Non-linear quantum-classical scheme to simulate non-equilibrium strongly correlated fermionic many-body dynamics

TL;DR

This paper introduces a hybrid quantum-classical method leveraging digital quantum simulation to efficiently model non-equilibrium dynamics of strongly correlated fermions within the Hubbard model, incorporating error mitigation.

Contribution

It presents a novel non-linear scheme combining quantum and classical computations to simulate complex fermionic systems with self-consistency and error handling.

Findings

Demonstrates the scheme's effectiveness in a specific example

Shows potential for scalable non-equilibrium fermionic simulations

Integrates quantum error considerations into the feedback loop

Abstract

We propose a non-linear, hybrid quantum-classical scheme for simulating non-equilibrium dynamics of strongly correlated fermions described by the Hubbard model in a Bethe lattice in the thermodynamic limit. Our scheme implements non-equilibrium dynamical mean field theory (DMFT) and uses a digital quantum simulator to solve a quantum impurity problem whose parameters are iterated to self-consistency via a classically computed feedback loop where quantum gate errors can be partly accounted for. We analyse the performance of the scheme in an example case.