# Autoregressive neural-network wavefunctions for ab initio quantum chemistry

arXiv: https://arxiv.org/abs/2109.12606 · HTML: https://mlsanity.com/paper/2109.12606/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 56 references that are in the map.
- First posted on arXiv 26 Sep 2021.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Monte Carlo Gradient Estimation in Machine Learning](https://mlsanity.com/paper/1906.10652/) (2019)
- [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)
- [Neural Autoregressive Distribution Estimation](https://mlsanity.com/paper/1605.02226/) (2016)
- [Deep autoregressive models for the efficient variational simulation of many-body quantum systems](https://mlsanity.com/paper/1902.04057/) (2019)
- [Quantum State Tomography with Conditional Generative Adversarial Networks](https://mlsanity.com/paper/2008.03240/) (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)
- [Scalable neural quantum states architecture for quantum chemistry](https://mlsanity.com/paper/2208.05637/) (2022)
- [Neural-network solutions to stochastic reaction networks](https://mlsanity.com/paper/2210.01169/) (2022)
- [The autoregressive neural network architecture of the Boltzmann distribution of pairwise interacting spins systems](https://mlsanity.com/paper/2302.08347/) (2023)
- [ANTN: Bridging Autoregressive Neural Networks and Tensor Networks for Quantum Many-Body Simulation](https://mlsanity.com/paper/2304.01996/) (2023)
- [NNQS-Transformer: an Efficient and Scalable Neural Network Quantum States Approach for Ab initio Quantum Chemistry](https://mlsanity.com/paper/2306.16705/) (2023)
- [m^ast of two-dimensional electron gas: a neural canonical transformation study](https://mlsanity.com/paper/2201.03156/) (2022)
- [Ab-initio variational wave functions for the time-dependent many-electron Schr"odinger equation](https://mlsanity.com/paper/2403.07447/) (2024)
- [Retentive Neural Quantum States: Efficient Ans"atze for Ab Initio Quantum Chemistry](https://mlsanity.com/paper/2411.03900/) (2024)
- [Tracking large chemical reaction networks and rare events by neural networks](https://mlsanity.com/paper/2512.10309/) (2025)
- [Convergence of variational Monte Carlo simulation and scale-invariant pre-training](https://mlsanity.com/paper/2303.11602/) (2023)
- [A Generative Neural Annealer for Black-Box Combinatorial Optimization](https://mlsanity.com/paper/2505.09742/) (2025)
- [Astral: training physics-informed neural networks with error majorants](https://mlsanity.com/paper/2406.02645/) (2024)
- [Large Language Model Scaling Laws for Neural Quantum States in Quantum Chemistry](https://mlsanity.com/paper/2509.12679/) (2025)
- [An Empirical Study of Quantum Dynamics as a Ground State Problem with Neural Quantum States](https://mlsanity.com/paper/2206.09241/) (2022)
- [Hybrid Ground-State Quantum Algorithms based on Neural Schr"odinger Forging](https://mlsanity.com/paper/2307.02633/) (2023)
- [Solving excited states for long-range interacting trapped ions with neural networks](https://mlsanity.com/paper/2506.08594/) (2025)
- [Enhanced Neural Quantum State via Annealed Gradient Descent](https://mlsanity.com/paper/2607.18865/) (2026)
- [Gradient-estimator design overcomes trainability barriers in neural-network-based variational optimization](https://mlsanity.com/paper/2609.22342/) (2026)
- [Foundation Neural-Network Quantum States for Molecular Potential Energy Surfaces in Second Quantization](https://mlsanity.com/paper/2609.37733/) (2026)
- [Neural Fourier Surrogates for Data Reuploading Quantum Neural Networks](https://mlsanity.com/paper/2610.00841/) (2026)

## Abstract (arXiv)

In recent years, neural network quantum states (NNQS) have emerged as powerful tools for the study of quantum many-body systems. Electronic structure calculations are one such canonical many-body problem that have attracted significant research efforts spanning multiple decades, whilst only recently being attempted with NNQS. However, the complex non-local interactions and high sample complexity are significant challenges that call for bespoke solutions. Here, we parameterise the electronic wavefunction with a novel autoregressive neural network (ARN) that permits highly efficient and scalable sampling, whilst also embedding physical priors reflecting the structure of molecular systems without sacrificing expressibility. This allows us to perform electronic structure calculations on molecules with up to 30 spin-orbitals -- at least an order of magnitude more Slater determinants than previous applications of conventional NNQS -- and we find that our ansatz can outperform the de-facto gold-standard coupled cluster methods even in the presence of strong quantum correlations. With a highly expressive neural network for which sampling is no longer a computational bottleneck, we conclude that the barriers to further scaling are not associated with the wavefunction ansatz itself, but rather are inherent to any variational Monte Carlo approach.