Derandomized shallow shadows: Efficient Pauli learning with bounded-depth circuits

TL;DR

The paper introduces the derandomized shallow shadows (DSS) algorithm, which efficiently estimates many non-commuting observables using shallow circuits, improving sample complexity and scalability for quantum chemistry and many-body physics tasks.

Contribution

The paper presents a novel derandomized algorithm that optimizes measurement circuits for estimating multiple Pauli observables with polynomial classical resource scaling.

Findings

DSS outperforms existing methods in energy estimation accuracy.

Performance of DSS improves with deeper measurement circuits.

DSS is applicable to quantum chemistry and quantum many-body verification.

Abstract

Efficiently estimating large numbers of non-commuting observables is an important subroutine of many quantum science tasks. We present the derandomized shallow shadows (DSS) algorithm for efficiently learning a large set of non-commuting observables, using shallow circuits to rotate into measurement bases. Exploiting tensor network techniques to ensure polynomial scaling of classical resources, our algorithm outputs a set of shallow measurement circuits that approximately minimizes the sample complexity of estimating a given set of Pauli strings. We numerically demonstrate systematic improvement, in comparison with state-of-the-art techniques, for energy estimation of quantum chemistry benchmarks and verification of quantum many-body systems, and we observe DSS's performance consistently improves as one allows deeper measurement circuits. These results indicate that in addition to being an efficient, low-depth, stand-alone algorithm, DSS can also benefit many larger quantum algorithms requiring estimation of multiple non-commuting observables.