Variance reduction methods in the estimation of Pauli sums

TL;DR

This paper presents a unified framework for variance reduction in quantum observable estimation, introducing heuristics and optimization techniques that improve measurement efficiency and accuracy in quantum computing applications.

Contribution

It develops a comprehensive framework that enhances existing measurement strategies and introduces heuristics to optimize information gain and measurement distribution.

Findings

Simple grouping algorithms can match or outperform state-of-the-art accuracy.

Measurement costs can be reduced by up to a factor of two.

The framework can augment recent measurement schemes like shadow grouping.

Abstract

Accurately estimating expectation values of quantum observables with as few measurements as possible is crucial to many quantum computing applications. We introduce a framework that covers many of existing measurement strategies and introduce heuristics that can be used to enhance randomized schemes, including those based on Pauli grouping with inverse probability weighting and variants of the classical shadow algorithm. We show how to maximize information gain from such schemes, while carefully optimizing the distribution of possible measurements, and show that simple grouping algorithms can get close to, and in some cases exceed, state-of-the-art accuracy for unbiased estimation of expectation values on a standard quantum chemistry benchmark. We show how these randomized methods may be compared to more recent measurement schemes, such as shadow grouping, derandomized shadow, and overlapped grouping measurement, we show how the same strategies can be used to augment these schemes, and we demonstrate that we can reduce measurement costs by up to a factor of two by allowing Clifford measurement circuits for otherwise Clifford-less methods.