Strip-Symmetric Quantum Codes for Biased Noise: Z-Decoupling in Stabilizer and Floquet Codes
Mohammad Rowshan · 2026 · arXiv
| 编号 QE243 | 主题 Floquet 与动态码 | 链接 arXiv:2601.03623 |
摘要
摘要保留原文（英文）
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Bias-tailored codes such as the XZZX surface code and the domain wall color code achieve high dephasing-biased thresholds because, in the infinite-bias limit, their syndromes decouple into one-dimensional repetition-like chains; the Floquet code shows an analogous strip-wise structure for detector events in spacetime. We capture this common mechanism by defining strip-symmetric biased codes, a class of static stabilizer and dynamical (Floquet) codes for which, under pure dephasing and perfect measurements, each elementary fault is confined to a strip and the Z-detector—fault incidence matrix is block diagonal. For such codes the Z-detector hypergraph decomposes into independent strip components and maximum-likelihood decoding factorizes across strips, yielding complexity savings for matching-based decoders. We characterize strip symmetry via per-strip stabilizer products, viewed as a 1-form symmetry, place XZZX, the domain wall color code, and in this framework, and introduce synthetic strip-symmetric detector models and domain-wise Clifford constructions that serve as design tools for new bias-tailored Floquet codes.
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