# Accurate Computation of Quantum Excited States with Neural Networks

arXiv: https://arxiv.org/abs/2308.16848 · HTML: https://mlsanity.com/paper/2308.16848/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 80 references that are in the map.
- First posted on arXiv 31 Aug 2023.

## 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)
- [A Self-Attention Ansatz for Ab-initio Quantum Chemistry](https://mlsanity.com/paper/2211.13672/) (2022)
- [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)
- [Ab-initio quantum chemistry with neural-network wavefunctions](https://mlsanity.com/paper/2208.12590/) (2022)
- [Electronic excited states in deep variational Monte Carlo](https://mlsanity.com/paper/2203.09472/) (2022)

## Built on by (most cited first, 17 of 17)

- [An ab initio foundation model of wavefunctions that accurately describes chemical bond breaking](https://mlsanity.com/paper/2506.19960/) (2025)
- [Neural Pfaffians: Solving Many Many-Electron Schr"odinger Equations](https://mlsanity.com/paper/2405.14762/) (2024)
- [Accurate Ab-initio Neural-network Solutions to Large-Scale Electronic Structure Problems](https://mlsanity.com/paper/2504.06087/) (2025)
- [Functional Neural Wavefunction Optimization](https://mlsanity.com/paper/2507.10835/) (2025)
- [On Representing Electronic Wave Functions with Sign Equivariant Neural Networks](https://mlsanity.com/paper/2403.05249/) (2024)
- [Is attention all you need to solve the correlated electron problem?](https://mlsanity.com/paper/2502.05383/) (2025)
- [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)
- [Benchmarking Simulacra AI's Quantum Accurate Synthetic Data Generation for Chemical Sciences](https://mlsanity.com/paper/2511.07433/) (2025)
- [Revisiting the Broken Symmetry Phase of Solid Hydrogen: A Neural Network Variational Monte Carlo Study](https://mlsanity.com/paper/2512.17703/) (2025)
- [Excited Pfaffians: Generalized Neural Wave Functions Across Structure and State](https://mlsanity.com/paper/2603.14515/) (2026)
- [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)
- [Fermionic neural Gibbs states](https://mlsanity.com/paper/2512.04663/) (2025)
- [Enabling ab initio geometry optimization of strongly correlated systems with transferable deep quantum Monte Carlo](https://mlsanity.com/paper/2603.25381/) (2026)
- [Physics-Informed Generative Solver: Bridging Data-Driven Priors and Conservation Laws for Stable Spatiotemporal Field Reconstruction](https://mlsanity.com/paper/2605.22338/) (2026)
- [Honeycomb Crystal in a Mass-Asymmetric Electron-Hole Bilayer](https://mlsanity.com/paper/2610.17030/) (2026)

## Abstract (arXiv)

We present a variational Monte Carlo algorithm for estimating the lowest excited states of a quantum system which is a natural generalization of the estimation of ground states. The method has no free parameters and requires no explicit orthogonalization of the different states, instead transforming the problem of finding excited states of a given system into that of finding the ground state of an expanded system. Expected values of arbitrary observables can be calculated, including off-diagonal expectations between different states such as the transition dipole moment. Although the method is entirely general, it works particularly well in conjunction with recent work on using neural networks as variational Ans"atze for many-electron systems, and we show that by combining this method with the FermiNet and Psiformer Ans"atze we can accurately recover vertical excitation energies and oscillator strengths on a range of molecules. Our method is the first deep learning approach to achieve accurate vertical excitation energies, including challenging double excitations, on benzene-scale molecules. Beyond the chemistry examples here, we expect this technique will be of great interest for applications to atomic, nuclear and condensed matter physics.