AI 中文总结
本研究针对多能级量子硬件的漏出误差，证明[[n,k,d]]稳定器码可等距嵌入D维系统，推导漏出修正充要条件，建立量子纠错统一框架。
AI 中文摘要
超出计算子空间的漏出是多能级量子硬件的主要误差来源。我们证明，任何[[n,k,d]]稳定器码均可等距嵌入单个D维系统，同时保留其完整的纠错结构。我们进一步推导了精确漏出修正的充要条件，证明当漏出无法区分逻辑态时，漏出可被修正。这些结果为多能级量子系统的量子纠错建立了统一框架。
英文摘要
Leakage beyond the computational subspace is a major source of error in multilevel quantum hardware. We show that any \( [[n,k,d]] \) stabilizer code can be embedded isometrically into a single \(D\)-dimensional system while preserving its complete error-correcting structure. We further derive a necessary and sufficient condition for exact leakage correction, proving that leakage is correctable precisely when it does not distinguish between logical states. These results establish a unified framework for quantum error correction in multilevel quantum systems.
