Do Quantum Models Scale Like LLMs?
Abstract
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.
Related
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BibTeX
@misc{berman2026quantum,
title = {{Do Quantum Models Scale Like LLMs?}},
author = {David S. Berman and Ying-Jer Kao and Roger G. Melko and Alexander G. Stapleton},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20912},
eprint = {2609.20912},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20912},
}
RIS
TY - UNPB
TI - Do Quantum Models Scale Like LLMs?
AU - David S. Berman
AU - Ying-Jer Kao
AU - Roger G. Melko
AU - Alexander G. Stapleton
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20912
UR - https://arxiv.org/abs/2609.20912
AB - 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.
ER -