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

2025-08-29

AI Summary

Long-term time series forecasting faces challenges in jointly addressing non-stationarity, multi-scale dependency modeling, and computational efficiency. Existing Transformer-based models (e.g., Autoformer, Informer) suffer from quadratic complexity and degraded long-horizon performance; while state space models (e.g., S-Mamba) achieve linear complexity, they exhibit training instability, sensitivity to initialization, and limited robustness for multivariate settings. This paper proposes the Quantum-optimized Selective State Space Model (Q-SSM), which innovatively incorporates a variational quantum circuit (RY-RX ansatz) as a lightweight gating mechanism. The quantum expectation value adaptively modulates memory updates, preserving O(L) recurrence efficiency while significantly improving training stability and long-range dependency modeling. Evaluated on ETT, Traffic, and Exchange Rate benchmarks, Q-SSM consistently outperforms LSTM, TCN, Reformer, Autoformer, Informer, and S-Mamba—delivering superior accuracy and robustness in multivariate long-horizon forecasting.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Intelligent Robots: State Estimation

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Long-range time series forecasting remains challenging, as it requires capturing non-stationary and multi-scale temporal dependencies while maintaining noise robustness, efficiency, and stability. Transformer-based architectures such as Autoformer and Informer improve generalization but suffer from quadratic complexity and degraded performance on very long time horizons. State space models, notably S-Mamba, provide linear-time updates but often face unstable training dynamics, sensitivity to initialization, and limited robustness for multivariate forecasting. To address such challenges, we propose the Quantum-Optimized Selective State Space Model (Q-SSM), a hybrid quantum-optimized approach that integrates state space dynamics with a variational quantum gate. Instead of relying on expensive attention mechanisms, Q-SSM employs a simple parametrized quantum circuit (RY-RX ansatz) whose expectation values regulate memory updates adaptively. This quantum gating mechanism improves convergence stability, enhances the modeling of long-term dependencies, and provides a lightweight alternative to attention. We empirically validate Q-SSM on three widely used benchmarks, i.e., ETT, Traffic, and Exchange Rate. Results show that Q-SSM consistently improves over strong baselines (LSTM, TCN, Reformer), Transformer-based models, and S-Mamba. These findings demonstrate that variational quantum gating can address current limitations in long-range forecasting, leading to accurate and robust multivariate predictions.

Problem

• Addressing long-range time series forecasting challenges
• Improving efficiency and stability in multivariate predictions
• Overcoming limitations of Transformer and state space models

Innovation

• Integrates state space dynamics with variational quantum gate
• Uses parametrized quantum circuit for adaptive memory updates
• Provides lightweight quantum alternative to attention mechanisms