An enhanced quantum reservoir computing framework for hydrological time series modeling

Abstract

Accurate streamflow forecasting is essential for water resource management, yet it remains challenging due to the highly non-stationary and volatile nature of hydrological time series. This study examines an enhanced Quantum Reservoir Computing (QRC) framework for one-step-ahead monthly dischage forecasting of the Buzău River across three periods. The framework implements a dual-axis rotation encoding scheme to map scalar inputs onto the Bloch sphere, coupled with a fixed, multi-layered parametric reservoir featuring a cyclic Controlled-Z (CZ) entanglement topology. Operating under a continuous state-passing strategy, the network processes historical dependencies through a single forward pass over a static 4-qubit system, shifting all learning optimization to a lightweight classical ridge regression readout. QRC achieved test NSE values of 0.693–0.738. While QNN and VQR yielded lower MAE and RMSE values across all three configurations, QRC consistently outperformed BPNN. ESN achieved slightly lower errors throughout, whereas performance comparisons with ELM and LSTM varied by configuration. The primary empirical contribution of this study is a compact, fixed-reservoir architecture that successfully avoids the iterative optimization of quantum-gate parameters.