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We investigate the quantum equation of motion (qEOM), a hybridquantum-classical algorithm for computing excitation properties of a fermionicmany-body system, with a particular emphasis on the strong-coupling regime. Themethod is designed as a stepping stone towards building more accurate solutionsfor strongly coupled fermionic systems, such as medium-heavy nuclei, usingquantum algorithms to surpass the current barrier in classical computation.Approximations of increasing accuracy to the exact solution of theLipkin-Meshkov-Glick Hamiltonian with $N=8$ particles are studied on digitalsimulators and IBM quantum devices. Improved accuracy is achieved by applyingoperators of growing complexity to generate excitations above the correlatedground state, which is determined by the variational quantum eigensolver (VQE).We demonstrate explicitly that the qEOM exhibits a quantum benefit due to theindependence of the number of required quantum measurements from theconfiguration complexity. Post-processing examination shows that quantum deviceerrors are amplified by increasing configuration complexity and couplingstrength. A detailed error analysis is presented, and error mitigation based onzero noise extrapolation is implemented.

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