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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Getting started\n",
        "\n",
        "This notebook will guide you through the basic steps necessary to generate and simulate a simple quantum circuit.\n",
        "\n",
        "\n",
        "## Writing a quantum circuit\n",
        "\n",
        "Let us write a circuit preparing a Bell state $(|00\\rangle + |11\\rangle)/\\sqrt{2}$:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {},
      "outputs": [
        {
          "data": {
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            "text/plain": [
              "<wand.image.Image: 8d66b60 'PDF' (153x76)>"
            ]
          },
          "execution_count": 1,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "from qat.lang.AQASM import Program, H, CNOT\n",
        "\n",
        "# Create a Program\n",
        "qprog = Program()\n",
        "# Number of qbits\n",
        "nbqbits = 2\n",
        "# Allocate some qbits\n",
        "qbits = qprog.qalloc(nbqbits)\n",
        "\n",
        "# Apply some quantum Gates\n",
        "qprog.apply(H, qbits[0]) \n",
        "qprog.apply(CNOT, qbits[0], qbits[1])\n",
        "\n",
        "# Export this program into a quantum circuit\n",
        "circuit = qprog.to_circ()\n",
        "# And display it!\n",
        "circuit.display()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Simulating the circuit\n",
        "\n",
        "To simulate our circuit, we use our linear-algebra-based simulator, linalg. We print out the states of the computational basis with a nonzero amplitude (here, we expect to see the state $|00\\rangle$ (= index 0) and the state $|11\\rangle$ (= index 3), both with amplitude $|1/\\sqrt{2}$)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "State |00> amplitude (0.7071067811865475+0j)\n",
            "State |11> amplitude (0.7071067811865475+0j)\n"
          ]
        }
      ],
      "source": [
        "# import one Quantum Processor Unit Factory\n",
        "from qat.qpus import PyLinalg\n",
        "\n",
        "# Create a Quantum Processor Unit\n",
        "pylinalgqpu = PyLinalg()\n",
        "\n",
        "# Create a job\n",
        "job = circuit.to_job()\n",
        "\n",
        "# Submit the job to the QPU\n",
        "result = pylinalgqpu.submit(job)\n",
        "\n",
        "# Iterate over the final state vector to get all final components\n",
        "for sample in result:\n",
        "    print(\"State %s amplitude %s\" % (sample.state, sample.amplitude))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "We can also sample the final state of the system to mimic the measure of the final state of a quantum processor. Here, we expect to see state 0 half of the time, and state 3 half of the time (on average)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "scrolled": true
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "We measured the state |00> (its probability is 0.4 and its amplitude None)\n",
            "We measured the state |11> (its probability is 0.6 and its amplitude None)\n"
          ]
        }
      ],
      "source": [
        "# Create a job where we specify the number of shots\n",
        "job = circuit.to_job(nbshots=10)\n",
        "\n",
        "# Submit to the QPU\n",
        "result = pylinalgqpu.submit(job)\n",
        "\n",
        "# And use it to draw 10 samples\n",
        "for sample in result:\n",
        "    print(\"We measured the state {} (its probability is {} and its amplitude {})\".format(sample.state, sample.probability, sample.amplitude))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "For more information about simulation options, in order to know what you can ask from a simulator, checkout [this tutorial](tutorials/simulation/simulation_overview.ipynb).\n",
        "\n",
        "In particular, you will learn how to **directly compute the average of an observable** or **return the state vector as a numpy array**."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "As for quantum programming, you can learn more about  [here](tutorials/lang/writing_quantum_program.ipynb).\n"
      ]
    }
  ],
  "metadata": {
    "authors": [
      "Simon Martiel",
      "Jerome Pioux"
    ],
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