发表机构
Centre for Quantum Software and Information (QSI), School of Computer Science, University of Technology Sydney; School of Electrical Engineering and Telecommunications, University of New South Wales (UNSW)（悉尼科技大学计算机科学学院量子软件与信息中心; 新南威尔士大学电气与电信学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究探讨双变量自行车码中依赖稳定子校验的元校验机制，分析其综合征修复能力与逻辑障碍，发现仅靠元综合征修复在高错误率下失效，并建议采用联合数据-测量解码以应对测量故障模糊性。
AI 中文摘要
错误的综合征测量可能破坏原本正确的量子纠错步骤。双变量自行车（BB）码包含相关的稳定子校验，因此其测量的综合征满足可用于元校验的奇偶约束。我们研究了这种内置冗余何时真正支持综合征修复，以及它如何与码的逻辑结构相互作用。零化子商识别出单块逻辑类，并表明何时不可避免地需要进行混合块搜索。对于综合征修复，元综合征等价于对有效综合征理想进行模归约。因此，平移群映射到维度为$k/2$的商代数的单位群，其核为$K_M$。这给出了距离为二的表征、可区分单故障的单位群界限，以及一个族级障碍：对于块长度增长的有界-$k$ BB族，在任意固定测量错误率下，仅依赖元综合征的精确修复失败概率趋于一。在没有中间数据故障的情况下，相同的轨道计数也给出了消除所有单故障模糊性所需的最小部分第二次测量。精确计算区分了标准示例。$[[72,12,6]]$码具有综合征距离三，最小权重修复可纠正每个单测量故障，而Gross $[[144,12,12]]$码有36个不可区分的单故障对。持续的唯象实验显示出相同的定性对比，并倾向于在具有更强模糊性的码上采用联合数据-测量解码，而非分离的修复阶段。该分析将我们早期的互素周期处理扩展到一般的双块BB码，并将测量模糊性与它可能引起的数据错误区分开来。
英文摘要
Faulty syndrome measurements can corrupt an otherwise correct quantum-error correction step. Bivariate bicycle (BB) codes contain dependent stabilizer checks, so every valid syndrome obeys additional parity constraints, or metachecks. We study how far this built-in redundancy can identify measurement faults and when the remaining ambiguity is unavoidable, while separately checking the code's logical structure. A logical decomposition is used as a preliminary safety check: it identifies a $k/2$-dimensional annihilator subspace and a $k/2$-dimensional colon quotient, and the minimum-weight logical need not be visible from the annihilator side alone. On the measurement side, translation symmetry partitions syndrome locations into classes that carry identical metacheck information. This gives an exact characterization of the leading single-fault ambiguity, a bound on how many fault locations can be distinguished, and a family-level repair limit when the encoded dimension stays bounded while the block length grows. Under a static-data assumption, the same calculation gives the minimum number of checks that must be remeasured to remove every single-fault ambiguity. Exact finite-code calculations illustrate both regimes: all single measurement faults are distinguishable in a 72-qubit BB code, whereas the 144-qubit Gross code merges its 72 syndrome locations into 36 indistinguishable pairs. In a 108-qubit example, one logical component first appears at weight 12 while the other contains a weight-10 logical. Sustained phenomenological experiments show that joint data--measurement decoding is more robust than a separated repair stage on the more ambiguous codes. The resulting tests apply to general two-block BB codes, including non-coprime periods and repeated-root cases.
Comments15 pages, 11 figures, 9 tables
