Calculation of the Green's function on near-term quantum computers
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.
Keywords
Cite
@article{arxiv.1909.12250,
title = {Calculation of the Green's function on near-term quantum computers},
author = {Suguru Endo and Iori Kurata and Yuya O. Nakagawa},
journal= {arXiv preprint arXiv:1909.12250},
year = {2020}
}