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.

Published version; Updated references

References in corpus (17)

• NICE: Non-linear Independent Components Estimation
• An introduction to quantum machine learning
• Learning phase transitions by confusion
• Neural-Network Approach to Dissipative Quantum Many-Body Dynamics
• Provably efficient machine learning for quantum many-body problems
• Variational Quantum Monte Carlo Method with a Neural-Network Ansatz for Open Quantum Systems
• Variational neural network ansatz for steady states in open quantum systems
• Constructing neural stationary states for open quantum many-body systems
• Variational Neural Annealing
• Flow-based sampling for fermionic lattice field theories
• Stochastic normalizing flows as non-equilibrium transformations
• Intrinsic dimension of path integrals: data mining quantum criticality and emergent simplicity
• Variational autoencoder reconstruction of complex many-body physics
• Inferring the quantum density matrix with machine learning
• Probing Criticality in Quantum Spin Chains with Neural Networks
• On the Mathematical Understanding of ResNet with Feynman Path Integral
• Generative models for sampling of lattice field theories

Cited by in corpus (9)

• Stochastic normalizing flows as non-equilibrium transformations
• Fourier-Flow model generating Feynman paths
• Exponentially improved efficient machine learning for quantum many-body states with provable guarantees
• Solving Schrodinger equations using physically constrained neural network
• Multiqubit state learning with entangling quantum generative adversarial networks
• Analogy between Boltzmann machines and Feynman path integrals
• Neural network expansion of Euclidean path integrals and its application to interacting scalar fields
• On the solution of Euclidean path integrals with neural networks
• Approximating Grassmann valued path integrals with radial basis function neural networks