Spatial prediction of reservoir parameters, especially permeability, is crucial for oil and gas exploration and development. However, the wide range and high variability of permeability prevent existing methods from providing reliable predictions. For the first time in subsurface spatial prediction, this study presents a quantum-enhanced long short-term memory with attention (QLSTMA) model that incorporates variational quantum circuits (VQCs) into the recurrent cell. Using quantum entanglement and superposition principles, the QLSTMA significantly improves the ability to predict complex geological parameters such as permeability. Two quantization structures, QLSTMA with Shared Gates (QLSTMA-SG) and with Independent Gates (QLSTMA-IG), are designed to investigate and evaluate the effects of quantum structure configurations and the number of qubits on model performance. Experimental results demonstrate that the 8-qubit QLSTMA-IG model significantly outperforms the traditional long short-term memory with attention (LSTMA), reducing Mean Absolute Error (MAE) by 19% and Root Mean Squared Error (RMSE) by 20%, with particularly strong performance in regions featuring complex well-logging data. These findings validate the potential of quantum-classical hybrid neural networks for reservoir prediction, indicating that increasing the number of qubits yields further accuracy gains despite the reliance on classical simulations. This study establishes a foundational framework for the eventual deployment of such models on real quantum hardware and their extension to broader applications in petroleum engineering and geoscience.