Efficient routing algorithm for trusted relay quantum key distribution networks via quantum reinforcement learning

Trusted relay quantum key distribution networks (TR-QKDNs) have emerged as one of the most practical solutions for implementing large-scale QKDNs. The development of efficient routing algorithms is crucial to ensure adaptability to diverse network parameters and topologies. However, current approaches suffer from multiple limitations, including insufficient consideration of key influencing factors, excessive reliance on manually configured parameters, and scalability bottlenecks caused by the exponential complexity of classical algorithms. In this paper, we propose a quantum reinforcement learning-based routing algorithm, named hybrid quantum deep deterministic policy gradient (HQ-DDPG) that integrates a custom-designed quantum neural network (QNN) with the deep deterministic policy gradient (DDPG), to intelligently balance multiple influencing factors and dynamically optimize routing decisions in TR-QKDNs. To reduce computational complexity, we further utilize a quantum single-source shortest path (QSSP) algorithm to compute the optimal routing path. Training results demonstrate that the proposed HQ-DDPG outperforms DDPG in terms of performance metrics, achieving nearly double the training convergence speed while reducing resource requirements by approximately 45 times and exhibiting superior network expressiveness. In typical network topology tests, the proposed algorithm consistently maintains a quantum key delivery ratio above 91.35% under high-load demand, significantly surpassing both DDPG and optimized link state routing (OLSR). Finally, leveraging distributed quantum computing, the proposed QNN enables efficient solutions for large-scale TR-QKDN problems with fewer quantum resources.