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Quantum Machine Learning

Adaptivity can help exponentially for shadow tomography

arXiv
Authors: Sitan Chen, Weiyuan Gong, Zhihan Zhang

Year

2024

Paper ID

56965

Status

Preprint

Abstract Read

~2 min

Abstract Words

110

Citations

N/A

Abstract

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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  • This paper contributes to the Quantum Machine Learning research area in the Quantum Articles archive.
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  • 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...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2412.19022 [2] arXiv https://arxiv.org/abs/2412.19022 [3] Publisher https://arxiv.org/abs/2412.19022

Local Citation Graph (Related-Paper Links)

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