Probing many-body localization on a noisy quantum computer

TL;DR

This paper demonstrates that spectral functions can be used as a robust diagnostic tool for many-body localization on noisy quantum computers, specifically using a trapped-ion setup for a disordered Heisenberg model.

Contribution

The authors compute spectral functions on a noisy quantum computer and introduce an effective error-mitigation technique to detect many-body localization signatures.

Findings

Spectral functions reveal localization signatures despite noise.

Error mitigation enhances the visibility of localization features.

Localization signatures increase with disorder strength.

Abstract

A disordered system of interacting particles exhibits localized behavior when the disorder is large compared to the interaction strength. Studying this phenomenon on a quantum computer without error correction is challenging because even weak coupling to a thermal environment destroys most signatures of localization. Fortunately, spectral functions of local operators are known to contain features that can survive the presence of noise. In these spectra, discrete peaks and a soft gap at low frequencies compared to the thermal phase indicate localization. Here, we present the computation of spectral functions on a trapped-ion quantum computer for a one-dimensional Heisenberg model with disorder. Further, we design an error-mitigation technique which is effective at removing the noise from the measurement allowing clear signatures of localization to emerge as the disorder increases. Thus, we show that spectral functions can serve as a robust and scalable diagnostic of many-body localization on the current generation of quantum computers.