###### Abstract  
Quantum key distribution (QKD) is a promising technique to resist the threat against quantum computers. However, the high loss of quantum signals over a long-distance optical fiber is an obstacle for QKD in the intercontinental domain. In this context, the quantum satellite network is preferred over the terrestrial quantum optical network. Due to the mobility of satellites, the satellite topology is dynamic in the quantum satellite network, which remains a challenge for routing. In hybrid geostationary-earth-orbit (GEO)/low-earth-orbit (LEO) quantum satellite networks, the lack of an efficient scheduling scheme for GEO/LEO satellites also limits the construction of quantum satellite networks. Therefore, this paper provides a topology abstraction-based routing scheme for secret-key provisioning, where the dynamic physical topology is translated into a quasi-static abstracted topology. This scheme contributes to saving the precious secret key resources. In order to improve the success probability of long-distance QKD requests, three novel resource-scheduling heuristic algorithms are proposed in hybrid GEO/LEO quantum satellite networks. Simulation results indicate that the proposed algorithms can improve the success probability of QKD requests by 47% compared to the benchmark. quantum key distribution; quantum satellite network; routing scheme 2023251047.10.3390/e25071047.10.3390/e25071047. practical for commercial use. Therefore, the optical fiber-based QKD is not an effective way to achieve a global quantum network. The free-space QKD is expected to become a critical technique for deploying the global quantum network. Compared to the optical fiber, the quantum signal loss over the free space in a vacuum can be omitted, which makes the long-distance QKD possible. When considering the satellite-to-ground QKD, it will suffer the atmospheric loss. However, since most of the space is vacuum instead of air, the quantum signal loss over the free space is still much lower than that over an optical fiber of the same distance [10]. In 2016, a quantum low-earth-orbit (LEO) satellite, namely Micius, has successfully demonstrated the satellite-to-ground QKD [11], which proved the feasibility of the satellite QKD. Some studies have been conducted on satellite QKD strategies in the intercontinental domain. However, they mostly focused on the free-space QKD based on only a single satellite, which cannot fulfill the requirements of global scale users. Meanwhile, due to the small coverage and flyover time of a single satellite, the conventional satellite QKD strategy may bring a large secret key provisioning delay. In order to achieve practical QKD in the global scale, it is necessary to deploy the quantum satellite network. The quantum satellite network consists of several satellites, which is currently based on the trusted-relay satellite QKD scheme [12; 13; 14]. Due to the mobility nature of satellites, the physical topology of the quantum satellite network is dynamic, which is a central obstacle for its construction. The topology of the fiber-based network is static; hence, the widely studied techniques (e.g., the routing scheme) for operating the fiber-based network cannot be directly applied to the quantum satellite network. Some preliminary works have been conducted; for example, [PERSON] et al. [15] analyzed the effectiveness of quantum satellites in different constellation arrangements. However, a large number of secret keys are wasted in existing routing strategies. The lack of the efficient routing scheme for key provisioning limits the construction of quantum satellite networks. The feasibility of quantum communication between the high-orbit satellite and the ground station has been attested in [16]. The quantum GEO satellite has a larger coverage area but with a relatively low secret key rate. On the contrary, the quantum LEO satellite has a relatively high secret key rate but with the limited coverage area.