On the Classical Shadow Nonparametric Bootstrap

TL;DR

This paper enhances classical shadow quantum state estimation with bootstrap resampling to better assess variability and accuracy, revealing significant differences from Gaussian assumptions and providing improved risk evaluation tools.

Contribution

It introduces bootstrap resampling techniques to classical shadows, offering a nonparametric way to evaluate estimator variability and improve error bounds in quantum state estimation.

Findings

Bootstrap distributions differ from Gaussian approximations

Theoretical error bounds are less tight than bootstrap percentiles

Resampling tools enable better risk assessment in quantum measurements

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.