AI 中文总结
本文研究滑动窗口译码（SWD）的动力学，提出将其描述为带ℤ₂电荷粒子的随机动力学过程，确定译码速率1/W为可译码相的相关扰动，且结果具有广泛适用性。
AI 中文摘要
量子纠错（QEC）的实际实现需要快速测量和连续处理校正子信息，以防止未处理数据积压。虽然“静态”QEC通过映射到平衡统计力学模型在理论上已被充分理解，但目前缺乏对“实时”QEC的这种理解。本文研究滑动窗口译码（SWD）的动力学，SWD是一种实时译码实现，作用于含噪校正子信息的时间局部窗口，并以非零速率不可逆地执行校正。我们提出了SWD的有效描述，将其视为随机动力学过程，其中带ℤ₂电荷的点粒子会发生宇称守恒的反应与扩散。该模型描述的是远大于窗口尺寸W的长度和时间尺度上的动力学，而小于W的尺度上的物理过程会导致有效参数呈现非平凡的W依赖标度。我们将译码速率1/W确定为可译码相的相关扰动，还通过改变SWD的许多微观细节且不影响有效描述，证明了本文结果具有广泛适用性。
英文摘要
Practical implementations of quantum error correction (QEC) require rapid measurement and continuous processing of the syndrome information in order to prevent a backlog of unprocessed data. While ``static'' QEC is theoretically well understood via mappings to equilibrium statistical mechanics models, such an understanding of ``real-time'' QEC is currently lacking. Here, we study the kinetics of sliding window decoding (SWD), an implementation of real-time decoding that acts on temporally local windows of noisy syndrome information and commits to corrections irreversibly at a nonzero rate. We propose an effective description of SWD in terms of a stochastic kinetic process, where $\mathbb{Z}_2$-charged point particles undergo parity-conserving reaction and diffusion. This model describes dynamics at length and time scales large compared to the window size $W$, whereas physics at scales smaller than $W$ leads to nontrivial $W$-dependent scaling of the effective parameters. We identify the rate of decoding $1/W$ as a relevant perturbation to the decodable phase. We also show broad applicability of our results by changing many microscopic details of SWD without affecting the effective description.
Comments8 pages, 3 pages of supplemental information
