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

## TL;DR

The paper introduces Q-SSM, a hybrid quantum-classical model that enhances long-range time series forecasting by improving stability and efficiency through quantum gating, outperforming existing models on benchmark datasets.

## Contribution

It presents a novel quantum-optimized state space model that replaces attention with a variational quantum circuit, improving stability and long-term dependency modeling in time series prediction.

## Key findings

- Q-SSM outperforms classical models on benchmarks
- Quantum gating improves training stability
- Enhanced long-term dependency capture

## 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.