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 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.

arXiv:2207.11821Jul 19, 20220 citations

LP Relaxation-Based Approximation Algorithms for Maximizing Entangled Quantum Routing Rate

Tu N. Nguyen, Dung H. P. Nguyen, Dang H. Pham +2 more

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 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.

International Conference on CommunicationsMay 16, 20225 citations

On Utility-Optimal Entanglement Routing in Quantum Networks

Sounak Kar, Arpan Mukhopadhyay

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.

International Conference on Quantum Communications, Networking, and Computing (QCNC)Apr 6, 20260 citations

On Utility-optimal Entanglement Routing in Quantum Networks

Sounak Kar, Arpan Mukhopadhyay

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.

quant-pharXiv:2603.01197Mar 3, 20260 citations

Entanglement Routing Based on Fidelity Curves

Bruno Coelho Coutinho, Monteiro, Raul, Luís Bugalho +1 more

How to efficiently distribute entanglement over large-scale quantum networks is still an open problem that greatly depends on the technology considered. In this work, we consider quantum networks where each link is characterized by a trade-off between the entanglement generation rate and fidelity. For such networks, we look at the two following problems: the one of finding the best path to connect any two given nodes, and the problem of finding the best starting node in order to connect three nodes in the network multipartite entanglement routing. Two entanglement distribution models are considered: one where entangled qubits are distributed one at a time, and a flow model where a large number of entangled qubits are distributed simultaneously. The paper proposes of a quite general methodology that uses continuous fidelity curves (i.e., entanglement generation fidelity vs. rate) as the main routing metric. Combined with multi-objective path-finding algorithms, the fidelity curves describing each link allow finding a set of paths that maximize both the end-to-end fidelity and the entanglement generation rate. For the link models and networks considered, it is proven that the algorithm always converges to the optimal solution. It is also shown through simulation that the execution time grows polynomially with the number of network nodes (growing with a power between $1$ and $1.4$ , depending on the network)How to efficiently distribute entanglement over large-scale quantum networks is still an open problem that greatly depends on the technology considered. In this work, we consider quantum networks where each link is characterized by a trade-off between the entanglement generation rate and fidelity. For such networks, we look at the two following problems: the one of finding the best path to connect any two given nodes, and the problem of finding the best starting node in order to connect three nodes in the network multipartite entanglement routing. Two entanglement distribution models are considered: one where entangled qubits are distributed one at a time, and a flow model where a large number of entangled qubits are distributed simultaneously. The paper proposes of a quite general methodology that uses continuous fidelity curves (i.e., entanglement generation fidelity vs. rate) as the main routing metric. Combined with multi-objective path-finding algorithms, the fidelity curves describing each link allow finding a set of paths that maximize both the end-to-end fidelity and the entanglement generation rate. For the link models and networks considered, it is proven that the algorithm always converges to the optimal solution. It is also shown through simulation that the execution time grows polynomially with the number of network nodes (growing with a power between $1$ and $1.4$, depending on the network)

arXiv:2303.12864Mar 22, 20231 citation

A Heuristic for Entanglement Routing in Quantum Networks

Wei-Hsun Huang, Dung H. P. Nguyen, Ting-Xiu Kuo +3 more

Due to the fact that quantum networks can provide higher security in communications, many related issues have been presented and addressed recently. One of the most important issues is to study the routing in quantum networks with multiple source-destination pairs while maximizing the total end-to-end entanglement rate. In previous studies, the shortest paths are typically selected as the entanglement paths for a source-destination pair to increase the total end-to-end entanglement rate. However, this approach is only efficient once the network resources are sufficient. Moreover, source-destination pairs only require a specific entanglement rate rather than the shortest paths. Therefore, in this paper, we suppose that each source-destination pair requires an upper bound of the entanglement rate. Under this assumption, a novel problem is proposed to construct entanglement paths for a set of multiple source-destination pairs such that the total end-to-end entanglement rate is maximized. We then propose a greedy algorithm to solve the problem. Finally, the simulation is conducted to evaluate the performance of the proposed algorithm.Due to the fact that quantum networks can provide higher security in communications, many related issues have been presented and addressed recently. One of the most important issues is to study the routing in quantum networks with multiple source-destination pairs while maximizing the total end-to-end entanglement rate. In previous studies, the shortest paths are typically selected as the entanglement paths for a source-destination pair to increase the total end-to-end entanglement rate. However, this approach is only efficient once the network resources are sufficient. Moreover, source-destination pairs only require a specific entanglement rate rather than the shortest paths. Therefore, in this paper, we suppose that each source-destination pair requires an upper bound of the entanglement rate. Under this assumption, a novel problem is proposed to construct entanglement paths for a set of multiple source-destination pairs such that the total end-to-end entanglement rate is maximized. We then propose a greedy algorithm to solve the problem. Finally, the simulation is conducted to evaluate the performance of the proposed algorithm.

International Conference on Applied System InnovationApr 21, 20230 citations

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