Numerical Optimization Strategies for the Variational Hamiltonian Ansatz in Noisy Quantum Environments

Abstract

The prevalence of variational methods in near-term quantum computing makes optimizer choice critical, yet selection is frequently intuition-based. We therefore present a systematic benchmark of eight classical optimization algorithms for variational quantum chemistry using the truncated Variational Hamiltonian Ansatz. Performance is evaluated on H$_2$, H$_4$, and LiH in both full and active-space representations under noiseless and finite-shot sampling noise. Sampling noise substantially reshapes cost landscapes, induces wandering near minima, and flips optimizer rankings: gradient-based methods perform best in noiseless simulations, whereas population-based optimizers, particularly CMA-ES, show greater robustness under finite-shot noise. Optimizer performance is strongly problem dependent: Hartree-Fock initialization aids small systems, but its advantage diminishes with system size. Also, we observe that finite shot sampling frequently violates the lower bound given by the variational principle, a principle that cannot be strictly held in the presence of noise. By exploiting the guaranteed convergence of Evolution Strategies to a steady state distribution defined by the noise floor, we utilize the symmetry of these violations to achieve energy estimation precision beyond the intrinsic sampling limit.