Classical optimisation of reduced density matrix estimations with classical shadows using N-representability conditions under shot noise considerations

TL;DR

This paper improves classical shadow tomography for quantum states by optimizing estimators and constraints, leading to better performance and resource savings in estimating reduced density matrices under shot noise.

Contribution

It introduces an improved estimator and reformulates optimization constraints, enhancing the efficiency of classical shadow methods for N-representability under shot noise.

Findings

Enhanced estimator yields better accuracy with fewer measurements

Rephrased constraints improve optimization efficiency

Numerical studies show potential measurement savings

Abstract

Classical shadow tomography has become a powerful tool in learning about quantum states prepared on a quantum computer. Recent works have used classical shadows to variationally enforce N-representability conditions on the 2-particle reduced density matrix. In this paper, we build upon previous research by choice of an improved estimator within classical shadow tomography and rephrasing the optimisation constraints, resulting in an overall enhancement in performance under comparable measurement shot budgets. We further explore the specific regimes where these methods outperform the unbiased estimator of the standalone classical shadow protocol and quantify the potential savings in numerical studies.