Quantum Internetworking is a recent field that promises numerous interesting applications, many of which require the distribution of entanglement between arbitrary pairs of users. This work deals with the problem of scheduling in an arbitrary entanglement swapping quantum network - often called first generation quantum network - in its general topology, multicommodity, loss-aware formulation. We introduce a linear algebraic framework that exploits quantum memory through the creation of intermediate entangled links. The framework is then employed to mathematically derive a natural class of quadratic scheduling policies for quantum networks by applying Lyapunov Drift Minimization, a standard technique in classical network science. Moreover, an additional class of Max-Weight inspired policies is proposed and benchmarked, reducing significantly the computation cost, at the price of a slight performance degradation. The policies are compared in terms of information availability, localization and overall network performance through an ad-hoc simulator that admits user-provided network topologies and scheduling policies in order to showcase the potential application of the provided tools to quantum network design.

翻译：量子互联网是一个新兴领域，有望实现众多引人注目的应用，其中许多应用需要在任意用户对之间分配纠缠态。本文研究任意纠缠交换量子网络（通常称为第一代量子网络）中的调度问题，涵盖其一般拓扑、多商品及考虑损耗的表述形式。我们引入一个线性代数框架，通过创建中间纠缠链来利用量子存储器。随后，该框架被用于数学推导量子网络的一类自然二次调度策略，该推导基于经典网络科学中的标准技术——李雅普诺夫漂移最小化。此外，我们还提出并基准测试了另一类受最大权重启发的策略，该策略以轻微性能下降为代价，显著降低了计算成本。通过一个允许用户自定义网络拓扑和调度策略的专用模拟器，我们从信息可用性、定位及整体网络性能方面对各类策略进行比较，以展示所提供工具在量子网络设计中的潜在应用。