This paper presents a quantum network routing technique based on the Partially Observable Markov Decision Process (POMDP) framework. It combines belief-state planning with graph neural networks (GNNs) to address partial observability, decoherence, and scalability challenges in dynamic quantum systems. Complex quantum network dynamics, including entanglement decay and time-varying channel noise, are encoded into a low-dimensional feature space, enabling efficient belief updates and scalable policy learning. Key elements include a hybrid GNN-POMDP architecture that learns routing policies by processing the graph-structured representation of entangled links, and a noise adaptation mechanism that fuses POMDP belief updates with GNN outputs for robust decision-making. A theoretical analysis is provided to ensure belief convergence, policy improvement, and robustness to noise. Experiments on simulated quantum networks with up to 100 nodes demonstrate that the proposed technique significantly improves routing fidelity and entanglement propagation compared to state-of-the-art baselines, particularly under high decoherence and non-stationary conditions.
