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

arXiv: https://arxiv.org/abs/2202.02750 · HTML: https://mlsanity.com/paper/2202.02750/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 72 references that are in the map.
- First posted on arXiv 6 Feb 2022.

## Builds on (most cited first, 25 of 25)

- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [GFlowNet Foundations](https://mlsanity.com/paper/2111.09266/) (2021)
- [Flow-based generative models for Markov chain Monte Carlo in lattice field theory](https://mlsanity.com/paper/1904.12072/) (2019)
- [Discovering physical concepts with neural networks](https://mlsanity.com/paper/1807.10300/) (2018)
- [Equivariant flow-based sampling for lattice gauge theory](https://mlsanity.com/paper/2003.06413/) (2020)
- [Solving Statistical Mechanics Using Variational Autoregressive Networks](https://mlsanity.com/paper/1809.10606/) (2018)
- [Provably efficient machine learning for quantum many-body problems](https://mlsanity.com/paper/2106.12627/) (2021)
- [Neural Network Renormalization Group](https://mlsanity.com/paper/1802.02840/) (2018)
- [Variational Neural Annealing](https://mlsanity.com/paper/2101.10154/) (2021)
- [Quantum State Tomography with Conditional Generative Adversarial Networks](https://mlsanity.com/paper/2008.03240/) (2020)
- [Equivalence of restricted Boltzmann machines and tensor network states](https://mlsanity.com/paper/1701.04831/) (2017)
- [Flow-based sampling for fermionic lattice field theories](https://mlsanity.com/paper/2106.05934/) (2021)
- [Stochastic normalizing flows as non-equilibrium transformations](https://mlsanity.com/paper/2201.08862/) (2022)
- [Experimental neural network enhanced quantum tomography](https://mlsanity.com/paper/1904.05902/) (2019)
- [Classification and reconstruction of optical quantum states with deep neural networks](https://mlsanity.com/paper/2012.02185/) (2020)
- [Machine learning assisted quantum state estimation](https://mlsanity.com/paper/2003.03441/) (2020)
- [Inferring the quantum density matrix with machine learning](https://mlsanity.com/paper/1904.05903/) (2019)
- [Probing Criticality in Quantum Spin Chains with Neural Networks](https://mlsanity.com/paper/2005.02104/) (2020)
- [Learning Principle of Least Action with Reinforcement Learning](https://mlsanity.com/paper/2011.11891/) (2020)
- [On the Mathematical Understanding of ResNet with Feynman Path Integral](https://mlsanity.com/paper/1904.07568/) (2019)

## Built on by (most cited first, 3 of 3)

- [Exponentially improved efficient machine learning for quantum many-body states with provable guarantees](https://mlsanity.com/paper/2304.04353/) (2023)
- [Analogy between Boltzmann machines and Feynman path integrals](https://mlsanity.com/paper/2301.06217/) (2023)
- [Quantum circuit complexity and unsupervised machine learning of topological order](https://mlsanity.com/paper/2508.04486/) (2025)

## Abstract (arXiv)

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.