# Electronic excited states in deep variational Monte Carlo

arXiv: https://arxiv.org/abs/2203.09472 · HTML: https://mlsanity.com/paper/2203.09472/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 104 references that are in the map.
- First posted on arXiv 17 Mar 2022.

## Builds on (most cited first, 7 of 7)

- [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)
- [Ab-Initio Potential Energy Surfaces by Pairing GNNs with Neural Wave Functions](https://mlsanity.com/paper/2110.05064/) (2021)
- [Machine learning for electronically excited states of molecules](https://mlsanity.com/paper/2007.05320/) (2020)
- [Better, Faster Fermionic Neural Networks](https://mlsanity.com/paper/2011.07125/) (2020)
- [Solving the electronic Schr"odinger equation for multiple nuclear geometries with weight-sharing deep neural networks](https://mlsanity.com/paper/2105.08351/) (2021)
- [Convergence to the fixed-node limit in deep variational Monte Carlo](https://mlsanity.com/paper/2010.05316/) (2020)

## Built on by (most cited first, 21 of 21)

- [Ab-initio quantum chemistry with neural-network wavefunctions](https://mlsanity.com/paper/2208.12590/) (2022)
- [Gold-standard solutions to the Schr"odinger equation using deep learning: How much physics do we need?](https://mlsanity.com/paper/2205.09438/) (2022)
- [Accurate Computation of Quantum Excited States with Neural Networks](https://mlsanity.com/paper/2308.16848/) (2023)
- [Operator SVD with Neural Networks via Nested Low-Rank Approximation](https://mlsanity.com/paper/2402.03655/) (2024)
- [Pairing-based graph neural network for simulating quantum materials](https://mlsanity.com/paper/2311.02143/) (2023)
- [Variational Monte Carlo on a Budget -- Fine-tuning pre-trained Neural Wavefunctions](https://mlsanity.com/paper/2307.09337/) (2023)
- [Towards a Foundation Model for Neural Network Wavefunctions](https://mlsanity.com/paper/2303.09949/) (2023)
- [Forward Laplacian: A New Computational Framework for Neural Network-based Variational Monte Carlo](https://mlsanity.com/paper/2307.08214/) (2023)
- [Analyzing the Performance of Deep Encoder-Decoder Networks as Surrogates for a Diffusion Equation](https://mlsanity.com/paper/2302.03786/) (2023)
- [Computing excited states of molecules using normalizing flows](https://mlsanity.com/paper/2308.16468/) (2023)
- [On Representing Electronic Wave Functions with Sign Equivariant Neural Networks](https://mlsanity.com/paper/2403.05249/) (2024)
- [Ab-initio simulation of excited-state potential energy surfaces with transferable deep quantum Monte Carlo](https://mlsanity.com/paper/2503.19847/) (2025)
- [Spin-Adapted Neural Network Wavefunctions in Real Space](https://mlsanity.com/paper/2511.01671/) (2025)
- [Artificial intelligence for artificial materials: moir'e atom](https://mlsanity.com/paper/2303.08162/) (2023)
- [Excited Pfaffians: Generalized Neural Wave Functions Across Structure and State](https://mlsanity.com/paper/2603.14515/) (2026)
- [A Score-Based Model for Learning Neural Wavefunctions](https://mlsanity.com/paper/2305.16540/) (2023)
- [A Theoretical Framework for an Efficient Normalizing Flow-Based Solution to the Electronic Schrodinger Equation](https://mlsanity.com/paper/2406.00047/) (2024)
- [Solving excited states for long-range interacting trapped ions with neural networks](https://mlsanity.com/paper/2506.08594/) (2025)
- [Revisiting Orbital Minimization Method for Neural Operator Decomposition](https://mlsanity.com/paper/2510.21952/) (2025)
- [Enabling ab initio geometry optimization of strongly correlated systems with transferable deep quantum Monte Carlo](https://mlsanity.com/paper/2603.25381/) (2026)
- [Position: The Inevitable Transition to Machine Learning in Quantum Chemistry](https://mlsanity.com/paper/2607.18281/) (2026)

## Abstract (arXiv)

Obtaining accurate ground and low-lying excited states of electronic systems is crucial in a multitude of important applications. One ab initio method for solving the Schr"odinger equation that scales favorably for large systems is variational quantum Monte Carlo (QMC). The recently introduced deep QMC approach uses ansatzes represented by deep neural networks and generates nearly exact ground-state solutions for molecules containing up to a few dozen electrons, with the potential to scale to much larger systems where other highly accurate methods are not feasible. In this paper, we extend one such ansatz (PauliNet) to compute electronic excited states. We demonstrate our method on various small atoms and molecules and consistently achieve high accuracy for low-lying states. To highlight the method's potential, we compute the first excited state of the much larger benzene molecule, as well as the conical intersection of ethylene, with PauliNet matching results of more expensive high-level methods.