A Quantum-Classical Hybrid Framework for Multivariate Time-Series Forecasting Complexity-Fidelity Trade-offs and Limitations

2026-07-17

AI Summary

This work addresses the trade-off between model complexity and prediction fidelity in multivariate time series multi-step forecasting on noisy intermediate-scale quantum (NISQ) devices by proposing the first quantum-native hybrid framework, comprising two architectures: Quantum Reservoir Computing with Fixed reservoir (QRC-F) and Variational Quantum Feedforward (VQF-F). The approach maps temporal sequences into quantum states via uniform quantization, RY-angle encoding, cross-channel entanglement, and a fixed random unitary reservoir, and employs a shared MIMO head for non-autoregressive multi-step prediction to circumvent error accumulation. By replacing self-attention with linear transformations, the method substantially reduces parameter count while enhancing training stability and noise resilience. Empirical results demonstrate that VQF-F achieves exceptional parameter efficiency, whereas QRC-F exhibits high robustness and circuit fidelity under quantum noise.

Abstract

This paper presents a unified quantum-classical hybrid framework for multi-horizon time-series forecasting, introducing two model variants Quantum Reservoir Forecaster (QRC-F) and Variational Quantum Forecaster (VQF-F). The proposed framework investigates the complexity-fidelity trade-off of quantum forecasting under near-term NISQ hardware constraints. Continuous time-series signals are transformed into binary representations through uniform quantization and encoded into quantum states using angle encoding with parameterized RY rotation gates. Cross-channel entanglement layers capture dependencies among multiple variables. QRC-F utilizes a fixed random unitary quantum reservoir for stable, gradient-free temporal feature extraction, whereas VQF-F employs a trainable variational quantum circuit optimized through the parameter-shift rule to learn temporal and inter-variable patterns from Pauli expectation values. Both models replace computationally expensive quadratic self-attention with efficient linear transformations, reducing parameter complexity. A shared MIMO-based multi-horizon prediction head simultaneously generates forecasts across multiple horizons, avoiding error accumulation in recursive forecasting. Experimental evaluations on benchmark datasets, including ETTh1, ETTh2, ETTm1, ETTm2, Weather, electricity, and exchange-rate, demonstrate that VQF-F achieves superior training stability and parameter efficiency, while QRC-F provides enhanced robustness and circuit fidelity under quantum noise. The results establish a practical quantum-native forecasting framework with strong potential for deployment on near-term NISQ devices.

Problem

• quantum-classical hybrid
• time-series forecasting
• complexity-fidelity trade-off
• NISQ devices
• multivariate forecasting

Innovation

• quantum-classical hybrid
• variational quantum forecasting
• quantum reservoir computing
• multi-horizon time-series forecasting
• NISQ