Estimating the Euclidean quantum propagator with deep generative modeling of Feynman paths

Abstract: Feynman path integrals provide an elegant, classically inspired representation for the quantum propagator and the quantum dynamics, through summing over a huge manifold of all possible paths. From computational and simulational perspectives, the ergodic tracking of the whole path manifold is a hard problem. Machine learning can help, in an efficient manner, to identify the relevant subspace and the intrinsic structure residing at a small fraction of the vast path manifold. In this work, we propose the Feynman path generator for quantum mechanical systems, which efficiently generates Feynman paths with fixed endpoints, from a (low-dimensional) latent space and by targeting a desired density of paths in the Euclidean space-time. With such path generators, the Euclidean propagator as well as the ground-state wave function can be estimated efficiently for a generic potential energy. Our work provides an alternative approach for calculating the quantum propagator and the ground-state wave function, paves the way toward generative modeling of quantum mechanical Feynman paths, and offers a different perspective to understand the quantum-classical correspondence through deep learning.