Machine learning of chaotic characteristics in classical nonlinear dynamics using variational quantum circuit

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.