Quantum_Entanglement.ipynb

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        "<a href=\"https://colab.research.google.com/github/Jayshah25/Quantum-Algorithms-and-Circuits/blob/master/Quantum_Entanglement.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "source": [
        "## **Quantum Entanglement**"
      ]
    },
    {
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      "source": [
        "In this notebook, we shall learn to entangle two Qubits and create 4 Bell States using the python library Qiskit. The circuit used for demonstration of Quantum Entanglement is simple and therefore, this notebook is a great way for a beginner to get into the World of Quantum Computing using Qiskit."
      ]
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    {
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      "source": [
        "**Prerequisites:**\n",
        "\n",
        "* Basic Python"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
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      "source": [
        "The Notebook is developed using the Google Colab. Therefore, if it is run in any other environment(like on a local machines), some steps may vary. However, this notebook may fail to render some images if tried to run Google Colab. Therefore, to run this code yourself, download this notebook from [Kaggle](https://www.kaggle.com/jaypradipshah/quantum-entanglement)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "S7ezZ6uXFRdt",
        "colab_type": "text"
      },
      "source": [
        "# What is Qiskit?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1YPYyxyyhlPA",
        "colab_type": "text"
      },
      "source": [
        "<img src =\"Images_Used/Quantum_Entanglement/qiskit.png\" />"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IWm7PVndXzhL",
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      },
      "source": [
        "**Credits: Github-Qiskit**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uz72CBxLGn_3",
        "colab_type": "text"
      },
      "source": [
        "[Qiskit](https://qiskit.org/) is an open-source framework for Quantum Computing. It provides tools for creating and manipulating quantum programs and running them on prototype quantum devices on IBM Q Experience or on simulators on a local computer.\n",
        "\n",
        "The version of Qiskit that we will be using is based on Python. The Swift and Javascript Versions of Qiskit are also in Development"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1arl1LnXHTPZ",
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      "source": [
        "Essentially, we will be building a Quantum Circuit that works on Qubits (Quantum Analogue of Classical bits). "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pZjxu_kyH7Z-",
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      },
      "source": [
        "# Quantum Gates"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9Qk0jaryIBoC",
        "colab_type": "text"
      },
      "source": [
        "Quantum Gates are the most important part of a Quantum Circuit. We manipulate the state of Qubits by applying Quantum Gates on them. This is similar to a Classical Circuit where we use Classical Gates like AND, OR, NOT, NAND, etc. for the purpose of manipulation. Some of the Quantum Gates have a classical analogue (like Quantum NOT Gate) and some are completely new gates with no classical analogues(like Hadamard Gate).\n",
        "\n",
        "In the Quantum Entanglement Circuit, we will be using two gates:\n",
        "* CNOT Gate\n",
        "* Hadamard Gate"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TqcMOxwUKBnD",
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      },
      "source": [
        "**CNOT Gate:**"
      ]
    },
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        "id": "R1Y9k52YkJu-",
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      },
      "source": [
        "<img src =\"Images_Used/Quantum_Entanglement/CNOT.png\" />"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "t0rLTkViJE_t",
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      "source": [
        "The CNOT Gate is one of the most commonly used gates in Quantum Circuits. It is the Quantum Analogue of the Classical XOR Gate. It operates on two Qubits namely, the control Qubit and the Target Qubit. The function of the Gate is simple! If the Control Qubit is in the state |1>, the CNOT Gate performs a NOT on the Target Qubit i.e it flips its state from |0> to |1> or from |1> to |0>. In the image above, the Control Qubit is denoted by **q0** and the Target Qubit is denoted by **q1**.\n",
        "\n",
        "Here, **\"|>\"** are a part of Dirac Notation and they distiguish the state of a Qubit from the state of a classical bit. They are pronounced as 'Ket'. For eg: |0> can be read out as \"Ket Zero\" or \"Ket of Zero\". As we know, the classical bit can take the values of either 0 or 1. Similarly, the Qubits can take either the state |0> or the state |1> or both at the same time(this is just a linear combination of these two states, popularly known as the concept of Superposition)\n",
        "\n",
        "Also, it is important to note that |0> and |1> are both 2X1 Vectors and not a scalar value."
      ]
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      "cell_type": "code",
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      "source": [
        "import numpy as np\n",
        "zero_state = np.array([[1],[0]])\n",
        "one_state = np.array([[0],[1]])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
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      "source": [
        "print(\"The |0> is \\n\", zero_state)\n",
        "print(\"The |1> is \\n\", one_state)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The |0> is \n",
            " [[1]\n",
            " [0]]\n",
            "The |1> is \n",
            " [[0]\n",
            " [1]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
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          "height": 50
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        "outputId": "52841780-b95d-4a11-acc3-76968b9052dc"
      },
      "source": [
        "print(\"The shape of the Vector |0> is\",zero_state.shape)\n",
        "print(\"The shape of the Vector |1> is\",one_state.shape)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The shape of the Vector |0> is (2, 1)\n",
            "The shape of the Vector |1> is (2, 1)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
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      "source": [
        "* At this point, a good question can be why is |0> equal to [[1],[0]]?\n",
        "\n",
        "The Question has a simple answer. There are two possible states 0 and 1. The value 1 on the first place indicates that it's the state zero. Similarly, in the state |1>, the value 1 is on the second position, indicating the state one. This is similar to the concept of **One-Hot Encoding**."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WEmNn_5EW2fy",
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      },
      "source": [
        "**Hadamard Gate:**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Wm937OFnki3A",
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      },
      "source": [
        "<img src =\"Images_Used/Quantum_Entanglement/Hadamard.png\" />"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "21VUrZjbk1JC",
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      },
      "source": [
        "**Image Credits- qiskit.org/textbook**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SpGuqQsEdeCK",
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      },
      "source": [
        "The Hadamard is a unique quantum gate and it transforms the state |0> to (|0>+|1>)/sqrt(2) and |1> to (|0>-|1>)/sqrt(2). Alternatively, this can be thought of as a 90 degree rotation around Y-Axis followed by a 180 degree rotation around X axis of the [Bloch Sphere](https://en.wikipedia.org/wiki/Bloch_sphere).\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oYbrjkVke34q",
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      "source": [
        "**Note:** Quantum Gates can be represented using a Unitary Matrix.\n",
        "\n",
        "The Unitary Matrix for CNOT and Hadamard Gates also exist. \n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "D0uVXd0ilG7W",
        "colab_type": "text"
      },
      "source": [
        "<img src =\"Images_Used/Quantum_Entanglement/Matrices.png\" />"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "uZmJ4UfllgMn"
      },
      "source": [
        "**Image Credits- qiskit.org/textbook**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DizRPyufgDBB",
        "colab_type": "text"
      },
      "source": [
        "# What is Quantum Entanglement?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sXOJavsvgMP3",
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      "source": [
        "Before getting into the coding, it is important to undestand what do we mean by the concept of Quantum Entanglement? This concept of Quantum Entanglement is one of the most important concepts in Quantum Mechanics and it was a topic of \n",
        "huge debate between Neil Bohr and Albert Einstein.\n",
        "\n",
        "The Principle states that two quantum particles, when entangled, can communicate with each other instantly irrespective of the distance between them. This means that if we place one qubit from the entangled pair on one edge of the Observable Universe and the other qubit on the other edge, they can still communicate. In simple words, this violates the law of General Theory of Relativity which states that faster than light communication or travel is not possible. Albert Einstein named this concept of Entanglement as \"Spooky Action at a distance\".\n",
        "\n",
        "With resect to Quantum Computing, the idea can be explained as, \"if you measure one qubit from the entangled pair, you instantly know the state of the second qubit\".\n",
        "\n",
        "In this notebook, we will develop four entangled States(also popularly known as [Bell States](https://en.wikipedia.org/wiki/Bell_state)) using two Qubits."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dT4x70QUjRFw",
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      "source": [
        "The four Bell States are:\n",
        "\n",
        "(Image Credits: Wikipedia)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "w93yFQvLli5Y",
        "colab_type": "text"
      },
      "source": [
        "<img src =\"Images_Used/Quantum_Entanglement/Bell1.png\" />"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "X85crbEvljB_",
        "colab_type": "text"
      },
      "source": [
        "<img src =\"Images_Used/Quantum_Entanglement/Bell2.png\" />"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2nca8jCYljI2",
        "colab_type": "text"
      },
      "source": [
        "<img src =\"Images_Used/Quantum_Entanglement/Bell3.png\" />"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "v9PnxEWYljp5",
        "colab_type": "text"
      },
      "source": [
        "<img src =\"Images_Used/Quantum_Entanglement/Bell4.png\" />"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qcCWdkDzkDEv",
        "colab_type": "text"
      },
      "source": [
        "**Note:**\n",
        "\n",
        "Here, two zeros in the notation |00> indicate the states of two Qubits."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "n28VOxFYkfH6",
        "colab_type": "text"
      },
      "source": [
        "# Quantum Circuits for Entanglement"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uE_Bgkezk1Sh",
        "colab_type": "text"
      },
      "source": [
        "Before we can use qiskit, we need to install the Qiskit in the Colab. If you want to install qiskit on your local machine, you can go through this [video](https://www.youtube.com/watch?v=M4EkW4VwhcI)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hVq6kMC3laeB",
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      },
      "source": [
        "!pip install qiskit #Install qiskit on colab\n",
        "!pip install pylatexenc #Required for matplotlib support to render the images of circuit\n",
        "from IPython.display import clear_output #Clear the output after installation\n",
        "clear_output()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FCTghaDskkun",
        "colab_type": "text"
      },
      "source": [
        "Now, this is the time to get into the cool coding part!"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7yZGUJfDm4f6",
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      "source": [
        "We shall build the first Entangled State."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "97ATklgytPiA",
        "colab_type": "text"
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      "source": [
        "**The First Bell State:**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "cwwozgE-r03-"
      },
      "source": [
        "<img src =\"Images_Used/Quantum_Entanglement/Bell1.png\" />"
      ]
    },
    {
      "cell_type": "code",
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        "id": "5EZw2ol2kxiH",
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      "source": [
        "#QuantumCircuit is the class that we shall use for our circuit\n",
        "#Aer is required to get the required backend support\n",
        "#execute will execute our circuit\n",
        "from qiskit import QuantumCircuit, Aer, execute"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cMAw-3f3ky0u",
        "colab_type": "code",
        "colab": {}
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      "source": [
        "circuit_es1 = QuantumCircuit(2,2) #initializing our circuit with two qubits and two bits"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
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          "height": 33
        },
        "outputId": "3c8e777a-ca34-4bce-ca2b-5cadd171fb1b"
      },
      "source": [
        "circuit_es1.h(0) #Applying hadamard Gate on the first qubit\n",
        "circuit_es1.cx(0,1) #Applying the CNOT Gate with zeroth qubit as the control qubit \n",
        "                    #and the first qubit as the target qubit\n",
        "circuit_es1.measure(0,0) #Measuring the zeroth qubit and storing its output to zeroth bit\n",
        "circuit_es1.measure(1,1)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<qiskit.circuit.instructionset.InstructionSet at 0x7fe66d7f95c0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 44
        }
      ]
    },
    {
      "cell_type": "code",
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        "id": "k7aumkAcoz3w",
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          "base_uri": "https://localhost:8080/",
          "height": 185
        },
        "outputId": "7dc0432e-2518-4d76-fbd5-5eab016c996d"
      },
      "source": [
        "#Let's visualize our circuit\n",
        "circuit_es1.draw('mpl')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 381.432x204.68 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 45
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "I_sEB0-avh04",
        "colab_type": "text"
      },
      "source": [
        "The only part of the circuit that we have not discussed yet is the **measurement**. \n",
        "\n",
        "The \"Measurement\" is also considered as an operation in Quantum Computing. In fact, a measurement is the only way to extract output from a qubit. Here, we extract the output from the qubit and store it in a bit.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wBzHmNY9oc65",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "simulator = Aer.get_backend('qasm_simulator') #Using qasm_simulator, we can simulate our circuit on an actual quantum device\n",
        "result = execute(circuit_es1,backend=simulator, shots = 1024).result() #shots = number of time we want to execute the circuit"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Rpipp6OQrBPV",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "counts = result.get_counts() #Get the results for each simulation"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zf-qqSpbrFGN",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 335
        },
        "outputId": "34e9ce17-937b-43b1-cc8e-f95d21069b8e"
      },
      "source": [
        "from qiskit.visualization import plot_histogram #To visualize our results\n",
        "plot_histogram(counts)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": 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/sAN4HphXbp8GPFvBuiRJ6nG6FJqZ+Q8RsRAYDTyemXvKi34N3FLp4iRJ6km6eqRJZjZRumq2bdv3K1aRJEk9VJcnN4iI6yNiSUS8GBHjym0fjYg/rXx5kiT1HF2d3OAm4BPA14Bos+g3wF9VsC5Jknqcrh5pXgdck5l3ArvbtDcDkytWlSRJPVBXQ/NUYHEH7S8D/Q6/HEmSeq6uhuZKYEoH7W8Dlh5+OZIk9VxdvXr2i8BdEfFqSuc0GyLiz4G/Aa6qdHGSJPUkXb1P8+sR0Re4HXg1pYkOfgPcmJkPHYH6JEnqMQ7lPs1ZwKyIOAk4LjM3Vb4sSZJ6ni6H5l6Z+UIlC5Ekqac7aGhGxDPA9MzcGhHPAtlZ38w8q5LFSZLUkxQ50nwYaGnzvtPQlCSpNztoaGbmp9q8v+2IViNJUg/W1Wn0fhIRJ3bQPjAiflK5siRJ6nm6OrnBhcDxHbSfAFxw2NVIktSDFbp6NiLazgJ0VkRsafO5DzATWFfJwiRJ6mmK3nLSROkCoATmdLB8J3BDpYqSJKknKhqaYylNm7cS+GPgt22W7QI2ZWZrhWuTJKlHKRSamfl8+W2XH1otSVJvUWRyg0uAf8vMl8vvO5WZ/1KxyiRJ6mGKHGl+GxgObCq/70xSuihIkqReqcjkBsd19F6SpGONIShJUkFFz2kW4jlNSVJvVvScZhGe05Qk9WpdOqcpSdKxzECUJKkg79OUJKkg79OUJKmggw7PZuZxmbmpzfvOXoUCMyKuj4hVEfFSRCyMiE4fKRYR0yPiqYjYHBE7I+KXEfGRDvq9OyKWRkRL+c93FalFkqSuqOo5zYi4HLgTuB04B3gKeDQiTulklR3Al4FpwCTgM8CnIuL6NttsAB4C/gk4u/zntyKi/kjthyTp2NTl0IyIKRFxX0Q0lV/3t3ve5oHcDMzOzFmZ+Vxm3gCsBz7YUefMXJiZD2bmksxclZnfAB5j/wde3wT8NDM/W97mZ4G55XZJkiqmS6EZEe8Ffg6cDPyg/BoGPB0Rf3aQdY8HzuWVz+OcA5xf8OefU+77RJvmhg62+VjRbUqSVFTR52nu9Vnglsy8vW1jRHyc0tDpNw6w7kmULhTa2K59I3DRgX5oRKwFXluu91OZeXebxcM72ebwTrZ1LXAtwIgRI5g7dy4A48aNY8CAASxatAiAIUOGMHnyZObNmwdA3759mTp1Ks3NzWzbtg2Auro6Nm7cCJx2oPJ1lGpqamLHjh0A1NfXs3btWtatWwfAxIkT6dOnD0uXLgVg+PDhjB07lsbGRgD69etHfX09CxYsYOfOnQA0NDSwatUqNmzYAMCkSZNobW1l2bJlAIwcOZJRo0axYMECAPr3709dXR2NjY20tLQAMHXqVJYvX86mTZsAOOOMM2hpaWHFihUAjB49mmHDhtHU1ATAwIEDmTJlCvPnz2f37t0ATJs2jSVLlrB582YAamtr2b59OytXrgRgzJgxDB48mObmZgAGDRpEbW0tTzzxBJlJRDB9+nQWLVrE1q1bAZgyZQpbtmxh9erVwOF9n9asWQPA+PHjqampYfHixQAMHTqUCRMmMH/+fABqampoaGg4pN8T1HTxb4OOBuvXr6/I9+lAIjMLFxQRfwBqM/NX7dpPB57JzFcfYN0RwDpgembOa9N+K/DezJx4gHXHAv2BNwB/C/x1Zt5fXrYLuDoz72vT/0pgVmYe8JtRV1eXe/9xORzX3HHYm1APNMsB/l7L72zvVKnvbEQszMy6jpZ19Ujzp8CFwK/atV/I/kOmHXkBaKU0nNvWMGDDgVbMzFXlt89GxDDgNuD+ctuGQ9mmJEld1dUJ2x8FPhcRdcDPym1vAC6hFGSdysxdEbEQmAF8q82iGcDDXaj5OPYfW2ksb+ML7bb5VBe2KUnSQR3qhO37zgu28RXgqwfZ1peA+yPiaeBJ4DpgBHA3QETcB5CZV5Y/3wCsApaV158GfKTdz7kTmBcRHwO+A7wLeBMwtcC+SZJUWFUnbM/MhyJiCPAJSlfgLgbelpnPl7u0v1+zD6VzmGOA3cCvgY9RDtnyNp+KiCsoXYj06XKfyzNzQaXqliQJun5O87Bl5lfp5Ig0My9s9/kO4KCn7DPz2xR/hJkkSYeky6EZEYOA/0rpqPD4tssy89MVqkuSpB6nS6EZEW8Avg+0ULpvch2lYdYWYDWl4VFJknqlrp6v/AKluV1HAi8Bb6Z0xNlE6dyjJEm9VldD8yzgrizNiNAK1GTmRuCjHOSWE0mSjnZdDc1dbd5vBE4tv99B6dYRSZJ6ra5eCNQMnAcsp/Qkkc+UZ+j5M+CZypYmSVLP0tUjzf8F/Kb8/hPAbylNajCIV052IElSr9KlI83MbGrz/reUbj2RJOmYcEiTG0TEacDryx+XZubKypUkSVLP1NX7NIcA/whcDOz5z+b4HnBVZm6ucH2SJPUYXT2neQ9wOnABcEL5NQ0YC8yqbGmSJPUsXR2enQn8l8xsbNP2ZET8D+BHlStLkqSep6tHmr8F/tBB+4uAQ7OSpF6tq6H5aeCOiBi5t6H8/u9w3llJUi930OHZiHgWyDZNY4HVEbGu/HnvPLRDKZ3zlCSpVypyTtPnVEqSRIHQzMxPVaMQSZJ6ukOd3ODNwCRKw7ZLMnNuJYuSJKkn6urkBiOBfwXO5T/noB0REU3AuzLzN52uLEnSUa6rV89+mdJzNE/PzNGZORoYX277cqWLkySpJ+nq8OwM4MLMXLW3ITNXRsSNwI8rWpkkST1MV480Yf/bTw7UJklSr9LV0Pwx8JWIGL23ISJOAe7AI01JUi/X1dC8EfgjYGVEPB8RzwO/LrfdWOniJEnqSbp6TnMz8MfAhcDrym3PZaaTtUuSer3CoRkRfYDfA7WZ+Tjw+BGrSpKkHqjw8GxmtgLPA8cfuXIkSeq5unpO838Dn4+Ik45EMZIk9WRdPaf5EUpPOVkXEWtp92zNzDyrUoVJktTTdDU0v03pnsw4ArVIktSjFQrNiHg18AXgT4BXUbon84bMfOEI1iZJUo9S9Jzmp4D3A98HHgAuAv7+CNUkSVKPVHR49hLgLzLzQYCI+CfgyYjoU76qVpKkXq/okeZo4P/t/ZCZTwO7gRFHoihJknqioqHZB9jVrm03h/gQa0mSjkZFQy+Ab0RES5u2E4BZEfHi3obMvLiSxUmS1JMUDc17O2j7RiULkSSppysUmpn5gSNdiCRJPd2hPIRakqRjkqEpSVJBhqYkSQUZmpIkFWRoSpJUkKEpSVJBhqYkSQUZmpIkFWRoSpJUkKEpSVJBhqYkSQUZmpIkFWRoSpJUkKEpSVJBhqYkSQUZmpIkFWRoSpJUkKEpSVJBhqYkSQVVPTQj4vqIWBURL0XEwoi44AB9T46If46IX0ZEa0TM7qDP+yMiO3idcER3RJJ0zKlqaEbE5cCdwO3AOcBTwKMRcUonq9QALwCfBxYcYNMvAie3fWXmS5WqW5IkqP6R5s3A7MyclZnPZeYNwHrggx11zszVmXljZs4Gthxgu5mZG9q+Kl+6JOlYV7XQjIjjgXOBOe0WzQHOP8zN94uI5yNibUR8LyLOOcztSZL0Cn2r+LNOAvoAG9u1bwQuOoztLgOuAhYBA4C/Bp6MiNrMXNG+c0RcC1wLMGLECObOnQvAuHHjGDBgAIsWLQJgyJAhTJ48mXnz5gHQt29fpk6dSnNzM9u2bQOgrq6OjRs3AqcdRvnqqZqamtixYwcA9fX1rF27lnXr1gEwceJE+vTpw9KlSwEYPnw4Y8eOpbGxEYB+/fpRX1/PggUL2LlzJwANDQ2sWrWKDRtKAyGTJk2itbWVZcuWATBy5EhGjRrFggWlMxH9+/enrq6OxsZGWlpaAJg6dSrLly9n06ZNAJxxxhm0tLSwYkXpr/ro0aMZNmwYTU1NAAwcOJApU6Ywf/58du/eDcC0adNYsmQJmzdvBqC2tpbt27ezcuVKAMaMGcPgwYNpbm4GYNCgQdTW1vLEE0+QmUQE06dPZ9GiRWzduhWAKVOmsGXLFlavXg0c3vdpzZo1AIwfP56amhoWL14MwNChQ5kwYQLz588HoKamhoaGhkP6PZXO/Ki3Wb9+fUW+TwcSmXkEd6HND4oYAawDpmfmvDbttwLvzcyJB1n/e8ALmfn+g/TrA/wC+Glm3nigvnV1dbn3H5fDcc0dh70J9UCzburuCnSk+J3tnSr1nY2IhZlZ19Gyap7TfAFoBYa1ax8GVOwcZGa2Ak3A+EptU5IkqGJoZuYuYCEwo92iGZSuoq2IiAjgLEoXGEmSVDHVPKcJ8CXg/oh4GngSuA4YAdwNEBH3AWTmlXtXiIizy28HAnvKn3dl5tLy8k8CPwNWlPvcSCk0O7wiV5KkQ1XV0MzMhyJiCPAJSvdTLgbelpnPl7t0dL/mv7f7/A7geWBM+fOJwNeA4cDvy/2nZebTla1eknSsq/aRJpn5VeCrnSy7sIO2OMj2PgR8qCLFSZJ0AM49K0lSQYamJEkFGZqSJBVkaEqSVJChKUlSQYamJEkFGZqSJBVkaEqSVJChKUlSQYamJEkFGZqSJBVkaEqSVJChKUlSQYamJEkFGZqSJBVkaEqSVJChKUlSQYamJEkFGZqSJBVkaEqSVJChKUlSQYamJEkFGZqSJBVkaEqSVJChKUlSQYamJEkFGZqSJBVkaEqSVJChKUlSQYamJEkFGZqSJBVkaEqSVJChKUlSQYamJEkFGZqSJBVkaEqSVJChKUlSQYamJEkFGZqSJBVkaEqSVJChKUlSQYamJEkFGZqSJBVkaEqSVJChKUlSQYamJEkFGZqSJBVkaEqSVJChKUlSQYamJEkFGZqSJBVkaEqSVJChKUlSQYamJEkFGZqSJBVkaEqSVFDVQzMiro+IVRHxUkQsjIgLDtJ/ernfSxGxMiKuO9xtSpJ0KKoamhFxOXAncDtwDvAU8GhEnNJJ/7HAD8r9zgE+B3wlIt59qNuUJOlQVftI82ZgdmbOysznMvMGYD3wwU76Xwf8JjNvKPefBdwLfOQwtilJ0iGpWmhGxPHAucCcdovmAOd3slpDB/0fA+oi4lWHuE1Jkg5J3yr+rJOAPsDGdu0bgYs6WWc48KMO+vctby+6us2IuBa4tvxxR0QsK1K89jkJeKG7i6iGez7U3RVIFeF3tutO7WxBNUOzR8jMrwFf6+46jlYR0ZSZdd1dh6Ri/M5WVjVD8wWgFRjWrn0YsKGTdTZ00n93eXtxCNuUJOmQVO2cZmbuAhYCM9otmkHpiteONHbSvykzXz7EbUqSdEiqPTz7JeD+iHgaeJLS1bEjgLsBIuI+gMy8stz/buCvIuIO4B+ANwLvB95TdJuqOIe2paOL39kKisys7g+MuB74G+BkYDHwocycV142FyAzL2zTfzrwf4HJwG+Av83Mu4tuU5KkSql6aEqSdLRy7llJkgoyNCVJKsjQlCSpIENTkqSCjrkZgdR1ETEKOJ3SZBJ7gGWZ6eQRko45Xj2rA4qIDwJXAbXAH4BfAWuBnwHfycxlEXFcZu7pxjIlqSocnlWnImIIpeeUfpfSPbANlB7N1gpcCXw5IiZl5p6IiO6rVBJA+elPEyKiprtr6a080lSnIuIG4M8ys76DZVMpPRR8JPDHmXlMPEVB6ski4ibgs8A3gX8Bfg78NjNb2/QZSGl2tR9l5svdUuhRzCNNHcguYEBEnAEQETXlZ5iSmfOB9wIvAW/pvhIltXE58DSlaxC+Q2n+7i9ExNSIeE25z38HPmlgHhpDUwfybUoX/twUEQMysyUzd0XEcQCZ+R/A74BR3VmkJIiI1wIvA7My8wJKz4T8R+C/AfOAn0TER4GbgAXdVuhRzuFZdajNOcp3AncCgykN+XwV+HdKQTkN+HvgzMxc3Q1lSiqLiJOBK4ClmflYu2XnAFeXlw8CRmfmuupXefQzNHVAEXEicApwPvAuSudCoPS80gDuz8zbuqc6SW1FRD8gM/OlthfnZfkf+oj4LPC2zDynu2o82nmfpl4hIoYCfw58mNLDvndSGoadD3wReBWlcyY/zMzl3VWnpP1l5s69YZntjogi4tXAu4Gvd0dtvYVHmnqFiJhN6VFs/wZsoTQ0eyYwAdgEfHxVGLoAAAHESURBVCIzPSci9RDlK2K3tw/Kdn1OoHSh0AOZuatqxfUyhqb2U/6/1O2UhnDmtWk7BaindF5kHPCnmdncbYVK2ici/oHSVbNPA89n5rYO+pyYmb+renG9jFfPqr1JwCpKt5sApWGezHw+M78JvIPSUO1l3VSfpDYi4j3ANcDfUZqI5AsR8a6IOK18jnPvuc57994+pkPnkab2U/5yfQ94NaVZf37dfoq88qQHf5GZZ3dDiZLaiIhZlGbp+j/AJcD7gNOAZcAPgB8DE4E7M/P47qqzt/BIU/vJzJ3A/wL6AfcBV0bE6IjoD/suJpgOLO6+KiUBRERfSiNDv8vMlZn5xcw8EzgPeIJSgH4T+Apwf/dV2nt4pKkOlYdxbgEupjRReyPwW+AiYD1wdWY+230VSgKIiEHAsMz8ZXnGrpfbXhAUEZcDDwBTMvMX3VVnb2Fo6oDKt5+8HfgTSlPmLQa+lZm/7NbCJHWqPGtXZGZrRFxDaWj21d1dV29gaKowHwEmHX0i4magT2Z+obtr6Q0MTUnqxSLiVUCr/8NbGYamJEkFefWsJEkFGZqSJBVkaEqSVJChKUlSQYamJEkFGZqSJBX0/wForhgCzdiwggAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 504x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 48
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wP6tagWyyica",
        "colab_type": "text"
      },
      "source": [
        "**Analyzing the results:**\n",
        "\n",
        "* Clearly, we have got two states |00> and |11> with the right most number representing the state of the zeroth qubit. The probability of getting the state |00> is 0.503 and for |11>, it's 0.497\n",
        "\n",
        "* Note that we can never get the state (|00>+|11>)/sqrt(2). As soon as we measure a qubit, the superposition state vanishes away and we get either |00> or |11>\n",
        "\n",
        "* Initially, all the qubits are in the |0> state. Therefore, initially before applying the Hadamard Gate, our circuit was in the state |00>. We transformed that state into the (|00>+|11>)/sqrt(2) state. However, after measurement we can either get |00> or |11>.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JsRnQ47s04qF",
        "colab_type": "text"
      },
      "source": [
        "**How does the state transformation take place?**\n",
        "\n",
        "* The Hadamard Gate transforms the state of the first qubit from state |0> to (|0>+|1>)/sqrt(2). Therefore, our two qubit circuit is in the state (|00>+|01>)/sqrt(2). The right most digit defines the state of zeroth qubit. \n",
        "\n",
        "* After the Hadamard Gate, we apply the CNOT Gate. Recall that the CNOT Gate performs a NOT on the target qubit if the control qubit is in the state |1>. Clearly, the CNOT Gate has no effect if the state is |00>. However, if the state is |01>, the NOT operation is performed and the |01> state is transformed to |11>. \n",
        "\n",
        "* Now, we finally achieve the state (|00>+|11>)/sqrt(2). However, the state collapses before we make a measurement and therefore, we either get |00> or |11>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VdLSYrqM3Ov3",
        "colab_type": "text"
      },
      "source": [
        "**Note**: For the next three Bell States, try to figure out yourself the state transformation process as a simple exercise."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2VeJTfm9z-j9",
        "colab_type": "text"
      },
      "source": [
        "**The Second Bell State:**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "bQK2SpEtr4OP"
      },
      "source": [
        "<img src =\"Images_Used/Quantum_Entanglement/Bell2.png\" />"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dFCl3VLpKI8K",
        "colab_type": "text"
      },
      "source": [
        "Before we start building the circuit for Second Bell state, a common question can be - \"Why do these 4 Bell States differ?\"\n",
        "\n",
        "The reason for the differences in the Bell States is the initial state. Each of the four Bell State has a different initial state.\n",
        "\n",
        "Bell State 1 - |00>\n",
        "\n",
        "Bell State 2 - |01>\n",
        "\n",
        "Bell State 3 - |10>\n",
        "\n",
        "Bell State 4 - |11>\n",
        "\n",
        "Therefore, the circuit for all the Bell States is the same. We only need to change the initial states of our qubits."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jyuYaEn6KHpl",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 33
        },
        "outputId": "654b43ae-bd7a-487a-ba51-eb73ccc73b77"
      },
      "source": [
        "circuit_es2 = QuantumCircuit(2,2)\n",
        "circuit_es2.x(0) #Applying the NOT Gate on the first qubit to get the state |01>\n",
        "circuit_es2.h(0) \n",
        "circuit_es2.cx(0,1)\n",
        "circuit_es2.measure(0,0) \n",
        "circuit_es2.measure(1,1)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<qiskit.circuit.instructionset.InstructionSet at 0x7fe6766cae48>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 52
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OypdQ7JP037o",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 185
        },
        "outputId": "68467387-78fc-425d-8254-90491f88cbde"
      },
      "source": [
        "#Let's visualize our circuit\n",
        "circuit_es2.draw('mpl')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 441.632x204.68 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 53
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IisWW_p4MBSy",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 333
        },
        "outputId": "caa6e364-acc4-43b5-bae6-a4fa87c68d76"
      },
      "source": [
        "simulator = Aer.get_backend('qasm_simulator') \n",
        "result = execute(circuit_es2,backend=simulator, shots = 1024).result() \n",
        "counts = result.get_counts()\n",
        "plot_histogram(counts)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 504x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 54
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dfnKp_OcNcLr",
        "colab_type": "text"
      },
      "source": [
        "**The Third Bell State:**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "EdAxxDKer8Z_"
      },
      "source": [
        "<img src =\"Images_Used/Quantum_Entanglement/Bell3.png\" />"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-nJHRZLXMaC-",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 33
        },
        "outputId": "617eca74-8db7-4f66-e91c-f0b8b8b8ddc5"
      },
      "source": [
        "circuit_es3 = QuantumCircuit(2,2)\n",
        "circuit_es3.x(1) #Applying the NOT Gate on the second qubit to get the state |10>\n",
        "circuit_es3.h(0) \n",
        "circuit_es3.cx(0,1)\n",
        "circuit_es3.measure(0,0) \n",
        "circuit_es3.measure(1,1)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<qiskit.circuit.instructionset.InstructionSet at 0x7fe66d59d048>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 55
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JZBT8VHXN0nx",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 185
        },
        "outputId": "93ae0eff-13bf-443a-fadc-03eee335190a"
      },
      "source": [
        "#Let's visualize our circuit\n",
        "circuit_es3.draw('mpl')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 381.432x204.68 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 56
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rDpbzR26N3Ir",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 331
        },
        "outputId": "80a6cbf8-2fc4-4483-b963-064211fb2361"
      },
      "source": [
        "simulator = Aer.get_backend('qasm_simulator') \n",
        "result = execute(circuit_es3,backend=simulator, shots = 1024).result() \n",
        "counts = result.get_counts()\n",
        "plot_histogram(counts)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 504x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 57
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qoWMAL_FOMUq",
        "colab_type": "text"
      },
      "source": [
        "**The Fourth Bell State:**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "JLvneDXQsABy"
      },
      "source": [
        "<img src =\"Images_Used/Quantum_Entanglement/Bell4.png\" />"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0uARVFN5OKuP",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 33
        },
        "outputId": "244b26e8-9888-43ab-cd0d-294576d361b9"
      },
      "source": [
        "circuit_es4 = QuantumCircuit(2,2)\n",
        "circuit_es4.x(0)\n",
        "circuit_es4.x(1) #Applying the NOT Gates on the two qubits to get the state |11>\n",
        "circuit_es4.h(0) \n",
        "circuit_es4.cx(0,1)\n",
        "circuit_es4.measure(0,0) \n",
        "circuit_es4.measure(1,1)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<qiskit.circuit.instructionset.InstructionSet at 0x7fe66d4a5ef0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 58
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8aPx1x_ROWhN",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 185
        },
        "outputId": "29416925-24fa-41e9-e655-7f0692370667"
      },
      "source": [
        "#Let's visualize our circuit\n",
        "circuit_es4.draw('mpl')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 441.632x204.68 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 59
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "42wKYxYSOaPy",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 335
        },
        "outputId": "2cd75ce2-23a5-4e24-bffb-2a596b771abf"
      },
      "source": [
        "simulator = Aer.get_backend('qasm_simulator') \n",
        "result = execute(circuit_es4,backend=simulator, shots = 1024).result() \n",
        "counts = result.get_counts()\n",
        "plot_histogram(counts)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 504x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 60
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xDRSNFxRO8BS",
        "colab_type": "text"
      },
      "source": [
        "If you find something incorrect in the notebook or feel that some concepts needed a better explaination or you need resources for better understanding, contact me on [LinkedIn](https://www.linkedin.com/in/jay-shah-mlpython/).\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gPsL7AXXSVuT",
        "colab_type": "text"
      },
      "source": [
        "**THANK YOU!**"
      ]
    }
  ]
}