Error and Sensitivity Estimation of Excited States of the Lipkin model on NISQ Devices

Building on prior work simulating excited states of the Lipkin model using the quantum equation of motion (qEOM) method, we present results estimating both the error introduced by running this method on a noisy intermediate-scale quantum computer (NISQ device) and the sensitivity of the results on the ground state parameterization. The qEOM is a quantum generalization of the EOM method on classical computers and is built of collective excitations based on quasiboson operators $hat{O}^dagger_n(alpha)$ of increasing configuration complexity $alpha$. The qEOM method shows promise in this context because increases in configuration complexity do not have a corresponding increase in the number of measurements needed on a quantum computer. However, increases in configuration complexity do potentially increase the sensitivity on the ground state parameterization and the uncertainty of excited state energy spectra. Utilizing the efficient encoding scheme of prior work we use IBM quantum computer to compute the energy spectra for a system of $N=8$ particles and complexities $alpha=1$, and 2 (corresponding to random phase approximation and second random phase approximation). We show, in particular, that the ground state wave function is robust to variations in the parameterization and that the error introduced by the quantum computer is a function of configuration complexity and effective interaction strength.