标题： 拓扑量子错误纠正中的非均匀噪声率和Griffiths相 显示英文标题

标题： Non-Uniform Noise Rates and Griffiths Phases in Topological Quantum Error Correction

摘要： 量子纠错(QEC)码的性能通常是在假设空间和时间上误差率均匀的条件下进行研究的。另一方面，实验实现几乎总是会产生异质的误差率，这可能是由于诸如制造不完美和/或宇宙射线等效应在空间或时间上产生的。因此，理解它们的存在是否以及如何以定性的方式影响QEC的性能是很重要的。在本工作中，我们研究了非均匀误差率在1D重复码和2D环面码的代表性例子中的影响，重点在于它们是否具有扩展的空间-时间相关性；这些可能来自稀有事件（如宇宙射线）暂时提高整个码块的误差率。这些影响可以在相应的解码统计力学模型中描述，其中误差率的长程相关性导致较弱耦合的扩展稀有区域。对于稀有区域为线性的1D重复码，我们发现两个不同的可解码相：一种是传统的有序相，在这种相中逻辑失败率随着码距呈指数衰减，另一种是稀有区域主导的Griffiths相，在这种相中失败率显著更大，并呈拉伸指数衰减。特别是，当稀有区域的误差率高于整体阈值时，后者相存在。对于稀有区域为平面的2D环面码，我们没有发现可解码的Griffiths相：提升误差率超过整体阈值的稀有事件会导致阈值的渐近损失和解码失败。揭示失败机制意味着，抑制扩展的重复稀有事件序列的技术（在没有干预的情况下，这些事件将以高概率统计存在）对于使用环面码的QEC将是至关重要的。 显示英文摘要

摘要： The performance of quantum error correcting (QEC) codes are often studied under the assumption of spatio-temporally uniform error rates. On the other hand, experimental implementations almost always produce heterogeneous error rates, in either space or time, as a result of effects such as imperfect fabrication and/or cosmic rays. It is therefore important to understand if and how their presence can affect the performance of QEC in qualitative ways. In this work, we study effects of non-uniform error rates in the representative examples of the 1D repetition code and the 2D toric code, focusing on when they have extended spatio-temporal correlations; these may arise, for instance, from rare events (such as cosmic rays) that temporarily elevate error rates over the entire code patch. These effects can be described in the corresponding statistical mechanics models for decoding, where long-range correlations in the error rates lead to extended rare regions of weaker coupling. For the 1D repetition code where the rare regions are linear, we find two distinct decodable phases: a conventional ordered phase in which logical failure rates decay exponentially with the code distance, and a rare-region dominated Griffiths phase in which failure rates are parametrically larger and decay as a stretched exponential. In particular, the latter phase is present when the error rates in the rare regions are above the bulk threshold. For the 2D toric code where the rare regions are planar, we find no decodable Griffiths phase: rare events which boost error rates above the bulk threshold lead to an asymptotic loss of threshold and failure to decode. Unpacking the failure mechanism implies that techniques for suppressing extended sequences of repeated rare events (which, without intervention, will be statistically present with high probability) will be crucial for QEC with the toric code.