# Ab-initio variational wave functions for the time-dependent many-electron Schr"odinger equation

arXiv: https://arxiv.org/abs/2403.07447 · HTML: https://mlsanity.com/paper/2403.07447/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 132 references that are in the map.
- First posted on arXiv 12 Mar 2024.

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

- [Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networks](https://mlsanity.com/paper/1909.02487/) (2019)
- [Deep neural network solution of the electronic Schr"odinger equation](https://mlsanity.com/paper/1909.08423/) (2019)
- [A Self-Attention Ansatz for Ab-initio Quantum Chemistry](https://mlsanity.com/paper/2211.13672/) (2022)
- [Ab-initio quantum chemistry with neural-network wavefunctions](https://mlsanity.com/paper/2208.12590/) (2022)
- [NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems](https://mlsanity.com/paper/2112.10526/) (2021)
- [Generalizing Neural Wave Functions](https://mlsanity.com/paper/2302.04168/) (2023)
- [Autoregressive neural-network wavefunctions for ab initio quantum chemistry](https://mlsanity.com/paper/2109.12606/) (2021)
- [Ab-initio study of interacting fermions at finite temperature with neural canonical transformation](https://mlsanity.com/paper/2105.08644/) (2021)
- [Neural Wave Functions for Superfluids](https://mlsanity.com/paper/2305.06989/) (2023)
- [Wasserstein Quantum Monte Carlo: A Novel Approach for Solving the Quantum Many-Body Schr"odinger Equation](https://mlsanity.com/paper/2307.07050/) (2023)
- [Pairing-based graph neural network for simulating quantum materials](https://mlsanity.com/paper/2311.02143/) (2023)

## Built on by (most cited first, 7 of 7)

- [Are queries and keys always relevant? A case study on Transformer wave functions](https://mlsanity.com/paper/2405.18874/) (2024)
- [Quantum computing and artificial intelligence: status and perspectives](https://mlsanity.com/paper/2505.23860/) (2025)
- [Spin-Adapted Neural Network Wavefunctions in Real Space](https://mlsanity.com/paper/2511.01671/) (2025)
- [Operator Learning for Schr"odinger Equation: Unitarity, Error Bounds, and Time Generalization](https://mlsanity.com/paper/2505.18288/) (2025)
- [Fermionic neural Gibbs states](https://mlsanity.com/paper/2512.04663/) (2025)
- [Transformer Learning of Chaotic Collective Dynamics in Many-Body Systems](https://mlsanity.com/paper/2601.19080/) (2026)
- [One More Time: Revisiting Neural Quantum States from a Reinforcement Learning Perspective](https://mlsanity.com/paper/2607.02292/) (2026)

## Abstract (arXiv)

Understanding the real-time evolution of many-electron quantum systems is essential for studying dynamical properties in condensed matter, quantum chemistry, and complex materials, yet it poses a significant theoretical and computational challenge. Our work introduces a variational approach for fermionic time-dependent wave functions, surpassing mean-field approximations by accurately capturing many-body correlations. Therefore, we employ time-dependent Jastrow factors and backflow transformations, which are enhanced through neural networks parameterizations. To compute the optimal time-dependent parameters, we utilize the time-dependent variational Monte Carlo technique and a new method based on Taylor-root expansions of the propagator, enhancing the accuracy of our simulations. The approach is demonstrated in three distinct systems. In all cases, we show clear signatures of many-body correlations in the dynamics. The results showcase the ability of our variational approach to accurately capture the time evolution, providing insight into the quantum dynamics of interacting electronic systems, beyond the capabilities of mean-field.