLgBAAAAAAAAAD6JAjcAAAAAAAAAwCdR4AYAAAAAAAAA+CQK3AAAAAAAAAAAn0SBGwAAAAAAAADgkyhwAwAAAAAAAAB8EgVuAAAAAAAAAIBPosBdBXz88cfq1KmTIiMjFRISopYtW+qVV16R0+k0OjQAAAAAAACglJdeekndu3dXZGSkatSooYsuukjffPON0WF51YoVKzRkyBA1aNBANptNzz77rNEhed3ixYvVoUMHBQUFKSEhQa+88oohcdgN6RWl1KpVS08++aSaN2+uoKAgrVy5Unfffbf8/f01btw4o8MDAAAAAAAASixfvlyjR49Wly5dFBoaqnfeeUdXXnmlfvzxR/Xs2dPo8LwiOztbrVq10o033qgHHnjA6HC8bu3atRoyZIgeeughzZo1S7/++qvuuusuhYaG6q677vJqLBS4q4DLL7+81OtGjRrpyy+/1A8//ECBGwAAAAAAAFXKkiVLSr1+8cUX9c033+iLL76wTIH7iiuu0BVXXCFJeuSRRwyOxvteeeUVdenSRVOnTpUktWzZUlu2bNELL7xAgdvqnE6n1qxZo1WrVmnixIlGhwMAAAAAAAAf4XQ6tfdAioodjlLvFxUXl/y5MzHpjNd/Vr1aqGJrRrnUr8PhUGZmpsLCws4jevc4euyE0jOzz3i/on8HNkmNE+LlZ7N5JV53KzhZqP2HDp/xvis5UDsmUhHhZ/9drlq1Srfffnup9wYMGKDp06crKSlJdevWPZ8fwyUUuKuIjIwMxcfH6+TJk3I4HJo0aZLuv/9+o8MCAAAAAACAj7DZbNp3KFXfrlxb5vbcvHy99/nicl/7+dl0901DXe73+eef14kTJzRmzBiX27qdTfr4i6UqLCouc/O5/g56dmqjpg29V5x1t8AAu35a88cZRevTzvXzR4SH6YHR15yzn5SUFMXGxpZ67/TrlJQUrxa4echkFREeHq4NGzZo7dq1ev311/XKK6/o3XffNTosAAAAAAAA+JDeF3ZQ/Tq1KtX20h6dVDeupktt3njjDT3//POaN2+eV4ua5akZVUOD+navVNta0TU04JKubo7Iu2w2m64ZeIlCgoMq1f7aQb0r3dYoFLirCD8/PzVp0kTt2rXTXXfdpQkTJuiJJ54wOiwAAAAAAAD4EH8/P103qI8CAlxbuKFeXC317t7BpTbTp0/Xww8/rAULFqhfv34utfWkbh1aqlnDei618fOz6borXf97q4qqh4dp2GUXudyuZ+c2atIgvkL7xsXFKTU1tdR7hw8fLtnmTRS4qyiHw6H8/HyjwwAAAAAAAICPiYmK0KA+F1Z4/4AAu667srf8/SpeKnzqqac0efJkLV68uEoVt6XTs5gvVqgLM5Ev7dlJdWNdm71elbVr2VgdWjWp8P61oiM14OKKz17v2bOnli5dWuq9b775Rg0aNPD6TH7f/0rCBCZNmqRevXqpUaNGKiws1IoVKzRt2jTddtttRocGAAAAAAAAH9StQ0tt271fO/YePOe+g/pcqJpRNSp87AceeEBvvfWWZs2apebNm5fM5A0JCVFERERlQ3ar6uFhGnp5L3321Xfn3Ld+nVrqfWEHl46fnZ2t3bt3S5JOnjyp1NRUbdiwQdWqVVOTJhUvLHvSVf17KvFgijKycs66n5+fTSMGuzZ7/cEHH1SPHj30xBNP6Oabb9avv/6qmTNn6tVXXz3fsF1mczqdTq/3ilIefPBBff311zp06JCCg4PVqFEjjR49WnfddZf8/f2NDg8AAAAAAAA+KDM7VzPem6vcvIJy92nWsJ5uu3aAbDZbhY9b3r6jRo3SBx984GqYHjVn4XL9vmV3udsDAuwad9twxUS6Vpj/4Ycf1KdPnzPev+SSS/TDDz+4GqbH7N53SO/MWXTWfS6/uIv6dO/o8rEXLVqkxx9/XNu3b1dsbKzGjRunv//975UNtdIocPuYgylHFB0Z4dItFgAAAAAAALCmTTv26tMvy57FHBocpAduv1bVq4V6OSrvycsv0Iz35pU7i3nY5RepW4dWXo7Ku77+7metWre5zG3169TWnSMHu7Q8TVXju5FbUFFxsT7597ea9uZnOnDosNHhAAAAAAAAoIpr27yROrZuWua2YZf3MnVxW5JCgoN07aDeZW5r3qieurZv6d2ADDDgkq6qFV3jjPcDK7H2elXk29FbzLpNO5SRlaPAwADF1Yo2OhwAAAAAAAD4gCH9e6pG9Wql3uvYuonatmhkUETe1aRBvHp2blPqvdCQIA0feIlLS7P4qlMPEe0jP7/SP+ugvt1dXpqlKqLAXQabzVaS3F9//bX69eun6Oho2Ww2w9bQKSou1vKff5ck9e7WwaVF3wEAAAAAAGBdwUGBuvaK3iWvI8LDdFW/nsYFZIABF3dVrejIktdWmL3+Z3Vja+rSnp1KXrdoXF9d27cwMCL3ocB9Fi+//LKuuuoqbdy4UY0bN1Z8fLxhsZyevR1eLdQ0yQcAAAAAAADvaNygji7q0laSdO2g3gqx2PPdAgLsGjH41CzmC9o0Vdvm1pi9/me9L+yg+nVqnZq9PuBi08xe5yGTZTj9yw0MDNQrr7yisWPHys/PT06nUydPnlRQkGsfADM//EJZ2XnnEZFTWTl5cjqdCg4KVGBAwHkcCwAAAAAAAFbkdDpVWFRk6drSycJCBdjtpinuusrhcKjY4VCAvWqtDhFeLUT3jbq6Um2r1k9Sxdxxxx265557Sl7bbDaXi9uSlJWdp8zssp/U6qr8gpPKLzjplmMBAAAAAADAeqxeW7L6zy9JeSowOgS3ocB9FrfeeqtbjhNeLeQ8WjN7GwAAAAAAAIB5nU/9lCVKynD6FoXs7GyFhYUZGsuvG7bp30tXKrxaqCaMuZ6HSwIAAAAAAADAf1HgLsPpAre7/moqvwY3s7cBAAAAAAAAmBtrcFdx7liDm7W3AQAAAAAAAKA0CtxeULk1ZJi9DQAAAAAAAMD8WIPbzdy9REllsPY2AAAAAAAAAJydn9EB4ExFxcX6/pffJUm9u3WguA0AAAAAAAAAZaDAXQWt27RTJzKzFV4tVF3btzA6HAAAAAAAAACokpgaXAUFBthVvVqYLunWntnbAAAAAAAAAFAO1uCuogqLimSTTXa7v9GhAAAAAAAAAECVRIEbAAAAAAAAAOCTWIMbAAAAAAAAAOCTKHADAAAAAAAAAHwSBW4AAAAAAAAAgE+iwA0AAAAAAAAA8EkUuAEAAAAAAAAAPokCNwAAAAAAAADAJ1HgBgAAAAAAAAD4JArcAAAAAAAAAACfRIEbAAAAAAAAAOCTKHADAAAAAAAAAHwSBW4AAAAAAAAAgE+iwA0AAAAAAAAA8EkUuAEAAAAAAAAAPokCNwAAAAAAAADAJ1HgBgAAAAAAAAD4JArcAAAAAAAAAACfRIEbAAAAAAAAAOCTKHADAAAAAAAAAHwSBW4AAAAAAAAAgE+iwA0AAAAAAAAA8EkUuAEAAAAAAAAAPokCNwAAAAAAAADAJ1HgBgAAAAAAAAD4JArcAAAAAAAAAACfRIEbAAAAAAAAAOCTKHADAAAAAAAAAHwSBW4AAAAAAAAAgE+iwA0AAAAAAAAA8EkUuAEAAAAAAAAAPokCNwAAAAAAAADAJ1HgBgAAAAAAAAD4JArcAAAAAAAAAACfRIEbAAAAAAAAAOCTKHADAAAAAAAAAHwSBW4AAAAAAAAAgE+iwA0AAAAAAAAA8EkUuAEAAAAAAAAAPokCNwAAAAAAAADAJ1HgBgAAAAAAAAD4pP8HL0ShSvVNLbEAAAAASUVORK5CYII=\n"
          },
          "metadata": {},
          "execution_count": 40
        }
      ],
      "source": [
        "# Test circuit drawing\n",
        "qw_c.draw_circuit()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 41,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fQZmUTfg136d",
        "outputId": "d3f4af67-90a0-4c74-e9b7-3c9636d6d4a6"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Probability distribution:\n",
            "001: 0.1461\n",
            "011: 0.8539\n"
          ]
        }
      ],
      "source": [
        "# Test probability distribution\n",
        "print(\"Probability distribution:\")\n",
        "probs = qw_c.get_probabilities(shots=shots)\n",
        "for state, prob in probs.items():\n",
        "    print(f\"{state}: {prob:.4f}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "As we can see from the above results, with a low number of steps, the quantum walk is biased towards the initialization state, making it unsuitable for generating a reliable quantum walk for a QKD protocol. 😔"
      ],
      "metadata": {
        "id": "nIf0XSGJKxvH"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Test probability distribution with a higher number of steps\n",
        "qw_c = QW_Circle(P=3, t=600, initial_position=2, phi=0, theta=np.pi/4, F='Y')\n",
        "print(\"Probability distribution:\")\n",
        "probs = qw_c.get_probabilities(shots=shots)\n",
        "for state, prob in probs.items():\n",
        "    print(f\"{state}: {prob:.4f}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Y7Mvgaz76BWd",
        "outputId": "d0f07c79-290d-4795-b72d-790dea631a8e"
      },
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Probability distribution:\n",
            "100: 0.2061\n",
            "110: 0.2472\n",
            "000: 0.2998\n",
            "010: 0.2469\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Yif1LgtmMhLe"
      },
      "source": [
        "Instead, with a higher number of steps, the probability distribution becomes less biased, which is an optimal result. This indicates that the approach is valid for constructing quantum walks for a secure QKD protocol. 🎉"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "shp5FUZWT-Ca"
      },
      "source": [
        "Let us now examine the paper of [C. Vlachou et alt.](https://arxiv.org/abs/1710.07979), where simulations of a QW on a circle are initially conducted to determine the $c$ parameter as $P$ varies.\n",
        "\n",
        "In fact, to demonstrate the security of 1W-QKD, we will construct an equivalent entanglement-based protocol, as is commonly done. Proving the security of this protocol will also validate the security of the prepare-and-measure version. The equivalence between entanglement-based and prepare-and-measure QKD protocols was firstly introduced by [C. H. Bennett et alt.](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.68.557). Since then, the connection between entanglement (specifically, the ability to certify or distill it) and the security of prepare-and-measure QKD protocols has been extensively explored. A frequent method for proving the security of prepare-and-measure QKD protocols, including those presented in this notebook, involves considering an equivalent entanglement-based protocol.\n",
        "\n",
        "Even in cases where the devices are untrusted (as in device-independent QKD), security holds under certain assumptions about the devices. For the entanglement-based protocol, in each of the $N$ iterations, we modify steps (1) and (2) as follows:\n",
        "\n",
        "- **New step (1)**: Alice prepares the entangled state:\n",
        "  $$\n",
        "  \\ket{\\Psi_0} = \\frac{1}{\\sqrt{2P}} \\sum_{i=0}^{2P-1} \\ket{i, i}_{AB}\n",
        "  $$\n",
        "\n",
        "  which resides in a $4P^2$-dimensional Hilbert space, $(H_p \\otimes H_c)^2$. Alice sends Bob the second half (the Bob portion) of $\\ket{\\Psi_0}$ while keeping the first half (the Alice portion) in her private lab;\n",
        "\n",
        "- **New step (2)**: Alice and Bob independently choose two random bits, $w_A$ and $w_B$. If $w_A = 0$, Alice measures her half of the entangled state in the computational $Z$ basis; otherwise, she measures in the QW basis. Bob similarly measures his half according to $w_B$. Their measurement outcomes are recorded as $i_A$ for Alice and $j_B$ for Bob.\n",
        "\n",
        "Next, we prove the security of this entanglement-based protocol by initially making three assumptions:\n",
        "\n",
        "- $A_1$: Alice and Bob only use iterations where $w_A = w_B = 0$ for their raw key;\n",
        "- $A_2$: Eve is limited to collective attacks, where she independently attacks each protocol iteration but can perform a joint measurement of her ancilla at any future time;\n",
        "- $A_3$: Eve prepares the states that Alice and Bob hold.\n",
        "\n",
        "Assumption $A_1$ simplifies computation and can be discarded later; alternatively, Alice and Bob may bias their basis choice to make $w_A = w_B = 0$ more likely, as done in the BB84 protocol. Assumption $A_2$ can be removed later using a de Finetti argument, yielding security in the asymptotic limit without degrading the key-rate. Assumption $A_3$ grants more power to Eve; if security is shown with $A_3$, it holds even when $A_3$ is removed.\n",
        "\n",
        "Given $A_2$ and $A_3$, Alice, Bob, and Eve, after $N$ iterations, share a quantum state $\\rho_{ABE}^N$, where $\\rho_{ABE} \\in H_A \\otimes H_B \\otimes H_E$ with $H_A \\simeq H_B \\simeq H_p \\otimes H_c$. Eve, as an all-powerful adversary, has no constraints on her Hilbert space $H_E$. After error correction and privacy amplification, Alice and Bob share a secret key of size $\\ell(N)$. Under collective attacks, the Devetak-Winter key-rate expression can compute:\n",
        "\n",
        "$$\n",
        "r = \\lim_{N \\to \\infty} \\frac{\\ell(N)}{N} = S(A|E) - H(A|B)\n",
        "$$\n",
        "\n",
        "Let $A_z$ and $A_w$ be random variables representing Alice's system when measured in the $Z$ or QW basis, respectively, with $B_z$ and $B_w$ defined similarly for Bob. Under $A_1$, we seek:\n",
        "\n",
        "$$\n",
        "r = S(A_z|E) - H(A_z|B_z)\n",
        "$$\n",
        "\n",
        "Computing $H(A_z|B_z)$ is straightforward, given the probabilities:\n",
        "\n",
        "$$\n",
        "p_{i,j}^z = \\mathbb{P}(i_A = i, \\: j_B = j | w_A = w_B = 0)\n",
        "$$\n",
        "\n",
        "The challenge lies in bounding the von Neumann entropy $S(A_z|E)$. For this, we use an uncertainty relation from which, given any density operator $\\rho_{ABE}$ on $H_A \\otimes H_B \\otimes H_E$, and measurements using POVMs $M_0 = \\{ M_x^{(0)} \\}_x$ or $M_1 = \\{ M_x^{(1)} \\}_x$:\n",
        "\n",
        "$$\n",
        "S(A_0|E) + H(A_1|B) \\geq \\log \\frac{1}{c}\n",
        "$$\n",
        "\n",
        "where $c = \\max_{x,y} \\| M_x^{(0)} M_y^{(1)} \\|_\\infty^2$; we define $\\| \\cdot \\|_\\infty$ as the operator norm, with $A_i$ representing the random variable that describes Alice's system after applying the measurement $M_i$. We will define $B_i$ similarly for Bob's system. Assuming measurements $M_0$ are used for key distillation, provides the Devetak-Winter key rate:\n",
        "\n",
        "$$\n",
        "r = S(A_0|E) - H(A_0|B_0) \\geq \\log \\frac{1}{c} - H(A_0|B_0) - H(A_1|B) \\geq \\log \\frac{1}{c} - H(A_0|B_0) - H(A_1|B_1)\n",
        "$$\n",
        "\n",
        "This final inequality results from the fundamental fact that measurements can only increase entropy. In our scenario, we set $M^{(0)}_x = \\ket{x} \\bra{x}$ and $M^{(1)}_x = \\ket{\\tilde{x}} \\bra{\\tilde{x}}$ for $x \\in \\{0, 1, \\dots, 2P - 1\\}$, where $\\ket{\\tilde{x}} = \\sum_{i}\\alpha_{x,i} \\ket{i}$. Thus, for all $x, y$:\n",
        "\n",
        "$$\n",
        "\\| M^{(0)}_x M^{(1)}_y \\|_\\infty = |\\alpha_{x, y}|^2\n",
        "$$\n",
        "\n",
        "This results in:\n",
        "\n",
        "$$\n",
        "c = \\max_{x,y} |\\alpha_{x, y}|^2\n",
        "$$\n",
        "\n",
        "which depends only on the QW parameters and not on the channel noise. Therefore, Alice and Bob should choose optimal values for $t$, $\\theta$, and $P$ to minimize $c$, thereby maximizing the key rate.\n",
        "\n",
        "As previously mentioned, the value of $c$ depends solely on the QW parameters, which are under Alice and Bob's control. They should select a QW setup that minimizes this value so that, after evolving for $t$ steps, the probability of the walker occupying any specific position remains low. It's evident that as $t \\to \\infty$, the values $|\\alpha_{x, y}|$ do not settle into a steady state, which is why time-averaged distributions are often considered when analyzing QWs on cycles.\n",
        "\n",
        "However, for our QKD protocol, we are not concerned with large $t$; instead, we seek an optimal, reasonably small $t$. Larger values of $t$ generally mean longer preparation and reversal times for Alice and Bob, respectively. In that case, the choice of $t$ affects noise resistance rather than making it more difficult for Eve to distinguish, also, even relatively small values of $t$ can yield secure systems. Different values of $t$ lead to various noise tolerances, and we seek optimal $t$ values, where “optimal” refers to maximizing theoretical noise tolerance for a given walk configuration.\n",
        "\n",
        "We will explore various walk parameters to find the minimum $c$ value, starting with $F = I_c$, the identity operator. Notably, on a circle, it is generally practical to consider odd $P$ values, as even $P$ forces the probability amplitudes onto only even or odd nodes, thereby increasing $|\\alpha_{x, y}|$. The complete results of these simulations can be found in our [GitHub](https://github.com/werefin/1W-QKD-Quantum-Walks/) repository."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4qQkD9XC9HUo"
      },
      "source": [
        "### QW on a hypercube with a predefined number of vertices $2^{P}$\n",
        "\n",
        "Following the analysis and methodology previously seen for quantum walks on hypercubes, we can implement the QW evolution here by strictly adhering to those procedures. In this case, the circuit design becomes more complex, as the increment and decrement gates must be applied in each \"direction\" of the walk. Unlike the previous scenario where the vertices were limited to $P$, the number of vertices now scales to $2^{P}$, meaning the probability distribution is spread across a significantly larger state space. Furthermore, the number of qubits required for the circuit increases substantially: with $2^{P}$ vertices, the number of qubits is $\\text{log}_{2}(2^{P}) = P$. Our previous analysis comparing the Grover coin and the generic rotation coin remains relevant here. We will examine both approaches to demonstrate the distinctions we identified earlier."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 43,
      "metadata": {
        "id": "U5oRgFYGcZT-"
      },
      "outputs": [],
      "source": [
        "class QW_Hypercube:\n",
        "    def __init__(self, P, t, initial_position=0, F='I', coin_type='generic_rotation',\n",
        "                 phi=0, theta=np.pi/4):\n",
        "        \"\"\"\n",
        "        Quantum walk on a hypercube with 2^{P} vertices\n",
        "        Args:\n",
        "        P (int): dimension of the hypercube (2^{P} vertices)\n",
        "        t (int): number of walk steps to perform\n",
        "        initial_position (int): initial position of the walker\n",
        "        F (string): F operator type. Choose 'I', 'X', or 'Y'\n",
        "        coin_type (str): type of coin operation. Choose 'generic_rotation' or 'grover'\n",
        "        phi (float): phase angle for the coin rotation operator\n",
        "        theta (float): rotation angle for the coin rotation operator\n",
        "        \"\"\"\n",
        "        self.P = P\n",
        "        self.t = t\n",
        "        self.initial_position = initial_position\n",
        "        self.coin_type = coin_type\n",
        "        self.phi = phi\n",
        "        self.theta = theta\n",
        "        self.F = F\n",
        "        self.n_qubits = int(np.ceil(np.log2(2 ** P)))\n",
        "        # Create registers and quantum circuit\n",
        "        self.walker_r, self.coin_r, self.classic_r, self.circuit = self.hypercube_walk_circuit(self.n_qubits)\n",
        "        # Initialize the quantum circuit\n",
        "        self._initialize_states()\n",
        "        # Build the quantum random walk circuit\n",
        "        self._build_circuit()\n",
        "\n",
        "    def _initialize_states(self):\n",
        "        \"\"\"\n",
        "        Initialize the walker's position\n",
        "        \"\"\"\n",
        "        # Set the walker to the initial position (in the range 0 to 2^{P} - 1)\n",
        "        for i in range(self.n_qubits):\n",
        "            if self.initial_position & (1 << i): # check if bit i is set in initial_position\n",
        "                self.circuit.x(self.walker_r[self.n_qubits - i - 1])\n",
        "        self.circuit.barrier()\n",
        "\n",
        "    def hypercube_walk_circuit(self, n_qubits):\n",
        "        \"\"\"\n",
        "        Create a quantum circuit for hypercube topology\n",
        "        \"\"\"\n",
        "        walker_r = QuantumRegister(n_qubits, name='q')\n",
        "        coin_r = QuantumRegister(n_qubits, name='c')\n",
        "        classic_r = ClassicalRegister(n_qubits, name='r')\n",
        "        q_circuit = QuantumCircuit(walker_r, coin_r, classic_r)\n",
        "        return walker_r, coin_r, classic_r, q_circuit\n",
        "\n",
        "    def coin_rotation_operator(self, coin_r):\n",
        "        \"\"\"\n",
        "        Create a quantum circuit for the coin rotation operator\n",
        "        \"\"\"\n",
        "        # Create a quantum circuit for the coin rotation operator\n",
        "        q_circuit = QuantumCircuit(len(coin_r))\n",
        "        # Apply the rotation to each coin qubit\n",
        "        for qubit in range(len(coin_r)):\n",
        "            q_circuit.u(self.theta, self.phi, 0, qubit)\n",
        "        # Convert the circuit to an operator\n",
        "        coin_rotation_operator = Operator(q_circuit)\n",
        "        return coin_rotation_operator\n",
        "\n",
        "    def grover_coin(self, coin_r):\n",
        "        \"\"\"\n",
        "        Create the Grover coin operator\n",
        "        \"\"\"\n",
        "        matrix_size = 2 ** len(coin_r)\n",
        "        grover_matrix = np.full((matrix_size, matrix_size), 2 / matrix_size) - np.eye(matrix_size)\n",
        "        return Operator(grover_matrix)\n",
        "\n",
        "    def shift_operator(self, walker_r, coin_r):\n",
        "        \"\"\"\n",
        "        Create a quantum circuit for the shift operator\n",
        "        \"\"\"\n",
        "        q_circuit = QuantumCircuit(walker_r, coin_r)\n",
        "        for i in reversed(range(len(walker_r))):\n",
        "            q_circuit.mcx(coin_r, walker_r[i])\n",
        "            q_circuit.x(coin_r[-1])\n",
        "            for j in range(1, len(coin_r)):\n",
        "                if i & ((1 << j) - 1) == 0:\n",
        "                    q_circuit.x(coin_r[-(j + 1)])\n",
        "        return q_circuit\n",
        "\n",
        "    def hypercube_walk_step(self, walker_r, coin_r):\n",
        "        \"\"\"\n",
        "        Create a quantum circuit for one step of the hypercube walk\n",
        "        \"\"\"\n",
        "        shift = self.shift_operator(walker_r, coin_r)\n",
        "        walk_step = QuantumCircuit(walker_r, coin_r)\n",
        "        if self.coin_type == 'generic_rotation':\n",
        "            coin_operator = self.coin_rotation_operator(coin_r)\n",
        "            walk_step.unitary(coin_operator, coin_r, label=\"R\")\n",
        "        elif self.coin_type == 'grover':\n",
        "            coin_operator = self.grover_coin(coin_r)\n",
        "            walk_step.unitary(coin_operator, coin_r, label=\"G\")\n",
        "        walk_step.compose(shift, inplace=True)\n",
        "        return walk_step\n",
        "\n",
        "    def apply_F(self, coin_r):\n",
        "        \"\"\"\n",
        "        Create an operator for the specified F operator to be applied to the coin register\n",
        "        \"\"\"\n",
        "        # Create a quantum circuit for the coin operation\n",
        "        q_circuit = QuantumCircuit(len(coin_r))\n",
        "        # Apply the specified operation to each qubit\n",
        "        for qubit in range(len(coin_r)):\n",
        "            if self.F == \"X\":\n",
        "                q_circuit.x(qubit)\n",
        "            elif self.F == \"Y\":\n",
        "                q_circuit.y(qubit)\n",
        "            # Identity operator is the default behavior (no gate added)\n",
        "        # Convert the circuit to an operator\n",
        "        operator_F = Operator(q_circuit)\n",
        "        return operator_F\n",
        "\n",
        "    def _build_circuit(self):\n",
        "        \"\"\"\n",
        "        Build the quantum random walk circuit for the hypercube\n",
        "        \"\"\"\n",
        "        if self.coin_type == 'generic_rotation':\n",
        "            # Apply the F operator before evolving the walk\n",
        "            self.circuit.unitary(self.apply_F(self.coin_r), self.coin_r, label=\"F\")\n",
        "            self.circuit.barrier()\n",
        "        # Perform the quantum walk for the specified number of steps\n",
        "        for _ in range(self.t):\n",
        "            walk_step = self.hypercube_walk_step(self.walker_r, self.coin_r)\n",
        "            self.circuit.compose(walk_step, inplace=True)\n",
        "        self.circuit.barrier()\n",
        "        # Measure the position qubits\n",
        "        self.circuit.measure(self.walker_r, reversed(self.classic_r))\n",
        "\n",
        "    def draw_circuit(self):\n",
        "        \"\"\"\n",
        "        Draw the quantum circuit\n",
        "        \"\"\"\n",
        "        return self.circuit.draw(\"mpl\")\n",
        "\n",
        "    def plot_states_hist(self, shots=50000, title=None):\n",
        "        \"\"\"\n",
        "        Plot a histogram of measurement results for valid states\n",
        "        \"\"\"\n",
        "        simulator = AerSimulator(max_parallel_experiments=0, max_memory_mb=None)\n",
        "        self.circuit = transpile(self.circuit, backend=simulator, optimization_level=1)\n",
        "        results = simulator.run(self.circuit, shots=shots).result()\n",
        "        counts = results.get_counts()\n",
        "        fig, ax = plt.subplots(figsize=(12, 6))\n",
        "        plot_histogram(counts, title=title or f'QW results (P={self.P})', sort='value_desc', ax=ax)\n",
        "        ax.set_xlabel('Measured states')\n",
        "        ax.set_ylabel('Counts')\n",
        "        plt.xticks(rotation=45)\n",
        "        plt.tight_layout()\n",
        "        plt.show()\n",
        "\n",
        "    def execute(self):\n",
        "        \"\"\"\n",
        "        Execute the circuit once and return a valid result state\n",
        "        \"\"\"\n",
        "        simulator = AerSimulator(max_parallel_experiments=0, max_memory_mb=None)\n",
        "        self.circuit = transpile(self.circuit, backend=simulator, optimization_level=1)\n",
        "        results = simulator.run(self.circuit, shots=1).result()\n",
        "        counts = results.get_counts()\n",
        "        return list(counts.keys())[0]\n",
        "\n",
        "    def get_probabilities(self, shots=50000):\n",
        "        \"\"\"\n",
        "        Get the probability distribution of valid states\n",
        "        \"\"\"\n",
        "        simulator = AerSimulator(max_parallel_experiments=0, max_memory_mb=None)\n",
        "        self.circuit = transpile(self.circuit, backend=simulator, optimization_level=1)\n",
        "        results = simulator.run(self.circuit, shots=shots).result()\n",
        "        counts = results.get_counts()\n",
        "        total_counts = sum(counts.values())\n",
        "        probabilities = {state: count / total_counts for state, count in counts.items()}\n",
        "        return probabilities"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fVZ5d4rO_PGU"
      },
      "source": [
        "Let's start using the generic rotation coin. In that case, we expect results similar to those observed with the circle topology: lower $t$ values will produce biased distributions, while increasing $t$ leads to distributions that approach uniformity."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 44,
      "metadata": {
        "id": "p8lC683rs2F8"
      },
      "outputs": [],
      "source": [
        "# Test QW on a hypercube with 2^{P} vertices (generic_rotation coin)\n",
        "qw_h = QW_Hypercube(P=3, t=1, initial_position=2, F='Y',\n",
        "                    coin_type='generic_rotation', phi=0, theta=np.pi/4)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 45,
      "metadata": {
        "id": "RsFfsuA8w0Zh",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "outputId": "915941ba-68ed-4890-a77d-e6eb7e2de4e8"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 1374.44x618.722 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {},
          "execution_count": 45
        }
      ],
      "source": [
        "# Test circuit drawing\n",
        "qw_h.draw_circuit()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 46,
      "metadata": {
        "id": "47blhdXzszkI",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "bf98aa49-c86c-477c-8628-6352610c8ec6"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Probability distribution:\n",
            "000: 0.0180\n",
            "010: 0.2540\n",
            "110: 0.1064\n",
            "011: 0.6216\n"
          ]
        }
      ],
      "source": [
        "# Test probability distribution\n",
        "print(\"Probability distribution:\")\n",
        "probs = qw_h.get_probabilities(shots=shots)\n",
        "for state, prob in probs.items():\n",
        "    print(f\"{state}: {prob:.4f}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "As we can see afrom the above results, with a low number of steps, the quantum walk exhibits a bias toward the initialization state, making it unsuitable for implementing a secure QKD protocol. 😢"
      ],
      "metadata": {
        "id": "QhDOewu8dBo1"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Test probability distribution with a higher number of steps\n",
        "qw_h = QW_Hypercube(P=3, t=900, initial_position=2, F='Y',\n",
        "                    coin_type='generic_rotation', phi=0, theta=np.pi/4)\n",
        "print(\"Probability distribution:\")\n",
        "probs = qw_h.get_probabilities(shots=shots)\n",
        "for state, prob in probs.items():\n",
        "    print(f\"{state}: {prob:.4f}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4Sz6IYx88RMV",
        "outputId": "671e4d27-d75e-4222-9eeb-2339b0f11916"
      },
      "execution_count": 47,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Probability distribution:\n",
            "100: 0.0470\n",
            "000: 0.0963\n",
            "010: 0.2163\n",
            "111: 0.1421\n",
            "011: 0.1628\n",
            "001: 0.0444\n",
            "110: 0.2284\n",
            "101: 0.0628\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7oe6CPV8ALOa"
      },
      "source": [
        "As observed above, increasing the number of steps results in a less biased probability distribution, which is an ideal outcome. This demonstrates that the approach is effective for designing quantum walks suitable for a secure QKD protocol. ✅"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now, consider the scenario where the coin is defined as a Grover coin. In this case, the results are less favorable compared to the rotation coin. As observed earlier, the Grover coin theoretically produces a more biased distribution, making it challenging to achieve uniformity without significantly increasing $t$ in our simulations."
      ],
      "metadata": {
        "id": "DDDzHizdjB4w"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Test QW on a hypercube with 2^{P} vertices (grover coin)\n",
        "qw_h = QW_Hypercube(P=3, t=1, initial_position=2, coin_type='grover')"
      ],
      "metadata": {
        "id": "r2VbL8VSiP4W"
      },
      "execution_count": 48,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Test circuit drawing\n",
        "qw_h.draw_circuit()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 486
        },
        "id": "o5lge8LdkB-X",
        "outputId": "e3893619-a4ad-423d-89dd-2e5285d7ef43"
      },
      "execution_count": 49,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Figure size 1207.22x618.722 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {},
          "execution_count": 49
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Test probability distribution\n",
        "print(\"Probability distribution:\")\n",
        "probs = qw_h.get_probabilities(shots=shots)\n",
        "for state, prob in probs.items():\n",
        "    print(f\"{state}: {prob:.4f}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "V7RaQQ57kFGE",
        "outputId": "75aca946-8dbe-4557-c6a3-1b69550741a2"
      },
      "execution_count": 50,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Probability distribution:\n",
            "011: 0.0634\n",
            "110: 0.0639\n",
            "000: 0.0617\n",
            "010: 0.8109\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "From the results presented above, it is evident that the Grover coin introduces significant bias, rendering it impractical for use in QKD protocols. However, let us examine its behavior over a large number of steps."
      ],
      "metadata": {
        "id": "WS-eyCiem6iB"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Test probability distribution with a higher number of steps\n",
        "qw_h = QW_Hypercube(P=3, t=900, initial_position=2, coin_type='grover')\n",
        "print(\"Probability distribution:\")\n",
        "probs = qw_h.get_probabilities(shots=shots)\n",
        "for state, prob in probs.items():\n",
        "    print(f\"{state}: {prob:.4f}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "NTUbnZDbkKLZ",
        "outputId": "66f3fc7c-0a6e-4c13-8737-638ac7e470c3"
      },
      "execution_count": 51,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Probability distribution:\n",
            "101: 0.0628\n",
            "011: 0.0384\n",
            "111: 0.0377\n",
            "100: 0.0381\n",
            "001: 0.0365\n",
            "110: 0.0366\n",
            "000: 0.0388\n",
            "010: 0.7111\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Even if the bias is smaller, it remains significant compared to the probabilities of states other than the initialization state. This indicates that this type of quantum walk on hypercubes is unsuitable for constructing a secure QKD protocol. Theoretically, with $P = 1$, we should achieve the minimum value of $c = 0.5$, where $c = \\max_{x,y} |\\alpha_{x, y}|^2$, as the protocol simplifies to BB84. For larger $P$, $c$ should approach zero as $P$ increases, given a reasonably small number of iterations. However, using a Grover coin with QW on hypercubes ensures that even as $P$ increases, the maximum value of $c$ will remain at $0.5$. In other words, as $P$ grows, the protocol combining QW on hypercubes using the Grover coin is equivalent (in terms of $c$ security analysis) to a BB84 protocol. 🤯"
      ],
      "metadata": {
        "id": "WZWIJ_fxnpPV"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ogb0_oTGBdcX"
      },
      "source": [
        "Next, we can conduct a similar analysis over a range of $P$ values from $1$ to $13$ (due to the limitations of the\n",
        "`AerSimulator` in terms of its qubits' capacity) to evaluate the security parameter $c$ as a function of $P$. Specifically, we aim to examine how the topology affects $c$, taking into account the exponential growth in the number of vertices and its impact on circuit complexity. In addition, the previous demonstration of the QKD protocol's security on circles also applies to hypercubes, with only minor adjustments, as outlined below.\n",
        "\n",
        "The equivalence between entanglement-based and prepare-and-measure QKD protocols was first introduced by [C. H. Bennett et alt.](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.68.557). Since then, the relationship between entanglement and the security of prepare-and-measure QKD protocols has been extensively studied. A common approach to proving the security of prepare-and-measure QKD protocols, including those discussed here, is to consider an equivalent entanglement-based protocol.\n",
        "\n",
        "Even when the devices are untrusted, as in device-independent QKD, security is maintained under specific assumptions about the devices. In the entanglement-based protocol, steps (1) and (2) of each of the $N$ iterations are modified as follows:\n",
        "\n",
        "- **New step (1)**: Alice prepares the entangled state:\n",
        "  $$\n",
        "  \\ket{\\Psi_0} = \\frac{1}{\\sqrt{2^{P}}} \\sum_{i=0}^{2^{P}-1} \\ket{i, i}_{AB}\n",
        "  $$\n",
        "\n",
        "  which resides in a $2^{2P}$-dimensional Hilbert space, $(H_p \\otimes H_c)^2$. Alice sends Bob the second half (the Bob portion) of $\\ket{\\Psi_0}$ while keeping the first half (the Alice portion) in her private lab;\n",
        "\n",
        "- **New step (2)**: Alice and Bob independently choose two random bits, $w_A$ and $w_B$. If $w_A = 0$, Alice measures her half of the entangled state in the computational $Z$ basis; otherwise, she measures in the QW basis. Bob similarly measures his half according to $w_B$. Their measurement outcomes are recorded as $i_A$ for Alice and $j_B$ for Bob.\n",
        "\n",
        "Next, we prove the security of this entanglement-based protocol by initially making three assumptions:\n",
        "\n",
        "- $A_1$: Alice and Bob only use iterations where $w_A = w_B = 0$ for their raw key;\n",
        "- $A_2$: Eve is limited to collective attacks, where she independently attacks each protocol iteration but can perform a joint measurement of her ancilla at any future time;\n",
        "- $A_3$: Eve prepares the states that Alice and Bob hold.\n",
        "\n",
        "Assumption $A_1$ simplifies computation and can be discarded later; alternatively, Alice and Bob may bias their basis choice to make $w_A = w_B = 0$ more likely, as done in the BB84 protocol. Assumption $A_2$ can be removed later using a de Finetti argument, yielding security in the asymptotic limit without degrading the key-rate. Assumption $A_3$ grants more power to Eve; if security is shown with $A_3$, it holds even when $A_3$ is removed.\n",
        "\n",
        "Given $A_2$ and $A_3$, Alice, Bob, and Eve, after $N$ iterations, share a quantum state $\\rho_{ABE}^N$, where $\\rho_{ABE} \\in H_A \\otimes H_B \\otimes H_E$ with $H_A \\simeq H_B \\simeq H_p \\otimes H_c$. Eve, as an all-powerful adversary, has no constraints on her Hilbert space $H_E$. After error correction and privacy amplification, Alice and Bob share a secret key of size $\\ell(N)$. Under collective attacks, the Devetak-Winter key-rate expression can compute:\n",
        "\n",
        "$$\n",
        "r = \\lim_{N \\to \\infty} \\frac{\\ell(N)}{N} = S(A|E) - H(A|B)\n",
        "$$\n",
        "\n",
        "Let $A_z$ and $A_w$ be random variables representing Alice's system when measured in the $Z$ or QW basis, respectively, with $B_z$ and $B_w$ defined similarly for Bob. Under $A_1$, we seek:\n",
        "\n",
        "$$\n",
        "r = S(A_z|E) - H(A_z|B_z)\n",
        "$$\n",
        "\n",
        "Computing $H(A_z|B_z)$ is straightforward, given the probabilities:\n",
        "\n",
        "$$\n",
        "p_{i,j}^z = \\mathbb{P}(i_A = i, \\: j_B = j | w_A = w_B = 0)\n",
        "$$\n",
        "\n",
        "The challenge lies in bounding the von Neumann entropy $S(A_z|E)$. For this, we use an uncertainty relation from which, given any density operator $\\rho_{ABE}$ on $H_A \\otimes H_B \\otimes H_E$, and measurements using POVMs $M_0 = \\{ M_x^{(0)} \\}_x$ or $M_1 = \\{ M_x^{(1)} \\}_x$:\n",
        "\n",
        "$$\n",
        "S(A_0|E) + H(A_1|B) \\geq \\log \\frac{1}{c}\n",
        "$$\n",
        "\n",
        "where $c = \\max_{x,y} \\| M_x^{(0)} M_y^{(1)} \\|_\\infty^2$; we define $\\| \\cdot \\|_\\infty$ as the operator norm, with $A_i$ representing the random variable that describes Alice's system after applying the measurement $M_i$. We will define $B_i$ similarly for Bob's system. Assuming measurements $M_0$ are used for key distillation, provides the Devetak-Winter key rate:\n",
        "\n",
        "$$\n",
        "r = S(A_0|E) - H(A_0|B_0) \\geq \\log \\frac{1}{c} - H(A_0|B_0) - H(A_1|B) \\geq \\log \\frac{1}{c} - H(A_0|B_0) - H(A_1|B_1)\n",
        "$$\n",
        "\n",
        "This final inequality results from the fundamental fact that measurements can only increase entropy. In our scenario, we set $M^{(0)}_x = \\ket{x} \\bra{x}$ and $M^{(1)}_x = \\ket{\\tilde{x}} \\bra{\\tilde{x}}$ for $x \\in \\{0, 1, \\dots, 2^{P} - 1\\}$, where $\\ket{\\tilde{x}} = \\sum_{i}\\alpha_{x,i} \\ket{i}$. Thus, for all $x, y$:\n",
        "\n",
        "$$\n",
        "\\| M^{(0)}_x M^{(1)}_y \\|_\\infty = |\\alpha_{x, y}|^2\n",
        "$$\n",
        "\n",
        "This results in:\n",
        "\n",
        "$$\n",
        "c = \\max_{x,y} |\\alpha_{x, y}|^2\n",
        "$$\n",
        "\n",
        "which depends only on the QW parameters and not on the channel noise. Therefore, Alice and Bob should choose optimal values for $t$, $\\theta$, and $P$ to minimize $c$, thereby maximizing the key rate.\n",
        "\n",
        "Similar to the circle topology, we will investigate different walk parameters to determine the minimum value of $c$, beginning with $F = I_c$, the identity operator. It's important to note that also for hypercubes, odd values of $P$ are typically preferred, as even values of $P$ restrict the probability amplitudes to either even or odd nodes, which increases $|\\alpha_{x, y}|$. The results of these simulations are available in our [GitHub](https://github.com/werefin/1W-QKD-Quantum-Walks/) repository."
      ]
    }
  ],
  "metadata": {
    "accelerator": "GPU",
    "colab": {
      "gpuType": "T4",
      "machine_shape": "hm",
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "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": "3.9.13"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}