发表机构
Ecole Polytechnique Fédérale de Lausanne (EPFL); Princeton University（洛桑联邦理工学院; 普林斯顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
基于输入分布一阶与二阶矩，提出分布外量子动力学学习通用框架，揭示酉性对泛化的关键作用，并给出紧致普适界与不可行性结果。
AI 中文摘要
一个未知酉动力学在一族态上的作用能在多大程度上揭示其在其他态上的作用？我们基于输入分布的一阶矩和二阶矩，为分布外量子动力学学习开发了一个通用框架。这些矩定义了系综的偏差和表达性的概念，二者共同控制任意纯态训练分布与测试分布之间的泛化。我们的框架表明，仅研究酉算子在随机实态上的作用即可学习其在随机复态上的作用，无偏纯态系综的张量积保持表达性，且单量子比特风险与偏差无关。该框架还恢复了早期局域置乱结果作为其宽松特例，并给出了紧致的乘积到哈达玛界。最后，我们得出一系列关于学习特定信道的不可行性结果和有限泛化界，进一步凸显了酉性在实现分布外泛化中的独特作用。
英文摘要
How much can the action of an unknown unitary dynamics on one family of states reveal about its action elsewhere? We develop a general framework for out-of-distribution quantum dynamics learning based on the first and second moments of the input distribution. These define a notion of the bias and expressivity of an ensemble, which together control generalization between arbitrary pure-state training and testing distributions. Our framework shows that only studying the action of a unitary on random real states can learn its action on random complex states, that tensor products of unbiased pure-state ensembles preserve expressivity, and that single-qubit risks are independent of bias. It also recovers earlier locally scrambling results as loose special cases and yields tight product-to-Haar bounds. We conclude with a series of no-go results and limited generalization bounds for learning certain channels, which further serve to underscore the distinctive role of unitarity in enabling out-of-distribution generalization.
Comments12 + 60 pages, 1 figure
