On Utility-optimal Entanglement Routing in Quantum Networks

2026-03-01

AI Summary

This work addresses the joint optimization of routing and resource allocation in quantum networks, moving beyond the conventional assumption of fixed paths by explicitly incorporating routing decisions into a network utility maximization framework. The authors formulate a mixed-integer convex programming (MICP) model that takes entanglement measures—such as Negativity—as input, and develop an efficient randomized rounding-based heuristic algorithm alongside an upper-bound estimation technique to significantly enhance computational efficiency without compromising solution accuracy. Experimental results on real-world network instances demonstrate that the proposed approach achieves approximation accuracy exceeding 99.99% for most entanglement metrics, while consistently outperforming baseline methods in both computational speed and overall performance. This study successfully extends classical QoS-aware routing principles to the domain of quantum networking.

Technology Category

• Machine Learning: Quantum Machine Learning
• Planning, Routing, and Scheduling: Routing
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

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.

Problem

• entanglement routing
• quantum networks
• network utility maximization
• optimal routing
• quantum internet

Innovation

• entanglement routing
• quantum network utility maximization
• mixed-integer convex programming
• randomized rounding heuristic
• min-congestion routing