Enhancing Open Quantum Dynamics Simulations Using Neural Network-Based Non-Markovian Stochastic Schr\"odinger Equation Method

TL;DR

This paper introduces a neural network-enhanced method for simulating open quantum systems, significantly reducing computational costs and improving convergence in long-time, low-temperature simulations of complex quantum models.

Contribution

It integrates CNNs, LSTMs, and iAFF techniques into NMSSE to decrease the number of trajectories needed for accurate long-time quantum dynamics simulations.

Findings

Reduced number of trajectories for long-time simulations

Enhanced convergence at low temperatures

Successful application to spin-boson and FMO models

Abstract

The Non-Markovian Stochastic Schrodinger Equation (NMSSE) offers a promising approach for open quantum simulations, especially in large systems, owing to its low scaling complexity and suitability for parallel computing. However, its application at low temperatures faces significant convergence challenges. While short-time evolution converges quickly, long-time evolution requires a much larger number of stochastic trajectories, leading to high computational costs. To this end,we propose a scheme that combines neural network techniques with simulations of the non-Markovian stochastic Schrodinger equation. By integrating convolutional neural networks (CNNs) and long short-term memory recurrent neural networks (LSTMs),along with the iterative attentional feature fusion (iAFF) technique, this approach significantly reduces the number of trajectories required for long-time simulations, particularly at low temperatures, thereby substantially lowering computational costs and improving convergence. To demonstrate our approach, we investigated the dynamics of the spin-boson model and the Fenna-Matthews-Olson (FMO) complex across a range of parameter variations.