Finding Key Nodes in Complex Networks Through Quantum Deep Reinforcement Learning.

Identifying key nodes in networks is a fundamental problem in network science. This study proposes a quantum deep reinforcement learning (QDRL) framework that integrates reinforcement learning with a variational quantum graph neural network, effectively identifying distributed influential nodes while preserving the network's fundamental topological properties. By leveraging principles of quantum computing, our method is designed to reduce model parameters and computational complexity compared to traditional neural networks. Trained on small networks, it demonstrated strong generalization across diverse scenarios. We compared the proposed algorithm with some classical node ranking and network dismantling algorithms on various synthetical and empirical networks. The results suggest that the proposed algorithm outperforms existing baseline methods. Moreover, in synthetic networks based on Erdős-Rényi and Watts-Strogatz models, QDRL demonstrated its capability to alleviate the issue of localization in network information propagation and node influence ranking. Our research provides insights into addressing fundamental problems in complex networks using quantum machine learning, demonstrating the potential of quantum approaches for network analysis tasks.