量子测量类学习中纠缠学习规则的优势
Advantage of Entangled Learning Rules in Quantum Measurement Class Learning
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中文总结 AI 辅助
本文研究量子测量PAC学习中，纠缠测量学习规则相比单副本规则的优势，证明其最多享有多项式样本复杂度优势，并构造了单副本规则渐近次优的场景。
中文摘要 AI 辅助
以量子态形式的数据进行学习是目前的研究热点，并已衍生出多种问题，这些问题归结为通过量子测量与可用数据交互，以及对观测到的经典结果进行经典后处理。在量子测量PAC学习中，给定一系列未知的、制备好的量子态和经典标签，以及一个候选测量的假设类。任务是从假设类中选择一个测量，通过所选假设对新态进行测量，以最小化预测经典标签的固定误差概念。在这项工作中，我们考虑了在测量学习框架中，使用由无法通过局域操作和经典通信（LOCC）实现的测量所给出的学习规则与给定数据交互的优势，而不是单副本学习规则。我们提供了一个构造，表明存在这样的学习场景，其中单副本学习规则相对于最优规则是渐近次优的。然后我们证明，在PAC学习设置下（在自然的联合可测性覆盖假设下），基于纠缠测量的学习规则相对于单副本学习规则最多享有多项式样本复杂度优势。
英文摘要
Learning with data in the form of quantum states is of current interest and has led to a variety of problems that boil down to interaction with the available data via quantum measurement and classical post-processing of observed classical outcomes. In quantum measurement PAC learning, one is given a sequence of unknown, prepared quantum states and classical labels, along with a hypothesis class of candidate measurements. The task is to select a measurement from the hypothesis class that minimizes a fixed notion of error in prediction of the classical labels via measurement of a new state by the selected hypothesis. In this work, we consider the advantage of interacting with the given data in the measurement learning framework using learning rules given by measurements that cannot be implemented using local operations and classical communication (LOCC), as opposed to single-copy learning rules. We provide a construction showing that there exist learning scenarios wherein single-copy learning rules are asymptotically suboptimal compared to optimal ones. We then show that learning rules based on entangled measurements enjoy at most a polynomial sample complexity advantage over single-copy learning rules in the PAC learning setting (under a natural joint measurability covering assumption).
发表机构
- University at Albany, State University of New York（纽约州立大学奥尔巴尼分校）
- AI Plus Institute（人工智能增强研究所）
机构由 AI 辅助整理，请以论文原文为准。
