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

TL;DR

This paper introduces a deep generative model for Feynman paths that efficiently estimates quantum propagators and ground-state wave functions, offering a novel approach to quantum simulation and understanding quantum-classical correspondence.

Contribution

It presents a Feynman path generator using deep learning to efficiently sample relevant quantum paths, enabling improved estimation of quantum propagators and wave functions.

Findings

Efficient generation of Feynman paths from a low-dimensional latent space.

Accurate estimation of Euclidean propagator for various potentials.

Provides a new perspective on quantum-classical correspondence via deep learning.

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.