{ "cells": [ { "cell_type": "markdown", "id": "5c38153e", "metadata": {}, "source": [ "# Photonic circuits in QISKIT" ] }, { "cell_type": "code", "execution_count": 1, "id": "e20f1af2", "metadata": {}, "outputs": [], "source": [ "import qoptkit # QOPTKIT module\n", "import numpy as np # Numpy\n", "from math import acos,sqrt,pi # Mathematical module\n", "from qiskit import QuantumCircuit # QISKIT Circuits \n", "from qiskit_aer import Aer # QISKIT Aer\n", "from qiskit.visualization import plot_distribution # QISKIT Visualization tools" ] }, { "cell_type": "markdown", "id": "f8dd8eb6", "metadata": {}, "source": [ "## 1 Designing photonic circuits" ] }, { "cell_type": "markdown", "id": "10bfc409", "metadata": {}, "source": [ "

We have shown how a linear optical circuit can be used to implement the general qubit rotations rx,ry,rz and also the two qubit CZ operation. Therefore, we can choose any logical circuit defined using QISKIT and translate that circuit into an optical circuit. As shown next, the process is straightforward.

" ] }, { "cell_type": "markdown", "id": "bea83835", "metadata": {}, "source": [ "### Translation by substitution" ] }, { "cell_type": "markdown", "id": "4e10939e", "metadata": {}, "source": [ "

A logical circuit defined in QISKIT can be transpiled into an equivalent version made of the four gates rx,ry,rx and CZ that we can implement with optical elements. Then each of these gates is substituted by its optical counterpart. Let's put an example. First we are going to create and arbitrary circuit,

" ] }, { "cell_type": "code", "execution_count": 2, "id": "05db7537", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "q_circuit=QuantumCircuit(2,2)\n", "q_circuit.u(1.2,1.5,0.9,0)\n", "q_circuit.u(0.9,3.1,0.2,1)\n", "q_circuit.cx(0,1)\n", "q_circuit.barrier()\n", "q_circuit.measure(0,1)\n", "q_circuit.measure(1,0)\n", "q_circuit.draw(output='mpl')" ] }, { "cell_type": "markdown", "id": "3e745bde", "metadata": {}, "source": [ "

It is usual in quantum optics literature that channel \"0\" is represented as the most significant bit of the result. By extension, this also applies for qubits. This is, a \"01\" outcome means q0=0 and q1=1. However, QISKIT works the other way around. Qubit 0 is the least significant bit of the result. Therefore, when comparison between the two kind of circuits has to be made it is important to remember to invert the order in which the qubits are measured into classical bits. In our example this means that qubit 0 is assigned to classical bit 1 q0->c1 and q1->c0.

" ] }, { "cell_type": "markdown", "id": "91d325b1", "metadata": {}, "source": [ "Now we can simulate this circuit and plot the results." ] }, { "cell_type": "code", "execution_count": 3, "id": "29125b02", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qiskitsim = Aer.get_backend('aer_simulator') \n", "result = qiskitsim.run(q_circuit, shots=100000).result()\n", "counts = result.get_counts()\n", "plot_distribution(counts)" ] }, { "cell_type": "markdown", "id": "acf2aaf4", "metadata": {}, "source": [ "This circut can be transpiled into its corresponding optical version." ] }, { "cell_type": "code", "execution_count": 4, "id": "7bb6369e", "metadata": {}, "outputs": [], "source": [ "compiler=qoptkit.compiler() \n", "opt_circuit,cond,ancillas,pselect, oV=compiler.transpile(q_circuit)" ] }, { "cell_type": "markdown", "id": "3329f870", "metadata": {}, "source": [ "The whole process has been done automatically. First the circuit is transpiled," ] }, { "cell_type": "code", "execution_count": 5, "id": "58481f52", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "oV.draw(output='mpl')" ] }, { "cell_type": "markdown", "id": "3f7cbf39", "metadata": {}, "source": [ "An then the substitution is carried out." ] }, { "cell_type": "code", "execution_count": 6, "id": "6a78f5fa", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "opt_circuit.show(depth=22,sizexy=80,font=18)" ] }, { "cell_type": "markdown", "id": "0e8435d2", "metadata": {}, "source": [ "

A simulation will show how both circuits (the logical and the optical) provide the same results. Note that the optical simulation is performed for an input state that corresponds to a logical qubit value 00. QISKIT assumes by default that qubits are initialized to zero because it is easier to initialize superconductor qubits to this value. This is the reason because the optical simulation has to be also initialized to 0 to make the results comparable.

" ] }, { "cell_type": "code", "execution_count": 7, "id": "5ada6539", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "qubit= qoptkit.state(2,st=[ [1.0,[0,0]] ])\n", "inputst=qubit.decode(cond,ancillas,opt_circuit)\n", "soqssim=qoptkit.simulator() \n", "outstate=soqssim.run(inputst,opt_circuit)\n", "pselected=outstate.post_selection(pselect)\n", "encoded_state=pselected.encode(cond, opt_circuit)\n", "encoded_state.normalize()\n", "encoded_state.show(sizex=6,sizey=4)" ] }, { "cell_type": "markdown", "id": "2b0374d6", "metadata": {}, "source": [ "## 2 Obtaining logic from optical circuits." ] }, { "cell_type": "markdown", "id": "81e04feb", "metadata": {}, "source": [ "

As an attentive reader you may be wondering if it is possible to perform the opposite operation. Given an optical circuit may I obtain the logic of this circuit? Let's draw a arbitrary linear circuit inspired by the CNOT [4] and to calculate its output for a 00 qubit input.

" ] }, { "cell_type": "code", "execution_count": 8, "id": "db424b25", "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Create circuit\n", "cond=[[1, 2],[3, 4]]\n", "opt_circuit = qoptkit.qocircuit(6);\n", "opt_circuit.bs(3,4, 45.0,0.0)\n", "opt_circuit.barrier()\n", "opt_circuit.bs(0,1,180*acos(1.0/sqrt(3.0))/pi,0.0)\n", "opt_circuit.bs(2,3,180*acos(1.0/sqrt(3.0))/pi,0.0)\n", "opt_circuit.bs(4,5,180*acos(1.0/sqrt(3.0))/pi,0.0)\n", "opt_circuit.barrier()\n", "opt_circuit.bs(3,4, 25.0,0.0)\n", "opt_circuit.barrier()\n", "opt_circuit.ph(3, 180)\n", "opt_circuit.ph(4, 180)\n", "opt_circuit.show(sizexy=80,depth=12)\n", "\n", "\n", "# Calculate probability distribution in QOKIT\n", "inputst= qoptkit.state(6,st=[ [1.0,[0,0,1,0,1,0]]])\n", "outstate=soqssim.run(inputst,opt_circuit )\n", "pselected=outstate.post_selection([0,-1,-1,-1,-1,0])\n", "encoded_state=pselected.encode(cond, opt_circuit)\n", "encoded_state.normalize()\n", "encoded_state.show(sizex=4,sizey=4)" ] }, { "cell_type": "markdown", "id": "356b9dcf", "metadata": {}, "source": [ "

Next, we obtain the corresponding logical circuit using the proper QoptKIT instruction. We have to specify the gates that are allowed to be used to build the resulting logical circuit,

" ] }, { "cell_type": "code", "execution_count": 9, "id": "5c248c85", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "q_circuit=compiler.assemble(cond,cond,[0,0,0,0,0,0],[0,-1,-1,-1,-1,0],['id','rx','ry','rz','cx'],opt_circuit,measure='qoptkit')\n", "q_circuit.draw(output=\"mpl\")" ] }, { "cell_type": "markdown", "id": "e1ff4931", "metadata": {}, "source": [ "Finally, we can perform a QISKIT simulation to check that both circuits are equivalent." ] }, { "cell_type": "code", "execution_count": 10, "id": "3bee08ad", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qiskitsim = Aer.get_backend('aer_simulator') \n", "result = qiskitsim.run(q_circuit).result()\n", "counts = result.get_counts()\n", "plot_distribution(counts)" ] }, { "cell_type": "markdown", "id": "6bfdcd35", "metadata": {}, "source": [ "

Note that after post-selection and encoding a linear optical circuit may not be represented by a unitary matrix. Therefore the process of translation will fail if the optical circuit does not have an equivalent logical circuit.

" ] }, { "cell_type": "markdown", "id": "8e668366", "metadata": {}, "source": [ "**THIS CODE IS PART OF QoptKIT**
\n", "\n", "**Copyright:**
\n", "Copyright © 2023 National University of Ireland Maynooth, Maynooth University.\n", "\n", "Licensed under the Apache License, Version 2.0 (the \"License\"); you may not use this file except in compliance with the License" ] } ], "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": "3.8.8" } }, "nbformat": 4, "nbformat_minor": 5 }