A Framework for Distributed Resource Allocation in Quantum Networks

Abstract: 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.