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

Abstract: We conduct a benchmark of eight optimization algorithms for variational quantum chemistry using the tVHA, evaluating performance on $H_2$, $H_4$, and $LiH$ (in both full and active spaces) under noiseless and sampling noise conditions. Sampling noise fundamentally alters optimizer behavior, with gradient-based methods performing best in ideal conditions, while population-based algorithms, such as CMA-ES, show greater resilience under noise. Hartree-Fock initialization reduces the number of function evaluations by 27-60% and consistently yields higher final accuracy compared to random starting points. We identify a precision limit set by sampling noise, with diminishing returns beyond approximately 1000 shots.