Bayesian optimisation with improved information sharing for the variational quantum eigensolver

TL;DR

This paper empirically analyzes Bayesian optimisation with information sharing for the variational quantum eigensolver, demonstrating improved resource efficiency and performance in computing molecular potential energy surfaces, including on real quantum hardware.

Contribution

It introduces a new information sharing scheme for BOIS that reduces quantum resource requirements and compares it with existing schemes through extensive simulations and hardware experiments.

Findings

Improved by a factor of 1.5 in H2 using the new sharing scheme.

Achieved at least a 5-fold reduction in resources for H2O.

Kernel choice and acquisition weight rate significantly affect quantum resource demands.

Abstract

This work presents a detailed empirical analysis of Bayesian optimisation with information sharing (BOIS) for the variational quantum eigensolver (VQE). The method is applied to computing the potential energy surfaces (PES) of the hydrogen and water molecules. We performed noise-free simulations and investigated the algorithms' performance under the influence of noise for the hydrogen molecule, using both emulated and real quantum hardware (IBMQ System One). Based on the noise free simulations we compared different existing information sharing schemes and proposed a new one, which trades parallelisability of the algorithm for a significant reduction in the amount of quantum computing resources required until convergence. In particular, our numerical experiments show an improvement by a factor of 1.5 as compared to the previously reported sharing schemes in H2, and at least by a factor of 5 as compared to no sharing in H2O. Other algorithmic aspects of the Bayesian optimisation, namely, the acquisition weight decrease rate and kernel, are shown to have an influence on the quantum computation (QC) demand of the same order of magnitude.