# Large Language Model Scaling Laws for Neural Quantum States in Quantum Chemistry

arXiv: https://arxiv.org/abs/2509.12679 · HTML: https://mlsanity.com/paper/2509.12679/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 34 references that are in the map.
- First posted on arXiv 16 Sep 2025.

## Builds on (most cited first, 23 of 23)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies](https://mlsanity.com/paper/2404.06395/) (2024)
- [Retentive Network: A Successor to Transformer for Large Language Models](https://mlsanity.com/paper/2307.08621/) (2023)
- [Scaling Data-Constrained Language Models](https://mlsanity.com/paper/2305.16264/) (2023)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [Scaling Laws for Transfer](https://mlsanity.com/paper/2102.01293/) (2021)
- [Beyond Chinchilla-Optimal: Accounting for Inference in Language Model Scaling Laws](https://mlsanity.com/paper/2401.00448/) (2023)
- [A Tale of Tails: Model Collapse as a Change of Scaling Laws](https://mlsanity.com/paper/2402.07043/) (2024)
- [Scaling Laws vs Model Architectures: How does Inductive Bias Influence Scaling?](https://mlsanity.com/paper/2207.10551/) (2022)
- [Chinchilla Scaling: A replication attempt](https://mlsanity.com/paper/2404.10102/) (2024)
- [Deep autoregressive models for the efficient variational simulation of many-body quantum systems](https://mlsanity.com/paper/1902.04057/) (2019)
- [Scaling Laws for Downstream Task Performance of Large Language Models](https://mlsanity.com/paper/2402.04177/) (2024)
- [Variational Neural Annealing](https://mlsanity.com/paper/2101.10154/) (2021)
- [Autoregressive neural-network wavefunctions for ab initio quantum chemistry](https://mlsanity.com/paper/2109.12606/) (2021)
- [Neural Error Mitigation of Near-Term Quantum Simulations](https://mlsanity.com/paper/2105.08086/) (2021)
- [Overcoming barriers to scalability in variational quantum Monte Carlo](https://mlsanity.com/paper/2106.13308/) (2021)
- [Scalable neural quantum states architecture for quantum chemistry](https://mlsanity.com/paper/2208.05637/) (2022)
- [NNQS-Transformer: an Efficient and Scalable Neural Network Quantum States Approach for Ab initio Quantum Chemistry](https://mlsanity.com/paper/2306.16705/) (2023)
- [Scaling of neural-network quantum states for time evolution](https://mlsanity.com/paper/2104.10696/) (2021)
- [Retentive Neural Quantum States: Efficient Ans"atze for Ab Initio Quantum Chemistry](https://mlsanity.com/paper/2411.03900/) (2024)
- [Toward Neural Network Simulation of Variational Quantum Algorithms](https://mlsanity.com/paper/2211.02929/) (2022)

## Built on by (most cited first, 1 of 1)

- [Holographic Quantum Transformer: A Generalist Neuro-Symbolic Architecture for Solving Frustrated Systems via Generative Attention](https://mlsanity.com/paper/2607.00398/) (2026)

## Abstract (arXiv)

Scaling laws have been used to describe how large language model (LLM) performance scales with model size, training data size, or amount of computational resources. Motivated by the fact that neural quantum states (NQS) has increasingly adopted LLM-based components, we seek to understand NQS scaling laws, thereby shedding light on the scalability and optimal performance--resource trade-offs of NQS ansatze. In particular, we identify scaling laws that predict the performance, as measured by absolute error and V-score, for transformer-based NQS as a function of problem size in second-quantized quantum chemistry applications. By performing analogous compute-constrained optimization of the obtained parametric curves, we find that the relationship between model size and training time is highly dependent on loss metric and ansatz, and does not follow the approximately linear relationship found for language models.