Text as Dynamics: Quantum-Inspired Non-Markovian Multimodal Time-Series Forecasting

Multimodal time-series forecasting requires capturing both long-range temporal dependencies and evolving interactions between numerical observations and textual context. Most existing approaches encode text as an auxiliary representation and inject it through static fusion or local cross-modal interactions, leaving delayed and history-dependent effects to be learned only implicitly. We introduce QMUSE, a Quantum-inspired Multimodal Time Series Evolution framework that instead treats text as a time-varying driver of quantum-state evolution. QMUSE encodes numerical observations as density operators, maps textual context to a time-dependent Hamiltonian, and evolves the latent states through projected stochastic dynamics inspired by the stochastic Liouville-von Neumann equation. Learnable quantum measurements decode the evolved states into multi-step forecasts, yielding an end-to-end differentiable framework for modeling persistent, dissipative, and history-dependent cross-modal interactions on classical hardware. Experiments on nine real-world datasets demonstrate aggregate performance across domains and improvements across the majority of backbone–dataset combinations. Ablation and diagnostic analyses further verify the complementary contributions of the text-driven Hamiltonian and non-Markovian evolution, demonstrating the effectiveness of QMUSE in capturing persistent cross-modal influences.