CoolMomentum mitigating local minima in variational quantum eigensolvers

Abstract

We compare the use of adaptive moment estimation (ADAM), simultaneous perturbation stochastic approximation (SPSA), Nakanishi–Fujii–Todo method (NFT), and CoolMomentum in a variational quantum eigensolver. Using a random weighted max-cut problem, we numerically analyze these methods and confirm that CoolMomentum performs better than the other methods. ADAM and SPSA tend to get trapped in local minima or exhibit infeasible optimization durations. Although NFT exhibits fast convergence, it tends to suffer from local minima similar to ADAM and SPSA. Contrarily, CoolMomentum shows a higher accuracy under noiseless and realistic hardware noise conditions.