Analytically Continuing the Randomized Measurement Toolbox

TL;DR

This paper introduces stabilized analytic continuation (SAC), a robust method for extracting non-polynomial functions of density matrices from randomized measurements, demonstrated on entanglement entropy estimation in quantum systems.

Contribution

The paper presents SAC, a novel framework for analytically continuing randomized measurement data to obtain nonlinear quantum diagnostics with noise robustness.

Findings

Successfully estimated von Neumann entropies from simulated and experimental data.

Demonstrated robustness of SAC against statistical noise in quantum measurements.

Showcased potential for generalizing SAC to other nonlinear quantum diagnostics.

Abstract

We develop a framework for extracting non-polynomial analytic functions of density matrices in randomized measurement experiments by a method of analytical continuation. A central advantage of this approach, dubbed stabilized analytic continuation (SAC), is its robustness to statistical noise arising from finite repetitions of a quantum experiment, making it well-suited to realistic quantum hardware. As a demonstration, we use SAC to estimate the von Neumann entanglement entropy of a numerically simulated quenched N\'eel state from R\'enyi entropies estimated via the randomized measurement protocol. We then apply the method to experimental R\'enyi data from a trapped-ion quantum simulator, extracting subsystem von Neumann entropies at different evolution times. Finally, we briefly note that the SAC framework is readily generalizable to obtain other nonlinear diagnostics, such as the logarithmic negativity and R\'enyi relative entropies.