Continuous Time Quantum Walk Propagation for Irregular Temporal Graph Forecasting

Abstract

Continuous time quantum walks built on graph Laplacians produce non monotonic graph propagation features through quantum interference during evolution, which classical diffusion cannot achieve. Such walks deliver a physically motivated propagation scheme for temporal graph signal modeling. We propose Quantum Walk Temporal Architecture (QWTA), which replaces classical graph propagation with a CTQW-type parameterized spectral propagator. QWTA embeds effective observation intervals into the spectral phase modulation of the propagation kernel. QWTA-Base preserves exact CTQW spectral evolution and serves as a physically faithful propagation reference. QWTA-GR further introduces phase soft clipping and gated residual fusion to stabilize propagation. The results show that explicit phase encoding of irregular time intervals, when combined with suitable stabilization, provides a physically motivated and competitive graph propagation design for temporal graph forecasting with missing historical observations.