Studying energy-resolved transport with wavepacket dynamics on quantum computers

TL;DR

This paper demonstrates using wavepackets on quantum computers to study energy-dependent transport and localization transitions, achieving improved energy resolution and error mitigation in finite-size models.

Contribution

It introduces a wavepacket approach for probing transport on quantum computers, including error mitigation techniques and applications to many-body systems.

Findings

Identified an energy-dependent localization transition in the Anderson model.

Wavepackets at different energies show localized or delocalized behavior.

Error mitigation via maximum-likelihood estimation improves result accuracy.

Abstract

Probing energy-dependent transport in quantum simulators requires preparing states with tunable energy and small energy variance. Existing approaches often study quench dynamics of simple initial states, such as computational basis states, which are far from energy eigenstates and therefore limit the achievable energy resolution. In this work, we propose using wavepackets to probe transport properties with improved energy resolution. To demonstrate the utility of this approach, we prepare and evolve wavepackets on Quantinuum's H2-2 quantum computer and identify an energy-dependent localization transition in the Anderson model on an 8x7 lattice--a finite-size mobility edge. We observe that a wavepacket initialized at low energy remains spatially localized under time evolution, while a high-energy wavepacket delocalizes, consistent with the presence of a mobility edge. Crucial to our experiments is an error mitigation strategy that infers the noiseless output bit string distribution using maximum-likelihood estimation. Compared to post-selection, this method removes systematic errors and reduces statistical uncertainty by up to a factor of 5. We extend our methods to the many-particle regime by developing a quantum algorithm for preparing quasiparticle wavepackets in a one-dimensional model of interacting fermions. This technique has modest quantum resource requirements, making wavepacket-based studies of transport in many-body systems a promising application for near-term quantum computers.