Probing many-body localization by excited-state VQE

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.