Variational Quantum Algorithms (VQAs) are a leading approach for near-term quantum computing but face major optimization challenges from noise, barren plateaus, and complex energy landscapes. We benchmarked more than fifty metaheuristic algorithms for the Variational Quantum Eigensolver (VQE) using a three-phase procedure: initial screening on the Ising model, scaling tests up to nine qubits, and convergence on a 192-parameter Hubbard model. Landscape visualizations revealed that smooth convex basins in noiseless settings become distorted and rugged under finite-shot sampling, explaining the failure of gradient-based local methods. Across models, CMA-ES and iL-SHADE consistently achieved the best performance, while Simulated Annealing (Cauchy), Harmony Search, and Symbiotic Organisms Search also showed robustness. In contrast, widely used optimizers such as PSO, GA, and standard DE variants degraded sharply with noise. These results identify a small set of resilient algorithms for noisy VQE and provide guidance for optimization strategies on near-term quantum devices.
Novák et al. (Mon,) studied this question.