Neural Network Approach for Non-Markovian Dissipative Dynamics of Many-Body Open Quantum Systems

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.