Improved Measurement Cost Scaling in the Nonorthogonal Quantum Eigensolver

The nonorthogonal quantum eigensolver (NOQE) is a promising quantum chemistry algorithm that estimates low-lying molecular energies using shallow circuits on near-term devices. We show that overlap thresholding improves the measurement cost of NOQE from O(M^3) to O(M) shots per matrix element, where M is the number of reference states. Source codes for the numerical simulations, based on PySCF and OpenFermion, are available online.