projectq.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ProjectQ\n",
    "\n",
    "[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/ionq-samples/getting-started/blob/main/projectq.ipynb)\n",
    "\n",
    "[ProjectQ](https://projectq.ch/) is an open-source software framework for quantum computing that allows users to design, simulate, and optimize quantum circuits on various backends."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "\n",
    "# First, we install the essential libraries to our current Python runtime.\n",
    "# \"%%capture\" (above) captures and in this case, hides the output of this \n",
    "# cell, so you can comment it out if you need help debugging this step.\n",
    "\n",
    "%pip install projectq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "from getpass import getpass\n",
    "\n",
    "import projectq.setups.ionq\n",
    "from projectq import MainEngine\n",
    "from projectq.backends import IonQBackend\n",
    "from projectq.libs.hist import histogram\n",
    "from projectq.ops import H, CNOT, Measure\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Before you begin, get your API key from https://cloud.ionq.com/settings/keys\n",
    "\n",
    "# If your API key is stored as \"IONQ_API_KEY\" in your local environment, this\n",
    "# should find it. Otherwise you'll be prompted to enter your API key manually.\n",
    " \n",
    "token = os.getenv('IONQ_API_KEY') or getpass('Enter your IonQ API key: ')\n",
    "\n",
    "# We need to specify the device where the circuit will be executed. In this \n",
    "# case we're using the `ionq_simulator`, but if you have QPU access you can\n",
    "# specify it here to run the job on a QPU directly.\n",
    "\n",
    "device = 'ionq_simulator'\n",
    "\n",
    "backend = IonQBackend(token=token, device=device)\n",
    "compiler_engines = projectq.setups.ionq.get_engine_list(token=token, device=device)\n",
    "eng = MainEngine(backend, engine_list=compiler_engines)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "qubit1 = eng.allocate_qubit()  # Allocate a quantum register with 1 qubit\n",
    "qubit2 = eng.allocate_qubit()\n",
    "\n",
    "H | qubit1  # Apply a Hadamard gate\n",
    "\n",
    "CNOT | (qubit1, qubit2)  # Entangle the qubits\n",
    "\n",
    "Measure | qubit1  # Measure the qubit\n",
    "Measure | qubit2\n",
    "\n",
    "eng.flush()  # Flush all gates (and execute measurements)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 440x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "histogram(eng.backend, qubit1 + qubit2)\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.11.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}