Towards Efficient Quantum Computation of Molecular Ground State Energies using Bayesian Optimization with Priors over Surface Topology

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.