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Abraham Asfaw
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Merge pull request #43 from ordmoj/master
09_23_19_Hassi_Norlen
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‎qiskit_advocates/meetups/09_23_19-Hassi_Norlen-Morgan_State_Uni/1_1_coin_toss.ipynb

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"source": [
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"# Coin toss quantum circuit\n",
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"In this exercise we create a quantum circuit that simulates the probabilistic nature of a single qubit in superposition. The one qubit circuit initializes the qubit in the ground state $|0\\rangle$ and then uses a Hadamard gate to put the qubit in superposition $|\\psi\\rangle = \\left(|0\\rangle+|1\\rangle\\right)/\\sqrt{2}.$ \n",
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"Measuring the qubit causes it to collapse into one of the states $|0\\rangle$ or $|1\\rangle$ with a 50% probability, i.e. a coin toss. \n",
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"In this exercise we introduce the Hadamard gate, which puts a qubit in superposition.\n",
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"```\n",
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" ┌───┐ \n",
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"q_0: |0>┤ H ├ \n",
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" └───┘ \n",
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"```\n",
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"\n",
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"We also introduce the X gate that flips the qubit from $|0\\rangle$ to $|1\\rangle$ and vice versa.\n",
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"```\n",
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" ┌───┐\n",
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"q_0: |0>┤ X ├\n",
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" └───┘\n",
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"```"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"source": [
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"Import the required libraries."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"slideshow": {
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"slide_type": "fragment"
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}
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},
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"outputs": [],
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"source": [
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"from qiskit import QuantumCircuit, execute, Aer\n",
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"\n",
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"# Import Blochsphere visualization\n",
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"from qiskit.visualization import plot_bloch_multivector, plot_histogram"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"source": [
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"As we will be using the Bloch sphere visualization (`plot_bloch_multivector`) a bit, here's a quick function that calculates the state vector ($|\\psi\\rangle$) for the circuit to let you display the Bloch vector for any given state.\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"slideshow": {
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"slide_type": "fragment"
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}
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},
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"outputs": [],
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"source": [
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"def get_psi(circuit): \n",
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" global psi\n",
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" backend = Aer.get_backend('statevector_simulator') \n",
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" psi = execute(circuit, backend).result().get_statevector(circuit)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"source": [
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"Create an empty quantum circuit. We start out with the qubit in the $|0\\rangle$ state."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"slideshow": {
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"slide_type": "fragment"
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}
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},
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"outputs": [],
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"source": [
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"qc = QuantumCircuit(1,1)\n",
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"\n",
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"# Print out the circuit\n",
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"print(qc)\n",
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"\n",
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"# Display the Bloch sphere\n",
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"get_psi(qc)\n",
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"plot_bloch_multivector(psi)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"source": [
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"Add a Hadamard (super position) gate to the quantum circuit. This puts the qubit in a superposition: $|\\psi\\rangle = \\left(|0\\rangle+|1\\rangle\\right)/\\sqrt{2}.$"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"slideshow": {
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"slide_type": "fragment"
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}
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},
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"outputs": [],
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"source": [
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"qc.h(0)\n",
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"\n",
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"# Print out the circuit\n",
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"print(qc)\n",
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"\n",
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"# Display the Bloch sphere\n",
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"get_psi(qc)\n",
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"plot_bloch_multivector(psi)\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"source": [
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"Finally, add a measurement gate to complete the circuit."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"slideshow": {
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"slide_type": "fragment"
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}
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},
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"outputs": [],
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"source": [
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"# Add measure gate\n",
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"qc.measure(0,0)\n",
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"print(qc)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"source": [
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"Set the backend to a local simulator."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"slideshow": {
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"slide_type": "fragment"
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}
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},
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"outputs": [],
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"source": [
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"backend = Aer.get_backend('qasm_simulator')"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"source": [
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"Create a quantum job that runs just one shot to simulate a coin toss. Then run the job and display the result; either 0 for up (base) or 1 for down (excited). Display the result as a histogram."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"slideshow": {
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"slide_type": "fragment"
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}
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},
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"outputs": [],
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"source": [
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"job = execute(qc, backend, shots=1)\n",
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"counts = job.result().get_counts()\n",
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"print(counts)\n",
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"plot_histogram(counts)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"source": [
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"Now, lets run a thousand coin tosses in a row and see what we get."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"slideshow": {
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"slide_type": "fragment"
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}
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},
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"outputs": [],
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"source": [
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"job = execute(qc, backend, shots=1000)\n",
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"counts = job.result().get_counts()\n",
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"print(counts)\n",
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"plot_histogram(counts)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"slideshow": {
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"slide_type": "fragment"
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}
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},
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"source": [
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"In the histogram we see that we get 0 and 1 with ~50% probability. Which is what we expect from tossing some coins."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"source": [
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"We can also do our coin flip with the qubit starting in the $|1\\rangle$ state by first flipping the qubit by using the X gate. The Hadamard gate still flips the qubit to the equator, but now on the -X side."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"slideshow": {
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"slide_type": "fragment"
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}
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},
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"outputs": [],
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"source": [
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"qc2 = QuantumCircuit(1,1)\n",
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"qc2.x(0)\n",
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"qc2.h(0)\n",
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"print(qc2)\n",
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"# Display the Bloch sphere\n",
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"get_psi(qc2)\n",
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"plot_bloch_multivector(psi)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"slideshow": {
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"slide_type": "slide"
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}
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},
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"source": [
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"Add the measure gate and run the circuit 1,000 times."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"slideshow": {
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"slide_type": "fragment"
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}
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},
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"outputs": [],
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"source": [
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"qc2.measure(0,0)\n",
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"\n",
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"job2 = execute(qc2, backend, shots=1000)\n",
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"counts2 = job2.result().get_counts()\n",
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"print(counts2)\n",
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"plot_histogram(counts2)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"slideshow": {
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"slide_type": "fragment"
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}
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},
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"source": [
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"As you can see, there is no real difference in the outcome. "
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]
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}
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],
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"metadata": {
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"celltoolbar": "Slideshow",
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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"language_info": {
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"codemirror_mode": {
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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