Estimating the Euclidean quantum propagator with deep generative modeling of Feynman paths
This provides an alternative computational method for quantum mechanics simulations, potentially benefiting researchers in physics and computational science, though it appears incremental as it builds on existing generative modeling techniques.
The authors tackled the computational challenge of estimating the Euclidean quantum propagator by developing a deep generative model called the Feynman path generator, which efficiently samples relevant Feynman paths from a low-dimensional latent space, enabling efficient estimation of the propagator and ground-state wave function for generic potentials.
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.