microsoft/qdk
Publicmirrored fromhttps://github.com/microsoft/qdkAvailable
samples/notebooks/noise.ipynb
208lines · modecode
| 1 | { |
| 2 | "cells": [ |
| 3 | { |
| 4 | "cell_type": "markdown", |
| 5 | "metadata": {}, |
| 6 | "source": [ |
| 7 | "# Simulating Pauli noise\n", |
| 8 | "This notebook shows how to run simulations with Pauli noise, such as bit-flip or depolarizing noise.\n", |
| 9 | "\n", |
| 10 | "First, make sure prerequisites are available. Packages `qsharp` and `qsharp_widgets` must be already installed." |
| 11 | ] |
| 12 | }, |
| 13 | { |
| 14 | "cell_type": "code", |
| 15 | "execution_count": 5, |
| 16 | "metadata": {}, |
| 17 | "outputs": [], |
| 18 | "source": [ |
| 19 | "import qsharp\n", |
| 20 | "import qsharp_widgets" |
| 21 | ] |
| 22 | }, |
| 23 | { |
| 24 | "cell_type": "markdown", |
| 25 | "metadata": {}, |
| 26 | "source": [ |
| 27 | "## Simulation with noise\n", |
| 28 | "\n", |
| 29 | "Define a simple program that creates a Bell state on two qubits and measures both qubits." |
| 30 | ] |
| 31 | }, |
| 32 | { |
| 33 | "cell_type": "code", |
| 34 | "execution_count": 6, |
| 35 | "metadata": { |
| 36 | "vscode": { |
| 37 | "languageId": "qsharp" |
| 38 | } |
| 39 | }, |
| 40 | "outputs": [], |
| 41 | "source": [ |
| 42 | "%%qsharp\n", |
| 43 | "\n", |
| 44 | "operation BellPair() : Result[] {\n", |
| 45 | " use q = Qubit[2];\n", |
| 46 | " H(q[0]);\n", |
| 47 | " CNOT(q[0], q[1]);\n", |
| 48 | " MResetEachZ(q)\n", |
| 49 | "}" |
| 50 | ] |
| 51 | }, |
| 52 | { |
| 53 | "cell_type": "markdown", |
| 54 | "metadata": {}, |
| 55 | "source": [ |
| 56 | "Run 20 shots without noise and display results." |
| 57 | ] |
| 58 | }, |
| 59 | { |
| 60 | "cell_type": "code", |
| 61 | "execution_count": null, |
| 62 | "metadata": {}, |
| 63 | "outputs": [], |
| 64 | "source": [ |
| 65 | "results = qsharp.run(\"BellPair()\", 20)\n", |
| 66 | "results" |
| 67 | ] |
| 68 | }, |
| 69 | { |
| 70 | "cell_type": "markdown", |
| 71 | "metadata": {}, |
| 72 | "source": [ |
| 73 | "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." |
| 74 | ] |
| 75 | }, |
| 76 | { |
| 77 | "cell_type": "code", |
| 78 | "execution_count": null, |
| 79 | "metadata": {}, |
| 80 | "outputs": [], |
| 81 | "source": [ |
| 82 | "results = qsharp.run(\"BellPair()\", 20, noise=qsharp.DepolarizingNoise(0.1))\n", |
| 83 | "results" |
| 84 | ] |
| 85 | }, |
| 86 | { |
| 87 | "cell_type": "markdown", |
| 88 | "metadata": {}, |
| 89 | "source": [ |
| 90 | "Note that measurements do not always agree within the shot." |
| 91 | ] |
| 92 | }, |
| 93 | { |
| 94 | "cell_type": "markdown", |
| 95 | "metadata": {}, |
| 96 | "source": [ |
| 97 | "## Histograms\n", |
| 98 | "\n", |
| 99 | "Define a program to prepare a cat state on five qubits and measure each qubit." |
| 100 | ] |
| 101 | }, |
| 102 | { |
| 103 | "cell_type": "code", |
| 104 | "execution_count": 9, |
| 105 | "metadata": { |
| 106 | "vscode": { |
| 107 | "languageId": "qsharp" |
| 108 | } |
| 109 | }, |
| 110 | "outputs": [], |
| 111 | "source": [ |
| 112 | "%%qsharp\n", |
| 113 | "\n", |
| 114 | "operation Cat5() : Result[] {\n", |
| 115 | " use q = Qubit[5];\n", |
| 116 | " H(q[0]);\n", |
| 117 | " ApplyCNOTChain(q);\n", |
| 118 | " MResetEachZ(q)\n", |
| 119 | "}" |
| 120 | ] |
| 121 | }, |
| 122 | { |
| 123 | "cell_type": "markdown", |
| 124 | "metadata": {}, |
| 125 | "source": [ |
| 126 | "First, run this program without noise. Roughly half of the outcomes should be $\\ket{00000}$ and another half should be $\\ket{11111}$." |
| 127 | ] |
| 128 | }, |
| 129 | { |
| 130 | "cell_type": "code", |
| 131 | "execution_count": null, |
| 132 | "metadata": {}, |
| 133 | "outputs": [], |
| 134 | "source": [ |
| 135 | "result = qsharp.run(\"Cat5()\", 1000)\n", |
| 136 | "qsharp_widgets.Histogram(result)\n" |
| 137 | ] |
| 138 | }, |
| 139 | { |
| 140 | "cell_type": "markdown", |
| 141 | "metadata": {}, |
| 142 | "source": [ |
| 143 | "Now, run the same program with bit-flip noise of 1%, 5%, 10%, 25%." |
| 144 | ] |
| 145 | }, |
| 146 | { |
| 147 | "cell_type": "code", |
| 148 | "execution_count": null, |
| 149 | "metadata": {}, |
| 150 | "outputs": [], |
| 151 | "source": [ |
| 152 | "for p in [0.01, 0.05, 0.1, 0.25]:\n", |
| 153 | " result = qsharp.run(\"Cat5()\", 1000, noise=qsharp.BitFlipNoise(p))\n", |
| 154 | " display(f\"Noise probability = {p}\")\n", |
| 155 | " display(qsharp_widgets.Histogram(result))" |
| 156 | ] |
| 157 | }, |
| 158 | { |
| 159 | "cell_type": "markdown", |
| 160 | "metadata": {}, |
| 161 | "source": [ |
| 162 | "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." |
| 163 | ] |
| 164 | }, |
| 165 | { |
| 166 | "cell_type": "markdown", |
| 167 | "metadata": {}, |
| 168 | "source": [ |
| 169 | "## Arbitrary Pauli noise\n", |
| 170 | "\n", |
| 171 | "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." |
| 172 | ] |
| 173 | }, |
| 174 | { |
| 175 | "cell_type": "code", |
| 176 | "execution_count": null, |
| 177 | "metadata": {}, |
| 178 | "outputs": [], |
| 179 | "source": [ |
| 180 | "result = qsharp.run(\"Cat5()\", 1000, noise=(0.1, 0.0, 0.1))\n", |
| 181 | "display(qsharp_widgets.Histogram(result))\n", |
| 182 | "result = qsharp.run(\"Cat5()\", 1000, noise=(0.0, 0.1, 0.0))\n", |
| 183 | "display(qsharp_widgets.Histogram(result))" |
| 184 | ] |
| 185 | } |
| 186 | ], |
| 187 | "metadata": { |
| 188 | "kernelspec": { |
| 189 | "display_name": "Python 3", |
| 190 | "language": "python", |
| 191 | "name": "python3" |
| 192 | }, |
| 193 | "language_info": { |
| 194 | "codemirror_mode": { |
| 195 | "name": "ipython", |
| 196 | "version": 3 |
| 197 | }, |
| 198 | "file_extension": ".py", |
| 199 | "mimetype": "text/x-python", |
| 200 | "name": "python", |
| 201 | "nbconvert_exporter": "python", |
| 202 | "pygments_lexer": "ipython3", |
| 203 | "version": "3.11.9" |
| 204 | } |
| 205 | }, |
| 206 | "nbformat": 4, |
| 207 | "nbformat_minor": 2 |
| 208 | } |
| 209 | |