Integrating machine learning with scattering calculations to improve molecular collision observable predictions

This thesis demonstrates that machine learning can be integrated with rigorous quantum scattering calculations to improve predictions of molecular collision observables, a problem important to fields ranging from cold-atom physics to vacuum metrology. Rigorous quantum scattering calculations are limited by the fitting of high-dimensional potential energy surfaces (PES), the sensitivity of collision observables to the uncertainty in PES fitting, and the computational demands of achieving full convergence with large basis sets. The thesis begins by fitting polyatomic PES using Gaussian process (GP) regression built on quantum kernels. To provide an unbiased comparison between classical and quantum kernels, I develop an algorithm that uses an analog of the Bayesian information criterion to optimize the sequence of quantum gates, increasing the complexity of the quantum circuits incrementally. The algorithm achieves much higher PES fitting accuracy with fewer quantum gates than a fixed quantum circuit ansatz, matching state-of-the-art classical GP regression models. To examine the response of collision observables to the uncertainty in PES fitting, I employ rigorous quantum scattering calculations to perform a comprehensive analysis of the universality in thermal atom-atom collision rate coefficients. I demonstrate that the rate coefficients for heavy, highly polarizable atoms are insensitive to the variations in the interatomic interactions at short range. I provide phase diagrams separating universal from non-universal collisions by treating collision observables as probabilistic predictions determined by a distribution of interaction potentials. I then extend the analysis of the universality to atom-molecule collisions. I demonstrate that the rate coefficients of total (elastic + inelastic) atom-molecule scattering are insensitive to the interaction anisotropy of the underlying PES. Specifically, I show that the rate coefficients for Rb-H2 and Rb-N2 scattering at room temperature can be computed to 1% accuracy with the anisotropy set to zero, reducing the basis set size in coupled-channel quantum scattering calculations to the single-channel limit. To improve collision observables calculated with reduced basis sets, I present a basis-set extrapolation method for quantum scattering calculations based on GP regression. I demonstrate that the method can extrapolate fully converged collision observables using those calculated with reduced basis sets, with accuracy matching experimental requirements and theoretical approximations.