stabilizer_qec 2.1.0

Quantum error-correction simulation and decoding: Stim-format circuits and error models, a bit-parallel sampler, sparse-blossom, correlated and belief matching, BP+OSD, window decoders, bivariate bicycle codes, lattice surgery, Clifford+T circuits with coherent noise, and sampling and BP on the GPU.
Documentation
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
// The lane program (src/lanes.rs) run on a GPU: one invocation per word of 32 shots, the
// same opcodes, the same integer draws in the same order as the CPU executor, so the two give
// the same bits. The program is interpreted from `code`; REPEAT blocks run on a small loop
// stack. Every word owns a slice of the frame, ring, detector, observable and record buffers.

struct Params {
    num_words: u32,
    num_qubits: u32,
    ring_mask: u32,
    num_detectors: u32,
    num_observables: u32,
    num_measurements: u32,
    keep_measurements: u32,
    code_len: u32,
}

@group(0) @binding(0) var<storage, read> code: array<u32>;
@group(0) @binding(1) var<uniform> params: Params;
// Four words of xoshiro128** state per word.
@group(0) @binding(2) var<storage, read> seeds: array<u32>;
// x frames then z frames per word: frames[word * 2 * nq + q] and frames[word * 2 * nq + nq + q].
@group(0) @binding(3) var<storage, read_write> frames: array<u32>;
@group(0) @binding(4) var<storage, read_write> ring: array<u32>;
// num_words * num_detectors words, then one DONE word per word that ran to its end.
@group(0) @binding(5) var<storage, read_write> dets: array<u32>;
@group(0) @binding(6) var<storage, read_write> obs: array<u32>;
@group(0) @binding(7) var<storage, read_write> meas: array<u32>;

const DONE: u32 = 0xC0DEu;
const OP_RESET: u32 = 1u;
const OP_H: u32 = 2u;
const OP_S: u32 = 3u;
const OP_CX: u32 = 4u;
const OP_CZ: u32 = 5u;
const OP_MEASURE: u32 = 6u;
const OP_PAULI_ERROR: u32 = 7u;
const OP_DEPOLARIZE1: u32 = 8u;
const OP_DEPOLARIZE2: u32 = 9u;
const OP_PAULI_CHANNEL1: u32 = 10u;
const OP_DETECTOR: u32 = 11u;
const OP_OBSERVABLE: u32 = 12u;
const OP_REPEAT: u32 = 13u;
const OP_CORRELATED: u32 = 14u;
const OP_PAULI_CHANNEL2: u32 = 15u;
const OP_PAD: u32 = 16u;
const OP_FEEDBACK: u32 = 17u;
const OP_HERALDED: u32 = 18u;

const PROB_NEVER: u32 = 0u;
const PROB_ALWAYS: u32 = 1u;

const STACK: u32 = 16u;

// xoshiro128** state, as `lanes::Rng32`.
var<private> s0: u32;
var<private> s1: u32;
var<private> s2: u32;
var<private> s3: u32;
var<private> xbase: u32;
var<private> zbase: u32;
var<private> rbase: u32;
var<private> rmask: u32;
var<private> m: u32;
var<private> chain: u32;
var<private> det_base: u32;
var<private> det: u32;
var<private> obs_base: u32;
var<private> meas_base: u32;
var<private> keep: bool;

fn rotl(x: u32, k: u32) -> u32 {
    return (x << k) | (x >> (32u - k));
}

fn next() -> u32 {
    let result = rotl(s1 * 5u, 7u) * 9u;
    let t = s1 << 9u;
    s2 ^= s0;
    s3 ^= s1;
    s1 ^= s2;
    s0 ^= s3;
    s2 ^= t;
    s3 = rotl(s3, 11u);
    return result;
}

fn bernoulli(kind: u32, thr: u32) -> u32 {
    if kind == PROB_NEVER {
        return 0u;
    }
    if kind == PROB_ALWAYS {
        return 0xFFFFFFFFu;
    }
    var w = 0u;
    for (var lane = 0u; lane < 32u; lane++) {
        if next() <= thr {
            w |= 1u << lane;
        }
    }
    return w;
}

fn reset(basis: u32, q: u32) {
    if basis == 0u {
        frames[xbase + q] = 0u;
        frames[zbase + q] = next();
    } else {
        frames[zbase + q] = 0u;
        frames[xbase + q] = next();
    }
}

fn pauli_on_lane(q: u32, lane: u32, pauli: u32) {
    let bit = 1u << lane;
    if (pauli & 1u) != 0u {
        frames[xbase + q] ^= bit;
    }
    if (pauli & 2u) != 0u {
        frames[zbase + q] ^= bit;
    }
}

fn pauli_word(q: u32, pauli: u32, w: u32) {
    if (pauli & 1u) != 0u {
        frames[xbase + q] ^= w;
    }
    if (pauli & 2u) != 0u {
        frames[zbase + q] ^= w;
    }
}

fn record(w: u32) {
    ring[rbase + (m & rmask)] = w;
    if keep {
        meas[meas_base + m] = w;
    }
    m += 1u;
}

fn lookback(k: u32) -> u32 {
    return ring[rbase + ((m - k) & rmask)];
}

fn lowest(w: u32) -> u32 {
    return countTrailingZeros(w);
}

@compute @workgroup_size(64)
fn main(@builtin(global_invocation_id) id: vec3<u32>) {
    let word = id.x;
    if word >= params.num_words {
        return;
    }
    let nq = params.num_qubits;
    s0 = seeds[4u * word];
    s1 = seeds[4u * word + 1u];
    s2 = seeds[4u * word + 2u];
    s3 = seeds[4u * word + 3u];
    xbase = word * 2u * nq;
    zbase = xbase + nq;
    rmask = params.ring_mask;
    rbase = word * (rmask + 1u);
    m = 0u;
    chain = 0u;
    det_base = word * params.num_detectors;
    det = 0u;
    obs_base = word * params.num_observables;
    meas_base = word * params.num_measurements;
    keep = params.keep_measurements != 0u;

    // Every qubit starts in |0>, to which Z is invisible: the x frame 0, the z frame random.
    for (var q = 0u; q < nq; q++) {
        frames[xbase + q] = 0u;
        frames[zbase + q] = next();
    }
    for (var i = 0u; i < params.num_observables; i++) {
        obs[obs_base + i] = 0u;
    }

    // The loop stack: where a REPEAT body starts, where it ends, how many runs remain.
    var stack_start: array<u32, 16>;
    var stack_end: array<u32, 16>;
    var stack_left: array<u32, 16>;
    var depth = 0u;

    var pc = 0u;
    let end = params.code_len;
    loop {
        // A finished loop body: run it again, or pop it.
        while depth > 0u && pc == stack_end[depth - 1u] {
            if stack_left[depth - 1u] > 1u {
                stack_left[depth - 1u] -= 1u;
                pc = stack_start[depth - 1u];
            } else {
                depth -= 1u;
            }
        }
        if pc >= end {
            break;
        }
        let op = code[pc];
        pc += 1u;
        switch op {
            case OP_RESET: {
                let basis = code[pc];
                let n = code[pc + 1u];
                pc += 2u;
                for (var k = 0u; k < n; k++) {
                    reset(basis, code[pc + k]);
                }
                pc += n;
            }
            case OP_H: {
                let n = code[pc];
                pc += 1u;
                for (var k = 0u; k < n; k++) {
                    let q = code[pc + k];
                    let x = frames[xbase + q];
                    frames[xbase + q] = frames[zbase + q];
                    frames[zbase + q] = x;
                }
                pc += n;
            }
            case OP_S: {
                let n = code[pc];
                pc += 1u;
                for (var k = 0u; k < n; k++) {
                    let q = code[pc + k];
                    frames[zbase + q] ^= frames[xbase + q];
                }
                pc += n;
            }
            case OP_CX: {
                let n = code[pc];
                pc += 1u;
                for (var k = 0u; k < n; k++) {
                    let c = code[pc + 2u * k];
                    let t = code[pc + 2u * k + 1u];
                    frames[xbase + t] ^= frames[xbase + c];
                    frames[zbase + c] ^= frames[zbase + t];
                }
                pc += 2u * n;
            }
            case OP_CZ: {
                let n = code[pc];
                pc += 1u;
                for (var k = 0u; k < n; k++) {
                    let a = code[pc + 2u * k];
                    let b = code[pc + 2u * k + 1u];
                    frames[zbase + b] ^= frames[xbase + a];
                    frames[zbase + a] ^= frames[xbase + b];
                }
                pc += 2u * n;
            }
            case OP_MEASURE: {
                let basis = code[pc];
                let do_reset = code[pc + 1u] != 0u;
                let kind = code[pc + 2u];
                let thr = code[pc + 3u];
                let n = code[pc + 4u];
                pc += 5u;
                for (var k = 0u; k < n; k++) {
                    let q = code[pc + k];
                    var rec = 0u;
                    if basis == 0u {
                        rec = frames[xbase + q];
                    } else {
                        rec = frames[zbase + q];
                    }
                    rec ^= bernoulli(kind, thr);
                    record(rec);
                    if basis == 0u {
                        frames[zbase + q] = next();
                    } else {
                        frames[xbase + q] = next();
                    }
                    if do_reset {
                        reset(basis, q);
                    }
                }
                pc += n;
            }
            case OP_PAULI_ERROR: {
                let pauli = code[pc];
                let kind = code[pc + 1u];
                let thr = code[pc + 2u];
                let n = code[pc + 3u];
                pc += 4u;
                for (var k = 0u; k < n; k++) {
                    let w = bernoulli(kind, thr);
                    pauli_word(code[pc + k], pauli, w);
                }
                pc += n;
            }
            case OP_DEPOLARIZE1: {
                let kind = code[pc];
                let thr = code[pc + 1u];
                let n = code[pc + 2u];
                pc += 3u;
                for (var k = 0u; k < n; k++) {
                    let q = code[pc + k];
                    var w = bernoulli(kind, thr);
                    while w != 0u {
                        let lane = lowest(w);
                        w &= w - 1u;
                        let pauli = 1u + next() % 3u;
                        pauli_on_lane(q, lane, pauli);
                    }
                }
                pc += n;
            }
            case OP_DEPOLARIZE2: {
                let kind = code[pc];
                let thr = code[pc + 1u];
                let n = code[pc + 2u];
                pc += 3u;
                for (var k = 0u; k < n; k++) {
                    let a = code[pc + 2u * k];
                    let b = code[pc + 2u * k + 1u];
                    var w = bernoulli(kind, thr);
                    while w != 0u {
                        let lane = lowest(w);
                        w &= w - 1u;
                        let r = 1u + next() % 15u;
                        pauli_on_lane(a, lane, r & 3u);
                        pauli_on_lane(b, lane, r >> 2u);
                    }
                }
                pc += 2u * n;
            }
            case OP_PAULI_CHANNEL1: {
                let kind = code[pc];
                let thr = code[pc + 1u];
                let cx = code[pc + 2u];
                let cxy = code[pc + 3u];
                let n = code[pc + 4u];
                pc += 5u;
                for (var k = 0u; k < n; k++) {
                    let q = code[pc + k];
                    var w = bernoulli(kind, thr);
                    while w != 0u {
                        let lane = lowest(w);
                        w &= w - 1u;
                        let u = next();
                        var pauli = 2u;
                        if u < cx {
                            pauli = 1u;
                        } else if u < cxy {
                            pauli = 3u;
                        }
                        pauli_on_lane(q, lane, pauli);
                    }
                }
                pc += n;
            }
            case OP_DETECTOR: {
                let n = code[pc];
                pc += 1u;
                var w = 0u;
                for (var k = 0u; k < n; k++) {
                    w ^= lookback(code[pc + k]);
                }
                dets[det_base + det] = w;
                det += 1u;
                pc += n;
            }
            case OP_OBSERVABLE: {
                let i = code[pc];
                let n = code[pc + 1u];
                pc += 2u;
                var w = 0u;
                for (var k = 0u; k < n; k++) {
                    w ^= lookback(code[pc + k]);
                }
                pc += n;
                let mm = code[pc];
                pc += 1u;
                for (var k = 0u; k < mm; k++) {
                    let q = code[pc + 2u * k];
                    let p = code[pc + 2u * k + 1u];
                    if (p & 1u) != 0u {
                        w ^= frames[zbase + q];
                    }
                    if (p & 2u) != 0u {
                        w ^= frames[xbase + q];
                    }
                }
                pc += 2u * mm;
                obs[obs_base + i] ^= w;
            }
            case OP_REPEAT: {
                let count = code[pc];
                let len = code[pc + 1u];
                pc += 2u;
                if count == 0u || len == 0u || depth >= STACK {
                    pc += len;
                } else {
                    stack_start[depth] = pc;
                    stack_end[depth] = pc + len;
                    stack_left[depth] = count;
                    depth += 1u;
                }
            }
            case OP_CORRELATED: {
                let kind = code[pc];
                let thr = code[pc + 1u];
                let chained = code[pc + 2u] != 0u;
                let n = code[pc + 3u];
                pc += 4u;
                var w = bernoulli(kind, thr);
                if chained {
                    w &= ~chain;
                    chain |= w;
                } else {
                    chain = w;
                }
                for (var k = 0u; k < n; k++) {
                    pauli_word(code[pc + 2u * k], code[pc + 2u * k + 1u], w);
                }
                pc += 2u * n;
            }
            case OP_PAULI_CHANNEL2: {
                let kind = code[pc];
                let thr = code[pc + 1u];
                let cuts = pc + 2u;
                pc += 17u;
                let n = code[pc];
                pc += 1u;
                for (var k = 0u; k < n; k++) {
                    let a = code[pc + 2u * k];
                    let b = code[pc + 2u * k + 1u];
                    var w = bernoulli(kind, thr);
                    while w != 0u {
                        let lane = lowest(w);
                        w &= w - 1u;
                        let u = next();
                        var cas = 15u;
                        for (var j = 0u; j < 15u; j++) {
                            if u < code[cuts + j] {
                                cas = j + 1u;
                                break;
                            }
                        }
                        pauli_on_lane(a, lane, pauli_code(cas / 4u));
                        pauli_on_lane(b, lane, pauli_code(cas % 4u));
                    }
                }
                pc += 2u * n;
            }
            case OP_PAD: {
                let kind = code[pc];
                let thr = code[pc + 1u];
                let count = code[pc + 2u];
                pc += 3u;
                for (var k = 0u; k < count; k++) {
                    record(bernoulli(kind, thr));
                }
            }
            case OP_FEEDBACK: {
                let pauli = code[pc];
                let k = code[pc + 1u];
                let q = code[pc + 2u];
                pc += 3u;
                pauli_word(q, pauli, lookback(k));
            }
            case OP_HERALDED: {
                let kind = code[pc];
                let thr = code[pc + 1u];
                let c0 = code[pc + 2u];
                let c1 = code[pc + 3u];
                let c2 = code[pc + 4u];
                let n = code[pc + 5u];
                pc += 6u;
                for (var k = 0u; k < n; k++) {
                    let q = code[pc + k];
                    let w = bernoulli(kind, thr);
                    record(w);
                    var lanes = w;
                    while lanes != 0u {
                        let lane = lowest(lanes);
                        lanes &= lanes - 1u;
                        let u = next();
                        var pauli = 2u;
                        if u < c0 {
                            pauli = 0u;
                        } else if u < c1 {
                            pauli = 1u;
                        } else if u < c2 {
                            pauli = 3u;
                        }
                        pauli_on_lane(q, lane, pauli);
                    }
                }
                pc += n;
            }
            default: {
                // An unknown opcode: stop this word (the CPU reference would have refused it).
                pc = end;
            }
        }
    }
    // The word ran to its end: a dispatch the driver cut short leaves this unwritten.
    dets[params.num_words * params.num_detectors + word] = DONE;
}

// Stim's case order I, X, Y, Z as the frame's bits (x = 1, z = 2).
fn pauli_code(k: u32) -> u32 {
    switch k {
        case 0u: { return 0u; }
        case 1u: { return 1u; }
        case 2u: { return 3u; }
        default: { return 2u; }
    }
}