Numerical Optimization Strategies for the Variational Hamiltonian Ansatz in Noisy Quantum Environments
Abstract
Abstract Variational quantum eigensolvers are considered promising approaches for quantum chemistry on near-term quantum hardware, yet their performance is strongly affected by sampling noise. Despite the widespread use of classical optimizers, their robustness under realistic finite-shot sampling conditions remains insufficiently understood.The optimization of the truncated Variational Hamiltonian Ansatz for H2, H4, and LiH is investigated using eight classical optimization algorithms. A total of 1,280 independent optimization runs are performed under both exact statevector and finite-shot sampling conditions.Finite-shot sampling is found to reshape optimization dynamics and reverse optimizer rankings observed in noiseless simulations. While gradient-based methods achieve near-machine precision in exact simulations, their performance deteriorates substantially under sampling noise. In contrast, population-based approaches, particularly the Covariance Matrix Adaptation Evolution Strategy, remain robust, achieving corrected errors below 5 x 10-4 Ha for H2 and below 10-2 Ha for LiH.Finite-shot sampling is further shown to frequently produce apparent violations of the variational principle. By reevaluating candidate solutions using 105 measurements, sampling-induced fluctuations are exploited to obtain energy estimates beyond the intrinsic sampling limit.These results provide practical guidelines for optimizer selection and highlight the importance of high-shot reevaluation in…
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