Probing many-body localization by excited-state VQE

TL;DR

This paper introduces a NISQ-friendly method using excited-state VQE to reliably identify many-body localization phases on quantum hardware, advancing non-equilibrium quantum physics research.

Contribution

It presents a systematic approach to probe MBL phases with excited-state VQE, demonstrating its effectiveness and robustness on quantum hardware beyond classical capabilities.

Findings

Successfully differentiates MBL from thermal phases

Works with shallow quantum circuits

Robust against quantum noise

Abstract

Non-equilibrium physics including many-body localization (MBL) has attracted increasing attentions, but theoretical approaches of reliably studying non-equilibrium properties remain quite limited. In this Letter, we propose a systematic approach to probe MBL phases via the excited-state variational quantum eigensolver (VQE) and demonstrate convincing results of MBL on a quantum hardware, which we believe paves a promising way for future simulations of non-equilibrium systems beyond the reach of classical computations in the noisy intermediate-scale quantum (NISQ) era. Moreover, the MBL probing protocol based on excited-state VQE is NISQ-friendly, as it can successfully differentiate the MBL phase from thermal phases with relatively-shallow quantum circuits, and it is also robust against the effect of quantum noises.