Dynamical mean-field theory for the Hubbard-Holstein model on a quantum device

TL;DR

This paper demonstrates solving the Hubbard-Holstein model's impurity problem using a quantum computer, showcasing the potential of quantum algorithms for strongly correlated electron systems with bosonic interactions.

Contribution

First implementation of DMFT impurity problem for Hubbard-Holstein model on a quantum device, integrating fermionic and bosonic degrees of freedom with a Krylov variational quantum algorithm.

Findings

Spectral function matches exact results

Outperforms standard Trotter-expansion methods

Shows potential for studying correlated electron systems

Abstract

Recent developments in quantum hardware and quantum algorithms have made it possible to utilize the capabilities of current noisy intermediate-scale quantum devices for addressing problems in quantum chemistry and condensed matter physics. Here we report a demonstration of solving the dynamical mean-field theory (DMFT) impurity problem for the Hubbard-Holstein model on the IBM 27-qubit Quantum Falcon Processor Kawasaki, including self-consistency of the DMFT equations. This opens up the possibility to investigate strongly correlated electron systems coupled to bosonic degrees of freedom and impurity problems with frequency-dependent interactions. The problem involves both fermionic and bosonic degrees of freedom to be encoded on the quantum device, which we solve using a recently proposed Krylov variational quantum algorithm to obtain the impurity Green's function. We find the resulting spectral function to be in good agreement with the exact result, exhibiting both correlation and plasmonic satellites and significantly surpassing the accuracy of standard Trotter-expansion approaches. Our results provide an essential building block to study electronic correlations and plasmonic excitations on future quantum computers with modern ab initio techniques.