QiskitCircuit.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "8e8ff792-c256-4eab-b6cf-ab27a633957a",
   "metadata": {},
   "source": [
    "This section is a brief exploration into quantum circuits and their implementation in Qiskit. We plan to use `qiskit` and a library `bosonic-qiskit` to program and simualte our quantum circuits. We first followed [Quantum Circuits](https://learning.quantum.ibm.com/course/basics-of-quantum-information/quantum-circuits) to gain some experience with `qiskit`. We also followed some lessons from the [Bosonic Qiskit Textbook](https://github.com/C2QA/bosonic-qiskit/tree/main/tutorials/bosonic-qiskit-textbook) present in the `bosonic-qiskit` Github repository alongside other [tutorials](https://github.com/C2QA/bosonic-qiskit/tree/main/tutorials). "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5193c5b-3078-4f3f-9d46-4eec0055898e",
   "metadata": {},
   "source": [
    "The following are some basic examples of things we can do with `qiskit`. We begin with a brief look at `qiskit`'s `Statevector` class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "efb80f30-5791-4aa1-87ba-b7d1c61bcb70",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.quantum_info import Statevector\n",
    "from numpy import sqrt\n",
    "\n",
    "x = Statevector([1 / sqrt(2), 1 / sqrt(2)])\n",
    "y = Statevector([1+3.0j, -1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "98bbee8f-c292-4350-b575-dc2429a35f5d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{\\sqrt{2}}{2} |0\\rangle+\\frac{\\sqrt{2}}{2} |1\\rangle$$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'\\\\frac{\\\\sqrt{2}}{2} |0\\\\rangle+\\\\frac{\\\\sqrt{2}}{2} |1\\\\rangle'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[ 1.+3.j,-1.+0.j]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X is a valid state: True\n",
      "Y is a valid state: False\n"
     ]
    }
   ],
   "source": [
    "display(x.draw(\"latex\"))\n",
    "display(x.draw(\"latex_source\"))\n",
    "display(y.draw(\"text\"))\n",
    "\n",
    "\n",
    "print(f\"X is a valid state: {x.is_valid()}\")\n",
    "print(f\"Y is a valid state: {y.is_valid()}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1cba1a2c-b1dc-45c8-8b0c-559b96eee55a",
   "metadata": {},
   "source": [
    "We used a variety of options with the `draw` method to display statevectors. We also tested if the statevectors were valid.\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c65e035-2fcf-499e-9f7d-1e890cba573f",
   "metadata": {},
   "source": [
    "Below we dive into basic quantum circuits, first starting with some neccessary imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "60ba99fd-f060-4761-8978-32c869326a39",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister\n",
    "from qiskit.primitives import Sampler\n",
    "from qiskit.visualization import plot_histogram"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ebef51e-607e-4716-8550-b9c4255d4da6",
   "metadata": {},
   "source": [
    "We then create a simple circuit composed of one qubit and draw it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f332fc38-316c-4191-9109-ca0716ce217f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">   ┌───┐┌───┐┌───┐\n",
       "q: ┤ S ├┤ H ├┤ T ├\n",
       "   └───┘└───┘└───┘</pre>"
      ],
      "text/plain": [
       "   ┌───┐┌───┐┌───┐\n",
       "q: ┤ S ├┤ H ├┤ T ├\n",
       "   └───┘└───┘└───┘"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "circuit = QuantumCircuit(1)\n",
    "\n",
    "circuit.s(0)\n",
    "circuit.h(0)\n",
    "circuit.t(0)\n",
    "\n",
    "display(circuit.draw())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d40d3b82-b106-4e91-b4ae-1a83534d3362",
   "metadata": {},
   "source": [
    "Next we show an example of a circuit with classical and quantum registers along with gates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2fcbbd2e-8558-4004-aa60-8e6267b6c159",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">     ┌───┐     ┌─┐   \n",
       "  X: ┤ H ├──■──┤M├───\n",
       "     └───┘┌─┴─┐└╥┘┌─┐\n",
       "  Y: ─────┤ X ├─╫─┤M├\n",
       "          └───┘ ║ └╥┘\n",
       "U: 1/═══════════╩══╬═\n",
       "                0  ║ \n",
       "V: 1/══════════════╩═\n",
       "                   0 </pre>"
      ],
      "text/plain": [
       "     ┌───┐     ┌─┐   \n",
       "  X: ┤ H ├──■──┤M├───\n",
       "     └───┘┌─┴─┐└╥┘┌─┐\n",
       "  Y: ─────┤ X ├─╫─┤M├\n",
       "          └───┘ ║ └╥┘\n",
       "U: 1/═══════════╩══╬═\n",
       "                0  ║ \n",
       "V: 1/══════════════╩═\n",
       "                   0 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = QuantumRegister(1,\"X\")\n",
    "Y = QuantumRegister(1,\"Y\")\n",
    "U = ClassicalRegister(1,\"U\")\n",
    "V = ClassicalRegister(1, \"V\")\n",
    "circuit = QuantumCircuit(X,Y,U,V)\n",
    "\n",
    "circuit.h(X)\n",
    "circuit.cx(X,Y[0])\n",
    "circuit.measure(X,U)\n",
    "circuit.measure(Y,V)\n",
    "display(circuit.draw())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ced3abe3-d1ec-4e1d-92f4-da2b5d114324",
   "metadata": {},
   "source": [
    "We can simulate this circuit using `Sampler` and display a histogram of the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "2b72343b-9cc3-4d7d-a71f-896fbe07c735",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results = Sampler().run(circuit).result()\n",
    "statistics = results.quasi_dists[0].binary_probabilities()\n",
    "display(plot_histogram(statistics))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09f724fb-4d7b-45f6-999c-fce0e9063dc5",
   "metadata": {},
   "source": [
    "***\n",
    "Next we explored `bosonic-qiskit`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "76f69185-f777-4cc6-b58e-b7b72f508828",
   "metadata": {},
   "outputs": [],
   "source": [
    "import c2qa #Bosonic-qiskit\n",
    "import qiskit\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "073e174f-1199-446c-8772-b2007fc0a4e5",
   "metadata": {},
   "source": [
    "We define a qumode using 4 qubit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "38a79396-3cef-4d96-bd58-7066fa076be9",
   "metadata": {},
   "outputs": [],
   "source": [
    "qmr = c2qa.QumodeRegister(\n",
    "    num_qumodes=1,\n",
    "    num_qubits_per_qumode=4\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64f90c2f-c2c0-4ab7-97fb-9ef1a4d30310",
   "metadata": {},
   "source": [
    "We can initalize this qumode to different states"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f0828fd5-1b71-444a-a96c-5d612e2bb3c1",
   "metadata": {},
   "outputs": [],
   "source": [
    "circuit = c2qa.CVCircuit(qmr)\n",
    "circuit.cv_initialize([1/np.sqrt(2),1/np.sqrt(2)],qmr[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76124ddd-d6b2-4dd3-b928-79c1e09775f9",
   "metadata": {},
   "source": [
    "Here are some examples of defining CV, DV, and Classical registers in `bosonic-qiskit`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "659ccc48-b309-4d21-befe-b88cb3961b2c",
   "metadata": {},
   "outputs": [],
   "source": [
    "qmr = c2qa.QumodeRegister(\n",
    "    num_qumodes=1,\n",
    "    num_qubits_per_qumode=4\n",
    ")\n",
    "\n",
    "qr = qiskit.QuantumRegister(\n",
    "    size=1\n",
    ")\n",
    "\n",
    "cr = qiskit.ClassicalRegister(\n",
    "    size = 1\n",
    ")\n",
    "\n",
    "circuit = c2qa.CVCircuit(qmr, qr, cr)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6aa5771c-900c-444e-89ea-56f337cd938d",
   "metadata": {},
   "source": [
    "Here is a visualization of the Wigner Function of a Fock State"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "f22abeb1-9a7e-45ee-b4eb-9935b42c2d9c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import qiskit.visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "08069772-5f13-4e24-9561-2116ca523b3e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qmr = c2qa.QumodeRegister(1, num_qubits_per_qumode=3) # Create a qumode register with one qumode\n",
    "circuit = c2qa.CVCircuit(qmr) # Create a CV circuit\n",
    "\n",
    "circuit.cv_initialize(4, qmr) # Initialize the qumode in the state |4>\n",
    "\n",
    "# Simulate and plot the wigner function\n",
    "state,_,_ = c2qa.wigner.simulate(circuit)\n",
    "plot = c2qa.wigner.plot_wigner(circuit, state) # 5 rings correspond to 4 quanta"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d99b5b9-afc1-4cd0-b5bb-2f040078e268",
   "metadata": {},
   "source": [
    "This brief exploration into `qiskit` and `bosonic-qiskit` demonstrated the ease of use of implementing quantum circuits in code. However, a deeper understanding of both packages is required to realize a CV-DV quantum circuit and build up further from there. Qiskit integrates nicely with `numpy` and `matplot-lib`, allowing for ample statistics to be gathered and plotted. Currently, we will be limited to simulators due to the lack of available hardware implementations of CV-DV quantum computing open to outside usage and testing."
   ]
  }
 ],
 "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": "3.12.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}