QEC Lab

Decoder results grouped by what they actually measured. Two decoders benchmarked at different code distances, round counts, error rates, noise models, or stopping rules are not competitors, so they never appear in the same table here.

To see what a decoder is given to work with, the syndrome explorer applies a Pauli error to a small code and shows the syndrome it produces, what the decoder infers from it, and whether the correction restored the logical state.

Three independent decoders, one hashed sample

Surface code d=3, 3 rounds, p=0.02, 20,000 shots — one shared Stim sample (SHA-256 2bac07a88b02), which every decoder provably consumed. Execution class SIMULATION; produced by ketqat/ketqat-benchmarks@4b77286a.

Per-decoder results. Rank uses unconditional risk (failures plus abstentions over all shots), so a decoder cannot climb the table by declining hard shots. Latency is single-shot with warm-up; throughput is the library batch API — different experiments, reported separately.
Decoder	Rank	Uncond. risk	Wilson 95%	p50 / p99 (µs)	Batch (shots/s)
tesseract vunknown	1	0.13020	[0.1256, 0.1349]	355 / 2458	1,562
beliefmatching vunknown	2	0.13465	[0.1300, 0.1395]	148 / 743	6,134
pymatching-mwpm v2.4.0	3	0.14185	[0.1371, 0.1468]	4 / 7	1,389,754

Paired per-shot inference. All decoders saw the same shots, so the discordant counts (A wrong where B right, and conversely) decide what overlapping marginal intervals cannot: an exact McNemar test with Bonferroni correction across the three pairs.
Pair	Risk diff.	Paired 95% CI	b01 / b10	McNemar p	Significant
pymatching-mwpm − beliefmatching	+0.00720	[0.00487, 0.00953]	355 / 211	1.52e-9	yes(α=0.0167)
pymatching-mwpm − tesseract	+0.01165	[0.00837, 0.01493]	679 / 446	4.62e-12	yes(α=0.0167)
beliefmatching − tesseract	+0.00445	[0.00186, 0.00704]	394 / 305	8.61e-4	yes(α=0.0167)

The finding is a tradeoff, not a winner: the most accurate decoder here has roughly a thousandth of the fastest one’s batch throughput. Marginal intervals overlap for two of the three pairs at this shot count — the paired test on shared shots is what separates all three, which is why both tables are shown.

Decoder comparison

rotated-surface-code · d=3 · p=0.001

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 3

rounds: 3

physical error rate: 0.001

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	3.000e-4	[1.02e-4, 8.82e-4]	3 / 10000	0.52 ms	surface-code-mwpm-baseline-d3-p001

Reading this table: A comparison needs at least two decoders measured under these identical conditions.

rotated-surface-code · d=3 · p=0.002

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 3

rounds: 3

physical error rate: 0.002

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	1.300e-3	[7.60e-4, 2.22e-3]	13 / 10000	0.66 ms	surface-code-mwpm-baseline-d3-p002

Reading this table: A comparison needs at least two decoders measured under these identical conditions.

rotated-surface-code · d=3 · p=0.002

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 3

rounds: 3

physical error rate: 0.002

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	1.020e-3	[8.89e-4, 1.17e-3]	204 / 200000	11.16 ms	surface-code-mwpm-sweep-d3-p002-s2
pymatching	1.030e-3	[8.99e-4, 1.18e-3]	206 / 200000	11.40 ms	surface-code-mwpm-sweep-d3-p002-s1
pymatching	1.085e-3	[9.50e-4, 1.24e-3]	217 / 200000	11.65 ms	surface-code-mwpm-sweep-d3-p002-s3

Reading this table: The confidence intervals for pymatching and pymatching overlap, so this data does not distinguish them. More shots would be needed to separate them.

rotated-surface-code · d=3 · p=0.003

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 3

rounds: 3

physical error rate: 0.003

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	2.200e-3	[1.45e-3, 3.33e-3]	22 / 10000	0.85 ms	surface-code-mwpm-baseline-d3-p003

Reading this table: A comparison needs at least two decoders measured under these identical conditions.

rotated-surface-code · d=3 · p=0.005

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 3

rounds: 3

physical error rate: 0.005

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	6.700e-3	[5.28e-3, 8.50e-3]	67 / 10000	1.29 ms	surface-code-mwpm-baseline-d3-p005

Reading this table: A comparison needs at least two decoders measured under these identical conditions.

rotated-surface-code · d=3 · p=0.005

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 3

rounds: 3

physical error rate: 0.005

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	5.440e-3	[5.00e-3, 5.92e-3]	544 / 100000	11.91 ms	surface-code-mwpm-sweep-d3-p005-s1
pymatching	6.120e-3	[5.66e-3, 6.62e-3]	612 / 100000	12.10 ms	surface-code-mwpm-sweep-d3-p005-s3
pymatching	6.220e-3	[5.75e-3, 6.73e-3]	622 / 100000	12.73 ms	surface-code-mwpm-sweep-d3-p005-s2

Reading this table: The confidence intervals for pymatching and pymatching overlap, so this data does not distinguish them. More shots would be needed to separate them.

rotated-surface-code · d=3 · p=0.008

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 3

rounds: 3

physical error rate: 0.008

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	1.670e-2	[1.44e-2, 1.94e-2]	167 / 10000	2.01 ms	surface-code-mwpm-baseline-d3-p008

Reading this table: A comparison needs at least two decoders measured under these identical conditions.

rotated-surface-code · d=3 · p=0.008

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 3

rounds: 3

physical error rate: 0.008

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	1.459e-2	[1.39e-2, 1.54e-2]	1459 / 100000	18.87 ms	surface-code-mwpm-sweep-d3-p008-s1
pymatching	1.472e-2	[1.40e-2, 1.55e-2]	1472 / 100000	18.59 ms	surface-code-mwpm-sweep-d3-p008-s2
pymatching	1.485e-2	[1.41e-2, 1.56e-2]	1485 / 100000	19.09 ms	surface-code-mwpm-sweep-d3-p008-s3

Reading this table: The confidence intervals for pymatching and pymatching overlap, so this data does not distinguish them. More shots would be needed to separate them.

rotated-surface-code · d=3 · p=0.01

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 3

rounds: 3

physical error rate: 0.01

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	2.210e-2	[1.94e-2, 2.52e-2]	221 / 10000	2.45 ms	surface-code-mwpm-baseline-d3-p01

Reading this table: A comparison needs at least two decoders measured under these identical conditions.

rotated-surface-code · d=3 · p=0.011

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 3

rounds: 3

physical error rate: 0.011

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	2.690e-2	[2.47e-2, 2.92e-2]	538 / 20000	5.30 ms	surface-code-mwpm-sweep-d3-p011-s1
pymatching	2.720e-2	[2.50e-2, 2.95e-2]	544 / 20000	5.20 ms	surface-code-mwpm-sweep-d3-p011-s3
pymatching	2.740e-2	[2.52e-2, 2.98e-2]	548 / 20000	5.50 ms	surface-code-mwpm-sweep-d3-p011-s2

Reading this table: The confidence intervals for pymatching and pymatching overlap, so this data does not distinguish them. More shots would be needed to separate them.

rotated-surface-code · d=3 · p=0.015

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 3

rounds: 3

physical error rate: 0.015

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	4.480e-2	[4.09e-2, 4.90e-2]	448 / 10000	3.68 ms	surface-code-mwpm-baseline-d3-p015

Reading this table: A comparison needs at least two decoders measured under these identical conditions.

rotated-surface-code · d=3 · p=0.015

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 3

rounds: 3

physical error rate: 0.015

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	4.560e-2	[4.28e-2, 4.86e-2]	912 / 20000	7.73 ms	surface-code-mwpm-sweep-d3-p015-s2
pymatching	4.690e-2	[4.41e-2, 4.99e-2]	938 / 20000	7.64 ms	surface-code-mwpm-sweep-d3-p015-s1
pymatching	4.730e-2	[4.44e-2, 5.03e-2]	946 / 20000	7.56 ms	surface-code-mwpm-sweep-d3-p015-s3

Reading this table: The confidence intervals for pymatching and pymatching overlap, so this data does not distinguish them. More shots would be needed to separate them.

rotated-surface-code · d=3 · p=0.02

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 3

rounds: 3

physical error rate: 0.02

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	7.340e-2	[6.85e-2, 7.87e-2]	734 / 10000	4.99 ms	surface-code-mwpm-baseline-d3-p02

Reading this table: A comparison needs at least two decoders measured under these identical conditions.

rotated-surface-code · d=3 · p=0.02

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 3

rounds: 3

physical error rate: 0.02

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	7.400e-2	[7.05e-2, 7.77e-2]	1480 / 20000	10.26 ms	surface-code-mwpm-sweep-d3-p02-s3
pymatching	7.590e-2	[7.23e-2, 7.97e-2]	1518 / 20000	10.64 ms	surface-code-mwpm-sweep-d3-p02-s2
pymatching	8.105e-2	[7.73e-2, 8.49e-2]	1621 / 20000	11.28 ms	surface-code-mwpm-sweep-d3-p02-s1

Reading this table: The confidence intervals for pymatching and pymatching overlap, so this data does not distinguish them. More shots would be needed to separate them.

rotated-surface-code · d=5 · p=0.001

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 5

rounds: 5

physical error rate: 0.001

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	< 3.84e-4 (upper bound; no failures in 10,000 shots)	[0.00e+0, 3.84e-4]	0 / 10000	2.25 ms	surface-code-mwpm-baseline-d5-p001

Reading this table: A comparison needs at least two decoders measured under these identical conditions.

rotated-surface-code · d=5 · p=0.002

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 5

rounds: 5

physical error rate: 0.002

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	2.000e-4	[5.48e-5, 7.29e-4]	2 / 10000	3.98 ms	surface-code-mwpm-baseline-d5-p002

Reading this table: A comparison needs at least two decoders measured under these identical conditions.

rotated-surface-code · d=5 · p=0.002

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 5

rounds: 5

physical error rate: 0.002

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	2.650e-4	[2.03e-4, 3.47e-4]	53 / 200000	79.45 ms	surface-code-mwpm-sweep-d5-p002-s1
pymatching	3.250e-4	[2.55e-4, 4.14e-4]	65 / 200000	92.99 ms	surface-code-mwpm-sweep-d5-p002-s3
pymatching	3.450e-4	[2.73e-4, 4.37e-4]	69 / 200000	82.11 ms	surface-code-mwpm-sweep-d5-p002-s2

Reading this table: The confidence intervals for pymatching and pymatching overlap, so this data does not distinguish them. More shots would be needed to separate them.

rotated-surface-code · d=5 · p=0.003

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 5

rounds: 5

physical error rate: 0.003

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	1.000e-3	[5.43e-4, 1.84e-3]	10 / 10000	5.77 ms	surface-code-mwpm-baseline-d5-p003

Reading this table: A comparison needs at least two decoders measured under these identical conditions.

rotated-surface-code · d=5 · p=0.005

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 5

rounds: 5

physical error rate: 0.005

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	4.400e-3	[3.28e-3, 5.90e-3]	44 / 10000	9.76 ms	surface-code-mwpm-baseline-d5-p005

Reading this table: A comparison needs at least two decoders measured under these identical conditions.

rotated-surface-code · d=5 · p=0.005

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 5

rounds: 5

physical error rate: 0.005

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	4.610e-3	[4.21e-3, 5.05e-3]	461 / 100000	99.87 ms	surface-code-mwpm-sweep-d5-p005-s3
pymatching	4.700e-3	[4.29e-3, 5.14e-3]	470 / 100000	102.06 ms	surface-code-mwpm-sweep-d5-p005-s1
pymatching	4.930e-3	[4.51e-3, 5.38e-3]	493 / 100000	97.63 ms	surface-code-mwpm-sweep-d5-p005-s2

Reading this table: The confidence intervals for pymatching and pymatching overlap, so this data does not distinguish them. More shots would be needed to separate them.

rotated-surface-code · d=5 · p=0.008

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 5

rounds: 5

physical error rate: 0.008

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	1.480e-2	[1.26e-2, 1.74e-2]	148 / 10000	16.78 ms	surface-code-mwpm-baseline-d5-p008

Reading this table: A comparison needs at least two decoders measured under these identical conditions.

rotated-surface-code · d=5 · p=0.008

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 5

rounds: 5

physical error rate: 0.008

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	1.731e-2	[1.65e-2, 1.81e-2]	1731 / 100000	183.56 ms	surface-code-mwpm-sweep-d5-p008-s3
pymatching	1.777e-2	[1.70e-2, 1.86e-2]	1777 / 100000	173.75 ms	surface-code-mwpm-sweep-d5-p008-s1
pymatching	1.822e-2	[1.74e-2, 1.91e-2]	1822 / 100000	173.56 ms	surface-code-mwpm-sweep-d5-p008-s2

Reading this table: The confidence intervals for pymatching and pymatching overlap, so this data does not distinguish them. More shots would be needed to separate them.

rotated-surface-code · d=5 · p=0.01

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 5

rounds: 5

physical error rate: 0.01

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	3.220e-2	[2.89e-2, 3.58e-2]	322 / 10000	22.50 ms	surface-code-mwpm-baseline-d5-p01

Reading this table: A comparison needs at least two decoders measured under these identical conditions.

rotated-surface-code · d=5 · p=0.011

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 5

rounds: 5

physical error rate: 0.011

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	3.980e-2	[3.72e-2, 4.26e-2]	796 / 20000	52.22 ms	surface-code-mwpm-sweep-d5-p011-s3
pymatching	4.125e-2	[3.86e-2, 4.41e-2]	825 / 20000	54.76 ms	surface-code-mwpm-sweep-d5-p011-s2
pymatching	4.165e-2	[3.90e-2, 4.45e-2]	833 / 20000	54.72 ms	surface-code-mwpm-sweep-d5-p011-s1

Reading this table: The confidence intervals for pymatching and pymatching overlap, so this data does not distinguish them. More shots would be needed to separate them.

rotated-surface-code · d=5 · p=0.015

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 5

rounds: 5

physical error rate: 0.015

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	8.990e-2	[8.45e-2, 9.57e-2]	899 / 10000	36.30 ms	surface-code-mwpm-baseline-d5-p015

Reading this table: A comparison needs at least two decoders measured under these identical conditions.

rotated-surface-code · d=5 · p=0.015

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 5

rounds: 5

physical error rate: 0.015

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	8.785e-2	[8.40e-2, 9.19e-2]	1757 / 20000	77.76 ms	surface-code-mwpm-sweep-d5-p015-s1
pymatching	8.840e-2	[8.45e-2, 9.24e-2]	1768 / 20000	75.98 ms	surface-code-mwpm-sweep-d5-p015-s2
pymatching	9.005e-2	[8.62e-2, 9.41e-2]	1801 / 20000	76.24 ms	surface-code-mwpm-sweep-d5-p015-s3

Reading this table: The confidence intervals for pymatching and pymatching overlap, so this data does not distinguish them. More shots would be needed to separate them.

rotated-surface-code · d=5 · p=0.02

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 5

rounds: 5

physical error rate: 0.02

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	1.541e-1	[1.47e-1, 1.61e-1]	1541 / 10000	51.94 ms	surface-code-mwpm-baseline-d5-p02

Reading this table: A comparison needs at least two decoders measured under these identical conditions.

rotated-surface-code · d=5 · p=0.02

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 5

rounds: 5

physical error rate: 0.02

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	1.580e-1	[1.53e-1, 1.63e-1]	3160 / 20000	111.05 ms	surface-code-mwpm-sweep-d5-p02-s1
pymatching	1.606e-1	[1.56e-1, 1.66e-1]	3213 / 20000	115.11 ms	surface-code-mwpm-sweep-d5-p02-s2
pymatching	1.610e-1	[1.56e-1, 1.66e-1]	3220 / 20000	110.31 ms	surface-code-mwpm-sweep-d5-p02-s3

Reading this table: The confidence intervals for pymatching and pymatching overlap, so this data does not distinguish them. More shots would be needed to separate them.

rotated-surface-code · d=7 · p=0.001

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 7

rounds: 7

physical error rate: 0.001

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	< 3.84e-4 (upper bound; no failures in 10,000 shots)	[0.00e+0, 3.84e-4]	0 / 10000	6.85 ms	surface-code-mwpm-baseline-d7-p001

Reading this table: A comparison needs at least two decoders measured under these identical conditions.

rotated-surface-code · d=7 · p=0.002

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 7

rounds: 7

physical error rate: 0.002

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	< 3.84e-4 (upper bound; no failures in 10,000 shots)	[0.00e+0, 3.84e-4]	0 / 10000	12.08 ms	surface-code-mwpm-baseline-d7-p002

Reading this table: A comparison needs at least two decoders measured under these identical conditions.

rotated-surface-code · d=7 · p=0.002

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 7

rounds: 7

physical error rate: 0.002

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	9.000e-5	[5.69e-5, 1.42e-4]	18 / 200000	244.31 ms	surface-code-mwpm-sweep-d7-p002-s3
pymatching	9.500e-5	[6.08e-5, 1.48e-4]	19 / 200000	260.41 ms	surface-code-mwpm-sweep-d7-p002-s1
pymatching	1.050e-4	[6.87e-5, 1.61e-4]	21 / 200000	256.72 ms	surface-code-mwpm-sweep-d7-p002-s2

Reading this table: The confidence intervals for pymatching and pymatching overlap, so this data does not distinguish them. More shots would be needed to separate them.

rotated-surface-code · d=7 · p=0.003

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 7

rounds: 7

physical error rate: 0.003

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	6.000e-4	[2.75e-4, 1.31e-3]	6 / 10000	19.33 ms	surface-code-mwpm-baseline-d7-p003

Reading this table: A comparison needs at least two decoders measured under these identical conditions.

rotated-surface-code · d=7 · p=0.005

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 7

rounds: 7

physical error rate: 0.005

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	2.600e-3	[1.77e-3, 3.81e-3]	26 / 10000	32.91 ms	surface-code-mwpm-baseline-d7-p005

Reading this table: A comparison needs at least two decoders measured under these identical conditions.

rotated-surface-code · d=7 · p=0.005

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 7

rounds: 7

physical error rate: 0.005

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	2.740e-3	[2.43e-3, 3.08e-3]	274 / 100000	379.15 ms	surface-code-mwpm-sweep-d7-p005-s2
pymatching	2.880e-3	[2.57e-3, 3.23e-3]	288 / 100000	427.75 ms	surface-code-mwpm-sweep-d7-p005-s1
pymatching	3.090e-3	[2.76e-3, 3.45e-3]	309 / 100000	363.36 ms	surface-code-mwpm-sweep-d7-p005-s3

Reading this table: The confidence intervals for pymatching and pymatching overlap, so this data does not distinguish them. More shots would be needed to separate them.

rotated-surface-code · d=7 · p=0.008

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 7

rounds: 7

physical error rate: 0.008

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	1.530e-2	[1.31e-2, 1.79e-2]	153 / 10000	58.25 ms	surface-code-mwpm-baseline-d7-p008

Reading this table: A comparison needs at least two decoders measured under these identical conditions.

rotated-surface-code · d=7 · p=0.008

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 7

rounds: 7

physical error rate: 0.008

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	1.680e-2	[1.60e-2, 1.76e-2]	1680 / 100000	645.32 ms	surface-code-mwpm-sweep-d7-p008-s2
pymatching	1.695e-2	[1.62e-2, 1.78e-2]	1695 / 100000	624.57 ms	surface-code-mwpm-sweep-d7-p008-s1
pymatching	1.723e-2	[1.64e-2, 1.81e-2]	1723 / 100000	621.51 ms	surface-code-mwpm-sweep-d7-p008-s3

Reading this table: The confidence intervals for pymatching and pymatching overlap, so this data does not distinguish them. More shots would be needed to separate them.

rotated-surface-code · d=7 · p=0.01

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 7

rounds: 7

physical error rate: 0.01

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	3.790e-2	[3.43e-2, 4.18e-2]	379 / 10000	83.64 ms	surface-code-mwpm-baseline-d7-p01

Reading this table: A comparison needs at least two decoders measured under these identical conditions.

rotated-surface-code · d=7 · p=0.011

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 7

rounds: 7

physical error rate: 0.011

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	4.870e-2	[4.58e-2, 5.18e-2]	974 / 20000	187.86 ms	surface-code-mwpm-sweep-d7-p011-s1
pymatching	4.980e-2	[4.69e-2, 5.29e-2]	996 / 20000	197.88 ms	surface-code-mwpm-sweep-d7-p011-s2
pymatching	5.150e-2	[4.85e-2, 5.47e-2]	1030 / 20000	200.33 ms	surface-code-mwpm-sweep-d7-p011-s3

Reading this table: The confidence intervals for pymatching and pymatching overlap, so this data does not distinguish them. More shots would be needed to separate them.

rotated-surface-code · d=7 · p=0.015

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 7

rounds: 7

physical error rate: 0.015

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	1.340e-1	[1.27e-1, 1.41e-1]	1340 / 10000	139.84 ms	surface-code-mwpm-baseline-d7-p015

Reading this table: A comparison needs at least two decoders measured under these identical conditions.

rotated-surface-code · d=7 · p=0.015

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 7

rounds: 7

physical error rate: 0.015

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	1.310e-1	[1.26e-1, 1.36e-1]	2619 / 20000	298.35 ms	surface-code-mwpm-sweep-d7-p015-s3
pymatching	1.315e-1	[1.27e-1, 1.36e-1]	2629 / 20000	300.15 ms	surface-code-mwpm-sweep-d7-p015-s2
pymatching	1.317e-1	[1.27e-1, 1.36e-1]	2634 / 20000	306.06 ms	surface-code-mwpm-sweep-d7-p015-s1

Reading this table: The confidence intervals for pymatching and pymatching overlap, so this data does not distinguish them. More shots would be needed to separate them.

rotated-surface-code · d=7 · p=0.02

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 7

rounds: 7

physical error rate: 0.02

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	2.436e-1	[2.35e-1, 2.52e-1]	2436 / 10000	198.16 ms	surface-code-mwpm-baseline-d7-p02

Reading this table: A comparison needs at least two decoders measured under these identical conditions.

rotated-surface-code · d=7 · p=0.02

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 7

rounds: 7

physical error rate: 0.02

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	2.478e-1	[2.42e-1, 2.54e-1]	4957 / 20000	486.46 ms	surface-code-mwpm-sweep-d7-p02-s3
pymatching	2.482e-1	[2.42e-1, 2.54e-1]	4963 / 20000	423.92 ms	surface-code-mwpm-sweep-d7-p02-s1
pymatching	2.604e-1	[2.54e-1, 2.66e-1]	5207 / 20000	423.10 ms	surface-code-mwpm-sweep-d7-p02-s2

Reading this table: The confidence intervals for pymatching and pymatching overlap, so this data does not distinguish them. More shots would be needed to separate them.

rotated-surface-code · d=9 · p=0.002

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 9

rounds: 9

physical error rate: 0.002

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	5.000e-6	[8.83e-7, 2.83e-5]	1 / 200000	580.85 ms	surface-code-mwpm-sweep-d9-p002-s1
pymatching	1.000e-5	[2.74e-6, 3.65e-5]	2 / 200000	579.38 ms	surface-code-mwpm-sweep-d9-p002-s2
pymatching	1.500e-5	[5.10e-6, 4.41e-5]	3 / 200000	582.74 ms	surface-code-mwpm-sweep-d9-p002-s3

Reading this table: The confidence intervals for pymatching and pymatching overlap, so this data does not distinguish them. More shots would be needed to separate them.

rotated-surface-code · d=9 · p=0.005

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 9

rounds: 9

physical error rate: 0.005

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	1.310e-3	[1.10e-3, 1.55e-3]	131 / 100000	778.97 ms	surface-code-mwpm-sweep-d9-p005-s1
pymatching	1.620e-3	[1.39e-3, 1.89e-3]	162 / 100000	784.96 ms	surface-code-mwpm-sweep-d9-p005-s3
pymatching	1.620e-3	[1.39e-3, 1.89e-3]	162 / 100000	803.00 ms	surface-code-mwpm-sweep-d9-p005-s2

Reading this table: The confidence intervals for pymatching and pymatching overlap, so this data does not distinguish them. More shots would be needed to separate them.

rotated-surface-code · d=9 · p=0.008

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 9

rounds: 9

physical error rate: 0.008

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	1.465e-2	[1.39e-2, 1.54e-2]	1465 / 100000	1479.53 ms	surface-code-mwpm-sweep-d9-p008-s2
pymatching	1.499e-2	[1.43e-2, 1.58e-2]	1499 / 100000	1553.57 ms	surface-code-mwpm-sweep-d9-p008-s1
pymatching	1.575e-2	[1.50e-2, 1.65e-2]	1575 / 100000	1542.73 ms	surface-code-mwpm-sweep-d9-p008-s3

Reading this table: The confidence intervals for pymatching and pymatching overlap, so this data does not distinguish them. More shots would be needed to separate them.

rotated-surface-code · d=9 · p=0.011

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 9

rounds: 9

physical error rate: 0.011

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	5.705e-2	[5.39e-2, 6.04e-2]	1141 / 20000	499.34 ms	surface-code-mwpm-sweep-d9-p011-s2
pymatching	5.810e-2	[5.49e-2, 6.14e-2]	1162 / 20000	498.21 ms	surface-code-mwpm-sweep-d9-p011-s3
pymatching	5.890e-2	[5.57e-2, 6.22e-2]	1178 / 20000	494.82 ms	surface-code-mwpm-sweep-d9-p011-s1

Reading this table: The confidence intervals for pymatching and pymatching overlap, so this data does not distinguish them. More shots would be needed to separate them.

rotated-surface-code · d=9 · p=0.015

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 9

rounds: 9

physical error rate: 0.015

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	1.681e-1	[1.63e-1, 1.73e-1]	3362 / 20000	809.84 ms	surface-code-mwpm-sweep-d9-p015-s2
pymatching	1.690e-1	[1.64e-1, 1.74e-1]	3380 / 20000	809.94 ms	surface-code-mwpm-sweep-d9-p015-s3
pymatching	1.702e-1	[1.65e-1, 1.75e-1]	3404 / 20000	811.67 ms	surface-code-mwpm-sweep-d9-p015-s1

Reading this table: The confidence intervals for pymatching and pymatching overlap, so this data does not distinguish them. More shots would be needed to separate them.

rotated-surface-code · d=9 · p=0.02

benchmark suite: surface-code-memory-mwpm

benchmark suite version: 0.1.0

code family: rotated-surface-code

code distance: 9

rounds: 9

physical error rate: 0.02

noise model: circuit-level-depolarizing

stopping rule: null

decoder version: null

Every decoder below was measured under these identical conditions. Runs that differ in any of them appear in their own table, never merged into this one.

Decoder logical error rates with 95 percent confidence intervals under identical conditions
Decoder	Logical error rate	95% interval	Failures / shots	Decode latency	Run
pymatching	3.326e-1	[3.26e-1, 3.39e-1]	6651 / 20000	1196.07 ms	surface-code-mwpm-sweep-d9-p02-s1
pymatching	3.332e-1	[3.27e-1, 3.40e-1]	6664 / 20000	1180.05 ms	surface-code-mwpm-sweep-d9-p02-s3
pymatching	3.337e-1	[3.27e-1, 3.40e-1]	6674 / 20000	1175.76 ms	surface-code-mwpm-sweep-d9-p02-s2

Reading this table: The confidence intervals for pymatching and pymatching overlap, so this data does not distinguish them. More shots would be needed to separate them.

Unranked measurements

These runs did not record a comparability key, so they are listed rather than ranked. Placing them in a table alongside runs whose conditions are known would imply a comparison that has not been established.

pymatching surface-code-mwpm-baseline-d7-p02
pymatching surface-code-mwpm-baseline-d7-p015
pymatching surface-code-mwpm-baseline-d7-p01
pymatching surface-code-mwpm-baseline-d7-p008
pymatching surface-code-mwpm-baseline-d7-p005
pymatching surface-code-mwpm-baseline-d7-p003
pymatching surface-code-mwpm-baseline-d7-p002
pymatching surface-code-mwpm-baseline-d7-p001
pymatching surface-code-mwpm-baseline-d5-p02
pymatching surface-code-mwpm-baseline-d5-p015
pymatching surface-code-mwpm-baseline-d5-p01
pymatching surface-code-mwpm-baseline-d5-p008
pymatching surface-code-mwpm-baseline-d5-p005
pymatching surface-code-mwpm-baseline-d5-p003
pymatching surface-code-mwpm-baseline-d5-p002
pymatching surface-code-mwpm-baseline-d5-p001
pymatching surface-code-mwpm-baseline-d3-p02
pymatching surface-code-mwpm-baseline-d3-p015
pymatching surface-code-mwpm-baseline-d3-p01
pymatching surface-code-mwpm-baseline-d3-p008
pymatching surface-code-mwpm-baseline-d3-p005
pymatching surface-code-mwpm-baseline-d3-p003
pymatching surface-code-mwpm-baseline-d3-p002
pymatching surface-code-mwpm-baseline-d3-p001

Codes and hardware

QEC codes and hardware

Each cell is derived from the device snapshot’s capability fields, so the claim can be checked against the snapshot it came from. This is a capability match, not a recommendation and not an experimental result: only a recorded run could raise a pairing to simulated or demonstrated, and none of these are backed by a run.

The devices below are synthetic topologies used for exploring routing, not observations of any physical hardware.

QEC code and device capability matches, derived from device capability fields
Code	Line, 5 qubits	Grid, 3x3	All-to-all, 6 qubits	Line, 5 qubits, no feed-forward
Rotated surface code (X memory) STABILIZER CSS TOPOLOGICAL	THEORETICALLY_SUITABLECapabilities match	THEORETICALLY_SUITABLECapabilities match	THEORETICALLY_SUITABLECapabilities match	INCOMPATIBLE_UNDER_ASSUMPTIONSMissing a required capability mid-circuit measurement is required for syndrome extraction
Rotated surface code (Z memory) STABILIZER CSS TOPOLOGICAL	THEORETICALLY_SUITABLECapabilities match	THEORETICALLY_SUITABLECapabilities match	THEORETICALLY_SUITABLECapabilities match	INCOMPATIBLE_UNDER_ASSUMPTIONSMissing a required capability mid-circuit measurement is required for syndrome extraction
Unrotated surface code (X memory) STABILIZER CSS TOPOLOGICAL	THEORETICALLY_SUITABLECapabilities match	THEORETICALLY_SUITABLECapabilities match	THEORETICALLY_SUITABLECapabilities match	INCOMPATIBLE_UNDER_ASSUMPTIONSMissing a required capability mid-circuit measurement is required for syndrome extraction
Repetition code (memory) STABILIZER CSS	THEORETICALLY_SUITABLECapabilities match	THEORETICALLY_SUITABLECapabilities match	THEORETICALLY_SUITABLECapabilities match	INCOMPATIBLE_UNDER_ASSUMPTIONSMissing a required capability mid-circuit measurement is required for syndrome extraction
Color code (XYZ memory) STABILIZER CSS TOPOLOGICAL	THEORETICALLY_SUITABLECapabilities match	THEORETICALLY_SUITABLECapabilities match	THEORETICALLY_SUITABLECapabilities match	INCOMPATIBLE_UNDER_ASSUMPTIONSMissing a required capability mid-circuit measurement is required for syndrome extraction

Code catalog

Rotated surface code (X memory)
STABILIZER
CSS
TOPOLOGICAL
SURFACE
Planar topological code on a rotated lattice, preserving one logical qubit through repeated rounds of syndrome extraction.
- Nearest-neighbour connectivity on a two-dimensional grid is sufficient.
Runnable distances: 3, 5, 7, 9 · reference
Rotated surface code (Z memory)
STABILIZER
CSS
TOPOLOGICAL
SURFACE
Rotated surface code memory experiment in the Z basis.
Runnable distances: 3, 5, 7, 9 · reference
Unrotated surface code (X memory)
STABILIZER
CSS
TOPOLOGICAL
SURFACE
Unrotated surface code memory; uses more physical qubits per distance than the rotated layout.
Runnable distances: 3, 5, 7 · reference
Repetition code (memory)
STABILIZER
CSS
One-dimensional classical repetition code protecting against a single error type. Useful as a control: it is not a full quantum code.
- Protects against one error type only, so a low logical error rate here is not evidence of quantum error correction.
Runnable distances: 3, 5, 7, 9, 11 · reference
Color code (XYZ memory)
STABILIZER
CSS
TOPOLOGICAL
COLOR
Triangular color code memory, admitting transversal Clifford gates.
- Syndrome extraction uses weight-six stabilizers on a three-colorable lattice.
Runnable distances: 3, 5, 7 · reference