  Variational Quantum Eigensolvers (VQEs) represent a promising approach to
computing molecular ground states and energies on modern quantum computers.
These approaches use a classical computer to optimize the parameters of a trial
wave function, while the quantum computer simulates the energy by preparing and
measuring a set of bitstring observations, referred to as shots, over which an
expected value is computed. Although more shots improve the accuracy of the
expected ground state, it also increases the simulation cost. Hence, we propose
modifications to the standard Bayesian optimization algorithm to leverage
few-shot circuit observations to solve VQEs with fewer quantum resources. We
demonstrate the effectiveness of our proposed approach, Bayesian optimization
with priors on surface topology (BOPT), by comparing optimizers for molecular
systems and demonstrate how current quantum hardware can aid in finding ground
state energies.
