HOPSO: A Robust Classical Optimizer for VQE

TL;DR

This paper introduces HOPSO, a modified particle swarm optimization algorithm tailored for VQE, improving classical optimization robustness and noise resilience, leading to better energy approximations for molecular Hamiltonians.

Contribution

It presents a novel adaptation of Harmonic Oscillator-based Particle Swarm Optimization for VQE, enhancing noise robustness and respecting quantum parameter periodicity.

Findings

HOPSO achieves competitive ground-state energy estimates.

HOPSO outperforms COBYLA, DE, and standard PSO under noise.

HOPSO shows promise for scalable quantum chemistry applications.

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.