量子码中的码可见Liouvillian模与相干逻辑错误
Code-Visible Liouvillian Modes and Coherent Logical Errors in Quantum Codes
- Innopolis University（因诺波利斯大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文应用线性系统理论分析量子码中的相干噪声，定义最小码可见空间，揭示Knill-Laflamme条件与谱特征，并估计量子存储时间。
AI中文摘要：
相干哈密顿漂移和系统性错误通过量子纠错的方式可能不同于随机泡利噪声：它们产生逻辑信道的相位分量，这些分量在全泡利twirling下会丢失。我们考虑n个物理量子比特的Lindbladian动力学，通过固定编码、恢复和解码方案的有效逻辑信道传播。本文具有方法论性质：将线性系统理论中可观测性和最小实现的标准思想应用于信道ω↦Φ_t(ω)=De^{tL}E(ω)，其中E编码逻辑态，D是带有最终解码的选定恢复映射。最小码可见空间K_code定义为可解码逻辑可观测量关于L†的Krylov闭包；其可观测性分解产生逻辑信道的最小实现。在这种形式下，Knill-Laflamme条件作为短时间一致性检查，稳定子码上的泡利噪声简化为综合征-逻辑类上的链，恢复映射的选择作为可见模上的谱滤波器。对于量子存储器，同样的语言通过校正周期逻辑信道的主导可见特征值给出存储时间的估计。特别关注相干噪声的谱特征以及这些特征如何依赖于所选解码器。
英文摘要：
Coherent Hamiltonian drifts and systematic errors can pass through quantum error correction differently than stochastic Pauli noise: they generate phase components of the logical channel that are lost under full Pauli twirling. We consider the Lindbladian dynamics of \(n\) physical qubits propagated through an effective logical channel of a fixed encoding, recovery, and decoding scheme. The work is methodological in character: standard ideas of observability and minimal realization from linear systems theory are applied to the channel \[ ω \mapsto Φ_t(ω) = \cD e^{t\cL}\cE(ω), \] where \(\cE\) encodes the logical state and \(\cD\) is the chosen recovery map with final decoding. The minimal code-visible space \(\cK_{\rm code}\) is defined as the Krylov closure of the decodable logical observables with respect to \(\cL^\dagger\); its observable factorization yields a minimal realization of the logical channel. In this form, the Knill--Laflamme conditions serve as a short-time consistency check, Pauli noise on stabilizer codes reduces to a chain on syndrome-logical classes, and the choice of recovery map acts as a spectral filter on the visible modes. For quantum memory, the same language yields an estimate of the storage time in terms of the dominant visible eigenvalues of the logical channel of the correction cycle. Particular attention is paid to the spectral signatures of coherent noise and to how these signatures depend on the chosen decoder.
