发表机构
Weizmann Institute of Science; The Hebrew University of Jerusalem（魏茨曼科学研究所; 耶路撒冷希伯来大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文建立经典随机过程与CSS量子记忆的等价框架，引入SPCA并首次严格证明4D环面码在Toom规则和局部泡利噪声下是自主量子记忆，为低维可证明量子记忆构建提供系统路径。
AI 中文摘要
对热平衡之外的量子记忆的研究，既源于容错量子计算机中需要能够承受现实噪声的记忆的需求，也源于自主多体系统中量子记忆何时能够涌现这一基本问题。我们建立了基于CSS的量子记忆在泡利噪声下与经典记忆之间通过两个关联的概率过程的一般等价性。在异步设置中，量子动力学由林德布拉德生成子产生，我们识别出一类广泛的基于综合征的林德布拉德生成子，使得量子记忆问题等价于连续时间经典马尔可夫动力学中的记忆问题。在同步设置中，我们引入基于综合征的概率元胞自动机（SPCAs），并建立其经典记忆与局部量子信道下基于CSS的量子记忆之间的一一对应关系。该框架提供了一条从经典概率过程推导和构建量子记忆的系统路径，并重现了已知结果，包括4维环面码在热噪声存在下是量子记忆这一事实。作为应用，我们首次严格证明了在局部泡利噪声存在下，采用Toom规则的4维环面码是量子记忆，前提是错误率低于一个常数阈值。我们既对相应的同步、PCA型量子动力学证明了这一点，也对Floquet林德布拉德生成子证明了这一点。更一般地，我们表明SPCA中的经典记忆可以在Floquet林德布拉德动力学下提升为量子记忆；是否可以用与时间无关的林德布拉德生成子实现这一点仍然悬而未决。我们的结果为关联经典与量子记忆提供了一般框架，揭示了完全自主量子记忆的条件，并可能指导在低维中构建可证明的自主量子记忆。
英文摘要
The study of quantum memories out of thermal equilibrium is motivated both by the need for memories that withstand realistic noise in fault-tolerant quantum computers and by the fundamental question of when quantum memory can emerge in autonomous many-body systems. We establish a general equivalence between CSS-based quantum memories subject to Pauli noise and classical memories via two associated probabilistic processes. In the asynchronous setting, where the quantum dynamics is generated by a Lindbladian, we identify a broad class of syndrome-based Lindbladians for which the quantum memory problem is equivalent to memory in continuous-time classical Markov dynamics. In the synchronous setting, we introduce syndrome-based probabilistic cellular automata (SPCAs) and establish a one-to-one correspondence between their classical memories and CSS-based quantum memories under local quantum channels. This framework provides a systematic route for deriving and constructing quantum memories from classical probabilistic processes, and recovers known results, including the fact that the 4D toric code is a quantum memory in the presence of thermal noise. As an application, we give the first rigorous proof that the 4D toric code with Toom's rule is a quantum memory in the presence of local Pauli noise, provided the error is below a constant threshold. We prove this both for the corresponding synchronous, PCA-type quantum dynamics and for a Floquet Lindbladian. More generally, we show that classical memory in an SPCA can be lifted to a quantum memory under Floquet Lindbladian dynamics; whether this can be done with a time-independent Lindbladian remains open. Our results provide a general framework for relating classical and quantum memory, shed light on the conditions for fully autonomous quantum memories, and may guide the construction of provable autonomous quantum memories in low dimensions.
Comments78 pages, 3 figures
