The increasing number of Low Earth Orbit (LEO) satellites, driven by lower manufacturing and launch costs, is proving invaluable for Earth observation missions and low-latency internet connectivity. However, as the number of satellites increases, the number of communication links to maintain also rises, making the management of this vast network increasingly challenging and highlighting the need for clustering satellites into efficient groups as a promising solution. This paper formulates the clustering of LEO satellites as a coalition structure generation (CSG) problem and leverages quantum annealing to solve it. We represent the satellite network as a graph and obtain the optimal partitions using a hybrid quantum-classical algorithm called GCS-Q. The algorithm follows a top-down approach by iteratively splitting the graph at each step using a quadratic unconstrained binary optimization (QUBO) formulation. To evaluate our approach, we utilize real-world three-line element set (TLE/3LE) data for Starlink satellites from Celestrak. Our experiments, conducted using the D-Wave Advantage annealer and the state-of-the-art solver Gurobi, demonstrate that the quantum annealer significantly outperforms classical methods in terms of runtime while maintaining the solution quality. The performance achieved with quantum annealers surpasses the capabilities of classical computers, highlighting the transformative potential of quantum computing in optimizing the management of large-scale satellite networks.

翻译：随着制造和发射成本的降低，低地球轨道（LEO）卫星数量的不断增加，在地球观测任务和低延迟互联网连接方面展现出巨大价值。然而，卫星数量的增长导致需要维护的通信链路数量同步上升，使得这一庞大网络的管理日益复杂，凸显了将卫星聚类为高效组群作为可行解决方案的必要性。本文将LEO卫星聚类问题建模为联盟结构生成（CSG）问题，并利用量子退火技术进行求解。我们将卫星网络表示为图结构，并通过一种名为GCS-Q的混合量子-经典算法获取最优划分。该算法采用自上而下的策略，通过二次无约束二进制优化（QUBO）模型在每一步迭代中对图进行分割。为评估该方法，我们采用Celestrak提供的星链卫星真实世界三行轨道要素集（TLE/3LE）数据。通过使用D-Wave Advantage退火器和当前最先进的求解器Gurobi进行实验，结果表明量子退火器在保持解质量的同时，其运行时间显著优于经典方法。量子退火器实现的性能超越了经典计算机的能力，彰显了量子计算在优化大规模卫星网络管理方面的变革性潜力。