On the Classical Shadow Nonparametric Bootstrap

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.