Exploration of the Global Minimum and Conical Intersection with Bayesian Optimization

Conventional molecular geometry searches on a potential energy surface (PES) utilize energies and energy gradients from quantum chemical calculations. However, replacing energy calculations with noisy quantum computer measurements generates errors in the energies, which makes geometry optimization using the energy gradient difficult. One gradient-free optimization method that can potentially solve this problem is Bayesian optimization (BO). To use BO in geometry search, a suitable acquisition function (AF) must be defined. In this study, we propose a strategy for geometry searches using BO and examine the appropriate AFs to explore two critical structures: the global minimum (GM) on the singlet ground state (S0) and the most stable conical intersection (CI) point between S0 and the singlet excited state. We applied our strategy to two molecules and found the GM and the most stable CI geometries with high accuracy for both molecules.