Single-shot and two-shot decoding with generalized bicycle codes

• URL: http://arxiv.org/abs/2502.19406v2
• Date: Fri, 28 Mar 2025 20:34:15 GMT
• Title: Single-shot and two-shot decoding with generalized bicycle codes
• Authors: Hsiang-Ku Lin, Xingrui Liu, Pak Kau Lim, Leonid P. Pryadko,
• Abstract summary: Generalized-bicycle (GB) quantum error-correcting codes have naturally redundant minimum-weight stabilizer generators.<n>We constructed several short GB codes with relatively large dimensions, distances, and syndrome, also admitting fault-tolerant near-time-optimal syndrome measurement schedules.
• Score: 0.027042267806481293
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Generalized-bicycle (GB) quantum error-correcting codes have naturally redundant minimum-weight stabilizer generators. To use this redundancy, we constructed several short GB codes with relatively large dimensions, distances, and syndrome distances, also admitting fault-tolerant near-time-optimal syndrome measurement schedules. We simulated their performance both under phenomenological noise and standard circuit noise, using sliding window sequential decoding protocol covering $T\ge 1$ measurement rounds at a time, based on an in-house binary BP+OSD decoder. While true single-shot decoding ($T=1$) may suffer from a significant loss of accuracy, already two-shot ($T=2$) decoding gives nearly the same logical error rates as multi-shot with much larger $T$. Comparison with the same codes but redundant stabilizer generators dropped show significantly improved decoding accuracy for all $T\ge1$.

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