发表机构
Centre for Computational Science, University College London; Advanced Research Computing Centre, University College London（计算科学中心，伦敦大学学院; 高级研究计算中心，伦敦大学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出基于BP与OSD分歧的自适应qLDPC码解码器，通过内部风险信号识别高价值实例，以20%升级恢复85%-94%性能增益，并降低3.6倍解码成本。
AI 中文摘要
量子低密度奇偶校验（qLDPC）码的准确解码通常依赖于昂贵的后处理搜索，尽管不同综合征的解码难度差异很大。我们发现，更深层后处理搜索的收益高度集中在一小部分解码实例上，并且这些实例可以直接从解码器本身识别出来。为此，我们引入了一种基于置信传播（BP）和有序统计解码（OSD）的自适应解码器，利用BP硬判决与综合征一致零阶OSD解之间的分歧作为内部风险信号，以确定何处需要更深入的搜索。在电路级去极化噪声下的一个[[144,12,12]]双变量自行车码上（在144个数据量子比特中编码12个逻辑量子比特，距离为12），仅升级风险最高的20%实例即可恢复完整单自由变量扫描可获得的逻辑错误率改进的85%至92%，同时相对于对每个实例应用相同的截断搜索，平均串行解码成本降低了3.6倍。在匹配预算下，分歧引导的路由也优于基于BP综合征残差、综合征权重和随机选择的路由。相同行为在从提升积构造获得的结构不同的径向qLDPC码上再次出现，升级20%实例可恢复87%至94%的可用增益。在Quantinuum H2离子阱处理器上进行的Z存储器实验（实现X型和Z型校验）进一步表明，该信号在设备噪声下仍具有预测性。这些结果表明，解码器内部的分歧可以揭示额外解码工作有价值之处，从而将经典计算集中在最可能受益的实例上。
英文摘要
Accurate decoding of quantum low-density parity-check (qLDPC) codes often relies on expensive post-processing search, although decoding difficulty varies strongly between syndromes. We find that the benefit of deeper post-processing search is highly concentrated in a small subset of decoding instances, and that these instances can be identified directly from the decoder itself. To this end, we introduce an adaptive decoder based on belief propagation (BP) and ordered-statistics decoding (OSD), using the disagreement between the BP hard decision and the syndrome-consistent order-zero OSD solution as an internal risk signal to determine where deeper search is required. On a $[[144,12,12]]$ bivariate bicycle code under circuit-level depolarising noise, encoding $12$ logical qubits in $144$ data qubits with distance $12$, escalating only the highest-risk $20\%$ of instances recovers $85\%$ to $92\%$ of the improvement in logical error rate available from a full one-free-variable sweep, while reducing the mean serial decoding cost by a factor of $3.6$ relative to applying the same truncated search to every instance. At matched budget, disagreement-guided routing also outperforms routing based on the BP syndrome residual, syndrome weight and random selection. The same behaviour reappears on a structurally distinct radial qLDPC code obtained from a lifted-product construction, where escalating $20\%$ of instances recovers $87\%$ to $94\%$ of the available gain. A $Z$-memory experiment on the Quantinuum H2 trapped-ion processor, implementing both $X$-type and $Z$-type checks, further shows that the signal remains predictive under device noise. These results show that decoder-internal disagreement can expose where additional decoding effort is valuable, allowing classical computation to be concentrated on the instances most likely to benefit from it.
