Hybrid quantum-classical algorithm for computing imaginary-time correlation functions

TL;DR

This paper introduces a hybrid quantum-classical algorithm to efficiently compute imaginary-time Green's functions for strongly correlated materials, addressing a key bottleneck in quantum embedding methods like DMFT.

Contribution

The paper presents the first practical hybrid quantum-classical algorithm for calculating imaginary-time Green's functions using variational quantum simulation.

Findings

Successfully computed Green's functions for a dimer model

Validated the approach on a four-site impurity model from DMFT

Demonstrated the method's applicability to general imaginary-time correlation functions

Abstract

Quantitative descriptions of strongly correlated materials pose a considerable challenge in condensed matter physics and chemistry. A promising approach to address this problem is quantum embedding methods. In particular, the dynamical mean-field theory (DMFT) maps the original system to an effective quantum impurity model comprising correlated orbitals embedded in an electron bath. The biggest bottleneck in DMFT calculations is numerically solving the quantum impurity model, i.e., computing Green's function. Past studies have proposed theoretical methods to compute Green's function of a quantum impurity model in polynomial time using a quantum computer. So far, however, efficient methods for computing the imaginary-time Green's functions have not been established despite the advantages of the imaginary-time formulation. We propose a quantum-classical hybrid algorithm for computing imaginary-time Green's functions on quantum devices with limited hardware resources by applying the variational quantum simulation. Using a quantum circuit simulator, we verified this algorithm by computing Green's functions for a dimer model as well as a four-site impurity model obtained by DMFT calculations of the single-band Hubbard model, although our method can be applied to general imaginary-time correlation functions.