Quantum Recurrent Neural Networks: Predicting the Dynamics of Oscillatory and Chaotic Systems

In this study, we investigate Quantum Long Short-Term Memory and Quantum Gated Recurrent Unit integrated with Variational Quantum Circuits in modeling complex dynamical systems, including the Van der Pol oscillator, coupled oscillators, and the Lorenz system. We implement these advanced quantum machine learning techniques and compare their performance with traditional Long Short-Term Memory and Gated Recurrent Unit models. The results of our study reveal that the quantum-based models deliver superior precision and more stable loss metrics throughout 100 epochs for both the Van der Pol oscillator and coupled harmonic oscillators, and 20 epochs for the Lorenz system. The Quantum Gated Recurrent Unit outperforms competing models, showcasing notable performance metrics. For the Van der Pol oscillator, it reports MAE 0.0902 and RMSE 0.1031 for variable x and MAE 0.1500 and RMSE 0.1943 for y; for coupled oscillators, Oscillator 1 shows MAE 0.2411 and RMSE 0.2701 and Oscillator 2 MAE is 0.0482 and RMSE 0.0602; and for the Lorenz system, the results are MAE 0.4864 and RMSE 0.4971 for x, MAE 0.4723 and RMSE 0.4846 for y, and MAE 0.4555 and RMSE 0.4745 for z. These outcomes mark a significant advancement in the field of quantum machine learning.