AI 中文总结
研究如何从恒定时间泡利响应中高效学习林德布拉德算符，开发学习框架及两种算法，通过处理局部泡利响应解决相干 - 耗散模糊性，能在短时间窗口内获取林德布拉德系数，确立了局部响应求逆的可扩展范式。
AI 中文摘要
学习开放多体系统的生成器比学习哈密顿量更具挑战性：在封闭系统动力学中能直接揭示相干相互作用项的局部响应，在开放系统动力学中可能也包含耗散贡献。本文通过为具有有界耗散支持且对偶相互作用图度数有界或无权重局部强度有界的已知局部候选生成器字典开发一个高效的林德布拉德算符学习框架来应对这一挑战。该框架通过将局部泡利响应视为两种生成器项上的线性系统来解决相干 - 耗散模糊性。对这个响应系统求逆可分离它们的贡献，并使各个林德布拉德系数能在固定的短时间窗口内从局部响应数据中获取。在此框架内，开发了两种高效学习算法：切比雪夫 - 洛巴托响应插值算法，它使用对数数量的短演化时间，后均值成本与\(M\)成线性关系，具有对\(\epsilon\)的特定依赖关系；单时间投影响应收缩算法，它使用单个固定演化时间并全局求逆截断响应函数。两种方法都使用\(\widetilde{\mathcal{O}}(M/\epsilon^2)\)样本和经典后处理复杂度将\(M\)个候选系数估计到逐元素精度\(\epsilon\)。我们的理论结果确立了局部响应求逆作为从实验可获取的短时间数据中学习、校准和诊断复杂量子系统的可扩展范式。
英文摘要
Learning the generator of an open many-body system is more challenging than Hamiltonian learning: local responses, which can directly reveal coherent interaction terms in closed-system dynamics, may also contain dissipative contributions in open-system dynamics. In this paper, we address this challenge by developing an efficient Lindbladian learning framework for a known local candidate generator dictionary with bounded dissipative support and either bounded dual-interaction-graph degree or bounded unweighted local strength. The framework resolves the coherent-dissipative ambiguity by treating local Pauli responses as a linear system over both types of generator terms. Inverting this response system separates their contributions and makes the individual Lindbladian coefficients accessible from local response data in a fixed short-time window. Within this framework, we develop two efficient learning algorithms: Chebyshev--Lobatto response interpolation, which uses logarithmically many short evolution times and has a post-mean cost linear in $M$, with the stated dependence on $ε$, and Single-time projected response contraction, which uses a single fixed evolution time and globally inverts a truncated response function. Both procedures estimate $M$ candidate coefficients to entrywise accuracy $ε$ using $\widetilde{\mathcal{O}}(M/ε^2)$ sample and classical post-processing complexity. Our theoretical results establish local response inversion as a scalable paradigm for learning, calibrating, and diagnosing complex quantum systems from experimentally accessible short-time data.
