We introduce a distributed resource allocation framework for the Quantum Internet that relies on feedback-based, fully decentralized coordination to serve multiple co-existing applications. We develop quantum network control algorithms under the mathematical framework of Quantum Network Utility Maximization (QNUM), where utility functions quantify network performance by mapping entanglement rate and quality into a joint optimization objective. We then introduce QPrimal-Dual, a decentralized, scalable algorithm that solves QNUM by strategically placing network controllers that operate using local state information and limited classical message exchange. We prove global asymptotic stability for concave, separable utility functions, and provide sufficient conditions for local stability for broader non-concave cases. To reduce control overhead and account for quantum memory decoherence, we also propose schemes that locally approximate global quantities and prevent congestion in the network. We evaluate the performance of our approach via simulations in realistic quantum network architectures. Results show that QPrimalDual significantly outperforms baseline allocation strategies, scales with network size, and is robust to latency and decoherence. Our observations suggest that QPrimalDual could be a practical, high-performance foundation for fully distributed resource allocation in quantum networks.

翻译：我们为量子互联网引入了一种分布式资源分配框架，该框架依赖基于反馈的完全去中心化协调来服务多个共存的应用。我们在量子网络效用最大化（QNUM）的数学框架下开发量子网络控制算法，其中效用函数通过将纠缠速率和质量映射到联合优化目标来量化网络性能。随后，我们提出了QPrimal-Dual算法，这是一种去中心化、可扩展的算法，通过策略性地部署仅使用本地状态信息和有限经典消息交换进行操作的网络控制器来解决QNUM问题。我们证明了在凹且可分离的效用函数下的全局渐近稳定性，并为更广泛的非凹情况提供了局部稳定性的充分条件。为了降低控制开销并考虑量子存储器退相干的影响，我们还提出了局部近似全局量并防止网络拥塞的方案。我们通过在现实量子网络架构中的仿真来评估所提方法的性能。结果表明，QPrimalDual算法显著优于基线分配策略，能够随网络规模扩展，并且对延迟和退相干具有鲁棒性。我们的观察表明，QPrimalDual有望成为量子网络中完全分布式资源分配的一个实用且高性能的基础框架。