Analyzing many-body localization with a quantum computer

TL;DR

This paper explores how small quantum computers can be used to study many-body localization by efficiently obtaining eigenstates and analyzing localization properties, overcoming classical computational limitations.

Contribution

It demonstrates that quantum computers can efficiently generate eigenstates at arbitrary energies to study localization, offering new methods beyond classical simulations.

Findings

Quantum computers can obtain eigenstates in polynomial time.

Localization can be observed through alternative tests on quantum hardware.

Limitations in measurement affect entanglement entropy analysis.

Abstract

Many-body localization, the persistence against electron-electron interactions of the localization of states with non-zero excitation energy density, poses a challenge to current methods of theoretical and numerical analysis. Numerical simulations have so far been limited to a small number of sites, making it difficult to obtain reliable statements about the thermodynamic limit. In this paper, we explore the ways in which a relatively small quantum computer could be leveraged to study many-body localization. We show that, in addition to studying time-evolution, a quantum computer can, in polynomial time, obtain eigenstates at arbitrary energies to sufficient accuracy that localization can be observed. The limitations of quantum measurement, which preclude the possibility of directly obtaining the entanglement entropy, make it difficult to apply some of the definitions of many-body localization used in the recent literature. We discuss alternative tests of localization that can be implemented on a quantum computer.