QWaveNet: Quantum-Enhanced Wavelet Network for Time Series Forecasting

Series decomposition aims to separate long-term trajectories and periodic patterns in time series, thereby improving the specificity and interpretability of forecasting models. However, mainstream approaches usually equate this functional separation with an operational split between a smoothed baseline and fluctuating residuals. One line of methods approximates the trend via low-pass smoothing, which assumes long-term trajectories to be purely smooth and may misassign nonlinear evolution, stage-wise transitions, and structural fluctuations to the residual. The other relies on heuristic nonlinear decompositions to capture complex dynamics, but is sensitive to noise and hyperparameters, leading to unstable and mixed component boundaries. To address this issue, we propose a forecasting framework, QWaveNet. It employs a quantum convolutional neural network to learn Dynamic Evolution, a long-term structural representation beyond low-pass smoothing priors, which preserves nonlinear evolution, stage-wise transitions, and structural fluctuations more coherently, while its complementary Evolutionary Residual captures localized variations and periodic dynamics. Guided by these complementary components, QWaveNet further performs adaptive multi-scale decomposition and reconstruction to support forecasting. Experiments on multiple benchmark datasets demonstrate the effectiveness of QWaveNet.