Efficient estimation of Pauli observables by derandomization

TL;DR

This paper introduces a derandomization method for efficiently estimating multiple Pauli observables in quantum algorithms, reducing resource requirements and outperforming previous randomized approaches.

Contribution

The authors develop a deterministic measurement protocol that guarantees at least as good performance as randomized methods, significantly reducing the number of copies needed for low-weight observables.

Findings

Deterministic measurement on O(log L) copies suffices for estimating L low-weight Pauli observables.

The derandomized protocol outperforms randomized methods in certain high-weight cases.

Numerical experiments demonstrate improved ground-state energy estimation for small molecules.

Abstract

We consider the problem of jointly estimating expectation values of many Pauli observables, a crucial subroutine in variational quantum algorithms. Starting with randomized measurements, we propose an efficient derandomization procedure that iteratively replaces random single-qubit measurements with fixed Pauli measurements; the resulting deterministic measurement procedure is guaranteed to perform at least as well as the randomized one. In particular, for estimating any $L$ low-weight Pauli observables, a deterministic measurement on only of order $\log(L)$ copies of a quantum state suffices. In some cases, for example when some of the Pauli observables have a high weight, the derandomized procedure is substantially better than the randomized one. Specifically, numerical experiments highlight the advantages of our derandomized protocol over various previous methods for estimating the ground-state energies of small molecules.