QCL-LNF: A Spatiotemporal Quantum CNN-LSTM Model for Long-Term NDVI Forecasting

The normalized difference vegetation index (NDVI), as a key remote sensing indicator for assessing vegetation growth conditions, plays a vital role in agricultural monitoring and ecological environment evaluation. In the context of global climate change, developing highly accurate and generalizable spatio-temporal NDVI forecasting models, particularly at the half-year scale, has emerged as a critical research challenge. Although deep learning methods have achieved notable progress in NDVI forecasting, they still face several limitations, particularly the complexity of temporal modeling and the insufficient ability to capture long-term dependencies. We propose a spatio-temporal quantum CNN-LSTM (QCL-LNF) model for long-term NDVI forecasting. The QCL-LNF integrates a quantum neural network (QNN), a convolutional neural network (CNN), and a long short-term memory (LSTM) network to enhance long-term NDVI forecasting performance. It leverages variational quantum circuit (VQC) to improve the modeling of high-dimensional spatio-temporal features and employs gating mechanisms to effectively fuse spatial and temporal representations. Experimental results across China demonstrate that the proposed model consistently outperforms several state-of-the-art (SOTA) methods in terms of forecasting accuracy and robustness. Consistent improvements in RMSE, MAE and R<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> across multiple forecasting horizons clearly validate its superiority for long-term NDVI prediction.