Calculation of the Green's function on near-term quantum computers

TL;DR

This paper introduces two shallow-circuit quantum algorithms for computing the Green's function of quantum many-body systems on near-term quantum computers, enabling analysis of strongly-correlated systems.

Contribution

It proposes the first near-term quantum algorithms for Green's function calculation, using variational dynamics and Lehmann representation methods.

Findings

Numerical simulations of the Fermi-Hubbard model validate the methods.

Both algorithms require shallow circuits suitable for near-term devices.

The approaches enable studying strongly-correlated quantum systems.

Abstract

The Green's function plays a crucial role when studying the nature of quantum many-body systems, especially strongly-correlated systems. Although the development of quantum computers in the near future may enable us to compute energy spectra of classically-intractable systems, methods to simulate the Green's function with near-term quantum algorithms have not been proposed yet. Here, we propose two methods to calculate the Green's function of a given Hamiltonian on near-term quantum computers. The first one makes use of a variational dynamics simulation of quantum systems and computes the dynamics of the Green's function in real time directly. The second one utilizes the Lehmann representation of the Green's function and a method which calculates excited states of the Hamiltonian. Both methods require shallow quantum circuits and are compatible with near-term quantum computers. We numerically simulated the Green's function of the Fermi-Hubbard model and demonstrated the validity of our proposals.