  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.
