A Hybrid Quantum-Classical Method for Electron-Phonon Systems

TL;DR

This paper introduces a hybrid quantum-classical algorithm that efficiently models strongly correlated electron-phonon systems, accurately capturing phase competition without increasing quantum resource requirements.

Contribution

It combines variational quantum eigensolver and non-Gaussian solvers to handle strong electron-phonon interactions in a resource-efficient manner.

Findings

Successfully applied to Hubbard-Holstein model at half filling

Accurately captures charge density wave and antiferromagnetic phases

Results are consistent with exact diagonalization

Abstract

Interactions between electrons and phonons play a crucial role in quantum materials. Yet, there is no universal method that would simultaneously accurately account for strong electron-phonon interactions and electronic correlations. By combining methods of the variational quantum eigensolver and the variational non-Gaussian solver, we develop a hybrid quantum-classical algorithm suitable for this type of correlated systems. This hybrid method tackles systems with arbitrarily strong electron-phonon coupling without increasing the number of required qubits and quantum gates, as compared to purely electronic models. We benchmark the new method by applying it to the paradigmatic Hubbard-Holstein model at half filling, and show that it correctly captures the competition between charge density wave and antiferromagnetic phases, quantitatively consistent with exact diagonalization.