1-Basics.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "0f5cce31-f168-428c-a5df-5ccd4cbf8923",
   "metadata": {},
   "source": [
    "# Pennylane installation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fc94bc9d-cfa1-44ba-841c-5bd9bed39677",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "pip install pennylane --upgrade"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c9883ae-ba81-4205-8ed6-6338018d2fa9",
   "metadata": {
    "tags": []
   },
   "source": [
    "# Quantum Circuits"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "efaa5a98-862e-492d-bab3-bf142592b34f",
   "metadata": {},
   "source": [
    "- Instead of the qubit, PennyLane uses the term wires to refer to a quantum subsystem. \n",
    "- A circuit is represented as a function. By default all qubits are initialized as |0>.\n",
    "- The quantum function returns either a single or a tuple of measured observable values by applying a **measurement function**, which in the function below is the **PauliZ operator** to the qubit 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "bad6199f-0433-4b72-a770-c3f5e043743e",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import pennylane as qml\n",
    "\n",
    "def quantum_function(x, y):\n",
    "    qml.RZ(x, wires=0)\n",
    "    qml.CNOT(wires=[0,1])\n",
    "    qml.RY(y, wires=1)\n",
    "    return qml.expval(qml.PauliZ(1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8022bb33-67d3-4967-a8c7-189c119c4213",
   "metadata": {
    "tags": []
   },
   "source": [
    "To run and optimize a quantum circuit, we need to specify the quantum device on which to execute the circuit. Here we use the ”default.qubit” device, which is a standard quantum simulator. It is instantiated using the device loader as follows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a4c57b90-61f7-41bf-a10f-2646f8ad9e6f",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "dev = qml.device('default.qubit', wires=2, shots=1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75a1cd00-a556-43d7-9626-4ee5c6dda592",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Creating a quantum node"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca8ab18c-ec8b-471a-9996-c58b7cd22bf4",
   "metadata": {},
   "source": [
    "Quantum computations are represented as quantum node objects in PennyLane. A quantum node is an initialization of the quantum circuit, and encapsulates the computation to the specific quantum device that executes the circuit. Quantum nodes can be easily created by using the qnode decorator.\n",
    "\n",
    "<p style=\"text-align: center\"><img src=\"images/Qnode.png\" width=\"200\" height=\"100\"></p>\n",
    "\n",
    "QNodes can interact with machine learning libraries such as PyTorch and TensorFlow. This is what allows it to connect the quantum circuit to data structures like TensorFlow tensors and optimizers. By default, QNodes use the NumPy interface.\n",
    "\n",
    "A QNode is initialized as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "31a2ad11-7466-4f50-a882-1c28f8a94caf",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "circuit = qml.QNode(quantum_function, dev)\n",
    "\n",
    "##Qnode can also be used as a decorator:\n",
    "#@qml.qnode(dev)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3fa6b8c-9c48-4a81-9870-d654243eb026",
   "metadata": {},
   "source": [
    "The QNode is used to compute the result of a quantum circuit and can calculate results classically. For example, we will run the results of the quantum_function by creating a QNode circuit and passing the parameters x and y in the function quantum_function. Then an RZ gate, CNOT and RY will be applied on the circuit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "88c68024-db40-49ba-81cd-3c916633c763",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(<Figure size 600x300 with 1 Axes>, <Axes: >)\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 600x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "result = qml.draw_mpl(circuit)(np.pi/3, 0.5)\n",
    "print(result)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}