Randomized measurement protocols for lattice gauge theories

TL;DR

This paper introduces symmetry-aware randomized measurement protocols for lattice gauge theories, enhancing efficiency and enabling direct analysis of entanglement and topological order without full state reconstruction.

Contribution

It proposes novel symmetry-conscious randomized measurement schemes that outperform traditional methods by reducing costs and allowing direct symmetry-based analysis.

Findings

Reduced measurement costs for gauge theories

Enables symmetry-based error mitigation

Allows direct verification of topological states

Abstract

Randomized measurement protocols, including classical shadows, entanglement tomography, and randomized benchmarking are powerful techniques to estimate observables, perform state tomography, or extract the entanglement properties of quantum states. While unraveling the intricate structure of quantum states is generally difficult and resource-intensive, quantum systems in nature are often tightly constrained by symmetries. This can be leveraged by the symmetry-conscious randomized measurement schemes we propose, yielding clear advantages over symmetry-blind randomization such as reducing measurement costs, enabling symmetry-based error mitigation in experiments, allowing differentiated measurement of (lattice) gauge theory entanglement structure, and, potentially, the verification of topologically ordered states in existing and near-term experiments. Crucially, unlike symmetry-blind randomized measurement protocols, these latter tasks can be performed without relearning symmetries via full reconstruction of the density matrix.