microsoft/qdk
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samples/notebooks/correlated_noise.ipynb
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| 1 | { |
| 2 | "cells": [ |
| 3 | { |
| 4 | "cell_type": "markdown", |
| 5 | "id": "b7675b9f", |
| 6 | "metadata": {}, |
| 7 | "source": [ |
| 8 | "# Correlated Noise Simulation\n", |
| 9 | "\n", |
| 10 | "This notebook demonstrates how to simulate **correlated (multi-qubit) noise** using the QDK simulators.\n", |
| 11 | "While the [noise.ipynb](noise.ipynb) notebook covers independent Pauli noise applied uniformly to all gates,\n", |
| 12 | "this notebook shows how to:\n", |
| 13 | "\n", |
| 14 | "1. Configure per-gate noise using `NoiseConfig`.\n", |
| 15 | "2. Define custom noise intrinsics to model multi-qubit noise for custom gates.\n", |
| 16 | "\n", |
| 17 | "First, make sure prerequisites are available. The package and extra `qdk[jupyter]` must be already installed." |
| 18 | ] |
| 19 | }, |
| 20 | { |
| 21 | "cell_type": "code", |
| 22 | "execution_count": null, |
| 23 | "id": "3f51ef59", |
| 24 | "metadata": {}, |
| 25 | "outputs": [], |
| 26 | "source": [ |
| 27 | "import qdk\n", |
| 28 | "from qdk import qsharp, openqasm\n", |
| 29 | "from qdk.simulation import NoiseConfig, run_qir\n", |
| 30 | "from qdk.widgets import Histogram" |
| 31 | ] |
| 32 | }, |
| 33 | { |
| 34 | "cell_type": "markdown", |
| 35 | "id": "3944616a", |
| 36 | "metadata": {}, |
| 37 | "source": [ |
| 38 | "## 1. Per-Gate Noise with `NoiseConfig`\n", |
| 39 | "\n", |
| 40 | "The convenience functions `DepolarizingNoise(p)` and `BitFlipNoise(p)` apply the same noise\n", |
| 41 | "to every gate. For more realistic modeling, you often need different error rates for different\n", |
| 42 | "gates, e.g., two-qubit gates are typically noisier than single-qubit gates, and they might apply\n", |
| 43 | "different noise to each qubit.\n", |
| 44 | "\n", |
| 45 | "`NoiseConfig` gives you a noise table for each gate (H, X, CNOT, etc.), and each table\n", |
| 46 | "supports arbitrary Pauli error strings." |
| 47 | ] |
| 48 | }, |
| 49 | { |
| 50 | "cell_type": "markdown", |
| 51 | "id": "fbbeb079", |
| 52 | "metadata": {}, |
| 53 | "source": [ |
| 54 | "### Bell pair with per-gate noise\n", |
| 55 | "\n", |
| 56 | "Define a Bell pair circuit in Q# and run it with different noise rates on single-qubit vs. two-qubit gates." |
| 57 | ] |
| 58 | }, |
| 59 | { |
| 60 | "cell_type": "code", |
| 61 | "execution_count": null, |
| 62 | "id": "65ae7014", |
| 63 | "metadata": { |
| 64 | "vscode": { |
| 65 | "languageId": "qsharp" |
| 66 | } |
| 67 | }, |
| 68 | "outputs": [], |
| 69 | "source": [ |
| 70 | "%%qsharp\n", |
| 71 | "\n", |
| 72 | "operation BellPair() : Result[] {\n", |
| 73 | " use qs = Qubit[2];\n", |
| 74 | " H(qs[0]);\n", |
| 75 | " CNOT(qs[0], qs[1]);\n", |
| 76 | " MResetEachZ(qs)\n", |
| 77 | "}" |
| 78 | ] |
| 79 | }, |
| 80 | { |
| 81 | "cell_type": "markdown", |
| 82 | "id": "e9d78333", |
| 83 | "metadata": {}, |
| 84 | "source": [ |
| 85 | "First, run without noise to establish a baseline. We expect only `[Zero, Zero]` and `[One, One]`." |
| 86 | ] |
| 87 | }, |
| 88 | { |
| 89 | "cell_type": "code", |
| 90 | "execution_count": null, |
| 91 | "id": "aa9be062", |
| 92 | "metadata": {}, |
| 93 | "outputs": [], |
| 94 | "source": [ |
| 95 | "result = qsharp.run(\"BellPair()\", 1000, seed=42)\n", |
| 96 | "Histogram(result)" |
| 97 | ] |
| 98 | }, |
| 99 | { |
| 100 | "cell_type": "markdown", |
| 101 | "id": "91fd10e8", |
| 102 | "metadata": {}, |
| 103 | "source": [ |
| 104 | "Now configure `NoiseConfig` with different noise rates per gate:\n", |
| 105 | "- H gate: 0.5% depolarizing (single-qubit gates are relatively clean)\n", |
| 106 | "- CNOT (cx): 5% depolarizing (two-qubit gates are typically 10× noisier)\n", |
| 107 | "- Measurement (mresetz): 1% bit-flip (measurement readout error)" |
| 108 | ] |
| 109 | }, |
| 110 | { |
| 111 | "cell_type": "code", |
| 112 | "execution_count": null, |
| 113 | "id": "e62c90e2", |
| 114 | "metadata": {}, |
| 115 | "outputs": [], |
| 116 | "source": [ |
| 117 | "noise = NoiseConfig()\n", |
| 118 | "noise.h.set_depolarizing(0.005)\n", |
| 119 | "noise.cx.set_depolarizing(0.05)\n", |
| 120 | "noise.mresetz.set_bitflip(0.01)\n", |
| 121 | "\n", |
| 122 | "result = qsharp.run(\"BellPair()\", 1000, noise=noise, seed=42)\n", |
| 123 | "Histogram(result)" |
| 124 | ] |
| 125 | }, |
| 126 | { |
| 127 | "cell_type": "markdown", |
| 128 | "id": "f231a569", |
| 129 | "metadata": {}, |
| 130 | "source": [ |
| 131 | "The histogram now shows some `[Zero, One]` and `[One, Zero]` outcomes from errors.\n", |
| 132 | "Since the CNOT has 10× more noise than the H gate, most errors come from the two-qubit gate." |
| 133 | ] |
| 134 | }, |
| 135 | { |
| 136 | "cell_type": "markdown", |
| 137 | "id": "443c3f27", |
| 138 | "metadata": {}, |
| 139 | "source": [ |
| 140 | "### Arbitrary Pauli errors on a gate\n", |
| 141 | "\n", |
| 142 | "Each `NoiseTable` supports arbitrary Pauli strings. For example, on a CNOT gate we can\n", |
| 143 | "set specific correlated errors using multi-character Pauli strings. Each character in the\n", |
| 144 | "string corresponds to a qubit argument of the gate:\n", |
| 145 | "\n", |
| 146 | "| Pauli string | Meaning |\n", |
| 147 | "|---|---|\n", |
| 148 | "| `xi` | X error on control, identity on target |\n", |
| 149 | "| `ix` | Identity on control, X error on target |\n", |
| 150 | "| `xx` | Correlated X error on both qubits simultaneously |\n", |
| 151 | "| `zz` | Correlated Z (dephasing) on both qubits |" |
| 152 | ] |
| 153 | }, |
| 154 | { |
| 155 | "cell_type": "code", |
| 156 | "execution_count": null, |
| 157 | "id": "6bbb9c77", |
| 158 | "metadata": {}, |
| 159 | "outputs": [], |
| 160 | "source": [ |
| 161 | "# Model a CNOT gate with 5% correlated IX and 2% correlated ZI on both qubits.\n", |
| 162 | "noise = NoiseConfig()\n", |
| 163 | "noise.cx.ix = 0.05 # 5% probability of correlated IX error\n", |
| 164 | "noise.cx.zi = 0.02 # 5% probability of correlated ZI error\n", |
| 165 | "\n", |
| 166 | "result = qsharp.run(\"BellPair()\", 1000, noise=noise, seed=42)\n", |
| 167 | "Histogram(result)" |
| 168 | ] |
| 169 | }, |
| 170 | { |
| 171 | "cell_type": "markdown", |
| 172 | "id": "aa361125", |
| 173 | "metadata": {}, |
| 174 | "source": [ |
| 175 | "You can also set multiple Pauli error channels at once using `set_pauli_noise`:" |
| 176 | ] |
| 177 | }, |
| 178 | { |
| 179 | "cell_type": "code", |
| 180 | "execution_count": null, |
| 181 | "id": "3bbbdbf0", |
| 182 | "metadata": {}, |
| 183 | "outputs": [], |
| 184 | "source": [ |
| 185 | "noise = NoiseConfig()\n", |
| 186 | "noise.cx.set_pauli_noise([\n", |
| 187 | " (\"XI\", 0.01), # 1% X error on control only\n", |
| 188 | " (\"IX\", 0.01), # 1% X error on target only\n", |
| 189 | " (\"XX\", 0.005), # 0.5% correlated XX\n", |
| 190 | " (\"ZZ\", 0.02), # 2% correlated ZZ crosstalk\n", |
| 191 | "])\n", |
| 192 | "\n", |
| 193 | "result = qsharp.run(\"BellPair()\", 1000, noise=noise, seed=42)\n", |
| 194 | "Histogram(result)" |
| 195 | ] |
| 196 | }, |
| 197 | { |
| 198 | "cell_type": "markdown", |
| 199 | "id": "130889ea", |
| 200 | "metadata": {}, |
| 201 | "source": [ |
| 202 | "## 2. Custom Noise Intrinsics\n", |
| 203 | "\n", |
| 204 | "For more complex noise models, you can define custom noise intrinsics. These\n", |
| 205 | "are no-op gates in the ideal circuit that act as insertion points for correlated noise during\n", |
| 206 | "simulation. This is useful for modeling correlated noise on custom gates (those not included in `NoiseConfig`).\n", |
| 207 | "\n", |
| 208 | "A noise intrinsic is declared with `@NoiseIntrinsic()` in Q# (or `@qdk.qir.noise_intrinsic`\n", |
| 209 | "in OpenQASM). The noise model is then configured in Python via `NoiseConfig.intrinsic()`." |
| 210 | ] |
| 211 | }, |
| 212 | { |
| 213 | "cell_type": "markdown", |
| 214 | "id": "adc6a923", |
| 215 | "metadata": {}, |
| 216 | "source": [ |
| 217 | "### Q# example: modeling crosstalk between qubits\n", |
| 218 | "\n", |
| 219 | "Imagine a 3-qubit register where applying a gate on qubit 0 causes crosstalk\n", |
| 220 | "(correlated ZZ dephasing) on qubits 1 and 2. We model this by inserting a noise\n", |
| 221 | "intrinsic after the gate." |
| 222 | ] |
| 223 | }, |
| 224 | { |
| 225 | "cell_type": "code", |
| 226 | "execution_count": null, |
| 227 | "id": "e0df5c17", |
| 228 | "metadata": {}, |
| 229 | "outputs": [], |
| 230 | "source": [ |
| 231 | "qdk.init(target_profile=qdk.TargetProfile.Adaptive_RIF)" |
| 232 | ] |
| 233 | }, |
| 234 | { |
| 235 | "cell_type": "code", |
| 236 | "execution_count": null, |
| 237 | "id": "51340462", |
| 238 | "metadata": { |
| 239 | "vscode": { |
| 240 | "languageId": "qsharp" |
| 241 | } |
| 242 | }, |
| 243 | "outputs": [], |
| 244 | "source": [ |
| 245 | "%%qsharp\n", |
| 246 | "\n", |
| 247 | "// A noise intrinsic representing crosstalk on 3 qubits.\n", |
| 248 | "// In the ideal circuit this is a no-op; the simulator injects\n", |
| 249 | "// Pauli errors according to the NoiseConfig.\n", |
| 250 | "@NoiseIntrinsic()\n", |
| 251 | "operation Crosstalk3Q(q0: Qubit, q1: Qubit, q2: Qubit) : Unit {\n", |
| 252 | " body intrinsic;\n", |
| 253 | "}\n", |
| 254 | "\n", |
| 255 | "// Prepare a GHZ state on 3 qubits, with crosstalk after each CNOT.\n", |
| 256 | "operation GHZ() : Result[] {\n", |
| 257 | " use qs = Qubit[3];\n", |
| 258 | " H(qs[0]);\n", |
| 259 | " CNOT(qs[0], qs[1]);\n", |
| 260 | " Crosstalk3Q(qs[0], qs[1], qs[2]); // crosstalk hits all 3 qubits\n", |
| 261 | " CNOT(qs[1], qs[2]);\n", |
| 262 | " Crosstalk3Q(qs[0], qs[1], qs[2]); // crosstalk again\n", |
| 263 | " MResetEachZ(qs)\n", |
| 264 | "}" |
| 265 | ] |
| 266 | }, |
| 267 | { |
| 268 | "cell_type": "markdown", |
| 269 | "id": "ce61b334", |
| 270 | "metadata": {}, |
| 271 | "source": [ |
| 272 | "Compile to QIR so we can run with a custom `NoiseConfig`:" |
| 273 | ] |
| 274 | }, |
| 275 | { |
| 276 | "cell_type": "code", |
| 277 | "execution_count": null, |
| 278 | "id": "1b211a19", |
| 279 | "metadata": {}, |
| 280 | "outputs": [], |
| 281 | "source": [ |
| 282 | "qir = qsharp.compile(\"GHZ()\")" |
| 283 | ] |
| 284 | }, |
| 285 | { |
| 286 | "cell_type": "markdown", |
| 287 | "id": "4e431ff4", |
| 288 | "metadata": {}, |
| 289 | "source": [ |
| 290 | "First, run without noise, we should see a clean GHZ state (`000` and `111` only):" |
| 291 | ] |
| 292 | }, |
| 293 | { |
| 294 | "cell_type": "code", |
| 295 | "execution_count": null, |
| 296 | "id": "6b7ed62a", |
| 297 | "metadata": {}, |
| 298 | "outputs": [], |
| 299 | "source": [ |
| 300 | "result = run_qir(qir, shots=1000, seed=42)\n", |
| 301 | "Histogram(result)" |
| 302 | ] |
| 303 | }, |
| 304 | { |
| 305 | "cell_type": "markdown", |
| 306 | "id": "3155ed57", |
| 307 | "metadata": {}, |
| 308 | "source": [ |
| 309 | "Now configure the crosstalk noise intrinsic. We'll model two types of correlated errors:\n", |
| 310 | "- `ixx`: correlated XX on qubits 1 and 2 (10% probability)\n", |
| 311 | "- `xxi`: correlated XX on qubits 0 and 1 (5% probability)" |
| 312 | ] |
| 313 | }, |
| 314 | { |
| 315 | "cell_type": "code", |
| 316 | "execution_count": null, |
| 317 | "id": "958335ff", |
| 318 | "metadata": {}, |
| 319 | "outputs": [], |
| 320 | "source": [ |
| 321 | "noise = NoiseConfig()\n", |
| 322 | "table = noise.intrinsic(\"Crosstalk3Q\", num_qubits=3)\n", |
| 323 | "table.ixx = 0.10 # 10% XX on qubits 1-2\n", |
| 324 | "table.xxi = 0.05 # 5% XX on qubits 0-1\n", |
| 325 | "\n", |
| 326 | "result = run_qir(qir, shots=1000, noise=noise, seed=42)\n", |
| 327 | "Histogram(result)" |
| 328 | ] |
| 329 | }, |
| 330 | { |
| 331 | "cell_type": "markdown", |
| 332 | "id": "f18d9f40", |
| 333 | "metadata": {}, |
| 334 | "source": [ |
| 335 | "The crosstalk breaks the perfect GHZ correlations, we now see outcomes like `001`, `010`,\n", |
| 336 | "etc. that would be impossible in the ideal circuit." |
| 337 | ] |
| 338 | }, |
| 339 | { |
| 340 | "cell_type": "markdown", |
| 341 | "id": "d9cd8528", |
| 342 | "metadata": {}, |
| 343 | "source": [ |
| 344 | "### OpenQASM example\n", |
| 345 | "\n", |
| 346 | "The same noise intrinsic pattern works in OpenQASM using the `@qdk.qir.noise_intrinsic`\n", |
| 347 | "annotation on a custom gate definition." |
| 348 | ] |
| 349 | }, |
| 350 | { |
| 351 | "cell_type": "code", |
| 352 | "execution_count": null, |
| 353 | "id": "8ec4beaa", |
| 354 | "metadata": {}, |
| 355 | "outputs": [], |
| 356 | "source": [ |
| 357 | "qasm_source = \"\"\"\n", |
| 358 | "OPENQASM 3.0;\n", |
| 359 | "include \"stdgates.inc\";\n", |
| 360 | "\n", |
| 361 | "// A noise intrinsic representing crosstalk on 3 qubits.\n", |
| 362 | "// In the ideal circuit this is a no-op; the simulator injects\n", |
| 363 | "// Pauli errors according to the NoiseConfig.\n", |
| 364 | "@qdk.qir.noise_intrinsic\n", |
| 365 | "gate crosstalk_3q q0, q1, q2 {}\n", |
| 366 | "\n", |
| 367 | "qubit[3] qs;\n", |
| 368 | "\n", |
| 369 | "// Prepare a GHZ state on 3 qubits, with crosstalk after each CNOT.\n", |
| 370 | "h qs[0];\n", |
| 371 | "cx qs[0], qs[1];\n", |
| 372 | "crosstalk_3q qs[0], qs[1], qs[2]; // crosstalk hits all 3 qubits\n", |
| 373 | "cx qs[1], qs[2];\n", |
| 374 | "crosstalk_3q qs[0], qs[1], qs[2]; // crosstalk again\n", |
| 375 | "\n", |
| 376 | "bit[3] res = measure qs;\n", |
| 377 | "\"\"\"\n", |
| 378 | "\n", |
| 379 | "qir_qasm = openqasm.compile(\n", |
| 380 | " qasm_source,\n", |
| 381 | " output_semantics=openqasm.OutputSemantics.OpenQasm,\n", |
| 382 | " target_profile=qdk.TargetProfile.Base,\n", |
| 383 | ")" |
| 384 | ] |
| 385 | }, |
| 386 | { |
| 387 | "cell_type": "code", |
| 388 | "execution_count": null, |
| 389 | "id": "a3d230ea", |
| 390 | "metadata": {}, |
| 391 | "outputs": [], |
| 392 | "source": [ |
| 393 | "noise = NoiseConfig()\n", |
| 394 | "table = noise.intrinsic(\"crosstalk_3q\", num_qubits=3)\n", |
| 395 | "table.ixx = 0.10 # 10% XX on qubits 1-2\n", |
| 396 | "table.xxi = 0.05 # 5% XX on qubits 0-1\n", |
| 397 | "\n", |
| 398 | "result = run_qir(qir_qasm, shots=1000, noise=noise, seed=42)\n", |
| 399 | "Histogram(result)" |
| 400 | ] |
| 401 | } |
| 402 | ], |
| 403 | "metadata": { |
| 404 | "language_info": { |
| 405 | "name": "python" |
| 406 | } |
| 407 | }, |
| 408 | "nbformat": 4, |
| 409 | "nbformat_minor": 5 |
| 410 | } |
| 411 | |