发表机构
University of Illinois Urbana-Champaign; Korea Institute for Advanced Study; Institute of Science Tokyo; Massachusetts Institute of Technology（伊利诺伊大学厄巴纳-香槟分校; 韩国高等研究院; 东京科学大学; 麻省理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对超高码率量子码的设计，提出基于配对划分和减半变换的模板，以列权重为关键参数，在紧凑块长下实现更大距离，并识别出多个参数优良的非CSS码。
AI 中文摘要
减少量子纠错的量子比特开销是可扩展容错量子计算的核心挑战。近期的超高码率量子码为实现这一目标提供了有前景的途径，其中一些构造每个逻辑量子比特仅需两个物理数据量子比特。然而，系统性地指导编码率、距离、校验权重和块长之间权衡的设计原理仍然缺乏。在此，我们开发并分析了探索这一设计空间的原理，并利用它们设计了性能更优的紧凑码构造。我们基于配对划分构造和进一步缩短块长的减半变换开发了码模板。受度分布系综分析的启发，我们识别出列权重是一个关键设计参数：增加列权重可以在紧凑块长下实现更大的距离，但代价是更重的校验。我们发现，在物理错误率为0.1%时，增加距离带来的好处往往超过更重校验带来的惩罚。应用这一框架，我们识别出众多参数优良的紧凑码，包括校验权重为10的[[90,21,11]]、[[140,31,15]]和[[200,43,20]]非CSS码。此外，我们开发了用于识别低权重逻辑基的对称性知情策略。这些结果为设计超高码率量子码和导航其帕累托前沿提供了系统性策略。
英文摘要
Reducing the qubit overhead of quantum error correction is a central challenge for scalable fault-tolerant quantum computing. Recent ultra-high-rate quantum codes offer a promising route toward this goal, with some constructions requiring as few as two physical data qubits per logical qubit. However, systematic principles for navigating the tradeoffs among encoding rate, distance, check weight, and blocklength remain lacking. Here, we develop and analyze principles for exploring this design space, and use them to design compact code constructions with improved performance. We develop code templates based on a pair-partition construction and a halving transformation that further reduces blocklength. Motivated by ensemble analysis of the degree distributions, we identify column weight as a key design parameter: increasing the column weight enables larger distances at compact blocklengths, at the cost of heavier checks. We find that at physical error rates of 0.1%, the benefits of increased distance often outweigh the penalty associated with heavier checks. Applying this framework, we identify numerous compact codes with favorable parameters, including [[90,21,11]], [[140,31,15]], and [[200,43,20]] non-CSS codes with check weight 10. Moreover, we develop symmetry-informed strategies for identifying low-weight logical bases. These results provide systematic strategies for designing ultra-high-rate quantum codes and navigating their Pareto frontier.
Comments20 + 16 pages. This work also subsumes the earlier results of arXiv preprint 2607.14091
