# Neural Quantum Propagators for Driven-Dissipative Quantum Dynamics

arXiv: https://arxiv.org/abs/2410.16091 · HTML: https://mlsanity.com/paper/2410.16091/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 56 references that are in the map.
- First posted on arXiv 21 Oct 2024.

## Builds on (most cited first, 9 of 9)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers](https://mlsanity.com/paper/2111.13587/) (2021)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [Enhancing Computational Fluid Dynamics with Machine Learning](https://mlsanity.com/paper/2110.02085/) (2021)
- [Machine learning for molecular simulation](https://mlsanity.com/paper/1911.02792/) (2019)
- [Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations](https://mlsanity.com/paper/2407.07218/) (2024)
- [Neural Stochastic PDEs: Resolution-Invariant Learning of Continuous Spatiotemporal Dynamics](https://mlsanity.com/paper/2110.10249/) (2021)
- [Scattering with Neural Operators](https://mlsanity.com/paper/2308.14789/) (2023)
- [Learning S-Matrix Phases with Neural Operators](https://mlsanity.com/paper/2404.14551/) (2024)

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

- [Machine Learning Time Propagators for Time-Dependent Density Functional Theory Simulations](https://mlsanity.com/paper/2508.16554/) (2025)
- [Operator Learning for Schr"odinger Equation: Unitarity, Error Bounds, and Time Generalization](https://mlsanity.com/paper/2505.18288/) (2025)
- [Learning spatially structured open quantum dynamics with regional-attention transformers](https://mlsanity.com/paper/2509.06871/) (2025)

## Abstract (arXiv)

Describing the dynamics of strong-laser driven open quantum systems is a very challenging task that requires the solution of highly involved equations of motion. While machine learning techniques are being applied with some success to simulate the time evolution of individual quantum states, their use to approximate time-dependent operators (that can evolve various states) remains largely unexplored. In this work, we develop driven neural quantum propagators (NQP), a universal neural network framework that solves driven-dissipative quantum dynamics by approximating propagators rather than wavefunctions or density matrices. NQP can handle arbitrary initial quantum states, adapt to various external fields, and simulate long-time dynamics, even when trained on far shorter time windows. Furthermore, by appropriately configuring the external fields, our trained NQP can be transferred to systems governed by different Hamiltonians. We demonstrate the effectiveness of our approach by studying the spin-boson and the three-state transition Gamma models.