Adaptivity can help exponentially for shadow tomography

Fuente: arXiv
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Main Authors: Chen, Sitan, Gong, Weiyuan, Zhang, Zhihan
Format: Preprint
Published: 2024
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author Chen, Sitan
Gong, Weiyuan
Zhang, Zhihan
author_facet Chen, Sitan
Gong, Weiyuan
Zhang, Zhihan
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2412_19022
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Adaptivity can help exponentially for shadow tomography
Chen, Sitan
Gong, Weiyuan
Zhang, Zhihan
Quantum Physics
Information Theory
Machine Learning
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.
title Adaptivity can help exponentially for shadow tomography
topic Quantum Physics
Information Theory
Machine Learning
url https://arxiv.org/abs/2412.19022