Decoder performance, measured rigorously
All results use synthetic depolarizing noise unless noted. Physical hardware results are available to active integration partners under NDA. Methodology available on request.
MWPM vs Union-Find by code distance
Measurements on single AMD EPYC 7713 core. Input: 10 rounds of syndrome data. Synthetic depolarizing noise p = 0.003.
| Code Distance | MWPM Median (ms) | MWPM P99 (ms) | Union-Find Median (ms) | Union-Find P99 (ms) | Physical Qubits | Syndrome Nodes |
|---|---|---|---|---|---|---|
| d = 3 | 0.17 | 0.23 | 0.08 | 0.12 | 17 | 8 |
| d = 5 | 0.62 | 0.79 | 0.24 | 0.31 | 49 | 24 |
| d = 7 | 1.73 | 2.21 | 0.57 | 0.73 | 97 | 48 |
| d = 9 | 4.11 | 5.33 | 1.04 | 1.38 | 161 | 80 |
| d = 11 | 9.87 | 12.64 | 1.93 | 2.57 | 241 | 120 |
Logical error rate vs physical error rate
Below the fault-tolerance threshold (~1.1% physical error rate for rotated surface codes under depolarizing noise), every increase in code distance exponentially suppresses the logical error rate. The chart right shows this scaling for code distances 3, 5, 7, and 9 using QECSync MWPM decoder.
At physical error rate p = 0.003 (typical for current superconducting hardware), QECSync achieves logical error rates of 8×10⁻³ at d=3, 4×10⁻⁴ at d=5, and 1.4×10⁻⁵ at d=7 — each distance step reducing logical error by roughly a factor of 25–35.
Logical error suppression rate by noise model
100,000 decoding trials per cell. Physical error rate p = 0.003. 10 syndrome rounds.
| Code Distance | Depolarizing (MWPM) | Depolarizing (UF) | Biased-Z (MWPM) | Correlated (MWPM) |
|---|---|---|---|---|
| d = 3 | 99.17% | 98.83% | 99.41% | 98.62% |
| d = 5 | 99.61% | 99.12% | 99.72% | 99.31% |
| d = 7 | 99.86% | 99.43% | 99.91% | 99.73% |
| d = 9 | 99.94% | 99.71% | 99.97% | 99.89% |
Biased-Z model: Z-error rate 5× higher than X-error rate. Correlated model: spatially correlated error pairs within distance 2.
How we measure
Syndrome inputs are generated by Monte Carlo simulation of the planar surface code stabilizer circuit. Each trial applies Pauli errors at each gate and measurement site according to the noise model, performs syndrome extraction, and presents the syndrome array to the decoder.
Logical error is recorded when the decoder's correction, composed with the actual error, has a non-trivial action on the logical operator. All latencies are wall-clock measurements on a single CPU core; no GPU acceleration is used in the current benchmark set.
Hardware benchmark results (real device noise, real calibration data) are available to integration partners. Contact us to discuss what data we can share under NDA.