Quantum benefit of the quantum equation of motion for the strongly coupled many-body problem

TL;DR

This paper explores the quantum equation of motion (qEOM) for strongly coupled many-body fermionic systems, demonstrating quantum advantage in measurement efficiency and analyzing error mitigation on quantum devices.

Contribution

It introduces an improved qEOM method for strongly coupled systems and shows quantum measurement efficiency is independent of configuration complexity.

Findings

qEOM achieves higher accuracy with complex operators

Quantum measurement count is independent of configuration complexity

Error mitigation improves results on noisy quantum devices

Abstract

We investigate the quantum equation of motion (qEOM), a hybrid quantum-classical algorithm for computing excitation properties of a fermionic many-body system, with a particular emphasis on the strong-coupling regime. The method is designed as a stepping stone towards building more accurate solutions for strongly coupled fermionic systems, such as medium-heavy nuclei, using quantum algorithms to surpass the current barrier in classical computation. Approximations of increasing accuracy to the exact solution of the Lipkin-Meshkov-Glick Hamiltonian with $N=8$ particles are studied on digital simulators and IBM quantum devices. Improved accuracy is achieved by applying operators of growing complexity to generate excitations above the correlated ground state, which is determined by the variational quantum eigensolver (VQE). We demonstrate explicitly that the qEOM exhibits a quantum benefit due to the independence of the number of required quantum measurements from the configuration complexity. Post-processing examination shows that quantum device errors are amplified by increasing configuration complexity and coupling strength. A detailed error analysis is presented, and error mitigation based on zero noise extrapolation is implemented.