Exploration of the Global Minimum and Conical Intersection with Bayesian Optimization

Conventional molecular geometry searches on a potential energy surface (PES) utilize 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, an acquisition function (AF), which involves an objective variable, must be defined suitably. 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 located the GM and the most stable CI geometries with high accuracy for both molecules. We also succeeded in the geometry searches even when artificial random noises were added to the energies to simulate geometry optimization using noisy quantum computer measurements.