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

Yuheng Xie, Yuanchen Hao, Yuefeng Lin, Yuchen Sun, Ding Wang, Cong Guo, Na Chen, Yang Liu, Jianjun Tang

Published Oct 20, 2025• 2 citations
Publisher

Abstract

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.

DOI
10.1364/oe.570196

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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.
Efficient and scalable quantum key scheduling remains a critical challenge in trusted-relay Quantum Key Distribution (QKD) networks due to imbalanced key resource utilization, dynamic key consumption, and topology-induced congestion. This paper presents a Q-learning-based adaptive routing framework designed to optimize quantum key delivery in dynamic QKD networks. The model formulates routing as a Markov Decision Process, with a compact state representation that combines the current node, destination node, and discretized key occupancy levels. Reward function is designed to jointly penalize resource imbalance and rapid key depletion while promoting traversal through links with sustainable key generation, guiding the agent toward balanced and congestion-aware decisions. Compared to Dijkstra, the Q-learning scheduler achieves significantly lower delivery latency, more effective key resource utilization, and greater reliability: maintaining 45.8 vs 118.5 hops in average delay under heavy load, sustaining 74.5\% vs 61.5\% in average key utilization, and reducing the failure ratio to 7.2\% vs 41.5\%, collectively confirming its advantages in scalability, congestion resilience, and resource-efficient decision making.
Due to the unavailability of quantum repeaters, end-to-end secret keys need to be relayed in a hop-by-hop manner using so called trusted nodes in long-distance QKD networks. Therefore, a sufficient number of secret keys is required between all QKD devices along the path until the destination node is reached. As key generation rates are typically limited to a few kbps depending on link lengths, constraint-based routing algorithms considering key availability levels are desirable. We show that centralized routing based on Deep Reinforcement Learning (DRL) combined with Graph Neural Networks (GNNs) is able to reduce blockings and enhance load-balancing compared to conventional shortest path algorithms. Additionally, because of the training on random topologies, the agent is able to act in topologies unseen during training.
Routing is a challenging problem in quantum key distribution (QKD)-secured optical networks (QKD-ONs) and involves the selection of an appropriate route that establishes a secure path between the QKD nodes for secret key distribution. Deep reinforcement learning (DRL) is a promising approach for solving decision-making problems in complex networking environments such as QKD-ONs. By leveraging the capabilities of DRL algorithms, the routing decisions can be optimized to enhance network performance. This paper proposes a DRL-based solution for routing in QKD-ONs that enables the routing agent to learn and adapt to changing network conditions by understanding the networking environment. The performance of the proposed scheme is compared with the baseline schemes on NSFNET in terms of blocking probability. Simulation results indicate that compared to the baseline schemes (shortest path (SP) and hop count (HC)), the proposed DRL-based routing scheme reduces the blocking by 14.31% and 8%, respectively.
Quantum Key Distribution (QKD) networks guarantee information-theoretical security of exchanged keys, but key rates are still limited. This makes efficient and adaptive routing a critical challenge, especially in meshed topologies without quantum repeaters. Conventional shortest path routing approaches struggle to cope with dynamic key store filling levels and changes in network topologies, which leads to load imbalance and blocked connections. In this work, we propose an adaptive routing framework based on Deep Reinforcement Learning (DRL) for hop-wise end-to-end routing in unknown meshed QKD networks. The agent leverages Graph Attention Networks (GATs) to process the network states of varying topologies, enabling generalization across previously unseen meshed networks without topology-specific retraining. The agent is trained on random graphs with 10 to 20 nodes and learns a routing policy that explicitly balances key consumption across the network by utilizing a reward function that is based on the entropy of key store filling levels. We evaluate the proposed approach on the 14-node NSFNET topology under time-varying traffic demands. Simulation results demonstrate that the DRL-based routing significantly outperforms hop-based and weighted shortest path benchmarks, achieving up to a 18.7% increase in mean key store filling levels while completely avoiding key store depletion. These results highlight the potential of graph-based DRL methods for scalable, adaptive, and resource-efficient routing in future QKD networks.
With the continuous development of quantum computing technology, Quantum Key Distribution (QKD) is an important means of secure communication in the post-quantum era. However, the high cost of trusted routing relays in QKD networks has hindered its widespread adoption in power systems. Reducing costs is the key to the popularization of QKD in large-scale data grid scenarios. Therefore, this paper proposes a routing scheme for QKD network in a hybrid trusted environment. Our scheme is based on SDN architecture, utilizing the characteristics of QKD network in hybrid trusted environment, through prioritizing the selection of trusted paths (composed entirely of trusted quantum nodes) and backup selection of hybrid trusted paths (composed of both trusted and semi-trusted quantum nodes), implementing a unified dynamic routing strategy to obtain the optimal quantum routing path. Furthermore, by collecting topology information and real-time link status of the power grid, a calculation method for the number of paths and link costs is proposed to maximize load balancing in the network. Finally, the simulation results demonstrate that our scheme outperforms routing schemes relying solely on trusted quantum nodes for key distribution, as well as other cooperative routing schemes involving semi-trusted quantum nodes, in terms of success rate of distribution and load balancing.
Quantum routing is crucial for future networks as it utilizes entanglement and swapping to establish efficient communication paths between nodes. Although machine learning has transformed various industries, its integration with quantum networking remains relatively underexplored. To address this gap, we present the Deep Quantum Routing Agent (DQRA), an innovative deep reinforcement learning framework that optimizes routing paths to maximize request fulfillment within constrained time windows. Our approach integrates a neural network with a qubit-preserving shortest-path algorithm, employing a reward-based training system to enhance connection success rates. Extensive experiments show DQRA achieves over 80% routing success in resource-limited networks and maintains approximately 60% effectiveness under challenging single-repeater conditions. Importantly, the model demonstrates polynomial-time complexity, ensuring scalable deployment and effectively merging machine learning with quantum network optimization