# Time Series Prediction of Open Quantum System Dynamics by Transformer Neural Networks

## TL;DR

This paper introduces a deep learning model using Transformer neural networks to predict the behavior of open quantum systems over time.

## Contribution

A novel deep learning approach using Transformers for time series prediction of open quantum system dynamics.

## Key findings

- The model achieves high-fidelity predictions for both short- and long-term system evolution.
- It generalizes well under varying initial states and coupling strengths.
- The method successfully predicts steady-state behavior, showing practical scalability.

## Abstract

The dynamics of open quantum systems play a crucial role in quantum information science. However, obtaining numerically exact solutions for the Lindblad master equation is often computationally expensive. Recently, machine learning techniques have gained considerable attention for simulating open quantum system dynamics. In this paper, we propose a deep learning model based on time series prediction (TSP) to forecast the dynamical evolution of open quantum systems. We employ the positive operator-valued measure (POVM) approach to convert the density matrix of the system into a probability distribution and construct a TSP model based on Transformer neural networks. This model effectively captures the historical evolution patterns of the system and accurately predicts its future behavior. Our results show that the model achieves high-fidelity predictions of the system’s evolution trajectory in both short- and long-term scenarios, and exhibits robust generalization under varying initial states and coupling strengths. Moreover, we successfully predicted the steady-state behavior of the system, further proving the practicality and scalability of the method.