  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.
