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arXiv:2603.01197

On Utility-optimal Entanglement Routing in Quantum Networks

Sounak Kar, Arpan Mukhopadhyay

quant-phcs.NISubmitted Mar 1, 2026• Announced Mar 3, 2026• 0 citations• Revised Mar 11, 2026 (v2)
v1 · Mar 1, 2026v2 · Mar 11, 2026
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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.

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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.
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.
Network utility maximization (NUM) addresses the problem of allocating resources fairly within a network and explores the ways to achieve optimal allocation in real-world networks. Although extensively studied in classical networks, NUM is an emerging area of research in the context of quantum networks. In this work, we consider the quantum network utility maximization (QNUM) problem in a static setting, where a user's utility takes into account the assigned quantum quality (fidelity) via a generic entanglement measure, as well as the corresponding rate of entanglement generation. Under certain assumptions, we demonstrate that the QNUM problem can be formulated as an optimization problem with the rate allocation vector as the only decision variable. Using a change-of-variable technique known in the field of geometric programming, we then establish sufficient conditions under which this formulation can be reduced to a convex problem: a class of optimization problems that can be solved efficiently and with certainty even in high dimensions. We further show that this technique preserves convexity, enabling us to formulate convex QNUM problems in networks where some routes have certain entanglement measures that do not readily admit convex formulation while others do. This allows us to compute the optimal resource allocation in networks where heterogeneous applications run over different routes.
There will be a fast-paced shift from conventional network systems to novel quantum networks that are supported by the quantum entanglement and teleportation, key technologies of the quantum era, to enable secured data transmissions in the next-generation of the Internet. Despite this prospect, migration to quantum networks cannot be done at once, especially on the aspect of quantum routing. In this paper, we study the maximizing entangled routing rate (MERR) problem. In particular, given a set of demands, we try to determine entangled routing paths for the maximum number of demands in the quantum network while meeting the network's fidelity. We first formulate the MERR problem using an integer linear programming (ILP) model to capture the traffic patent for all demands in the network. We then leverage the theory of relaxation of ILP to devise two efficient algorithms including HBRA and RRA with provable approximation ratios for the objective function. To deal with the challenge of the combinatorial optimization problem in big scale networks, we also propose the path-length-based approach (PLBA) to solve the MERR problem. Using both simulations and an open quantum network simulator platform to conduct experiments with real-world topologies and traffic matrices, we evaluate the performance of our algorithms and show up the success of maximizing entangled routing rate.
There will be a fast-paced shift from conventional network systems to novel quantum networks that are supported by the quantum entanglement and teleportation, key technologies of the quantum era, to enable secured data transmissions in the next-generation of the Internet. Despite this prospect, migration to quantum networks cannot happen all at once, especially when it comes to quantum routing. In this paper, we focus on the maximizing entanglement routing rate (MERR) problem, which aims to determine entangled routing paths for the maximum number of demands in the quantum network while meeting the network's fidelity. To tackle this problem, we first formulate the MERR problem using an integer linear programming (ILP) model. We then leverage the method of linear programming relaxation to devise two efficient algorithms, including the half-based rounding algorithm (HBRA) and the randomized rounding algorithm (RRA) with a provable approximation ratio for the objective function. Furthermore, to address the challenge of the combinatorial optimization problem in big scale networks, we also propose the path-length-based approach (PLBA) to solve the MERR problem. Finally, we evaluate the performance of our algorithms and show up the success of maximizing the entanglement routing rate.
Quantum networks are essential infrastructure for enabling large-scale and long-distance quantum communications but face significant challenges in routing optimization and resource allocation due to their probabilistic nature and quantum resource limitations. Existing approaches typically tackle these problems in isolation, often by simply applying classical routing algorithms, maximizing the overall profit to allocate resources without considering fairness, or improving fairness in an ad-hoc way without a rigorous model. This paper proposes a general framework to systematically address these challenges. First, we conduct a thorough analysis of quantum network metrics using routing algebra as the mathematical foundation, and design provably optimal routing algorithms to tackle the unique challenges arising from their probabilistic characteristics. Second, we formulate an optimization model that simultaneously considers fairness among concurrent requests while respecting various quantum resource constraints, and design efficient near-optimal heuristics to solve it. The proposed framework provides both theoretical insights and practical solutions for the design and management of future quantum networks.
Quantum networks are essential infrastructure for enabling large-scale and long-distance quantum communications but face significant challenges in routing optimization and resource allocation due to their probabilistic nature and quantum resource limitations. Existing approaches typically tackle these problems in isolation, often by simply applying classical routing algorithms, maximizing the overall profit to allocate resources without considering fairness, or improving fairness in an ad-hoc way without a rigorous model. This paper proposes a general framework to systematically address these challenges. First, we conduct a thorough analysis of quantum network metrics using routing algebra as the mathematical foundation, and design provably optimal routing algorithms to tackle the unique challenges arising from their probabilistic characteristics. Second, we formulate an optimization model that simultaneously considers fairness among concurrent requests while respecting various quantum resource constraints, and design efficient near-optimal heuristics to solve it. The proposed framework provides both theoretical insights and practical solutions for the design and management of future quantum networks.