Quantum Many-Body Dynamics and its Long Time Behavior with Quantum Inspired Recurrent Neural Network

Kuan-Ting Chou^1*, Daw-Wei Wang^1,2,3

¹Physics Division, National Center for Theoretical Sciences, Hsinchu, Taiwan
²Department of Physics, National Tsing Hua University, Hsinchu, Taiwan
³Center for Quantum Technology, National Tsing Hua University, Hsinchu, Taiwan

* Presenter:Kuan-Ting Chou, email:stu95.40801@gmail.com

Over the past few years, experiments in closed quantum many-body systems, such as ultracold atoms, have been developed rapidly, and provide opportunities for simulating many-body systems with dynamically controllable parameters. However, to have an efficient numerical method of real-time evolution is still a main challenge in quantum many-body systems due to its large Hilbert space. In this work, we construct a Quantum Inspired Recurrent Neural Network (QI-RNN) that can predict long-term dynamics of physical observables in general systems. Our architecture involves an encoder mapping the initial configuration of a given system to the initial hidden variables of RNN, and a decoder following the successive layers extracting the information of hidden variables and giving prediction of targeted quantities. A quantum U(1) gauge phase is introduced to remove the divergence of gradient appearing in traditional RNN, and therefore can accurately predict the long time behavior. We apply this method to 1D Ising Model and anisotropic Heisenberg model with a time-dependent transverse magnetic field. We train the model in a certain parameter regime for a short time but could simulate physical quantities (such as transverse magnetization, and total energy etc.) in some other parameter regime for a long time behavior. Our model shows a completely new approach to apply machine learning for the study of many-body dynamics.

Keywords: Quantum Many-Body System, Quantum Many-Body Dynamics, Machine Learning