Applications of neural networks to the simulation of dynamics of open quantum systems

• Main Authors: Bandyopadhyay, Sayantan, Huang, Zhongkai, Sun, Kewei, Zhao, Yang
• Other Authors: School of Materials Science & Engineering
• Format: Article
• Language: English
• Published: 2020
• Subjects: Engineering::Materials; Neural Networks; Open Quantum Systems
• Online Access: https://hdl.handle.net/10356/136768
• Institution: Nanyang Technological University

Despite neural networks’ success, their applications to open-system dynamics are few. In this work, non-linear autoregressive neural networks are adopted to generalize time series of expectation values of observables of interest in open quantum systems. Using Dirac-Frenkel time-dependent variation with the multiple Davydov D2 Ansatz, we obtain first stages of dynamical states of both the spin-boson model and the dissipative Landau-Zener model. With calculated data, careful training of the non-linear neural networks is performed. It is shown that the training quality of the networks is sufficient to ensure a least mean square error of 1×10-11. Subsequently, the network is cross validated by testing with additional data. Successes of the network training demonstrate that initial data of simulated open-system dynamics contain sufficient knowledge regarding its future propagation. We use the first-stage information and the trained network to predict future values of target observables in the series, and succeed with considerable accuracy.