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Machine learning of chaotic characteristics in classical nonlinear dynamics using variational quantum circuit |
| Sheng-Chen Bai(白生辰) and Shi-Ju Ran(冉仕举)† |
| Center for Quantum Physics and Intelligent Sciences, Department of Physics, Capital Normal University, Beijing 100048, China |
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Abstract Replicating the chaotic characteristics inherent in nonlinear dynamical systems via machine learning (ML) is a key challenge in this rapidly advancing interdisciplinary field. In this work, we explore the potential of variational quantum circuits (VQC) for learning the stochastic properties of classical nonlinear dynamical systems. Specifically, we focus on the one- and two-dimensional logistic maps, which, while simple, remain under-explored in the context of learning dynamical characteristics. Our findings reveal that, even for such simple dynamical systems, accurately replicating long-term characteristics is hindered by a pronounced sensitivity to overfitting. While increasing the parameter complexity of the ML model typically enhances short-term prediction accuracy, it also leads to a degradation in the model's ability to replicate long-term characteristics, primarily due to the detrimental effects of overfitting on generalization power. By comparing the VQC with two widely recognized classical ML techniques, which are long short-term memory (LSTM) networks for time-series processing and reservoir computing, we demonstrate that VQC outperforms these methods in terms of replicating long-term characteristics. Our results suggest that for the ML of dynamics, it is demanded to develop more compact and efficient models (such as VQC) rather than more complicated and large-scale ones.
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Received: 15 April 2025
Revised: 12 June 2025
Accepted manuscript online: 03 July 2025
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PACS:
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03.67.Ac
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(Quantum algorithms, protocols, and simulations)
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07.05.Mh
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(Neural networks, fuzzy logic, artificial intelligence)
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05.45.-a
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(Nonlinear dynamics and chaos)
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| Fund: Sheng-Chen Bai is grateful to Qing Lv, Peng-Fei Zhou, Yong Qing, Zhang-Xu Chen, Guo-Dong Cheng, Ke Li, Rui Hong, Ying Lu, Yi-Cheng Tang, and Yu-Jia An for helpful discussions. Project supported in part by Beijing Natural Science Foundation (Grant No. 1232025), Peng Huanwu Visiting Professor Program, and Academy for Multidisciplinary Studies, Capital Normal University. |
Corresponding Authors:
Shi-Ju Ran
E-mail: sjran@cnu.edu.cn
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Cite this article:
Sheng-Chen Bai(白生辰) and Shi-Ju Ran(冉仕举) Machine learning of chaotic characteristics in classical nonlinear dynamics using variational quantum circuit 2026 Chin. Phys. B 35 020303
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