Time-series analysis and network analysis are now used extensively in diverse areas of science. In this paper, we applythese techniques to quantum dynamics in an optomechanical system: specifically, the long-time dynamics of the mean photon number in an archetypal tripartite quantum system comprising a single-mode radiation field interacting with a two-level atom and an oscillating membrane. We also investigate a classical system of interacting Duffing oscillators which effectively mimics several of the features of tripartite quantum-optical systems. In both cases, we examine the manner in which the maximal Lyapunov exponent obtained from a detailed time-series analysis varies with changes in an appropriate tunable parameter of the system. Network analysis is employed in both the quantum and classical models to identify suitable network quantifiers which will reflect these variations with the system parameter. This is a novel approach towards (i) examining how a considerably smaller data set (the network) obtained from a long time series of dynamical variables captures important aspects of the underlying dynamics, and (ii) identifying the differences between classical and quantum dynamics.
Quantum vs. classical: A comprehensive benchmark study for predicting time series with variational quantum machine learning
Institute for Computational Physics, University of Stuttgart（斯图加特大学计算物理研究所）；Fraunhofer Institute for Manufacturing Engineering and Automation（弗劳恩霍夫制造工程和自动化研究所）；Heilbronn University of Applied Sciences（海尔布隆应用科学大学）
Hybrid Quantum-Classical Machine Learning Algorithms for Multi-Output Time-Series Forecasting at Utility Scale
The Washington Institute for STEM, Entrepreneurship, and Research (WISER)（华盛顿STEM、创业与研究研究所）；Universidad de Guadalajara（瓜达拉哈拉大学）；Oklahoma State University（俄克拉荷马州立大学）；South Asian University（南亚大学）；E.ON Digital Technology GmbH（E.ON数字技术有限公司）
