# Learning quantum dynamics with latent neural ODEs

arXiv: https://arxiv.org/abs/2110.10721 · HTML: https://mlsanity.com/paper/2110.10721/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 47 references that are in the map.
- First posted on arXiv 20 Oct 2021.

## Builds on (most cited first, 11 of 11)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Explainable Machine Learning for Scientific Insights and Discoveries](https://mlsanity.com/paper/1905.08883/) (2019)
- [Discovering physical concepts with neural networks](https://mlsanity.com/paper/1807.10300/) (2018)
- [Latent-space Physics: Towards Learning the Temporal Evolution of Fluid Flow](https://mlsanity.com/paper/1802.10123/) (2018)
- [Noisy intermediate-scale quantum (NISQ) algorithms](https://mlsanity.com/paper/2101.08448/) (2021)
- [Learning Interpretable Representations of Entanglement in Quantum Optics Experiments using Deep Generative Models](https://mlsanity.com/paper/2109.02490/) (2021)
- [Deploying a Top-100 Supercomputer for Large Parallel Workloads: the Niagara Supercomputer](https://mlsanity.com/paper/1907.13600/) (2019)
- [Physicist's Journeys Through the AI World - A Topical Review. There is no royal road to unsupervised learning](https://mlsanity.com/paper/1905.01023/) (2019)

## Built on by (most cited first, 4 of 4)

- [Emulating Quantum Dynamics with Neural Networks via Knowledge Distillation](https://mlsanity.com/paper/2203.10200/) (2022)
- [Robust Moment Identification for Nonlinear PDEs via a Neural ODE Approach](https://mlsanity.com/paper/2506.05245/) (2025)
- [Fourier Neural Differential Equations for learning Quantum Field Theories](https://mlsanity.com/paper/2311.17250/) (2023)
- [Reconstruction of dynamical systems from data without time labels](https://mlsanity.com/paper/2312.04038/) (2023)

## Abstract (arXiv)

The core objective of machine-assisted scientific discovery is to learn physical laws from experimental data without prior knowledge of the systems in question. In the area of quantum physics, making progress towards these goals is significantly more challenging due to the curse of dimensionality as well as the counter-intuitive nature of quantum mechanics. Here, we present the QNODE, a latent neural ODE trained on expectation values of closed and open quantum systems dynamics. It can learn to generate such measurement data and extrapolate outside of its training region that satisfies the von Neumann and time-local Lindblad master equations for closed and open quantum systems respectively in an unsupervised means. Furthermore, the QNODE rediscovers quantum mechanical laws such as the Heisenberg's uncertainty principle in a data-driven way, without any constraint or guidance. Additionally, we show that trajectories that are generated from the QNODE that are close in its latent space have similar quantum dynamics while preserving the physics of the training system.