AI 中文总结
研究固态容错量子计算中对损伤的高容忍度方法，针对半导体电子自旋量子比特系统，采用CAbLECAR方法，通过路径求解软件找到有效路径，经转换获得逻辑错误率，结果表明构建超大阵列可容忍大量损伤，还可推广到其他量子低密度奇偶校验码。
AI 中文摘要
这是一项关于固态容错量子计算中一种对损伤（即缺陷或‘掉线’）具有高容忍度方法的简短研究。我们的方法主要针对半导体电子自旋量子比特系统，其已被证明能支持沿预定义路径的快速且高保真穿梭。我们采用了Chadwick和Chong最近的CAbLECAR方法：由辅助量子比特执行稳定器操作，每个辅助量子比特遵循定制的预编程路径。我们考虑简单的表面码，但对物理晶格造成损伤，并依靠路径求解软件在强制稳定器对易和避免挂钩错误的约束下找到有效路径。然后将解决方案转换为用于Stim的探测器错误模型并获得逻辑错误率。我们通过使用约化等效表面码距离的概念，将逻辑性能与原始晶格的性能进行比较来表达结果；对于合理的基础错误率，我们发现10%的损伤会使原始等效距离减少约一半（在大阵列极限下$d_\text{equiv}\approx0.48\,d_\text{pristine}$，对于我们最小的阵列则升至$\approx0.60$）。这表明通过构建超大阵列可以容忍大量损伤。我们指出，研究其他量子低密度奇偶校验码的损伤容限是一个直接的推广，并且有可能适应运行时出现的损伤。
英文摘要
This is a short study of an approach offering high tolerance to damage (i.e. defects or 'drop outs') in solid state fault-tolerant quantum computing. Our method is primarily aimed at semiconductor electron spin-qubit systems, which have been shown to support fast and high-fidelity shuttling along pre-defined paths. We adapt the recent CAbLECAR method of Chadwick and Chong: stabilisers are performed by ancillas which each follow a bespoke pre-programmed path. We consider the simple surface code but we damage the physical lattice, and rely on route-solving software to find efficient pathways under constraints enforcing stabiliser commutation and hook error avoidance. Solutions are then converted to detector error models for Stim and logical error rates are obtained. We express our results by gauging the logical performance against that of a pristine lattice, using the notion of a reduced equivalent surface-code distance; for reasonable underlying error rates we find that $10\%$ damage leaves roughly half of the pristine equivalent distance ($d_\text{equiv}\approx0.48\,d_\text{pristine}$ in the large-array limit, rising to $\approx0.60$ for our smallest array). This suggests that one can tolerate substantial damage by building oversized arrays. We note that investigating damage tolerance of other qLDPC codes is a straightforward generalisation, and potentially one could adapt to damage emerging at runtime.
Comments15 pages, 10 figures
