Quantum-Optimized Selective State Space Model for Efficient Time Series Prediction

Long-range time series forecasting remains challenging due to non-stationarity, multi-scale dependencies, and efficiency constraints in real-world Big Data settings. Transformerbased models improve accuracy by modeling global dependencies, but their quadratic complexity in sequence length and degraded performance on very long horizons limit scalability. Recent state space models (SSMs) offer linear-time inference, yet can exhibit unstable training dynamics and reduced accuracy on high-dimensional multivariate series. We propose the Quantum-Optimized Selective State Space Model (Q-SSM), a hybrid recurrent architecture in which a variational single-qubit quantum gate regulates memory updates within a linear-time SSM backbone. The gate produces smooth, bounded, and contractive dynamics that stabilize training, mitigate vanishing/exploding gradients, and enhance long-term dependency modeling without attention. Q-SSM further combines calendaraware input encoding and residual decoding to better capture seasonal patterns and reduce long-horizon drift. Experiments on six benchmarks (four ETT variants, Traffic, Exchange) show that Q-SSM achieves up to 57 % lower mean squared error (MSE) than strong Transformer and SSM baselines while retaining linear complexity, offering an accurate and efficient solution for long-horizon multivariate forecasting.