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 apply Lyapunov Drift Minimization (a standard technique in classical network science) to mathematically derive a natural class of scheduling policies for quantum networks minimizing the square norm of the user demand backlog. 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，有望带来众多有趣的应用，其中许多应用需要在任意用户对之间分发纠缠态。本文研究在任意纠缠交换量子网络（通常称为第一代量子网络）中，针对其通用拓扑、多商品及考虑损耗的调度问题。我们引入了一个线性代数框架，通过创建中间纠缠链路来利用量子存储器。该框架随后被用于应用李雅普诺夫漂移最小化方法（一种经典网络科学中的标准技术），从数学上推导出量子网络调度策略的一类自然形式，以最小化用户需求积压的平方范数。此外，本文提出并评估了另一类基于最大加权思想的策略，该策略在计算成本显著降低的同时，仅以轻微的性能损失为代价。通过一个专用仿真器，从信息可用性、本地化及整体网络性能角度对各类策略进行比较，该仿真器允许用户自定义网络拓扑和调度策略，以展示所提供工具在量子网络设计中的潜在应用。