Abstract:Federated learning (FL), as an emerging distributed machine learning paradigm, enables collaborative model training across institutions and devices by retaining data locally on clients and exchanging only model parameters or gradients. However, existing client selection strategies exhibit notable limitations in large-scale heterogeneous environments. Random selection results in unstable and slow convergence, weighted policies based on data scale or computational resources may fail to guarantee global optimality, and traditional privacy preservation mechanisms may become ineffective under quantum computing threats. Moreover, achieving a proper balance among efficiency, security, and fairness remains challenging. To address these issues, this study proposes a client selection framework based on the quantum approximate optimization algorithm (QAOA). In this framework, the client selection problem is formulated as a quantum combinatorial optimization problem and is efficiently solved through a hybrid quantum-classical optimization process to obtain near-optimal solutions. In addition, the quantum secure multi-party computation (QSMPC) protocol is integrated to safeguard gradient updates, effectively preventing gradient inversion and eavesdropping attacks during the training process. Experimental evaluations on multiple benchmark datasets demonstrate that, compared with classical baseline methods, the proposed method improves model precision by approximately 2%–5%, accelerates convergence by 27%–44%, and significantly enhances client fairness. These results confirm the application potential of quantum optimization in federated learning. Furthermore, this study provides a novel methodological perspective for efficient client selection in heterogeneous environments and establishes both theoretical and practical foundations for deploying quantum-secure privacy-preserving mechanisms in distributed machine learning.