发表机构
Brandeis University; Brigham Young University（布兰迪斯大学; 杨百翰大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究构建ZY表面码，在电路级偏置及串扰噪声下与ZX码对比，发现偏置提升X阈值但降低Z阈值，串扰主要损害Z存储，并强调联合推理解码器的必要性。
AI 中文摘要
研究表面码在偏置噪声模型下的阈值行为是一个活跃的研究领域。此前Tuckett等人（2018年）的工作使用最优张量网络解码器，证明了在码容量级退相位噪声下，将$Z$型稳定子替换为$Y$型稳定子能显著提高表面码的阈值。在本工作中，我们通过将$X$型稳定子替换为$Y$型稳定子，构建并研究了一种$ZY$表面码。我们在电路级Pauli-$X$偏置噪声下，分别在有和没有额外基于门的$XX$串扰噪声的情况下，将其与标准$ZX$表面码进行比较。我们发现，对于$ZX$表面码，$X$存储阈值随偏置单调增加，而$Z$存储阈值则下降并趋于饱和。对于$ZY$表面码，$Y$存储阈值在所有偏置值下几乎保持不变。$ZX$和$ZY$码的$Z$存储阈值在不确定度范围内一致。添加$XX$串扰会使$Z$存储阈值降低超出拟合不确定度，而对$X$存储阈值影响不大。CNOT排序的选择会在两个逻辑存储之间重新分配阈值性能。我们的工作将先前的观察从码容量级噪声扩展到电路级噪声。这也表明需要能够联合推理相关综合征信息的解码器，以便充分利用定制的稳定子结构进行量子纠错。
英文摘要
Studying the threshold behavior of surface codes under biased noise models is an active area of research. Previous work Tuckett et al. (2018), using an optimal tensor-network decoder, demonstrated that replacing $Z$-type stabilizers with $Y$-type stabilizers significantly improves the surface code threshold under code-capacity level dephasing noise. In this work, we construct and study a $ZY$ surface code by replacing the $X$-type stabilizers with $Y$-type stabilizers. We compare it with the standard $ZX$ surface code under circuit-level Pauli-$X$ biased noise, with and without an additional gate-based $XX$ crosstalk noise. We find that for the $ZX$ surface code, the $X$-memory threshold increases monotonically with bias while the $Z$-memory threshold decreases and saturates. For the $ZY$ surface code, the $Y$-memory threshold is nearly constant across all bias values. The $Z$-memory thresholds of the $ZX$ and $ZY$ codes are consistent within the uncertainty. Adding $XX$ crosstalk reduces the $Z$-memory threshold beyond the fitting uncertainty while leaving the $X$ memory threshold largely unaffected. The choice of CNOT ordering redistributes threshold performance between the two logical memories. Our work extends prior observations from code-capacity level noise to circuit-level noise. It also indicates the need for decoders capable of jointly reasoning over correlated syndrome information so that tailored stabilizer structures could be fully utilized for quantum error correction.
