Quantum networks are envisioned to enable reliable distribution and manipulation of quantum information across distances, forming the foundation of a future quantum internet. The fair and efficient allocation of communication resources in such networks has been addressed through the quantum network utility maximization (QNUM) framework, which optimizes network utility under the assumption of predetermined routes for competing user demands. In this work, we relax this assumption and aim to identify optimal routes that correspond to the maximum achievable network utility. Specifically, we formulate the single-path utility-based entanglement routing problem as a Mixed-Integer Convex Program (MICP). The formulation is exact when negativity is chosen as the entanglement measure for utility quantification or the network supports sufficiently high entanglement generation rates across demands. For other entanglement measures considered, the formulation approximates the problem with over 99.99% accuracy on evaluated real-world examples. To improve computational tractability, we propose a randomized rounding-based heuristic and an upper bound via the relaxation of the MICP. Furthermore, based on min-congestion routing, we introduce an alternative randomized heuristic and upper bound. This heuristic is computationally faster, while both the heuristic and the upper bound often outperform their counterparts on considered real-world networks. Our work provides the framework for extending classical flow-based and quality of service-aware routing concepts to quantum networks.

翻译：量子网络被设想为实现量子信息在远距离间的可靠分发与操控，构成未来量子互联网的基础。此类网络中通信资源的公平高效分配问题已通过量子网络效用最大化框架得到处理，该框架在假设竞争性用户需求具有预定路由的前提下优化网络效用。本研究放宽该假设，旨在识别与最大可达网络效用相对应的最优路由。具体而言，我们将基于单路径效用的纠缠路由问题建模为混合整数凸规划。当选择负性作为效用量化的纠缠度量或网络支持足够高的跨需求纠缠生成率时，该模型为精确表述。对于所考虑的其他纠缠度量，该模型在评估的真实案例中以超过99.99%的精度逼近原问题。为提升计算可处理性，我们提出基于随机舍入的启发式算法及通过松弛混合整数凸规划获得的上界。此外，基于最小拥塞路由，我们引入了另一种随机启发式算法与上界。该启发式算法计算速度更快，且在处理所考察的真实网络时，其算法性能与上界结果常优于对应方法。本研究为将经典基于流及服务质量感知的路由概念扩展至量子网络提供了框架基础。