Neural Network Solution of Non-Markovian Quantum State Diffusion and Operator Construction of Quantum Stochastic Process

Non-Markovian quantum state diffusion provides a wavefunction-based framework for modeling open quantum systems. In this work, we introduce a novel machine learning approach based on an operator construction algorithm. This algorithm employs a neural network as a universal generator to reconstruct the stochastic time evolution operator from an ensemble of quantum trajectories. Unlike conventional machine learning methods that merely approximate time-dependent wavefunctions or expectation values, our operator-based approach yields broader applications and enhanced interpretability of the stochastic process. We benchmark the algorithm on the spin-boson model across diverse spectral densities, demonstrating its accuracy. Furthermore, we showcase the operator's utility in calculating absorption spectra and reconstructing reduced density matrices at extended timescales. These results establish a new paradigm for the application of machine learning in quantum dynamics.