Comparative Analysis of Optimization Methods for Variational Quantum Eigensolvers

Abstract

This thesis presents a comparative evaluation of optimization methods for Variational Quantum Eigensolvers (VQEs), a hybrid quantum-classical algorithm designed to compute ground state energies of quantum systems. The study explores six optimizers—COBYLA, Powell, SLSQP, BFGS, SPSA, and AQNGD—across both noiseless statevector simulations and noisy quantum hardware simulators. The hydrogen molecule (H2) serves as the benchmark, with performance evaluated through metrics such as accuracy, resource efficiency, and robustness to noise. The results highlight significant performance differences among optimizers. Gradient-based methods (BFGS, SLSQP) exhibit exceptional accuracy in noiseless conditions but suffer catastrophic degradation under noise, while AQNGD demonstrates superior performance in noisy environments. The study also investigates initialization strategies and noise impacts, providing practical guidelines for selecting optimization algorithms based on quantum resource constraints. This work establishes a systematic framework for evaluating optimization methods in the NISQ era, contributing essential insights for achieving reliable quantum advantage in computational chemistry and related fields.