Channel-agnostic finite-temperature phase estimation averaged over variable grids: reconstruction of Green's function for dynamical mean-field theory

Abstract

For treating correlated electronic systems on quantum computers, we propose a quantum-classical hybrid scheme for dynamical mean-field theory (DMFT). In the quantum part of the scheme, we use modified quantum phase estimation (QPE) circuits suitable for the one-particle Green's function (GF) at a finite temperature so that we can extract spectral amplitudes and the excitation energies without knowing the excitation channel invoked at each measurement. In the classical part of the scheme, we adopt an approach that estimates reasonably the GF based on the data collected from the QPE sampling. We dub the approach the QPE averaged over variable grids (QAVG), that may help one to reconstruct the GF via optimization of trial parameters and modeling the probability distributions for various settings of the QPE circuits. We apply the QAVG-DMFT scheme to SrVO$_3$ to demonstrate its validity via numerical simulations.