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.
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.
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) is a mathe-matical framework that has endowed researchers with powerful methods for designing and analyzing classical communication protocols. NUM has also enabled the development of distributed algorithms for solving the resource allocation problem, while at the same time providing certain guarantees, e.g., that of fair treatment, to the users of a network. We extend here the notion of NUM to quantum networks, and propose three quantum utility functions - each incorporating a different entanglement measure. We aim both to gain an understanding of some of the ways in which quantum users may perceive utility, as well as to explore structured and theoretically-motivated methods of simultaneously servicing multiple users in distributed quantum systems. Using our quantum NUM constructions, we develop an optimization framework for networks that use the single-photon scheme for entanglement generation, which enables us to solve the resource allocation problem while exploring rate-fidelity tradeoffs within the network topologies that we consider. We learn that two of our utility functions, which are based on distillable entanglement and secret key fraction, are in close agreement with each other and produce similar solutions to the optimization problems we study. While these two utilities place a higher emphasis on end-to-end fidelity, our third utility- based on entanglement negativity - has more favorable mathematical properties, and tends to place a higher value on the rate at which users receive entangled resources. These contrasting behaviors thus provide ideas regarding the suitability of quantum network utility definitions to different quantum applications.
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.
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.
In this paper, we study the utility-cost ratio (UCR) maximization problem in quantum networks, with a particular focus on secure quantum key distribution (QKD). We propose the Quantum Utility-Cost Optimization (QUCO) algorithm to address the challenge of balancing network utility with operational and infrastructure costs. The utility of the network is measured based on the secret key fraction, a key performance metric in QKD, while the costs considered include operational and maintenance expenses, transceiver deployment, auxiliary equipment, and wavelength channel usage. The QUCO algorithm transforms the original non-convex problem into a convex optimization through a series of transformations, enabling efficient resource allocation across quantum network routes. Our simulation results, conducted on a realistic quantum network topology, demonstrate the algorithm’s ability to improve the utility-cost ratio while maintaining high network performance. The QUCO algorithm strikes a balance between minimizing costs and maintaining high end-to-end entanglement fidelity, which is effective for optimizing UCR in quantum networks.
From the perspective of user experience, when optimizing resource provisioning in networks, we have to maximize social utility, which is an abstraction of what users can obtain from the service provided by a network. In quantum networks, unlike their counterparts, circuit-switched classical networks, (i) the utility obtained by a demand is not always concave for the number of Entanglement Connections (ECs) we provision to it; and (ii) each demand requires a different amount of quantum resources over each link along the path to establish an EC. As a result, the Social Utility Maximization (SUM) problem is more challenging than in classic circuit-switched networks. In this paper, we propose an approach also called SUM to maximize social utility in quantum networks by provisioning an appropriate number of ECs (and corresponding resources) to demands. We first formulate the SUM problem and analyze it based on Lagrangian relaxation and duality techniques. Accordingly, we derive the optimal EC provisioning scheme for a given Lagrangian multiplier, depending on whether the utility function of each demand is convex, concave, or sigmoid-like. After that, a primal-dual iteration algorithm is proposed to determine the optimal EC provisioning scheme to maximize social utility. We conduct extensive simulations to demonstrate that SUM outperforms the state-of-the-art approach to maximizing quantum network throughput,i.e., EFiRAP, by up to 58.4%.