量子马尔可夫态模型用于亚稳态动力学
Quantum Markov State Models for Metastable Dynamics
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中文总结 AI 辅助
针对开放量子系统长时间动力学中仅少数慢自由度起主导作用的现象，构建量子马尔可夫态模型，在包含经典扇区和量子矩阵块的小物理态空间上描述存留信息及其演化，实现精确压缩与重构，并给出最优误差界，用于预测亚稳态动力学。
中文摘要 AI 辅助
开放量子系统会迅速丢失大部分微观信息，仅留下少数自由度主导其长时间动力学。经典马尔可夫态模型（MSMs）将此类亚稳态动力学描述为少数代表性相之间的跃迁，是凝聚态物理和化学物理中成熟的方法。然而，仅凭相标签无法捕捉亚稳态之间可能持续存在的量子相干性。即使慢模式已知，其谱投影也未必产生有效的量子态。我们构建了量子马尔可夫态模型（QMSMs），在包含经典扇区和量子矩阵块的小物理态空间上描述存留信息及其演化。我们假设演化通道$\mathcal C$在第二次应用时变化很小，缺陷$\eta=\|\mathcal C^2-\mathcal C\|_\diamond$足够小，且慢自由度的数量独立于整个系统大小而有界。在这些假设下，我们构造压缩与重构通道，其复合能精确恢复每个约化态，而反向复合给出精确幂等的通道近似$\mathcal C$，回答了Kitaev的精确舍入问题\cite{Kitaev2025}。我们的构造对所有输入态给出最优的钻石范数界$\mathcal{O}(\eta^{1/3})$，并对由$\mathcal C$制备的亚稳态给出改进的界$\mathcal{O}(\eta^{1/2})$，常数仅依赖于慢维度。约化跃迁通道可迭代以受控误差预测微观动力学。我们通过一个弱驱动耗散自旋链说明QMSM，该链支持亚稳态逻辑量子比特或长寿命经典相。
英文摘要
Open quantum systems can rapidly lose most microscopic information, leaving only a few degrees of freedom to govern their long-time dynamics. Classical Markov state models (MSMs) describe such metastable dynamics as transitions among a few representative phases and are widely used to reduce complex-system dynamics in condensed matter and chemical physics. In quantum systems, however, phase labels alone are insufficient when coherence persists between metastable states. Even when the slow modes are known, their spectral projection need not produce valid quantum states. We construct quantum Markov state models (QMSMs) that describe the surviving information and its evolution on a small physical state space containing classical sectors and quantum matrix blocks. We quantify metastability by assuming that the evolution channel $\mathcal C$ changes little when applied a second time, with sufficiently small defect $η=\|\mathcal C^2-\mathcal C\|_\diamond$, and that the number of slow degrees of freedom is bounded independently of the full system size. Under these assumptions, we construct compression and reconstruction channels whose composition recovers every reduced state exactly, while the reverse composition gives an exactly idempotent channel approximating $\mathcal C$, answering Kitaev's exact-rounding question [Kit25]. Our constructions give an optimal diamond-norm bound of $\mathcal{O}(η^{1/3})$ on all input states, as well as an improved bound of $\mathcal{O}(η^{1/2})$ on metastable states prepared by $\mathcal C$, with constants depending only on the slow dimension. The reduced transition channel can be iterated to predict the microscopic dynamics with controlled error. We illustrate the QMSM through a weakly driven dissipative spin chain supporting either a metastable logical qubit or long-lived classical phases.
发表机构
- University of California, Berkeley（加州大学伯克利分校）
- California Institute of Technology（加州理工学院）
- Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
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