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October 11, 2025Open Access

HOPSO: A Robust Classical Optimizer for VQE

Key Points

HOPSO achieves competitive ground-state energy approximations for hydrogen and lithium hydride molecules, enhancing performance.
It demonstrates improved robustness against measurement stochastic noise when compared to COBYLA and Differential Evolution methods.
The study adapts the dynamics of HOPSO to respect periodicity in quantum parameters, facilitating better optimization outcomes.
Tailored classical optimization methods may enable scalable variational quantum eigensolver applications for larger systems in practical settings.

Abstract

Variational Quantum Eigensolver (VQE) algorithm is one of few approaches where the hope for near-term quantum advantage concentrates. However, they face challenges connected with measurement stochastic noise, barren plateaus, and optimization difficulties in periodic parameter spaces. While most of the efforts concentrates on optimizing the quantum part of the procedure, here we aim to enhance the classical optimization by utilizing a modified version of Harmonic Oscillator-based Particle Swarm Optimization (HOPSO). By adapting its dynamics to respect the periodicity of quantum parameters and enhance noise resilience, we show its strengths on hydrogen (H2) and lithium hydride (LiH) molecules modeled as 4- and 8-qubit Hamiltonians. HOPSO achieves competitive ground-state energy approximations and demonstrates improved robustness compared to COBYLA, Differential Evolution (DE), and standard Particle Swarm Optimization (PSO) methods in all situations and outperforms other methods under realistic noise conditions. These results suggest that a properly tailored classical part of VQE algorithms can tackle with current problems and gives hope for its scalability for larger systems.

HOPSO: A Robust Classical Optimizer for VQE

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Abstract

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