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This study demonstrates that simple linear models can accurately forecast observables in chaotic quantum many-body systems, challenging the assumption that complex nonlinear architectures like Transformers are necessary for such tasks. The findings suggest that high-fidelity prediction of quantum dynamics may be achievable through straightforward linear mappings, offering a computationally efficient alternative to classical simulation methods.
On linearity or non-linearity in machine learning for quantum chaotic dynamics
arXiv:2610.10697v1 Announce Type: cross Abstract: Accurately simulating chaotic quantum many-body dynamics remains a major computational challenge for classical methods, due to the rapid buildup and spatial spreading of entanglement during the evolution. This raises the question of whether machine learning can provide an effective alternative for predicting quantum dynamics. We address this question by formulating quantum dynamics as a time-series forecasting problem, using a few-qubit PXP chain, realizable with Rydberg-atom arrays, as a benchmark. By varying the initial state, the system spans dynamical regimes ranging from ergodic behavior to quantum many-body scarring, providing a controlled setting for testing forecasting models across qualitatively different dynamics. We compare two contrasting architectures: an expressive nonlinear Transformer and DLinear, a simple linear forecasting model. The Transformer accurately predicts dynamics in the more ergodic regime, but its performance progressively deteriorates as the initial state approaches the scarred limit. In contrast, DLinear remains accurate across the entire family of initial states, with its main deviations consisting of small high-frequency oscillations that have little effect on the overall prediction error. Remarkably, these results show that observables generated by complex quantum many-body dynamics can be forecast with high accuracy through a simple linear mapping from past to future observations. This reveals that the complexity of the underlying quantum evolution need not translate into an equally complex forecasting problem.
Abstract:Accurately simulating chaotic quantum many-body dynamics remains a major computational challenge for classical methods, due to the rapid buildup and spatial spreading of entanglement during the evolution. This raises the question of whether machine learning can provide an effective alternative for predicting quantum dynamics. We address this question by formulating quantum dynamics as a time-series forecasting problem, using a few-qubit PXP chain, realizable with Rydberg-atom arrays, as a benchmark. By varying the initial state, the system spans dynamical regimes ranging from ergodic behavior to quantum many-body scarring, providing a controlled setting for testing forecasting models across qualitatively different dynamics. We compare two contrasting architectures: an expressive nonlinear Transformer and DLinear, a simple linear forecasting model. The Transformer accurately predicts dynamics in the more ergodic regime, but its performance progressively deteriorates as the initial state approaches the scarred limit. In contrast, DLinear remains accurate across the entire family of initial states, with its main deviations consisting of small high-frequency oscillations that have little effect on the overall prediction error. Remarkably, these results show that observables generated by complex quantum many-body dynamics can be forecast with high accuracy through a simple linear mapping from past to future observations. This reveals that the complexity of the underlying quantum evolution need not translate into an equally complex forecasting problem.
Francesco Perciavalle and Agostino Gallo contributed equally to this work. 11 pages, 5 figures
Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Machine Learning (cs.LG)
arXiv:2610.10697 [quant-ph]
(or arXiv:2610.10697v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2610.10697 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 329 words
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