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Quantum Machine Learning

On the Classical Shadow Nonparametric Bootstrap

arXiv

Authors: Eric Ghysels, Jack Morgan

Year

2025

Paper ID

17231

Status

Preprint

Abstract Read

~2 min

Abstract Words

100

Citations

N/A

Abstract

Classical shadows are an efficient method for constructing an approximate classical description of a quantum state using very few measurements. In the paper we propose to enhance classical shadow methods using bootstrap resampling methods. We apply nonparametric bootstrapping to assess the variability and accuracy of estimators by repeatedly sampling with replacement from the observed data, i.e. in our case the classical shadow measurements. We show that the bootstrap distributions are very different from the Gaussian approximations. Likewise, the theoretical error bounds are not tight compared to the bootstrap percentiles. Finally, we suggest using resampling tools to make risk assessments.

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This paper contributes to the Quantum Machine Learning research area in the Quantum Articles archive.
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Classical shadows are an efficient method for constructing an approximate classical description of a quantum state using very few measurements.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2511.09793 [2] arXiv https://arxiv.org/abs/2511.09793 [3] Publisher https://arxiv.org/abs/2511.09793

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