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DmitryVasilevskyDmitry Vasilevsky
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Dmitry Vasilevsky
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Added sample notebook with noise (#1980)
Demonstrates use of Pauli noise in Python and display histogram widget in the notebook. --------- Co-authored-by: Dmitry Vasilevsky <[email protected]>
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‎samples/notebooks/noise.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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"source": [
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"# Simulating Pauli noise\n",
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"This notebook shows how to run simulations with Pauli noise, such as bit-flip or depolarizing noise.\n",
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"\n",
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"First, make sure prerequisites are available. Packages `qsharp` and `qsharp_widgets` must be already installed."
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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": 5,
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"metadata": {},
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"outputs": [],
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"source": [
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"import qsharp\n",
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"import qsharp_widgets"
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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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"source": [
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"## Simulation with noise\n",
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"\n",
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"Define a simple program that creates a Bell state on two qubits and measures both qubits."
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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": 6,
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"metadata": {
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"vscode": {
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"languageId": "qsharp"
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}
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},
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"outputs": [],
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"source": [
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"%%qsharp\n",
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"\n",
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"operation BellPair() : Result[] {\n",
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" use q = Qubit[2];\n",
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" H(q[0]);\n",
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" CNOT(q[0], q[1]);\n",
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" MResetEachZ(q)\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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"source": [
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"Run 20 shots without noise and display results."
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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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"outputs": [],
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"source": [
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"results = qsharp.run(\"BellPair()\", 20)\n",
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"results"
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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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"source": [
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"Note that measurements always agree within a shot as expected. Now run 20 shots of the same program with 10% [depolarizing noise](https://en.wikipedia.org/wiki/Quantum_depolarizing_channel). Depolarizing noise is applied to each gate and each measurement."
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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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"outputs": [],
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"source": [
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"results = qsharp.run(\"BellPair()\", 20, noise=qsharp.DepolarizingNoise(0.1))\n",
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"results"
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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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"source": [
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"Note that measurements do not always agree within the shot."
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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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"source": [
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"## Histograms\n",
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"\n",
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"Define a program to prepare a cat state on five qubits and measure each qubit."
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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": 9,
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"metadata": {
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"vscode": {
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"languageId": "qsharp"
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}
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},
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"outputs": [],
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"source": [
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"%%qsharp\n",
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"\n",
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"operation Cat5() : Result[] {\n",
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" use q = Qubit[5];\n",
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" H(q[0]);\n",
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" ApplyCNOTChain(q);\n",
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" MResetEachZ(q)\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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"source": [
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"First, run this program without noise. Roughly half of the outcomes should be $\\ket{00000}$ and another half should be $\\ket{11111}$."
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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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"outputs": [],
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"source": [
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"result = qsharp.run(\"Cat5()\", 1000)\n",
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"qsharp_widgets.Histogram(result)\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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"source": [
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"Now, run the same program with bit-flip noise of 1%, 5%, 10%, 25%."
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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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"outputs": [],
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"source": [
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"for p in [0.01, 0.05, 0.1, 0.25]:\n",
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" result = qsharp.run(\"Cat5()\", 1000, noise=qsharp.BitFlipNoise(p))\n",
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" display(f\"Noise probability = {p}\")\n",
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" display(qsharp_widgets.Histogram(result))"
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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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"source": [
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"We can see that with 1% noise, cat state can still be clearly seen, but when noise approaches 25%, the cat state is indistinguishable from noise."
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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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"source": [
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"## Arbitrary Pauli noise\n",
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"\n",
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"Standard bit-flip, phase-flip, and [depolarizing](https://en.wikipedia.org/wiki/Quantum_depolarizing_channel) noise are available, but arbitrary Pauli noise is also possible. The following example runs the same Cat5 program. First it applies noise with 20% probability (bit-flip half the time and phase-flip half the time). In a second experiment it applies Pauli-Y noise with 10% probability."
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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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"outputs": [],
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"source": [
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"result = qsharp.run(\"Cat5()\", 1000, noise=(0.1, 0.0, 0.1))\n",
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"display(qsharp_widgets.Histogram(result))\n",
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"result = qsharp.run(\"Cat5()\", 1000, noise=(0.0, 0.1, 0.0))\n",
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"display(qsharp_widgets.Histogram(result))"
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]
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}
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],
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"metadata": {
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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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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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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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"version": "3.11.9"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}

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