Efficient Entanglement Routing for Satellite-Aerial-Terrestrial Quantum Networks

In the era of 6G and beyond, space-aerial-terrestrial quantum networks (SATQNs) are poised to advance the development of a global-scale quantum Internet. These networks leverage free space optical satellite and aerial quantum networks to complement optical fiber-based terrestrial quantum networks to enable the distribution of high-fidelity quantum entanglement over long distances. However, establishing multi-hop end-to-end quantum entanglement remains highly challenging, not only due to time-varying link conditions and structural heterogeneity inherent in SATQNs, but also because noise in quantum channels and imperfections in quantum operations can degrade the quality of entanglement. To address this challenge, we formulate an optimization problem that maximizes SATQN throughput by jointly optimizing routing path selection and entanglement generation rates (PS-EGR) while ensuring high entanglement fidelity. The resulting problem is a mixed-integer linear programming (MILP) formulation, which is NP-hard. We propose a Benders’ decomposition (BD)-based approach to solve this problem efficiently. Specifically, the MILP is decomposed into a master problem for binary routing path selection and a subproblem for continuous entanglement generation rate optimization. Numerical results validate the effectiveness of the proposed PS-EGR scheme, offering critical insights into the optimization and deployment of SATQNs.