AI 中文总结
研究稳定器码中相关相干噪声，推导相关逻辑信道及通用累积量框架，引入PROSE编码抑制误差，表明其能有效识别本征空间，与逻辑泡利旋转结合可匹配或超越标准技术，还指出噪声相关性可成资源。
AI 中文摘要
稳定器码中的相干误差通常在量子比特和量子纠错（QEC）循环之间相关。对这种噪声进行一般的分析处理非常有价值。我们推导了在相关相干\(Z\)噪声下重复QEC循环所诱导的精确逻辑信道，并开发了一个广泛通用的累积量展开框架，该框架产生了一个易于处理的噪声平均逻辑保真度表达式。此表达式在噪声中是非微扰的，适用于任意稳定器码和相关结构。它揭示了标准随机泡利误差模型中没有的特征：诱导信道取决于选择哪个稳定器本征空间作为码空间。利用这一点，我们引入了受保护稳定器本征空间（PROSE）编码，一种选择最优码空间的误差抑制策略。我们表明，在许多相关情况下可以有效地识别此本征空间。此外，可以与逻辑泡利旋转相结合，PROSE匹配或优于标准误差抑制技术（动态解耦、物理量子比特的泡利旋转）。我们还表明，通常认为对QEC有害的噪声相关性，反而可以成为一种资源：通过正确的编码，即使是正相关性也能将逻辑保真度降低到低于不相关基线的水平。我们的结果为稳定器码中的相关相干噪声提供了一个新的、广泛适用的视角。
英文摘要
Coherent errors in stabilizer codes are often correlated across qubits and QEC cycles. Having a general analytical treatment of such noise would thus be extremely valuable. We derive here the exact logical channel induced by repeated QEC cycles under correlated coherent $Z$ noise, and develop a broadly general cumulant-expansion framework that yields a tractable expression for the noise-averaged logical infidelity. Crucially, this expression is non-perturbative in the noise, and applies to arbitrary stabilizer codes and correlation structures. It reveals a feature with no analogue in standard stochastic Pauli error models: the induced channel depends on which stabilizer eigenspace is chosen as the codespace. Exploiting this, we introduce protected stabilizer eigenspace (PROSE) encoding, an error-suppression strategy that selects the optimal codespace. We show that this eigenspace can be efficiently identified in many relevant situations. Further, when combined with logical Pauli twirling, PROSE matches or outperforms standard error suppression techniques (dynamical decoupling, Pauli twirling of physical qubits). We also show that noise correlations, usually assumed to be harmful to QEC, can instead be a resource: with the right encoding, even positive correlations reduce the logical infidelity below the uncorrelated baseline. Our results offer a new, broadly applicable lens on correlated coherent noise in stabilizer codes.
Comments27 pages, 11 figures
