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arXiv:2509.12679 · Machine Learning Science and Technology

Large language model scaling laws for neural quantum states in quantum chemistry

Oliver Knitter, Dan Zhao, Stefan Leichenauer, Shravan Veerapaneni

Published Mar 17, 2026• 0 citations
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Abstract

Abstract 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 the field of 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 ansätze. 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 using a simplified compute estimate model, 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 compute-optimal tradeoff found by the Chinchilla laws.

DOI
10.1088/2632-2153/ae538f

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Abstract 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 the field of 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 ansätze. 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 using a simplified compute estimate model, 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 compute-optimal tradeoff found by the Chinchilla laws.
Scaling laws, the power-law relations between loss, architecture size, and compute observed in modern neural networks, offer a quantitative way to characterize the complexity of a learning problem, with the exponent governing the decay of the loss reflecting how rapidly additional resources translate into improved accuracy, and thus how hard the target is to learn. Whether an analogous framework can characterize the complexity of physical problems remains open. We address this question for Neural-Network Quantum States, a leading variational approach for strongly correlated quantum many-body systems. Using transformer wave functions to approximate ground states of the J1J_1J1​-J2J_2J2​ Heisenberg model on triangular and square lattices with up to 20×2020\times 2020×20 sites, we find that the VVV-score, a measure of accuracy of a variational state, decays as a power law in training compute. Under an appropriate rescaling of compute, results for different system sizes collapse onto a single curve, analogous to scaling collapse in critical phenomena. The resulting power law is, to a good approximation, independent of the number of sites, showing that the transformer Ansatz is size-consistent for the systems considered. The exponent decreases systematically with frustration, identifying it as a quantitative measure of representational difficulty of the ground state and establishing scaling laws as a general framework for benchmarking variational ansätze.
Quantum machine learning (QML) is a promising application of quantum computing, yet when and how practical learning models can achieve quantum advantage remains poorly understood. Even a polynomial improvement in the resources needed to attain a given predictive performance would be significant. In this work, we investigate empirical scaling laws of quantum vision transformers (QViTs), which connect QML to the transformer architecture underlying modern large language models. We ask whether QViTs exhibit scaling behavior analogous to classical models and how this behavior changes when qubit number is included alongside dataset size and model parameters. The validation losses in our numerical image-classification experiments are well described by a joint shifted power-law model in qubit number, transformer depth, and training dataset size. Expressing this fit in terms of the classical encoder parameter budget identifies a regime in which increasing the number of qubits can compensate for fewer classical encoder parameters at comparable predicted performance. This finding is consistent with earlier observations of parameter efficiency in quantum learning models and suggests a direction for exploring possible resource savings in QML.
In this work, we study the neural scaling laws of RydbergGPT, an autoregressive transformer model trained on qubit projective measurement data gathered from interacting Rydberg atom arrays. The quantum system is known to exhibit a finite-size remnant of a critical point as the laser detuning parameter is varied. We find that near the critical point the transformer loss as a function of training dataset size is well described by a power-law with a loss floor correction. However, away from criticality the quality of the power-law description is substantially reduced. We then compare the statistical structure of both Rydberg measurements and natural-language corpora using an entropy-normalised, finite sample corrected mutual information "two-point" function. We find that near-critical statistics of the two point functions are closest to those observed in natural-language, whilst other qubit configurations far from the critical point have two-point functions that decay more rapidly. This supports the hypothesis that multi-scale dependence contributes to stable neural scaling, and that scaling behaviour should be viewed as a property of the model-data pair.
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Large Language Models (LLMs) contribute significantly to the development of conversational AI and has great potentials to assist the scientific research in various areas. This paper attempts to address the following questions: What opportunities do the current generation of generative pre-trained transformers (GPTs) offer for the developments of noisy intermediate-scale quantum (NISQ) technologies? Additionally, what potentials does the forthcoming generation of GPTs possess to push the frontier of research in fault-tolerant quantum computing (FTQC)? In this paper, we implement a QGAS model, which can rapidly propose promising ansatz architectures and evaluate them with application benchmarks including quantum chemistry and quantum finance tasks. Our results demonstrate that after a limited number of prompt guidelines and iterations, we can obtain a high-performance ansatz which is able to produce comparable results that are achieved by state-of-the-art quantum architecture search methods. This study provides a simple overview of GPT's capabilities in supporting quantum computing research while highlighting the limitations of the current GPT at the same time. Additionally, we discuss futuristic applications for LLM in quantum research.
Large Language Models (LLMs) such as GPT and LLaMA have transformed artificial intelligence, but their rapid growth has brought major challenges in computation, energy use, and scalability. Quantum computing (QC) offers a fundamentally different way to process information, with the potential to accelerate key operations in training, inference, optimization, and representation learning. This survey provides a structured and comprehensive review of how QC can support the future development of LLMs. It examines quantum algorithms, hybrid quantum-classical methods, quantum neural networks, quantum embeddings, and security applications. It also evaluates their feasibility in both the current noisy intermediate-scale quantum (NISQ) era and the future fault-tolerant era. The survey highlights current progress, identifies major technical barriers, and outlines practical research directions needed to build scalable, efficient, and secure quantum-enhanced language models.