project.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Emerging Technologies Project\n",
        "\n",
        "**By Ethan Conneely (G00393941)**\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "**Table of contents**    \n",
        "- Emerging Technologies Project    \n",
        "  - Introduction    \n",
        "    - Quantum Computing    \n",
        "    - Deutsch's algorithm    \n",
        "  - Library Imports    \n",
        "  - Function Input    \n",
        "  - Deutsch Algorithm circuit creation    \n",
        "  - Real Hardware    \n",
        "    - Jobs    \n",
        "  - References    \n",
        "\n",
        "<!-- vscode-jupyter-toc-config\n",
        "\tnumbering=false\n",
        "\tanchor=false\n",
        "\tflat=false\n",
        "\tminLevel=1\n",
        "\tmaxLevel=6\n",
        "\t/vscode-jupyter-toc-config -->\n",
        "<!-- THIS CELL WILL BE REPLACED ON TOC UPDATE. DO NOT WRITE YOUR TEXT IN THIS CELL -->"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Introduction\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Quantum Computing\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Quantum computing is a new way of performing computation.  \n",
        "It differs from classical computation by utilizing qubits instead of traditional bits  \n",
        "to perform a new type of computation that classical computation would  \n",
        "take much longer to compute.\n",
        "\n",
        "The main advantage of quantum computing is that it can perform many computations  \n",
        "simultaneously, whereas classical computing can only perform one computation.  \n",
        "The way this is achieved is by using the properties of quantum mechanics,  \n",
        "The ability to put a qubit in a superposition of states allows the qubit to  \n",
        "effectively act as a 1 and a 0 at the same time. This allows for many computations  \n",
        "to be performed at the same time.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Deutsch's algorithm\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Deutsch's algorithm is a quantum algorithm that determines whether a given Boolean function is constant or balanced.\n",
        "\n",
        "- A constant function is one that always returns the same value, regardless of the input.\n",
        "- A balanced function returns 0 for half of the inputs and 1 for the other half.\n",
        "\n",
        "It can be represented using the following equation:\n",
        "\n",
        "Deutsch's algorithm takes in 1 bit that is 0 or 1 and outputs a 1 bit also 0 or 1\n",
        "\n",
        "$\\Sigma = \\{0,1\\}$\n",
        "\n",
        "$f : \\Sigma\\rightarrow \\Sigma$\n",
        "\n",
        "The algorithm outputs 0 for constant and 1 for balanced\n",
        "\n",
        "It is effectively doing the xor operation from classical computing.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Library Imports\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "For quantum simulation in Python, Qiskit can be used.  \n",
        "It is a library that we can use to run quantum simulations and make circuits.\n",
        "\n",
        "Matplotlib will be used for visualising the circuit diagrams generated from qiskit.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {},
      "outputs": [],
      "source": [
        "from qiskit import QuantumCircuit, Aer\n",
        "from qiskit.result import Result\n",
        "import matplotlib.pyplot as plt\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Function Input\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Below are all the possible input function in a table [[1]](#1)\n",
        "\n",
        "| function $f(x)$ | $x=0$ | $x=1$ | $f(0) ⨁ f(1)$ |\n",
        "| --------------- | ----- | ----- | ------------- |\n",
        "| $f_0$           | 0     | 0     | 0             |\n",
        "| $f_1$           | 0     | 1     | 1             |\n",
        "| $f_2$           | 1     | 0     | 1             |\n",
        "| $f_3$           | 1     | 1     | 0             |\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "This is the first circuit it does nothing and is of type constant.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Below is the 4 complete circuits for each function [[1]](#1)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 161.878x200.667 with 1 Axes>"
            ]
          },
          "execution_count": 14,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "constantCircuitA = QuantumCircuit(2)\n",
        "constantCircuitA.draw(output='mpl',style=\"clifford\")\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAALAAAACuCAYAAACWa4e1AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/SrBM8AAAACXBIWXMAAA9hAAAPYQGoP6dpAAAJ90lEQVR4nO3df0zU9x3H8ef3gIo/MBVpcjb8rmARARORiGlcMLiks3WurVVD0S32v7malHL7u38Zpm0XY5Nhl85uyRiJNR2FbNkS/igxbYMjrqZcZW3EAnKJV2m1V12F++yPpSQEtHLAXd9fXo//+H6+3+ONPrn73vfg8JxzDhGjAqkeQGQuFLCYpoDFNAUspilgMU0Bi2kKWExTwGKaAhbTFLCYpoDFNAUspilgMU0Bi2kKWExTwGKaAhbTFLCYpoDFNAUspilgMU0Bi2kKWExTwGKaAhbTFLCYpoDFNAUspilgMU0Bi2kKWExTwGKaAhbTFLCYpoDFNAUspilgMU0Bi2kKWExTwGKaAhbTFLCYpoDFNAUspilgMU0Bi2kKWExTwGKaAhbTFLCYpoDFNAUspvk+4Gg0SigUYu3atWRmZpKXl8eRI0eIxWIcOnQIz/M4efJkqseUBKWneoCFdOHCBR5//HEikQjLly9n/fr1XL16lRMnTvDZZ59x/fp1ADZu3JjaQSVxzqeuXbvmcnNzHeCamprcjRs3JtdaWloc4NLT053nee6rr75K4aQyF74NeP/+/Q5whw8fnnG9qqrKAa6oqCjJk8l88uU5cDgcpr29nZycHI4ePTrjPps2bQKgqqpqyvbLly+za9cusrKyWLVqFQcOHOCLL75Y8JklMb4MuK2tjXg8TkNDAytWrJhxn6VLlwJTA7558yZ1dXUMDw/T1tbGqVOn6Onp4YknniAejydldpkdXz6J6+7uBqCuru6u+wwPDwNTAz516hQjIyO899575OfnA5Cbm8vWrVvp6Ohg9+7dCze0JMSXAV+5cgWAgoKCGdfHx8c5d+4cMDXgzs5OHnvsscl4AWpraykuLubdd99NOODq6moikUhCxy4GwWCQ8+fPJ3SsLwOOxWIA3Lp1a8b19vZ2otEoWVlZFBUVTW7v7+9nz5490/YvLy+nv78/4XkikQgjIyMJHy9358uAg8EgY2Nj9PX1UVtbO2VtdHSU5uZmACorK/E8b3JtbGyMBx98cNrtZWdnc+nSpTnNI3c3l38fXwZcX19POBympaWFHTt2UFpaCkBvby+NjY1Eo1EgeS9gJPrwKN/Pl1chQqEQq1evZmhoiPLycioqKigpKaGmpobi4mK2b98OTL+EtmrVKr788stpt3f9+nWys7OTMbrMki8Dzs3Npaenh507d5KZmcng4CDZ2dm0trbS1dXFwMAAMD3gsrKyGc91+/v7KSsrS8rsMkupfiUl2W7evOk8z3OBQMDFYrEpa8eOHXMZGRluaGhoctsHH3zgAHf27Nlkjyr3wXPOuVR/EyXThx9+yJYtW1i3bh2ffPLJlLUbN25QUVFBTk4OL7/8Mrdv3yYUCvHQQw/x/vvvEwj48gHLtEX3P3Lx4kVg+ukDwMqVK+nu7mbNmjXs27eP559/nq1bt9LZ2al4f6B8eRXiXu4VMMAjjzxCZ2dnMkeSOVh0dyvfF7DYsujOgcVfFt09sPiLAhbTFLCYpoDFNAUspilgMU0Bi2kKWExTwGKaAhbTFLCYpoDFNAUspilgMU0Bi2kKWExTwGKaAhbTFLCYpoDFNAUspilgMU0Bi2kKWExTwGKaAhbTFLCYpoDFNAUspilgMW3RvcG1Bc45volPpHqMWVkWSJvyN/eSRQH/AH0Tn2BV9z9TPcasjG3fwfK05OekUwgxTQGLaQpYTFPAYpoCFtMUsJimgMU0BSymKWAxTQGLaQpYTFPAYpoCFtMWRcDRaJRQKMTatWvJzMwkLy+PI0eOEIvFOHToEJ7ncfLkyVSPKQnwfcAXLlygoqKCY8eOEYlEWL9+PXfu3OHEiRPs3buXcDgMwMaNG1M76AKZePM0d378E+J//8e0Necc4y/9mjs7d+EuDyZ/uHng64Cj0ShPPvkkkUiEpqYmRkdH6evrIxKJ0NLSQldXF729vXieR2VlZarHXRCBxgYoLGCi9Q3cteiUtfjZd3AfXSTQ+BxeUWFqBpwjXwf8wgsvMDw8zOHDhzl+/DhZWVmTa6FQiKqqKsbHxyksLGTlypUpnHTheBkZpDc3we3bTLz628ntbmiY+Ok/4j26jsCep1M34Bz5NuBwOEx7ezs5OTkcPXp0xn02bdoEQFVV1eS274KvqalhyZIlKfk1mfnmlawlsO9Z3L/6iHf9DTcxwcRvjoNzpDU34aWlpXrEhPk24La2NuLxOA0NDaxYsWLGfZYuXQpMDfjTTz/l7bffJhgMsnnz5qTMmgyBhv1QXMzEG78n/vrvcJcGCPz8AF5ebqpHmxPfBtzd3Q1AXV3dXfcZHh4Gpga8bds2RkdH6ejooL6+fmGHTCIvPZ305hfh2zvEO7vwNpQTeGp3qseaM9/+UueVK1cAKCgomHF9fHycc+fOAVMDDgTm/3u6urqaSCRy3/u7Bx6A1tfnfQ6WL4eMDBgfx9tcjTePX2tpSSnet98mdGwwGOT8+fMJHevbgGOxGAC3bt2acb29vZ1oNEpWVhZFRUULOkskEmFkZOT+D8hcQsY8z+CcY+KV12D8DuTnEf/zXwj8aBvew2vm5favjl6F2/+dl9uaDd8GHAwGGRsbo6+vj9ra2ilro6OjNDc3A1BZWbngT9SCweCs9ncPPMC1eZ4h/k4H7t8fEfjFQQK1Wxj/5a+YeOU10o63zMvX//Cah+d0D5wo3wZcX19POBympaWFHTt2UFpaCkBvby+NjY1Eo/+/JpqMFzBm+/AYmxif1/eFcCMjxN88jbeulMCzz+ClpRF4roH4H94i/k4HaT/76Zw/x8B/BvS+EPMpFAqxevVqhoaGKC8vp6KigpKSEmpqaiguLmb79u3A1PNfP3LxOBPHXoV4nLTmFycvmQWefQavtIT4m6dxV0dTPGXifBtwbm4uPT097Ny5k8zMTAYHB8nOzqa1tZWuri4GBgYA/wccP3MW1x8mcPA5vPz8ye1eWhppL70I8QkmXnkN51wKp0ycb08hAMrKyujs7Jy2/euvv2ZwcJBAIMCGDRtSMFlyuM8/J/7Wn/DKHiXw9FPT1r3Cgnk/lUg2Xwd8Nx9//DHOOUpLS1m2bNm09TNnzgDQ398/5ePCwkKqq6uTN+gcefn5ZHT99Z77pO3fS9r+vUmaaP4tyoAvXrwI3P30Yc+ePTN+fPDgQU6fPr2gs8nsKOAZWD0fXIx8+yTuXr4vYLFjUd4Df/dzEmLforwHFv9QwGKaAhbTFLCYpoDFNAUspilgMU0Bi2kKWExTwGKaAhbTPKcfvfrB0R/7vn8KWEzTKYSYpoDFNAUspilgMU0Bi2kKWExTwGKaAhbTFLCYpoDFNAUspilgMU0Bi2kKWExTwGKaAhbTFLCYpoDFNAUspilgMU0Bi2kKWExTwGKaAhbTFLCY9j890Z1oCcI0+AAAAABJRU5ErkJggg==",
            "text/plain": [
              "<Figure size 203.683x200.667 with 1 Axes>"
            ]
          },
          "execution_count": 16,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "constantCircuitB = QuantumCircuit(2)\n",
        "constantCircuitB.x(1)\n",
        "constantCircuitB.draw(output='mpl',style=\"clifford\")\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 203.683x200.667 with 1 Axes>"
            ]
          },
          "execution_count": 5,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "balancedCircuitA = QuantumCircuit(2)\n",
        "balancedCircuitA.cx(0, 1)\n",
        "balancedCircuitA.draw(output='mpl',style=\"clifford\")\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 287.294x200.667 with 1 Axes>"
            ]
          },
          "execution_count": 6,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "balancedCircuitB = QuantumCircuit(2)\n",
        "balancedCircuitB.cx(0, 1)\n",
        "balancedCircuitB.x(1)\n",
        "balancedCircuitB.draw(output='mpl',style=\"clifford\")\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Deutsch Algorithm circuit creation\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The algorithm is made up of 2 qubits and 1 classical bit.  \n",
        "It creates the circuit and combines in the function to be tested.\n",
        "\n",
        "The basic layout for the diagram was gotten from this diagram i added in the function composition. [[2]](#2)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {},
      "outputs": [],
      "source": [
        "def deutsch_algorithm_circuit(function: QuantumCircuit) -> QuantumCircuit:\n",
        "    \"\"\"\n",
        "    Implements Deutsch's algorithm to determine whether a function f is constant or balanced.\n",
        "\n",
        "    Arguments:\n",
        "        function (QuantumCircuit): The function to evaluate.\n",
        "\n",
        "    Returns:\n",
        "        QuantumCircuit: The Deutsch algorithm circuit.\n",
        "    \"\"\"\n",
        "\n",
        "    qc = QuantumCircuit(2, 1)\n",
        "\n",
        "    # flipt the second qubit\n",
        "    qc.x(1)\n",
        "\n",
        "    # Apply Hadamard gates to both qubits\n",
        "    qc.h(range(2))\n",
        "\n",
        "    qc.barrier()  # for visual separation\n",
        "\n",
        "    # Combine the functions into a single circuit\n",
        "    qc.compose(function, range(2), inplace=True)\n",
        "\n",
        "    qc.barrier()  # for visual separation\n",
        "\n",
        "    # Apply Hadamard gates to qubit 0\n",
        "    qc.h(0)\n",
        "\n",
        "    qc.barrier()  # for visual separation\n",
        "\n",
        "    # # Measure the first qubit\n",
        "    qc.measure(0, 0)\n",
        "\n",
        "    return qc\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Run the simulation with Aer's qasm simulator the results  \n",
        "are returned from measuring the qubits.\n",
        "\n",
        "The possible results:\n",
        "\n",
        "- 0 - constant\n",
        "- 1 - balanced\n",
        "\n",
        "With real quantum computers the results are not always accurate\n",
        "due to noise and other factors.\n",
        "The values can be\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {},
      "outputs": [],
      "source": [
        "def simulate_deutsch_algorithm(deutsch_circuit: QuantumCircuit) -> Result:\n",
        "    \"\"\"\n",
        "    Aer simulation of Deutsch's algorithm.\n",
        "\n",
        "    Arguments:\n",
        "        deutsch_circuit (QuantumCircuit): The Deutsch algorithm circuit.\n",
        "\n",
        "    Returns:\n",
        "        Result: The simulation result.\n",
        "    \"\"\"\n",
        "\n",
        "    # Simulate the circuit\n",
        "    simulator = Aer.get_backend('qasm_simulator')\n",
        "\n",
        "    return simulator.run(deutsch_circuit).result()\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {},
      "outputs": [],
      "source": [
        "input_functions = [\n",
        "    constantCircuitA, constantCircuitB, balancedCircuitA, balancedCircuitB\n",
        "]\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {},
      "outputs": [],
      "source": [
        "circuits = [deutsch_algorithm_circuit(f) for f in input_functions]\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {},
      "outputs": [],
      "source": [
        "def count_to_type(count):\n",
        "    # Determine whether the function is constant or balanced\n",
        "    # if there are more 0s than 1s, the function is constant\n",
        "    if int(count.get(\"0\", 0)) > int(count.get(\"1\", 0)):\n",
        "        return \"constant\"  # Function is constant\n",
        "    else:\n",
        "        return \"balanced\"  # Function is balanced\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Below is all the diagrams for the 4 circuits and the results of the simulation.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 705.35x284.278 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 788.961x284.278 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 788.961x284.278 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAArMAAAELCAYAAADKlg6eAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/SrBM8AAAACXBIWXMAAA9hAAAPYQGoP6dpAAAxQklEQVR4nO3deVyVdd7/8fcBWQQRd0URccENR51SJ8tccsndbHKrJptM20xr5lb7VTM6d5ZLm1N2Z6a2mWW3WrllUzc6lalZJqVgiiIKgsmICIIInOv3B+MZEVAOHri4rvN6Ph4+8FznWj6H8/1evLn4Xt/jMAzDEAAAAGBBPmYXAAAAAFQUYRYAAACWRZgFAACAZRFmAQAAYFmEWQAAAFgWYRYAAACWRZgFAACAZRFmAQAAYFmEWQAAAFgWYRawsTlz5sjhcCg9Pd1j++zbt6/69u3rsf2ZZdu2bXI4HNq2bZtb27366qtq166dAgICNGfOnEqpzc6OHj0qX19fNWzYUOPHj9eZM2fMLgmAxRFmAaCcDh8+rGnTpikwMFCLFi3S7bffXuz5vn376t577y227PXXX9eYMWMUEREhh8NR4vmL5syZo8jIyArX9o9//EOTJk1Sp06d5Ovre8V9OZ1OLVy4UC1btlRgYKA6d+6sDz74oMQ6b7/9tkaOHKnmzZsrODhYnTp10ty5c3X+/Pkr1vLNN9/I4XCU+otUw4YNtXz5co0fP16rV6/WSy+9VOHXDAASYRYAyu3HH3+UJD377LN66KGH1Llz56tus2DBAsXExCg6Olo1atSotNpWrVqlVatWKTQ0VE2bNr3iuk899ZRmzZqlgQMH6tVXX1VERITuvPNOffjhh651cnJy9Mc//lGnTp3Sgw8+qEWLFqlHjx6aPXu2hgwZIsMwSt230+nUo48+quDg4FKfDw4O1r333qtXX31VUVFR2rt3b4VfMwBIUuWdWQHAZs6dOydJaty4cbm3+ec//+m6KlurVq3KKk3PPfec3nzzTfn5+Wn48OHat29fqeulpKToxRdf1COPPKLFixdLku6//3716dNHM2bM0JgxY+Tr6yt/f39t375dN954o2vbyZMnKzIyUrNnz9b//d//acCAASX2v3TpUh0/flz333+//v73v1+x5iZNmigrK+saXjUAcGUW8Arp6ekaO3asateurfr162v69Okl/lT81ltv6ZZbblGjRo0UEBCgjh076vXXX7/qvi9cuKC//vWvuv766xUaGqrg4GDdfPPN2rp1a7H1jh49KofDoRdeeEFLly5V69atFRAQoO7du2v37t0l9nvgwAGNHTtWDRs2VM2aNdWuXTs99dRTxdZJSUnRfffdp8aNGysgIEDR0dFasWJFiX0lJyfrtttuU3BwsBo1aqTHH39ceXl55fnWFXPxaqTD4Sj3Ni1atHBr/Uulp6frwIEDysnJueq6TZs2lZ+f31XX+/TTT5Wfn6+HH37YtczhcOihhx5ScnKyduzYIUny9/cvFmQvGj16tCQpPj6+xHOnT5/W008/rf/+7/9WnTp1rlqLj49PmVd4AaC8uDILeIGxY8cqMjJS8+bN086dO/XKK68oIyND7777rmud119/XdHR0Ro5cqRq1KihDRs26OGHH5bT6dQjjzxS5r7Pnj2rZcuWacKECZo8ebKysrK0fPly3Xrrrfruu+/UtWvXYuuvWrVKWVlZeuCBB+RwOLRw4ULdfvvtOnLkiCuM/fTTT7r55pvl5+enKVOmKDIyUocPH9aGDRv07LPPSpJOnjypG264QQ6HQ1OnTlXDhg312WefadKkSTp79qwee+wxSVJubq769++vY8eOadq0aWratKnee+89xcTEuP19dDqdkopCWFVYvHix/va3v2nr1q0eu+nuxx9/VHBwsDp06FBseY8ePVzP9+rVq8zt09LSJEkNGjQo8dxf/vIXNWnSRA888ICeeeaZq9bicDhUWFjoTvkAUJIBwLZmz55tSDJGjhxZbPnDDz9sSDJiY2Ndy3Jyckpsf+uttxqtWrUqtqxPnz5Gnz59XI8LCgqMvLy8YutkZGQYjRs3Nu677z7XssTEREOSUb9+feP06dOu5Z9++qkhydiwYYNrWe/evY2QkBAjKSmp2H6dTqfr/5MmTTLCwsKM9PT0YuuMHz/eCA0Ndb2eRYsWGZKMjz76yLXOuXPnjDZt2hiSjK1bt5Z43WV55plnDEnG4cOHy73NpYKDg42JEyeWe/2L7587NRqGYQwbNsxo0aJFmc9d/p4aRtH3RJLxxBNPXHHfAwYMMGrXrm1kZGQUWx4bG2v4+voan3/+ebHaT506Vea+Ro0aZbRp0+bKLwYAroJhBoAXuPzK6qOPPipJ2rx5s2tZzZo1Xf/PzMxUenq6+vTpoyNHjigzM7PMfV8cXykVXbk8ffq0CgoK1K1bN+3Zs6fE+uPGjVPdunVdj2+++WZJ0pEjRyRJp06d0ldffaX77rtPERERxba9+Od6wzC0du1ajRgxQoZhKD093fXv1ltvVWZmpuvYmzdvVlhYmO644w7XfoKCgjRlypQyX9Pl0tPT9fXXX2vZsmVq1aqVWrZsWe5tr8WcOXNkGIZHp0LLzc1VQEBAieWBgYGu58vy3HPP6csvv9T8+fNLDCOYNm2ahgwZokGDBpW7lj59+ighIUGLFy/W8ePHlZ+fX+5tAeAihhkAXiAqKqrY49atW8vHx0dHjx51Ldu+fbtmz56tHTt2lBijmZmZqdDQ0DL3/8477+jFF1/UgQMHigWS0kLf5QH1YrDNyMiQ9J9Q26lTpzKPd+rUKZ05c0ZLly7V0qVLS13n119/lSQlJSWpTZs2JcattmvXrsz9X65bt25KSkpSWFiYtmzZUuExsNVBzZo1Sx0vfHEM9aW/1Fxq9erVevrppzVp0iQ99NBDJZ779ttvy7zprCzTp0/Xjh079Oijj+rRRx/16HAKAN6DMAt4ocvD2OHDh9W/f3+1b99eL730kpo3by5/f39t3rxZL7/8smusaGlWrlype++9V7fddptmzJihRo0aydfXV/PmzdPhw4dLrO/r61vqfgw3bgS6WM/dd9+tiRMnlrpOeabNKq93331X+/bt01//+ldNnDhRe/bssWygDQsL09atW2UYRrHXkJqaKkmlTuv1xRdf6J577tGwYcO0ZMmSEs9fnAXB39/f9QvSxQ9DOH78uC5cuFDqft966y397//+r6ZOnapBgwapS5cuHniFALwNYRbwAocOHSp2lTQhIUFOp9M1sf6GDRuUl5en9evXF7tyevmMBKVZs2aNWrVqpXXr1hULR7Nnz65Qra1atZKkK17la9iwoUJCQlRYWFjq9FCXatGihfbt21civP3yyy/lrql3797q3bu3fv31V/3tb3/TkSNH1Lp163JvX5107dpVy5YtU3x8vDp27OhavmvXLtfzl9q1a5dGjx6tbt266aOPPip1rtzjx4+75rm93HXXXacuXbqUOp/s+vXr1bJlS7366qvX9qIAeDXGzAJe4LXXXiv2+GJ4GDJkiKT/XC299OpoZmam3nrrravuu7Rtd+3a5ZriyV0NGzZU7969tWLFCh07dqzYcxeP4evrq9///vdau3ZtqaH31KlTrv8PHTpUJ06c0Jo1a1zLcnJyyhyecCUXg35VfQSrO1NzldeoUaPk5+en//mf/3EtMwxDS5YsUbNmzYpNxxUfH69hw4YpMjJSGzduLHMIwscff1zi37hx4yQVXdV++eWXS93u7NmzCg8P99hrA+CduDILeIHExESNHDlSgwcP1o4dO7Ry5Urdeeedrj/rDho0SP7+/hoxYoQeeOABZWdn680331SjRo1cf34uy/Dhw7Vu3TqNHj1aw4YNU2JiopYsWaKOHTsqOzu7QvW+8sor6tWrl6677jpNmTJFLVu21NGjR7Vp0ybXFb758+dr69at+t3vfqfJkyerY8eOOn36tPbs2aMvv/xSp0+fllQ00f/ixYt1zz336IcfflBYWJjee+89BQUFuV3XxSm53BkSsWHDBsXGxkqS8vPz9dNPP2nu3LmSpJEjR15xOIQ7U3P99NNPWr9+vaSiK++ZmZmu43Tp0kUjRoyQJIWHh+uxxx7T888/r/z8fHXv3l2ffPKJvv76a73//vuuX06ysrJ06623KiMjQzNmzNCmTZuKHa9169bq2bOnJOm2224rUc/F92nIkCGlTuMlFX0fq2qaMwA2Zs4kCgCqwsXpkeLi4ow77rjDCAkJMerWrWtMnTrVyM3NLbbu+vXrjc6dOxuBgYFGZGSksWDBAmPFihWGJCMxMdG13uVTczmdTuO5554zWrRoYQQEBBi//e1vjY0bNxoTJ04sNj3Uxam5nn/++RJ1SjJmz55dbNm+ffuM0aNHG3Xq1DECAwONdu3aGX/5y1+KrXPy5EnjkUceMZo3b274+fkZTZo0Mfr3728sXbq02HpJSUnGyJEjjaCgIKNBgwbG9OnTjS1btrg97dW7775rSDK+/vrrcm8zceJEQ1Kp/956660rbuvO1FxvvfVWmce5fDqwwsJC13vm7+9vREdHGytXriy2zsX3q7z7LKv2K03N1aNHD6N///5XfW0AcCUOw+DjVwCgPGJiYtS/f39NmTJFTz75pBo2bFihK7zezOl06tSpU4qPj9fQoUM1ZswYvfPOO2aXBcDCCLMAUE75+fnq16+ftm/fLqnoJrc5c+aYW5TFHD161HUzYmhoqLZs2aIbbrjB5KoAWBlhFgDclJCQoJSUFDVv3tw1+wLK5/z58/r2228VGhqq6Oho14c1AEBFEWYBAABgWdxGCgAAAMsizAIAAMCyCLMAAACwLMIsAAAALIswCwAAAMsizAIAAMCyCLMAAACwLMIsAAAALIswCwAAAMsizAIAAMCyCLMAAACwLMIsAAAALIswCwAAAMsizAIAAMCyCLMAAACwLMIsAAAALIswCwAAAMsizAIAAMCyCLMAAACwLMIsAAAALIswCwAAAMsizAIAAMCyCLMAAACwLMIsAAAALIswCwAAAMsizAIAAMCyCLMAAACwLMIsAAAALIswCwAAAMuqYXYBAK7NgQMHyr3ur7/+qo8++khjx45Vo0aNyr1d+/btK1IaUCXoA97Nnfdfog3YEVdmAS9y6tQpvfbaazp16pTZpQCmoA+ANmA/hFkAAABYFmEWAAAAlkWYBQAAgGURZgEvEhoaqhEjRig0NNTsUgBT0AdAG7Afh2EYhtlFAKg4d+/krQju4kV1Rh/wblXx/ku0geqMK7OAF8nLy1NSUpLy8vLMLgUwBX0AtAH7IcwCXiQhIUGDBw9WQkKC2aUApqAPgDZgP4RZAAAAWBafAFYNGYZ0odDsKtzj7ys5HGZXAQD2wc8C72YYhnJycswuwy1BQUFymNAACLPV0IVCadZqs6twz4JxUgCtCQA8hp8F3i0nJ0e1atUyuwy3ZGdnKzg4uMqPyzADAAAAWBa/PwFeJDo6WvHx8WaXAZiGPgDagP1wZRYAAACWRZgFvEhiYqLGjx+vxMREs0sBTEEfAG3AfgizgBfJyclRbGys5e6QBTyFPgDagP0QZgEAAGBZhFkAAABYFmEWAAAAlkWYBbxIs2bNtGDBAjVr1szsUgBT0AdAG7Af5pkFvEidOnU0cuRIs8sATEMfAG3AfrgyC3iR06dP6/3339fp06fNLgUwBX0A3twGgoODFRERodatWys8PFx+fn5ubd+rVy8NGTKkkqqrOMIs4EVSU1M1d+5cpaamml0KYAr6ALypDQQFBem+++7TypUrFR8fr7NnzyopKUkJCQk6fvy4srKytHv3br3xxhsaMWKEfHzKjoW9evXSZ599po8//rjaBVrbh9n09HTNnDlTbdq0UWBgoJo3b67p06fr3LlzmjRpkhwOhxYvXmx2mQAAAB4RERGhRYsW6cSJE1q+fLnuuusutW/fvkRYDQgIULdu3TRlyhStX79eR44c0f/7f/9PtWrVKrbexSBbq1YtBQQEaPLkyVX5cq7K1mF27969+s1vfqPnn39eaWlp6tixo/Lz8/XKK69o3Lhxrs9m7tq1q7mFVpLkuG36+90O/bDphTLX+fvdDn36wvAqrAqoeufzpe0HpXe/kd7cVvR1R4KUV2B2ZUDl42eBd3nggQe0b98+TZ8+XaGhoa7leXl52r17t1avXq2VK1dq7dq1iouLk9PpdK3TokULPffcc/r555/Vr18/ScWDrCR99tlnmjBhQtW+qKuw7Q1g6enpGjFihNLS0vTnP/9Zs2fPVkhIiCRp4cKFmjVrlmrUqCGHw6HOnTubXC2AylDolDbFFgXZy4PrniTp0z3SzW2lwZ0lX1v/ag/A7urUqaPVq1dr0KBBrmU5OTlatWqVli9frh9++EH5+fkltqtVq5b69OmjBx98UEOHDpWPj48iIyMVExOjjz76SEOHDi0WZEePHq28vLwqe13lYdvT97Rp05ScnKypU6fqhRdecAVZSZo5c6a6dOmigoICRUZGqnbt2iZWClSd4OBg3XTTTQoODja7lEpXUCgt/6cUE1f2Fdjz+dIX+6W3vy4KvrA/b+oDKJ0d20D9+vW1devWYkF26dKlCg8P1+TJk7Vz585Sg6wkZWdna9OmTRoxYoTatWunrVu3up4bO3ZstQ+ykk3DbHx8vFavXq0GDRpo3rx5pa5z/fXXS5K6dOlSbHliYqJGjhypkJAQ1a1bV/fcc4/+9a9/VXrNQFWIjIzUsmXLFBkZaXYple6TPVLcifKt+3OytOHHyq0H1YM39QGUzm5tICgoSJ999plryOSvv/6qQYMG6YEHHlBGRoZb+0pISFD//v21aNEiGYbhWn78+PFqG2Qlmw4z+OCDD+R0OnXXXXeVGMR8Uc2aNSUVD7NZWVnq16+f6tWrpw8++EC5ubmaOXOmhg8fru3bt1/xLr/qrOBCjnKz0s0uA9VAYWGhcnNzVbNmTfn6+ppdTqXJyi0aE+uObw5JAztJwQGVUxOqB2/pA6XhZ0ERu7WBefPmqXv37pKkEydOqG/fvjp06FCF93fTTTfp/vvvl8PhcC1r3ry5Ro8erQ8//PCa660MtgyzMTExkuQavFya5ORkScXD7NKlS5WSkqKvvvpKERERkqTw8HDdeOONWr9+vW677bbKK7oS7Vw7WzvXzja7DFQDBw4c0B133KE1a9YoOjra7HIqzc7D7g8bKCiUvjsi9etQOTWhevCWPlAafhYUsVMb6N27t6ZNmyapaHzsoEGDrinIXn6zV2xsrCsnLV68WDExMfr111+vvXAPs2WYTUpKklR0V15pCgoKtH37dknFw+zGjRvVq1cvV5CVpJ49e6pVq1basGGDZcNsp35TFPW7MaU+9/H8gVVcDVD54ss5vKC07QizsCt+FtiLw+HQkiVLXI+ffPJJ7d+/v8L7K23WgtGjR+udd97RuHHjVL9+fc2fP1/33XffNdfuabYMs+fOnZMk5ebmlvr86tWrlZ6erpCQELVs2dK1PC4uTmPGlOzo0dHRiouLq3A93bp1U1paWrnX9/WrqdFzK/6b1eXqNIlSRKcBHttfadpGRakwv/TvNyrXvffeW+51L04SvnnzZv34Y/kHib799ttuVmWuAY99oTph7qfSnbv36rmJTE9kNXbtA/wsKB933n/JOm3g0imzStO/f3916FB0ntu5c6deeeWVCh+rrCCbl5enqVOnauDAgapXr57uvPNOzZgxo8x7iaKioio8JLNJkyb6/vvvK7StLcNskyZNlJGRoT179qhnz57FnktNTdWMGTMkSZ07dy42JiQjI0N16tQpsb969erpl19+qXA9aWlpSklJKff6NQKCKnwss5xIPaGCvByzy/BKOTnl/76fP3/e9dWd7dxpv9VBbvYZ1anAdjnZZyz3WmHfPsDPgvJx532UrNUGruSRRx5x/X/hwoXFbthyx5WCrFQ01eny5cs1Y8YMBQQEaNKkSVq4cGGp+zLrU9VsGWYHDBig+Ph4LViwQAMHDlTbtm0lSbt379Yf/vAHpacXDYCvqg9LaNKkiVvr+/rVrKRKKk/TsKZcmTVJUFD5f+AFBga6vrqzXbNmzdyuy0zZJ+OkqJ5XX/Ey507GW+61wr59gJ8F5ePO+yhZpw04nc4yw2GtWrU0YsQISUX3AK1fv75Cx7hakL1oyZIlrguBEyZMKDPMhoWFXdOV2YqyZZidOXOmVq1apePHjys6Olrt27fX+fPnlZCQoCFDhigyMlKff/55iWm56tatqzNnzpTY3+nTp1WvXr0K1+PuZfO8AmnW6gofzhQHDx1SgC1bU/V34MCBcq+bn5+vSZMmKSQkRH5+fuXebu7cuRUpzTRpmdL8je5t45D03ksPqcGbD1VKTag8du0D/CwoH3fef8k6beDcuXNlzsj029/+1jUTw8aNG1VYWOj2/ssbZCXpyJEj+umnn9S5c2d16tRJgYGBrivclzp06JAp8/dac66pqwgPD9fXX3+tYcOGKTAwUEePHlW9evX0xhtvaNOmTTp48KCkknPMdujQodSxsXFxca5xKYCV+fn5qV69em6dwK2oSajUPsy9baLDpQYhV18P1uYtfQBls0MbuDhXviT98MMPbm/vTpC9/Dg1atSodp+casswKxUF040bNyorK0tZWVnatWuXpkyZonPnzuno0aPy8fFRp06dim0zfPhwffPNN65puyRp165dOnz4sOtyPmBlx44d08MPP6xjx46ZXUqlu+vG8ofTRrWlCTdUbj2oHrypD6B0dmgD7du3d/0/NjbWrW0rEmQlae/eva7/V7cLfLYNs2XZv3+/DMNQVFRUibEyU6ZMUVhYmEaNGqWNGzdqzZo1mjBhgnr06KFRo0aZVHHFhXfsq+krDV0/7L/KXGf6SkOj/svNv8fCsrKysrR161ZlZWWZXUqlCwmUpg+UWjW88npRjaVpA/mwBG/hTX3gIn4WFGeHNpCZmamkpCSdPHnSrU8p7dmzZ4WCrCSdPHlSqampSkxMrHafBOZ1oxx//vlnSSWHGEhS7dq1FRMTo+nTp2v8+PGqUaOGhg8frpdfftmyn/4FeLOQmtK0QdKxf0nfHJR2J0qGITkc0u9aSTdFSc3rm10lALhn1qxZmjVrltvbHTt2TKmpqYqKinIryEpF05quXl09B3ETZi/TunVrbdzoHb+dAt4ior50Z0/pl1QpM1eqHSiNZ1gBAC+TkpKifv366amnntLjjz9e7a6wVhRhFgAAwEukpKTo4YcfNrsMj/K6MBsTE2N2CYBpGjdurFmzZqlx48ZmlwKYgj4A2oD9eF2YBbxZgwYN3P7oR8BO6AOgDdgPdzUBXiQzM1NbtmxRZmam2aUApqAPgDZgP4RZwIskJyfr8ccfLzaXMuBN6AOgDdgPYRYAAACWRZgFAACAZRFmAQAAYFmEWcCLBAYGqkOHDgoMDDS7FMAU9AHQBuyHqbkAL9K6dWutW7fO7DIA09AHQBuwH67MAgAAwLIIs4AXiYuLU+fOnRUXF2d2KYAp6AOgDdgPYRbwIoZhKD8/X4ZhmF0KYAr6AGgD9kOYBQAAgGVxA1g15O8rLRhndhXu8fc1uwIAsBd+Fni3oKAgZWdne2x/z7/xoc6ey1Ht4CDNeGB8iceeEBQU5JH9uIswWw05HFIA7wwAeDV+Fng3h8Oh4OBgj+3PPyBQ/vmF8g8IVHBwcInHVkY3AbxI69attX79ejVv3tzsUgBT0AdAG7AfwizgRQIDAxUVFWV2GYBp6AOgDdgPN4ABXiQlJUVPP/20UlJSzC4FMAV9ALQB+yHMAl7kzJkzWrt2rc6cOWN2KYAp6AOgDdgPYRYAAACWRZgFAACAZRFmAQAAYFmEWcCLNGjQQJMnT1aDBg3MLgUwBX0AtAH7IcwCXsThcMjf318Oh8PsUgBT0AdAG7AfwizgRU6dOqXXXntNp06dMrsUwBT0AdAG7IcwCwAAAMsizAIAAMCyCLMAAACwLMIs4EVCQ0M1YsQIhYaGml0KYAr6AGgD9lPD7AIAVJ3w8HAtXLjQ7DIA09AHQBuwH67MAl4kLy9PSUlJysvLM7sUwBT0AdAG7IcwC3iRhIQEDR48WAkJCWaXApiCPgDagP0wzKAaMgxDOc5Cs8twS5CPr0cnoDYM6YK1vgXy95WYgxuewnkAAMqHMFsN5TgLVTfmC7PLcEvGLQMV7Ou55nShUJq12mO7qxILxkkB9Ch4COcBACgfhhkAAADAsgizAAAAsCz+HgR4kejoaMXHx5tdBmAa+gBoA/bDlVkAAABYFmEW8CKJiYkaP368EhMTzS7FFIZR/Cu8j7f3AdAG7IhhBoAXycnJUWxsrHJycswupdIZhpTwq3QwVTp+uujfuX/PkX72vPT0Gim8ntS8ntS+qdSqIVOreQNv6gMoHW3AfgizAGwlr0DadVjaflA6ebbs9bLzpAOpRf++2C81CZV6tZV6tJL8OTMCgGVwygZgGwknpQ92Sv/Kdn/btExpzW7pnwekO3tKLRt6vj4AgOcRZgFYntMpffpjURC9VqeypFf+IfXrKA3vKvkw9AAAqjXCLOBFmjVrpgULFqhZs2Zml+IxhU7p3e1S7DHP7dOQFBMnZeYUXaX15VZZ27BjH4B7aAP2Q5gFvEidOnU0cuRIs8vwGMOQVu3wbJC91A9Hi4LshBu4Ocwu7NYH4D7agP1wvQHwIqdPn9b777+v06dPm12KR3x7qChwVqbvjhT9gz3YrQ/AfbQB+yHMAl4kNTVVc+fOVWpqqtmlXLN/ZUvrf3Rvmz8NluaMLvrqjo9/kM4wi48t2KkPoGJoA/bjFWE2PT1dM2fOVJs2bRQYGKjmzZtr+vTpOnfunCZNmiSHw6HFixebXWalKFzxtvIHDZVzyz9KPGcYhgr+a5byh42UkXi06ourAslx2/T3ux36YdMLZa7z97sd+vSF4VVYFTxh3fdF03C5o3ZNqU5Q0Vd3nM8vCrRW5O3nAAD2Z/sxs3v37tWQIUOUlpam4OBgdezYUSdOnNArr7yiw4cPu/7M0LVrV3MLrSQ+f7hLzp27VPjGm3Jcf50cDRu4nnOu+0TGTz/L57575WgZaV6RgJtOZUn7U6r2mD8dlzLOSXWDq/a414pzAAC7s/WV2fT0dI0YMUJpaWn685//rNTUVO3Zs0dpaWlasGCBNm3apN27d8vhcKhz585ml1spHH5+qjHjz9L58yp8aZFruXE8Wc6335WjfTv5jPm9eQUCFfDtoao/pmGYc9xrxTkAgN3ZOsxOmzZNycnJmjp1ql544QWFhIS4nps5c6a6dOmigoICRUZGqnbt2iZWWrkcUW3kM36sjB/2yLnpMxmFhSpc+IJkGPKd8Wc5fH3NLhFVJDg4WDfddJOCgy12efEShiHtNukj1c067rXiHPAfdugDuDa0Afux7TCD+Ph4rV69Wg0aNNC8efNKXef6669XbGysunTp4lqWnJys+fPn67vvvlNsbKwuXLggwzCqquxK43PXBDl37FLhm8vkc/iIjF8OymfK/XI0Dze7tCpRcCFHuVnpZpdhusjISC1btszsMq5Jxjkp+7w5xz6TI53NdX/MbXXg7eeAi+zQB3BtaAP2Y9sw+8EHH8jpdOquu+5SrVq1Sl2nZs2in0iXhtmEhAStXbtW3bt3l7+/v7Zv314l9VY2R40aqjHjTyp49DE5N26So1O0fG6/zeyyqszOtbO1c+1ss8swXWFhoXJzc1WzZk35WvRq3HGTZ9M5flqKtuBc695+DrjIDn0A14Y2YD+2HWYQExMjSerXr1+Z6yQnJ0sqHmZ79+6t1NRUrV+/XgMGDKjcIqtacLDk5ydJcnTvJoePbd/+Ejr1m6LRT3xR6j9vcuDAAXXv3l0HDnjgc19Nkppp7vHTzph7/GvixeeAi+zQB3BtaAP2Y9srs0lJSZKkFi1alPp8QUGB66rrpWHWpxJO7t26dVNaWlq51zf8/aU3XvNoDYZhqPDFl6WCfCmiuZyrPpRPn95yNA3zyP7bRrWV48IFj+xLknz9amr0XM/dbVOnSZQiOlXuLydto6JUmJ9bqccozb333lvudS/Oq7h582b9+GP5J2l9++233ayq8vxmyFNq1/ehUp/70+ArDwGoHfifr3NGX/k4Z3Oll7aUXL7ghUWa+EXZU715iqfPA5V9DpA8fx4oL2/rAyjOnfdf8t42MPqPjym4Vm2lpqUqPDy8xGOzNWnSRN9//32FtrVtmD137pwkKTe39HCxevVqpaenKyQkRC1btqzUWtLS0pSS4sY8QoEB8vNwDc5P1suI/Uk+f5won543qOCRR1X44svyfWGBHB74nM4TqSek83keqLRIjYAgj+2rqpxIPaGCvKqfWT8np/zHPH/+vOurO9u51X4rWWTW2TKfuziP7NX4+JRvvdJknc2smu+Hh88DlX0OkDx/Higvb+sDKM6d91Hy3jbgLCx0fU1JSSnx2MpsG2abNGmijIwM7dmzRz179iz2XGpqqmbMmCFJ6ty5s8dO5FeqxR2Gv79OefD4RkqKnCvelqNdW/mMvUMOX1/53H2XnG+9I+cn6+U7etQ1H6NpWFOPX5m1mqZhTU25MhsUVP5UFhgY6PrqznbNmlWfQaI1A8r+68nZq3z7awcWBVmnUzp7lZvIytpXzcAaVfL98OR5oCrOAZLnzwPl5W19AMW58z5K3tsGfP49PtjH11fNmjUr8dhs7malS9k2zA4YMEDx8fFasGCBBg4cqLZt20qSdu/erT/84Q9KTy+6s70qPizB3cvm5woLVDfGM2M5DadThc+/JDmd8p3xJ9cUPD5j75Cx/Vs5V7wtn9/1uOY/NR48dFDBvp5rTnkF0qzVHttdlTh46JACTOhR7oz72r9/v1asWKGhQ4cqOjq63NvNnTu3IqVVithj0ltfl/5cacMCLjVndNEV2bPnpTkfV+z4ixc+pY7NnqrYxm7w1Hmgqs4BkufPA+XlbX0Axbk79tVb28Bzr72vs9nnFNYkTMnJySUeW5ltR//PnDlT9evX1/HjxxUdHa3f/OY3ioqKUo8ePdSqVSvdcsstkoqPl7Uj55p1MuLi5TPxbjkiIlzLHb6+8v2vP0nOQhW++LItph/D1bVt21bbt293/XJnRc3reffx3cU5oDg79AFcG9qA/dg2zIaHh+vrr7/WsGHDFBgYqKNHj6pevXp64403tGnTJh08eFCSvcOsceyYnO+8J0eH9vL5/e0lnndEtpDP3XfJ+HmfnJ+sN6FCVDU/Pz/Vq1dPfn6eHpVddeoGSyGBJh07SAqx0AgYzgEl2aEP4NrQBuzHtsMMJKlDhw7auHFjieXZ2dk6evSofHx81KlTJxMqqxqOiAj5bfr0iuv4Thgn3wnjqqiiqhfesa+mr7zyFaerPW8nx44d0/z58/XEE08o4pKrdFbicEjdW0ox8VV/7O6tqv6Y14JzQEl26AO4NrQB+7Htldkr2b9/vwzDUFRUVKmDv9esWaM1a9YoLi6u2OOKThkBVBdZWVnaunWrsrKyzC7lmtwYJVXubZslORxSzzZVfFB4nF36ACqONmA/tr4yW5aff/5ZUtlDDMaMGVPq44kTJ1p+njnADhqESNHh0r4qvGehS/OiIQ4AgOqFMFsKb7kRArCy33eTDqUVzXxR2Wr6S6Ovr/zjAADc55XDDK4WZgFUf3WDpdvcDJhnc6UzOVefj/Zyt18vhVrvczwAwCt45ZXZmJgYs0sATNG4cWPNmjVLjRs3NrsUj7ihtXTklLT7SPnWv9o8tKXp2UbqVrkfEogqZLc+APfRBuzHK8Ms4K0aNGjg9ueYV2cOhzT+d1JBofRjkuf3372lNKZ70XFgD3brA3AfbcB+vHKYAeCtMjMztWXLFmVmZppdisf4+kh/uFG6pYPnZjhwOKSB0dKEnkUffwv7sGMfgHtoA/bDaRrwIsnJyXr88cct/9GFl/PxkUZeJz06UGoYcm37alxbmj5IGtZV8uGKrO3YtQ+g/GgD9sMwAwC20aqRNGOotDtR+uaglHqm/Ns2qyv1als0PtbPt9JKBAB4GGEWgK3415BuipJubCMlnpJ+SZOST0vHT0tZuZKhouEItWtK4fWk5vWk9k2lFvUZGwsAVkSYBWBLDkfRldpWjf6zzDAkp1E0fIDgCgD2QJgFvEhgYKA6dOigwMBAs0sxhcMh+RJivZq39wHQBuyIMAt4kdatW2vdunVmlwGYhj4A2oD9MJsBAAAALIswC3iRuLg4de7cWXFxcWaXApiCPgDagP0QZgEvYhiG8vPzZRiG2aUApqAPgDZgP4yZrYaCfHyVcctAs8twS5CPZyfm9PeVFozz6C4rnT9zk8KDOA8AQPkQZqshh8OhYF/vfmscDinAu78F8HKcBwCgfBhmAAAAAMvi137Ai7Ru3Vrr169X8+bNzS4FMAV9ALQB+yHMAl4kMDBQUVFRZpcBmIY+ANqA/TDMAPAiKSkpevrpp5WSkmJ2KYAp6AOgDdgPYRbwImfOnNHatWt15swZs0sBTEEfAG3AfgizAAAAsCzCLAAAACyLMAsAAADLYjYDwOLat29f7nVDQ0M1e/Zs3XjjjQoLC6vEqoCqQx/wbu68/xJtwI4Is4AXCQsL05w5c8wuAzANfQC0AfthmAEAAAAsizALAAAAyyLMAgAAwLIIswAAALAswiwAAAAsizALAAAAyyLMAgAAwLIIswAAALAswiwAAAAsizALAAAAyyLMAgAAwLIIs9XEV199pVGjRqlFixZyOByaO3eu2SUBAACUafPmzeratasCAgIUGRmpl156yZQ6CLPVRHZ2tjp27KiFCxeqSZMmZpcDAABQpu+//16jRo3SkCFDtHfvXs2ZM0dPPvmklixZUuW11KjyI6JUQ4cO1dChQyVJs2bNMrkaAACAsr300kvq3r275s2bJ0nq0KGD9u/fr/nz5+vBBx+s0lq4MgsAAAC3bN++XYMHDy62bPDgwUpKSlJycnKV1sKVWQAAABs5cuyECgqdxZYVFBa6vh5MTC7x+FK1gmuqaaP6VzxGampqiWGRFx+npqYqPDz8ml6DOwizAAAANpKSlq5NW3eW+lxO7nmt+GhzmY8dkh64a2Rll+hRDDMAAACwkZu6/0atIsIqtG2fG7oqMvzqN6KHhYUpLS2t2LKTJ0+6nqtKhFkAAAAb8XE4NGZoXwX4+7m1XVij+hrQ6/pyrXvTTTfp888/L7Zsy5YtatGiRZUOMZAIs9VGdna29u7dq7179+rChQtKS0vT3r17lZCQYHZpAADAYuqGhmjkwJvKvb6vr4/GDe+nGr6+5Vr/8ccf13fffaennnpKBw4c0DvvvKNXX31VTzzxREVLrjCHYRhGlR8VJWzbtk39+vUrsbxPnz7atm1b1RcEAAAszTAMvf/Jl9p3MPGq6w7td4N69+js1v43bdqkJ598UgcOHFCTJk00ffp0/elPf6pouRVGmAUAALCpcznn9fKK/1X2udwy12kVEab7xw+Xj8NRhZV5DsMMLCbxeKry8wvMLgMAAFhAcFCg7hjSp8znA/z9NGZoX8sGWYkwaylZ2Tla/tFmLVz6oTLPZptdDgAAsID2rSP0u64dSn1u5MCbVDc0pIor8izC7CUKCwv13nvvadCgQWrYsKECAgIUERGhwYMHa9myZSr89wTDZvnnrlgVFBSqbu0Q1Q4JNrUWAABgHUP73aD6dWsXWxbdNlLXRUeZVJHnEGb/7ezZsxo4cKDuueceffHFF/L391eXLl3kdDr1j3/8Q5MnT1ZWVpZp9WVl52jn3jhJ0oBe18th4T8HAACAqhXg76dxw/q58kOt4Jq6/dbetsgThNl/mzRpkrZu3arw8HDFxMQoJSVF3333nZKTk5Wamqpnn31Wfn7uzdfmSRevykY0bayoyGam1QEAAKwpollj9buhqyTpjiF9FBwUaG5BHsJsBpJ++OEHdevWTTVq1NCPP/6oTp06eXT/r76zTlnZZd9FeDWGYSjrXI4kKahmYLnngAMAALiUYRjKzy+Qv5sfqFDZQmrV1KMTb6/QtjU8XIslffLJJ5KkYcOGeTzISlJWdq7OZp/zyL5ycs97ZD8AAMB7nb9wwewSPIYwKykurmgsas+ePStl/yG1alZ4W67KAgAAu7uWrESYVdHNX5IUGhpaKfuv6GVzSdr4fzv0zfc/K6JpYz1090hbDNQGAADwFMKspNq1i6aqyMzMrJT9V3TM7KVXZdMzMjXvf1Z5ujQAAADTMWb2GkVHR2vdunXasWNHpezfE2NmGSsLAABQEmFW0ujRo/XMM89o8+bNiouLU8eOHT26/4qMA2GsLAAA8BbXMmaWqbn+bdy4cfroo48UERGhd999V336/OdzjE+ePKkVK1Zo2rRpCg6umk/eYqwsAADA1RFm/+3s2bMaNWqUtm3bJklq1qyZmjZtqtTUVKWkpMgwDGVkZKhOnTqVXktWdo4WvPGBCgoKdd/YoWrbMrzSjwkAAGBFfALYv9WuXVtffvmlli9frr59+yonJ0exsbHy8fHRrbfequXLlyskJKRKauHTvgAAAMqHK7PV0Lade7Vt517dOWoAV2UBAACugDBbTZ3Pu6AAfz/GygIAAFwBYRYAAACWxZhZAAAAWBZhFgAAAJZFmAUAAIBlEWYBAABgWYRZAAAAWBZhFgAAAJZFmAUAAIBlEWYBAABgWYRZAAAAWBZhFgAAAJZFmAUAAIBlEWYBAABgWYRZAAAAWBZhFgAAAJZFmAUAAIBlEWYBAABgWYRZAAAAWBZhFgAAAJZFmAUAAIBlEWYBAABgWYRZAAAAWBZhFgAAAJZFmAUAAIBlEWYBAABgWYRZAAAAWBZhFgAAAJZFmAUAAIBlEWYBAABgWYRZAAAAWBZhFgAAAJZFmAUAAIBlEWYBAABgWYRZAAAAWBZhFgAAAJZFmAUAAIBlEWYBAABgWYRZAAAAWBZhFgAAAJZFmAUAAIBl/X/XKuGfMiWKcwAAAABJRU5ErkJggg==",
            "text/plain": [
              "<Figure size 872.572x284.278 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "for circuit in circuits:\n",
        "    # Create a figure\n",
        "    fig = plt.figure(circuit.draw(output='mpl'))\n",
        "    # Determine whether the circuit is constant or balanced\n",
        "    state = simulate_deutsch_algorithm(circuit)\n",
        "    count = state.get_counts()\n",
        "\n",
        "    # Add the title to the figure\n",
        "    fig.suptitle(count_to_type(count) + \" \" + str(count))\n",
        "\n",
        "    # Show the figure\n",
        "    plt.show()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "As you can see above the results are perfect which is not realistic to quantum computers.  \n",
        "Next up is the results from a real quantum computer.  \n",
        "Where the results are not perfect.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Real Hardware\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Run the simulation on real quantum computers and compare the results. [[3]](#3)\n",
        "\n",
        "The results are not always accurate due to noise and other factors.  \n",
        "This gives a real world usecase of how a quantumn computer would perform.\n",
        "\n",
        "I went with ibm_lagos which has 7 qubits (which is more than enough for the algorithm) and would be the cheapest to run in terms of time usage. [[4]](#4)\n",
        "\n",
        "![Quantum Hardware](imgs/QuantumHardware.png)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Below the connection to the quantum computer is made and the circuit is sent to the quantum computer to be run.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "job id: cna3n8dyzmv0008w8zxg\n"
          ]
        }
      ],
      "source": [
        "from qiskit_ibm_runtime import QiskitRuntimeService, Sampler\n",
        "\n",
        "# Create a runtime program from my saved credentials\n",
        "service = QiskitRuntimeService()\n",
        "backend = service.backend(\"ibm_lagos\")\n",
        "\n",
        "# Run circuits on the real quantum system\n",
        "job = Sampler(backend).run(circuits=circuits)\n",
        "print(f\"job id: {job.job_id()}\")\n",
        "quantumResult = job.result()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Render out the results from the quantum computer and print out the value to show the noise."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "{0: 1.002514367816092, 1: -0.002514367816092}\n"
          ]
        },
        {
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAiMAAAGdCAYAAADAAnMpAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/SrBM8AAAACXBIWXMAAA9hAAAPYQGoP6dpAAAhj0lEQVR4nO3df1DUdeLH8RegLJou2KCLGoWWaZaiaexhOX6bNtEcq7luIuuUGLWrc8qirqAUMu9CS82Zorg8f3RzZ2pNmXN6mHF5XUVyod5ZamVqYrUoOrKIBcm+v380brcJyCL4duH5mNlJPrw/n32//Qg8290PG2GMMQIAALAk0vYEAABAx0aMAAAAq4gRAABgFTECAACsIkYAAIBVxAgAALCKGAEAAFYRIwAAwKpOtifQHH6/X9988426d++uiIgI29MBAADNYIxRdXW1+vTpo8jIxh//CIsY+eabb5SYmGh7GgAAoAXKy8t10UUXNfr5sIiR7t27S/pxMU6n0/JsAABAc/h8PiUmJgZ+jjcmLGLk1FMzTqeTGAEAIMyc6SUWvIAVAABYRYwAAACriBEAAGAVMQIAAKwiRgAAgFXECAAAsIoYAQAAVhEjAADAKmIEAABYRYwAAACrQo6R9957TxMnTlSfPn0UERGhtWvXnnGfzZs36+qrr5bD4dBll12mFStWtGCqAACgPQo5RmpqapScnKyCgoJmjd+3b58mTJig66+/Xtu3b9eDDz6oadOmaePGjSFPFgAAtD8hv1He+PHjNX78+GaPLywsVL9+/bRw4UJJ0hVXXKH3339fzz33nNLS0kK9ewAA0M60+bv2lpSUyOPxBG1LS0vTgw8+2Og+tbW1qq2tDXzs8/naanpKyl7fZscG2oP98ybYngKAdq7NX8Dq9XrlcrmCtrlcLvl8Pn333XcN7pOfn6/Y2NjALTExsa2nCQAALDkvr6bJyclRVVVV4FZeXm57SgAAoI20+dM0CQkJqqioCNpWUVEhp9OpLl26NLiPw+GQw+Fo66kBAIDzQJs/MpKamqri4uKgbZs2bVJqampb3zUAAAgDIcfI8ePHtX37dm3fvl3Sj5fubt++XQcOHJD041MsU6ZMCYy/9957tXfvXj366KPavXu3XnzxRa1Zs0YPPfRQ66wAAACEtZBj5OOPP9bw4cM1fPhwSVJWVpaGDx+u3NxcSdK3334bCBNJ6tevn9avX69NmzYpOTlZCxcu1J/+9Ccu6wUAAJKkCGOMsT2JM/H5fIqNjVVVVZWcTmerHptLe4GmcWkvgJZq7s/v8/JqGgAA0HEQIwAAwCpiBAAAWEWMAAAAq4gRAABgFTECAACsIkYAAIBVxAgAALCKGAEAAFYRIwAAwCpiBAAAWEWMAAAAq4gRAABgFTECAACsIkYAAIBVxAgAALCKGAEAAFYRIwAAwCpiBAAAWEWMAAAAq4gRAABgFTECAACsIkYAAIBVxAgAALCKGAEAAFYRIwAAwCpiBAAAWEWMAAAAq4gRAABgFTECAACsIkYAAIBVxAgAALCKGAEAAFYRIwAAwCpiBAAAWEWMAAAAq4gRAABgFTECAACsIkYAAIBVxAgAALCKGAEAAFYRIwAAwCpiBAAAWEWMAAAAq4gRAABgFTECAACsIkYAAIBVxAgAALCKGAEAAFYRIwAAwCpiBAAAWEWMAAAAq4gRAABgFTECAACsIkYAAIBVxAgAALCqRTFSUFCgpKQkxcTEyO12q7S0tMnxixcv1sCBA9WlSxclJibqoYce0vfff9+iCQMAgPYl5BhZvXq1srKylJeXp61btyo5OVlpaWk6dOhQg+NXrlyp7Oxs5eXladeuXVq6dKlWr16txx9//KwnDwAAwl/IMbJo0SJNnz5dmZmZGjx4sAoLC9W1a1ctW7aswfEffvihrr32Wt15551KSkrS2LFjNWnSpDM+mgIAADqGkGKkrq5OZWVl8ng8Px0gMlIej0clJSUN7jNq1CiVlZUF4mPv3r3asGGDbrrppkbvp7a2Vj6fL+gGAADap06hDK6srFR9fb1cLlfQdpfLpd27dze4z5133qnKykpdd911Msbo5MmTuvfee5t8miY/P19z5swJZWoAACBMtfnVNJs3b9bTTz+tF198UVu3btUbb7yh9evXa+7cuY3uk5OTo6qqqsCtvLy8racJAAAsCemRkfj4eEVFRamioiJoe0VFhRISEhrcZ/bs2Zo8ebKmTZsmSRoyZIhqamp0zz336IknnlBk5Ok95HA45HA4QpkaAAAIUyE9MhIdHa0RI0aouLg4sM3v96u4uFipqakN7nPixInTgiMqKkqSZIwJdb4AAKCdCemREUnKyspSRkaGRo4cqZSUFC1evFg1NTXKzMyUJE2ZMkV9+/ZVfn6+JGnixIlatGiRhg8fLrfbrT179mj27NmaOHFiIEoAAEDHFXKMpKen6/Dhw8rNzZXX69WwYcNUVFQUeFHrgQMHgh4JmTVrliIiIjRr1ix9/fXX6tmzpyZOnKg//OEPrbcKAAAQtiJMGDxX4vP5FBsbq6qqKjmdzlY9dlL2+lY9HtDe7J83wfYUAISp5v785r1pAACAVcQIAACwihgBAABWESMAAMAqYgQAAFhFjAAAAKuIEQAAYBUxAgAArCJGAACAVcQIAACwihgBAABWESMAAMAqYgQAAFhFjAAAAKuIEQAAYBUxAgAArCJGAACAVcQIAACwihgBAABWESMAAMAqYgQAAFhFjAAAAKuIEQAAYBUxAgAArCJGAACAVcQIAACwihgBAABWESMAAMAqYgQAAFhFjAAAAKuIEQAAYBUxAgAArCJGAACAVcQIAACwihgBAABWESMAAMAqYgQAAFhFjAAAAKuIEQAAYBUxAgAArCJGAACAVcQIAACwihgBAABWESMAAMAqYgQAAFhFjAAAAKuIEQAAYBUxAgAArCJGAACAVcQIAACwihgBAABWESMAAMAqYgQAAFhFjAAAAKuIEQAAYBUxAgAArGpRjBQUFCgpKUkxMTFyu90qLS1tcvyxY8c0Y8YM9e7dWw6HQ5dffrk2bNjQogkDAID2pVOoO6xevVpZWVkqLCyU2+3W4sWLlZaWps8++0y9evU6bXxdXZ1uvPFG9erVS6+//rr69u2rr776SnFxca0xfwAAEOZCjpFFixZp+vTpyszMlCQVFhZq/fr1WrZsmbKzs08bv2zZMh09elQffvihOnfuLElKSko6u1kDAIB2I6Snaerq6lRWViaPx/PTASIj5fF4VFJS0uA+69atU2pqqmbMmCGXy6WrrrpKTz/9tOrr6xu9n9raWvl8vqAbAABon0KKkcrKStXX18vlcgVtd7lc8nq9De6zd+9evf7666qvr9eGDRs0e/ZsLVy4UL///e8bvZ/8/HzFxsYGbomJiaFMEwAAhJE2v5rG7/erV69eevnllzVixAilp6friSeeUGFhYaP75OTkqKqqKnArLy9v62kCAABLQnrNSHx8vKKiolRRURG0vaKiQgkJCQ3u07t3b3Xu3FlRUVGBbVdccYW8Xq/q6uoUHR192j4Oh0MOhyOUqQEAgDAV0iMj0dHRGjFihIqLiwPb/H6/iouLlZqa2uA+1157rfbs2SO/3x/Y9vnnn6t3794NhggAAOhYQn6aJisrS0uWLNErr7yiXbt26b777lNNTU3g6popU6YoJycnMP6+++7T0aNHNXPmTH3++edav369nn76ac2YMaP1VgEAAMJWyJf2pqen6/Dhw8rNzZXX69WwYcNUVFQUeFHrgQMHFBn5U+MkJiZq48aNeuihhzR06FD17dtXM2fO1GOPPdZ6qwAAAGErwhhjbE/iTHw+n2JjY1VVVSWn09mqx07KXt+qxwPam/3zJtieAoAw1dyf37w3DQAAsIoYAQAAVhEjAADAKmIEAABYRYwAAACriBEAAGAVMQIAAKwiRgAAgFXECAAAsIoYAQAAVhEjAADAKmIEAABYRYwAAACriBEAAGAVMQIAAKwiRgAAgFXECAAAsIoYAQAAVhEjAADAKmIEAABYRYwAAACriBEAAGAVMQIAAKwiRgAAgFXECAAAsIoYAQAAVhEjAADAKmIEAABYRYwAAACriBEAAGAVMQIAAKwiRgAAgFXECAAAsIoYAQAAVhEjAADAKmIEAABYRYwAAACriBEAAGAVMQIAAKwiRgAAgFXECAAAsIoYAQAAVhEjAADAKmIEAABYRYwAAACriBEAAGAVMQIAAKwiRgAAgFXECAAAsIoYAQAAVhEjAADAKmIEAABYRYwAAACriBEAAGAVMQIAAKwiRgAAgFUtipGCggIlJSUpJiZGbrdbpaWlzdpv1apVioiI0K233tqSuwUAAO1QyDGyevVqZWVlKS8vT1u3blVycrLS0tJ06NChJvfbv3+/HnnkEY0ePbrFkwUAAO1PyDGyaNEiTZ8+XZmZmRo8eLAKCwvVtWtXLVu2rNF96uvrddddd2nOnDnq37//WU0YAAC0LyHFSF1dncrKyuTxeH46QGSkPB6PSkpKGt3vqaeeUq9evTR16tRm3U9tba18Pl/QDQAAtE8hxUhlZaXq6+vlcrmCtrtcLnm93gb3ef/997V06VItWbKk2feTn5+v2NjYwC0xMTGUaQIAgDDSplfTVFdXa/LkyVqyZIni4+ObvV9OTo6qqqoCt/Ly8jacJQAAsKlTKIPj4+MVFRWlioqKoO0VFRVKSEg4bfyXX36p/fv3a+LEiYFtfr//xzvu1EmfffaZLr300tP2czgccjgcoUwNAACEqZAeGYmOjtaIESNUXFwc2Ob3+1VcXKzU1NTTxg8aNEg7duzQ9u3bA7ebb75Z119/vbZv387TLwAAILRHRiQpKytLGRkZGjlypFJSUrR48WLV1NQoMzNTkjRlyhT17dtX+fn5iomJ0VVXXRW0f1xcnCSdth0AAHRMIcdIenq6Dh8+rNzcXHm9Xg0bNkxFRUWBF7UeOHBAkZH8YlcAANA8EcYYY3sSZ+Lz+RQbG6uqqio5nc5WPXZS9vpWPR7Q3uyfN8H2FACEqeb+/OYhDAAAYBUxAgAArCJGAACAVcQIAACwihgBAABWESMAAMAqYgQAAFhFjAAAAKuIEQAAYBUxAgAArCJGAACAVcQIAACwihgBAABWESMAAMAqYgQAAFhFjAAAAKuIEQAAYBUxAgAArCJGAACAVcQIAACwihgBAABWESMAAMAqYgQAAFhFjAAAAKuIEQAAYBUxAgAArCJGAACAVcQIAACwihgBAABWESMAAMAqYgQAAFhFjAAAAKuIEQAAYBUxAgAArCJGAACAVcQIAACwihgBAABWESMAAMAqYgQAAFhFjAAAAKuIEQAAYBUxAgAArCJGAACAVcQIAACwihgBAABWESMAAMAqYgQAAFhFjAAAAKuIEQAAYBUxAgAArCJGAACAVcQIAACwihgBAABWESMAAMAqYgQAAFhFjAAAAKtaFCMFBQVKSkpSTEyM3G63SktLGx27ZMkSjR49Wj169FCPHj3k8XiaHA8AADqWkGNk9erVysrKUl5enrZu3ark5GSlpaXp0KFDDY7fvHmzJk2apHfffVclJSVKTEzU2LFj9fXXX5/15AEAQPiLMMaYUHZwu9265ppr9MILL0iS/H6/EhMTdf/99ys7O/uM+9fX16tHjx564YUXNGXKlGbdp8/nU2xsrKqqquR0OkOZ7hklZa9v1eMB7c3+eRNsTwFAmGruz++QHhmpq6tTWVmZPB7PTweIjJTH41FJSUmzjnHixAn98MMPuvDCCxsdU1tbK5/PF3QDAADtU0gxUllZqfr6erlcrqDtLpdLXq+3Wcd47LHH1KdPn6Cg+bn8/HzFxsYGbomJiaFMEwAAhJFzejXNvHnztGrVKr355puKiYlpdFxOTo6qqqoCt/Ly8nM4SwAAcC51CmVwfHy8oqKiVFFREbS9oqJCCQkJTe67YMECzZs3T++8846GDh3a5FiHwyGHwxHK1AAAQJgK6ZGR6OhojRgxQsXFxYFtfr9fxcXFSk1NbXS/Z555RnPnzlVRUZFGjhzZ8tkCAIB2J6RHRiQpKytLGRkZGjlypFJSUrR48WLV1NQoMzNTkjRlyhT17dtX+fn5kqT58+crNzdXK1euVFJSUuC1Jd26dVO3bt1acSkAACAchRwj6enpOnz4sHJzc+X1ejVs2DAVFRUFXtR64MABRUb+9IDLSy+9pLq6Ov3qV78KOk5eXp6efPLJs5s9AAAIeyH/nhEb+D0jgD38nhEALdUmv2cEAACgtREjAADAKmIEAABYRYwAAACriBEAAGAVMQIAAKwiRgAAgFXECAAAsIoYAQAAVhEjAADAKmIEAABYRYwAAACriBEAAGAVMQIAAKwiRgAAgFXECAAAsIoYAQAAVhEjAADAKmIEAABYRYwAAACriBEAAGAVMQIAAKwiRgAAgFXECAAAsIoYAQAAVhEjAADAKmIEAABYRYwAAACriBEAAGAVMQIAAKwiRgAAgFXECAAAsIoYAQAAVhEjAADAKmIEAABYRYwAAACriBEAAGAVMQIAAKwiRgAAgFXECAAAsIoYAQAAVhEjAADAKmIEAABYRYwAAACriBEAAGAVMQIAAKwiRgAAgFXECAAAsIoYAQAAVhEjAADAKmIEAABYRYwAAACriBEAAGAVMQIAAKwiRgAAgFUtipGCggIlJSUpJiZGbrdbpaWlTY5/7bXXNGjQIMXExGjIkCHasGFDiyYLAADan5BjZPXq1crKylJeXp62bt2q5ORkpaWl6dChQw2O//DDDzVp0iRNnTpV27Zt06233qpbb71Vn3zyyVlPHgAAhL8IY4wJZQe3261rrrlGL7zwgiTJ7/crMTFR999/v7Kzs08bn56erpqaGv3tb38LbPvFL36hYcOGqbCwsFn36fP5FBsbq6qqKjmdzlCme0ZJ2etb9XhAe7N/3gTbUwAQppr78zukR0bq6upUVlYmj8fz0wEiI+XxeFRSUtLgPiUlJUHjJSktLa3R8QAAoGPpFMrgyspK1dfXy+VyBW13uVzavXt3g/t4vd4Gx3u93kbvp7a2VrW1tYGPfT5fKNMEAABhJKQYOVfy8/M1Z86cc3JfPAQNAIBdIT1NEx8fr6ioKFVUVARtr6ioUEJCQoP7JCQkhDReknJyclRVVRW4lZeXhzJNAAAQRkKKkejoaI0YMULFxcWBbX6/X8XFxUpNTW1wn9TU1KDxkrRp06ZGx0uSw+GQ0+kMugEAgPYp5KdpsrKylJGRoZEjRyolJUWLFy9WTU2NMjMzJUlTpkxR3759lZ+fL0maOXOmxowZo4ULF2rChAlatWqVPv74Y7388sutuxIAABCWQo6R9PR0HT58WLm5ufJ6vRo2bJiKiooCL1I9cOCAIiN/esBl1KhRWrlypWbNmqXHH39cAwYM0Nq1a3XVVVe13ioAAEDYCvn3jNjQlr9nBAAAtI02+T0jAAAArY0YAQAAVhEjAADAKmIEAABYRYwAAACriBEAAGAVMQIAAKwiRgAAgFXECAAAsIoYAQAAVoX83jQ2nPqN9T6fz/JMAABAc536uX2md54Jixiprq6WJCUmJlqeCQAACFV1dbViY2Mb/XxYvFGe3+/XN998o+7duysiIsL2dNqcz+dTYmKiysvLO9QbA3bUdUusvSOuvaOuW2LtHWntxhhVV1erT58+ioxs/JUhYfHISGRkpC666CLb0zjnnE5nh/jH+nMddd0Sa++Ia++o65ZYe0dZe1OPiJzCC1gBAIBVxAgAALCKGDkPORwO5eXlyeFw2J7KOdVR1y2x9o649o66bom1d9S1NyUsXsAKAADaLx4ZAQAAVhEjAADAKmIEAABYRYwAAACriBELjh49qrvuuktOp1NxcXGaOnWqjh8/3uT4+++/XwMHDlSXLl108cUX64EHHlBVVVXQuIiIiNNuq1atauvlNKmgoEBJSUmKiYmR2+1WaWlpk+Nfe+01DRo0SDExMRoyZIg2bNgQ9HljjHJzc9W7d2916dJFHo9HX3zxRVsuocVCWfuSJUs0evRo9ejRQz169JDH4zlt/N13333a+R03blxbLyNkoax7xYoVp60pJiYmaEx7Pef/93//1+DX7IQJEwJjwuGcv/fee5o4caL69OmjiIgIrV279oz7bN68WVdffbUcDocuu+wyrVix4rQxoX7vsCHUtb/xxhu68cYb1bNnTzmdTqWmpmrjxo1BY5588snTzvmgQYPacBXnCYNzbty4cSY5Odl89NFH5l//+pe57LLLzKRJkxodv2PHDvPLX/7SrFu3zuzZs8cUFxebAQMGmNtuuy1onCSzfPly8+233wZu3333XVsvp1GrVq0y0dHRZtmyZebTTz8106dPN3FxcaaioqLB8R988IGJiooyzzzzjNm5c6eZNWuW6dy5s9mxY0dgzLx580xsbKxZu3at+c9//mNuvvlm069fP6vrbEioa7/zzjtNQUGB2bZtm9m1a5e5++67TWxsrDl48GBgTEZGhhk3blzQ+T169Oi5WlKzhLru5cuXG6fTGbQmr9cbNKa9nvMjR44ErfuTTz4xUVFRZvny5YEx4XDON2zYYJ544gnzxhtvGEnmzTffbHL83r17TdeuXU1WVpbZuXOnef75501UVJQpKioKjAn179KWUNc+c+ZMM3/+fFNaWmo+//xzk5OTYzp37my2bt0aGJOXl2euvPLKoHN++PDhNl6JfcTIObZz504jyfz73/8ObPv73/9uIiIizNdff93s46xZs8ZER0ebH374IbCtOV8M51JKSoqZMWNG4OP6+nrTp08fk5+f3+D422+/3UyYMCFom9vtNr/5zW+MMcb4/X6TkJBgnn322cDnjx07ZhwOh3n11VfbYAUtF+raf+7kyZOme/fu5pVXXglsy8jIMLfccktrT7VVhbru5cuXm9jY2EaP15HO+XPPPWe6d+9ujh8/HtgWDuf8fzXne9Cjjz5qrrzyyqBt6enpJi0tLfDx2f5d2tDS77+DBw82c+bMCXycl5dnkpOTW29iYYKnac6xkpISxcXFaeTIkYFtHo9HkZGR2rJlS7OPU1VVJafTqU6dgt9eaMaMGYqPj1dKSoqWLVt2xrdtbit1dXUqKyuTx+MJbIuMjJTH41FJSUmD+5SUlASNl6S0tLTA+H379snr9QaNiY2NldvtbvSYNrRk7T934sQJ/fDDD7rwwguDtm/evFm9evXSwIEDdd999+nIkSOtOvez0dJ1Hz9+XJdccokSExN1yy236NNPPw18riOd86VLl+qOO+7QBRdcELT9fD7nLXGmr/PW+LsMF36/X9XV1ad9nX/xxRfq06eP+vfvr7vuuksHDhywNMNzhxg5x7xer3r16hW0rVOnTrrwwgvl9XqbdYzKykrNnTtX99xzT9D2p556SmvWrNGmTZt022236be//a2ef/75Vpt7KCorK1VfXy+XyxW03eVyNbpOr9fb5PhT/w3lmDa0ZO0/99hjj6lPnz5B35DHjRunP//5zyouLtb8+fP1z3/+U+PHj1d9fX2rzr+lWrLugQMHatmyZXrrrbf0l7/8RX6/X6NGjdLBgwcldZxzXlpaqk8++UTTpk0L2n6+n/OWaOzr3Ofz6bvvvmuVr59wsWDBAh0/fly33357YJvb7daKFStUVFSkl156Sfv27dPo0aNVXV1tcaZtLyzetTccZGdna/78+U2O2bVr11nfj8/n04QJEzR48GA9+eSTQZ+bPXt24M/Dhw9XTU2Nnn32WT3wwANnfb84d+bNm6dVq1Zp8+bNQS/mvOOOOwJ/HjJkiIYOHapLL71Umzdv1g033GBjqmctNTVVqampgY9HjRqlK664Qn/84x81d+5cizM7t5YuXaohQ4YoJSUlaHt7POf40cqVKzVnzhy99dZbQf+DOn78+MCfhw4dKrfbrUsuuURr1qzR1KlTbUz1nOCRkVby8MMPa9euXU3e+vfvr4SEBB06dCho35MnT+ro0aNKSEho8j6qq6s1btw4de/eXW+++aY6d+7c5Hi3262DBw+qtrb2rNcXqvj4eEVFRamioiJoe0VFRaPrTEhIaHL8qf+GckwbWrL2UxYsWKB58+bp7bff1tChQ5sc279/f8XHx2vPnj1nPefWcDbrPqVz584aPnx4YE0d4ZzX1NRo1apVzfpBc76d85Zo7Ovc6XSqS5curfLv6Hy3atUqTZs2TWvWrDntKaufi4uL0+WXXx7W57w5iJFW0rNnTw0aNKjJW3R0tFJTU3Xs2DGVlZUF9v3HP/4hv98vt9vd6PF9Pp/Gjh2r6OhorVu37rTLHxuyfft29ejRw8obMkVHR2vEiBEqLi4ObPP7/SouLg76P+H/lZqaGjRekjZt2hQY369fPyUkJASN8fl82rJlS6PHtKEla5ekZ555RnPnzlVRUVHQa4oac/DgQR05ckS9e/dulXmfrZau+3/V19drx44dgTW193Mu/Xg5e21trX7961+f8X7Ot3PeEmf6Om+Nf0fns1dffVWZmZl69dVXgy7jbszx48f15ZdfhvU5bxbbr6DtiMaNG2eGDx9utmzZYt5//30zYMCAoEt7Dx48aAYOHGi2bNlijDGmqqrKuN1uM2TIELNnz56gS75OnjxpjDFm3bp1ZsmSJWbHjh3miy++MC+++KLp2rWryc3NtbJGY368PM/hcJgVK1aYnTt3mnvuucfExcUFLt2cPHmyyc7ODoz/4IMPTKdOncyCBQvMrl27TF5eXoOX9sbFxZm33nrL/Pe//zW33HLLeXuZZyhrnzdvnomOjjavv/560Pmtrq42xhhTXV1tHnnkEVNSUmL27dtn3nnnHXP11VebAQMGmO+//97KGhsS6rrnzJljNm7caL788ktTVlZm7rjjDhMTE2M+/fTTwJj2es5Pue6660x6evpp28PlnFdXV5tt27aZbdu2GUlm0aJFZtu2bearr74yxhiTnZ1tJk+eHBh/6tLe3/3ud2bXrl2moKCgwUt7m/q7PF+Euva//vWvplOnTqagoCDo6/zYsWOBMQ8//LDZvHmz2bdvn/nggw+Mx+Mx8fHx5tChQ+d8fecSMWLBkSNHzKRJk0y3bt2M0+k0mZmZgR86xhizb98+I8m8++67xhhj3n33XSOpwdu+ffuMMT9eHjxs2DDTrVs3c8EFF5jk5GRTWFho6uvrLazwJ88//7y5+OKLTXR0tElJSTEfffRR4HNjxowxGRkZQePXrFljLr/8chMdHW2uvPJKs379+qDP+/1+M3v2bONyuYzD4TA33HCD+eyzz87FUkIWytovueSSBs9vXl6eMcaYEydOmLFjx5qePXuazp07m0suucRMnz79vPvmbExo637wwQcDY10ul7npppuCfueCMe33nBtjzO7du40k8/bbb592rHA55419fzq11oyMDDNmzJjT9hk2bJiJjo42/fv3D/rdKqc09Xd5vgh17WPGjGlyvDE/Xubcu3dvEx0dbfr27WvS09PNnj17zu3CLIgwxtK1nwAAAOI1IwAAwDJiBAAAWEWMAAAAq4gRAABgFTECAACsIkYAAIBVxAgAALCKGAEAAFYRIwAAwCpiBAAAWEWMAAAAq4gRAABg1f8DqSMmlVy99hIAAAAASUVORK5CYII=",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "{0: 0.017104039891819, 1: 0.982895960108181}\n"
          ]
        },
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "for data in quantumResult.quasi_dists:\n",
        "    bar = plt.bar([0, 1], list(data.values()), align='center')\n",
        "    print(data)\n",
        "    plt.show()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "As you can see a real Quantum computer is not perfect and the results are not always accurate.  \n",
        "When using the simulator this doesn't happen as the simulator is perfect and has no noise."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Jobs\n",
        "\n",
        "Here are the jobs that were run on the quantum computer.  \n",
        "I first ran them on the simulator to get the results and make sure it works before running on real quantum computers.\n",
        "\n",
        "![Alt text](imgs/QuantumJobs.png)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## References\n",
        "\n",
        "- <a id=\"1\">[1]:</a> Input table reference https://anonymousket.medium.com/quantum-algo-deutsch-algorithm-ccc119c69c08#b0aa\n",
        "- <a id=\"2\">[2]:</a> Circuit diagram reference https://i.ytimg.com/vi/7MdEHsRZxvo/maxresdefault.jpg\n",
        "- <a id=\"3\">[3]:</a> How to setup account and token for real hardware https://docs.quantum-computing.ibm.com/run\n",
        "- <a id=\"4\">[4]:</a> How to run on real hardware https://qiskit.org/ecosystem/ibm-runtime/how_to/backends.html\n"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.11.6"
    },
    "orig_nbformat": 4
  },
  "nbformat": 4,
  "nbformat_minor": 2
}