自适应测量可让量子态重构效率提升指数级
Adaptivity can help exponentially for shadow tomography
- 用自适应策略选择双拷贝测量，显著减少样本需求
- 自适应方案比非自适应方案节省指数级样本量
- 适合关注量子态估计高效算法的研究者
近年来，人们广泛关注在仅能进行无纠缠测量的约束下，从量子数据中学习的统计复杂性。尽管建立紧致下界的关键挑战在于测量可自适应选择，但普遍观点认为自适应性对非自适应协议的优势有限。本文提出反例：对于基础的阴影谱重建任务，采用自适应双拷贝测量的协议，其样本效率相比任何非自适应双拷贝测量协议可实现指数级提升。
原文摘要 · Abstract (English)
In recent years there has been significant interest in understanding the statistical complexity of learning from quantum data under the constraint that one can only make unentangled measurements. While a key challenge in establishing tight lower bounds in this setting is to deal with the fact that the measurements can be chosen in an adaptive fashion, a recurring theme has been that adaptivity offers little advantage over more straightforward, nonadaptive protocols. In this note, we offer a counterpoint to this. We show that for the basic task of shadow tomography, protocols that use adaptively chosen two-copy measurements can be exponentially more sample-efficient than any protocol that uses nonadaptive two-copy measurements.
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