Neural Network Approach for Non-Markovian Dissipative Dynamics of
  Many-Body Open Quantum Systems
Long Cao Liwei Ge Daochi Zhang Xiang Li Yao Wang Rui-Xue Xu YiJing Yan Xiao Zheng
Simulating the dynamics of open quantum systems coupled to non-Markovian
environments remains an outstanding challenge due to exponentially scaling
computational costs. We present an artificial intelligence strategy to overcome
this obstacle by integrating the neural quantum states approach into the
dissipaton-embedded quantum master equation in second quantization (DQME-SQ).
Our approach utilizes restricted Boltzmann machines (RBMs) to compactly
represent the reduced density tensor, explicitly encoding the combined effects
of system-environment correlations and nonMarkovian memory. Applied to model
systems exhibiting prominent effects of system-environment correlation and
non-Markovian memory, our approach achieves comparable accuracy to conventional
hierarchical equations of motion, while requiring significantly fewer dynamical
variables. The novel RBM-based DQME-SQ approach paves the way for investigating
non-Markovian open quantum dynamics in previously intractable regimes, with
implications spanning various frontiers of modern science.