发表机构
University of Copenhagen; Niels Bohr Institute, University of Copenhagen（哥本哈根大学; 尼尔斯·玻尔研究所，哥本哈根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文从子系统码分解的量子信息视角，推导了理想 GKP 哈密顿量的自校正行为，其逻辑寿命呈 Arrhenius 型标度，边界项被 Gibbs 权重指数抑制，实现了模相空间中的有效弦张力。
AI 中文摘要
被动量子纠错，也称为自校正，是量子信息科学中的一个圣杯。最近的理论进展表明，Gottesman-Kitaev-Preskill（GKP）码可以展现出自校正特性，使其成为实现自校正量子存储器的候选方案。在本文中，我们基于子系统码分解的量子信息视角，对理想 GKP 哈密顿量的自校正行为（表现为逻辑寿命的 Arrhenius 型标度）提供了自包含的推导。当通过物理正交分量 $q$ 和 $p$ 耦合时，细致平衡跳变算符分解为一个仅作用于规范子系统的主导部分和一个对逻辑量子比特非平凡作用的边界项。该边界项随后被模胞边缘附近的 Gibbs 权重指数抑制。与基于自旋的量子存储器（如二维表面码）相比，GKP 哈密顿量在模相空间中实现了有效的弦张力，从而使得当误差接近逻辑扇区边界时能量代价增加。
英文摘要
Passive quantum error correction, also known as self-correction, is a holy grail in quantum information science. Recent theoretical advances suggest that the Gottesman-Kitaev-Preskill (GKP) code can exhibit self-correction properties, positioning it as a candidate for the realization of self-correcting quantum memories. In this article, we provide a self-contained derivation of the self-correcting behavior of the ideal GKP Hamiltonian, manifested in the Arrhenius type scaling of the logical lifetime, from a quantum-information perspective based on the subsystem code decomposition. When coupling through the physical quadrature $q$ and $p$, the detailed-balance jump operators decompose into a dominant part acting only on the gauge subsystem and a boundary term that acts non-trivially on the logical qubit. The boundary term is then exponentially suppressed by the Gibbs weights near the edge of the modular cells. In contrast to spin-based quantum memories such as the two-dimensional surface code, the GKP Hamiltonian realizes an effective string tension in modular phase space, whereby the energy cost increases as an error approaches the boundary of a logical sector.
