AI 中文总结
本文提出从热亚稳态学习量子相互作用的统一框架，将吉布斯态学习机制推广至亚稳态，实现近乎最优的样本与计算复杂度。
AI 中文摘要
从有限温度多体系统学习量子相互作用是新兴量子平台中的核心任务。近期，从晶格量子吉布斯态学习的问题已找到严格且高效的协议。然而，精确的吉布斯态作为输入前提，实际上在计算上难以制备，且可能无法忠实代表一般的有限温度量子系统。相反，与热浴耦合的系统在真正达到平衡之前，可能长期停留在近似稳态（亚稳态）。在此，我们提出一个物理上和算法上一致的替代方案：从由系统-浴相互作用产生的细致平衡主方程（林德布拉德方程）的此类亚稳态中学习。我们提炼了吉布斯态学习背后的算法机制和结构条件，并将其完全推广到亚稳态，实现了在系统尺寸和精度上近乎最优的样本和计算复杂度。更广泛地，我们深化了亚稳态的概念，并发展了一个统一的有限温度学习框架。
英文摘要
Learning quantum interactions from finite-temperature many-body systems is a central task in emerging quantum platforms. Recently, the problem of learning from lattice quantum Gibbs states has found rigorous, efficient protocols. Nevertheless, exact Gibbs states, as the input premise, are in fact computationally intractable to prepare and may not faithfully represent generic finite-temperature quantum systems. In contrast, a system coupled to a heat bath can be stuck at an approximate stationary state (metastable state) long before it truly equilibrates. Here, we formulate a physically and algorithmically consistent alternative: learning from such metastable states of detailed-balanced master equations (Lindbladians) arising from system-bath interactions. We distill the algorithmic mechanism and structural condition underlying Gibbs-state learning and extend it in full to metastable states, attaining nearly optimal sample and computational complexity (in the system size and the precision). More broadly, we sharpen notions of metastability and develop a unified framework for finite-temperature learning.
