GKP-级联qLDPC码的电路级基准测试

中文摘要 AI 辅助

基于Gottesman-Kitaev-Preskill（GKP）码的可扩展容错量子纠错需要有限速率的外码，这些外码能够在现实电路噪声下利用模拟GKP信息。然而，量子低密度奇偶校验（qLDPC）外码作为电路级GKP级联的候选方案尚未被系统比较。在此，我们使用一个统一的模拟框架对BB码和三轮车码进行基准测试，该框架从码容量噪声逐步推进到重复的噪声综合征提取和调度解析的位移传播。在所有三种噪声模型下，采用有序统计解码的模拟信息信念传播（BP-OSD）比硬判决解码产生更高的有限尺寸交叉估计。在完整电路模型中，所选BB序列的模拟信息交叉阈值为σ_th≈0.212，三轮车序列为0.142，分别对应约10.46 dB和13.94 dB的压缩需求。这些结果表明，模拟GKP信息在电路级噪声下持续改进解码性能。在此使用的常见模拟假设下，所选BB序列也比所选三轮车序列产生更高的有限尺寸交叉估计。

英文摘要

Scalable fault-tolerant quantum error correction based on Gottesman-Kitaev-Preskill (GKP) codes requires finite-rate outer codes that can exploit analog GKP information under realistic circuit noise. However, quantum low-density parity-check (qLDPC) outer codes have not been systematically compared as candidates for circuit-level GKP concatenation. Here, we benchmark BB and tricycle codes using a unified simulation framework that progresses from code-capacity noise to repeated noisy syndrome extraction and schedule-resolved displacement propagation. Across all three noise models, analog-informed belief-propagation with ordered-statistics decoding (BP-OSD) yields higher finite-size crossing estimates than hard-decision decoding. In the full circuit model, the analog-informed crossings are \(σ_{\mathrm{th}}\simeq0.212\) for the selected BB sequence and \(0.142\) for the tricycle sequence, corresponding to squeezing requirements of approximately \(10.46\,\mathrm{dB}\) and \(13.94\,\mathrm{dB}\), respectively. These results show that analog GKP information continues to improve decoding under circuit-level noise. Under the common simulation assumptions used here, the selected BB sequence also yields a higher finite-size crossing estimate than the selected tricycle sequence.

发表机构

• Center on Frontiers of Computing Studies, School of Computer Science, Peking University（北京大学计算机科学学院前沿计算研究中心）

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