Efficient resource allocation and optical switching promise high key rates, network adaptability, and cost reduction in repeaterless quantum communication networks. However, identifying optimal switching configurations remains a significant challenge due to the combinatorial complexity. We introduce a novel graph formulation to model the physical and logical structure of repeaterless quantum networks, enabling the systematic optimization of switching strategies. The problem is posed as a linear program and solved using a column generation approach. This method enables scalable computation despite the exponential number of possible network configurations. Our results not only provide a formal foundation but also a practical algorithm for the optimization of switching. Empirical tests confirm the solver's scalability with network size, demonstrating the framework's effectiveness and laying the groundwork for future optimization of quantum network control.

翻译：高效的资源分配与光交换技术有望在无中继量子通信网络中实现高密钥率、网络适应性及成本降低。然而，由于组合复杂性，识别最优交换配置仍是一项重大挑战。我们提出了一种新颖的图论建模方法，用于刻画无中继量子网络的物理与逻辑结构，从而实现对交换策略的系统性优化。该问题被表述为线性规划模型，并通过列生成方法求解。尽管可能的网络配置数量呈指数级增长，该方法仍能实现可扩展的计算。我们的研究不仅为交换优化提供了形式化基础，还给出了实用的算法实现。实证测试验证了求解器随网络规模扩展的可伸缩性，证明了该框架的有效性，并为未来量子网络控制的优化奠定了基础。