A variational quantum circuits architecture with multi-head attention for chaotic time series prediction

Abstract

Traditional deep learning approaches that rely on analyzing single-dimensional time sequences face extraordinary challenges in predicting chaotic time sequences due to their primary properties, which include considerable nonlinearity, high sensitivity to initial conditions, and dynamic variability. This paper presents a novel prediction model for Quantum Multi-head attention (QMulti-Attn) for chaotic time sequences. The model combines a variational quantum circuit (VQC) with multi-headed self-attention mechanisms. The model is specifically designed to integrate the diversity and complexity of VQC quantum state space with multi-headed self-attention mechanisms. This enables the model to identify and handle critical dynamic features in chaotic time sequences while improving its predictive accuracy and generalization capabilities. Initially, the data that has been received is transformed into a meta group of a predetermined size. The input for QMulti-Attn consists of a multidimensional array with embedded dimensions and a time delay. The model’s capacity for chaotic time series prediction is augmented by the incorporation of the VQC. As a result, the introduction of VQC improved the model’s capacity to identify and solve intricate patterns in chaotic time sequence prediction tasks. This enhancement was achieved by maintaining the integrity of the original features and simplifying the deep network’s training process through residual connections. The long-term dependency mechanism is employed to replicate the dynamic behavior of the chaotic system. The QMulti-Attn model outperforms the Recurrent Neural Network (RNN), Time-Series Mixer (TSMixer), and Long Short-Term Memory (LSTM) models in two simulated chaotic time sequence datasets (Lorenz and Rossler) and a real chaos time sequencing dataset, Sea Clutter. The model’s standardized mean square error on the Sea Clutter test set exhibits a 7.46% relative improvement compared to TSMixer. The QMulti-Attn model synergistically integrates quantum learning with deep learning to achieve remarkable performance in predicting chaotic temporal sequences. The model is anticipated to significantly enhance our comprehension and forecasting of intricate nonlinear dynamic systems in the actual world.