Hybrid quantum-classical algorithm for computing 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.

sparse-ir: optimal compression and sparse sampling of many-body propagators

“…Precomputed IRs for different cutoffs Λ have been released previously as the irbasis library [14]. Using this library, IR and sparse sampling has been successfully employed in numerous physics and chemistry applications [15,16,17,18,19,20,21,22,23,24,25,26,27,28].…”

A Near-Term Quantum Algorithm for Computing Molecular and Materials Properties based on Recursive Variational Series Methods

“…Following the same design principles as their fault-tolerant counterparts, most of the known NISQ algorithms for property estimation were derived by replacing demanding computational subroutines with their near-term versions. For example, Variational Quantum Simulation [23] and Quantum Imaginary Time Evolution [24] were used to calculate correlation functions in real [25] and imaginary time [26][27][28], respectively. Similarly, variational linear system solvers were applied to response function calculations [29].…”