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

TL;DR

This paper systematically benchmarks classical optimization algorithms for variational quantum chemistry, revealing how noise impacts optimizer performance and proposing strategies to improve energy estimation accuracy in noisy quantum environments.

Contribution

It provides a comprehensive comparison of eight classical optimizers under realistic noise conditions and introduces a novel approach using Evolution Strategies to surpass sampling limits.

Findings

Gradient-based methods excel in noiseless conditions.

Population-based optimizers like CMA-ES are more robust under noise.

Finite-shot sampling can violate the variational principle bounds.

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.