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Computer Networks

A two-step linear programming approach for repeater placement in large-scale quantum networks

Romtham Sripotchanart, Weisheng Si, Rodrigo Neves Calheiros, Qing Cao, Tie Qiu

Published Sep 19, 2024• 4 citations
Publisher

Abstract

Thanks to the applications such as Quantum Key Distribution and Distributed Quantum Computing, the deployment of quantum networks is gaining great momentum. A major component in quantum networks is repeaters, which are essential for reducing the error rate of qubit transmission for long-distance links. However, repeaters are expensive devices, so minimizing the number of repeaters placed in a quantum network while satisfying performance requirements becomes an important problem. Existing solutions typically solve this problem optimally by formulating an Integer Linear Program (ILP). However, the number of variables in their ILPs is O ( n 2 ) , where n is the number of nodes in a network. This incurs infeasible running time when the network scale is large. To overcome this drawback, this paper proposes to solve the repeater placement problem by two steps, with each step using a linear program of a much smaller scale with O ( n ) variables. Although this solution is not optimal, it dramatically reduces the time complexity, making it practical for large-scale networks. Moreover, it constructs networks that have higher node connectivity than those by existing solutions, since it deploys slightly more number of repeaters into networks. Our extensive experiments on both synthetic and real-world network topologies verified our claims.

DOI
10.1016/j.comnet.2024.110795

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Thanks to the applications such as Quantum Key Distribution and Distributed Quantum Computing, the deployment of quantum networks is gaining great momentum. A major component in quantum networks is repeaters, which are essential for reducing the error rate of qubit transmission for long-distance links. However, repeaters are expensive devices, so minimizing the number of repeaters placed in a quantum network while satisfying performance requirements becomes an important problem. Existing solutions typically solve this problem optimally by formulating an Integer Linear Program (ILP). However, the number of variables in their ILPs is O ( n 2 ) , where n is the number of nodes in a network. This incurs infeasible running time when the network scale is large. To overcome this drawback, this paper proposes to solve the repeater placement problem by two steps, with each step using a linear program of a much smaller scale with O ( n ) variables. Although this solution is not optimal, it dramatically reduces the time complexity, making it practical for large-scale networks. Moreover, it constructs networks that have higher node connectivity than those by existing solutions, since it deploys slightly more number of repeaters into networks. Our extensive experiments on both synthetic and real-world network topologies verified our claims.
Quantum networks rely on repeaters to distribute entangled qubit pairs for applications such as quantum key distribution and distributed quantum computing. Minimizing the number of repeaters—while meeting connectivity and range constraints—is central to making deployments practical at scale. This thesis unifies three complementary lines of work toward that goal for terrestrial and non-terrestrial quantum networks. Two-Step Linear Programming (TSLP) is a scalable optimization framework that decomposes complex problems into two sequential linear programming steps to reduce computational complexity. First, a TSLP approach for repeater placement on existing infrastructure (terrestrial networks) is presented. Integer Linear Programming (ILP) is a mathematical modeling technique where variables are restricted to be integers to find the best possible outcome in a set of requirements. This work contributes a scalable optimization framework that addresses the computational limitations of traditional ILP models. While existing ILP solutions face O(n2) complexity, the proposed TSLP approach reduces this to O(n) variables. Simulation results on synthetic and real-world topologies show that TSLP dramatically decreases running time while achieving higher node connectivity through a strategic, slight increase in the number of repeaters. This advances research by enabling the design of large-scale fiber-based quantum networks that were previously computationally inaccessible. Second, a drone-based (non-terrestrial) repeater network for serving ground stations is studied. A key contribution of this work is the development of a polynomial-time, two- stage algorithm that decouples coverage and connectivity requirements. Stage 1 optimizes the coverage of ground terminals, while Stage 2 ensures the network backbone is fully connected. Third, the thesis addresses the need for fault tolerance in error-prone quantum net- works by extending the 1-connected drone model to achieve 2-connectedness. The Delaunay Triangulation with pruning, Steiner points, and pruning again (DT-PSP) is a geometry-aware heuristic that minimizes the number of required drone-based repeaters by leveraging geometric properties. The major contribution here is the introduction of the DT-PSP approach based on Delaunay Triangulation and Steiner node placement. Collectively, the proposed algorithms improve network connectivity and reduce deployment cost across diverse quantum-network settings. By bridging the gap between theoretical optimality and practical scalability, this PhD work provides a comprehensive toolkit for the real-world deployment of future large-scale quantum networks.
Long-distance quantum communication presents a significant challenge due to the degrading fidelity of transmitted qubits. Quantum repeaters are proposed to overcome this issue through Bell measurements on entangled qubit pairs. However, despite its necessity to enable wide-area quantum internet, the deployment cost of quantum repeaters can be prohibitively expensive; thus, developing a quantum repeater deployment model that can strike a balance between cost and effectiveness is essential. In this work, we present novel heuristic models to quickly determine a minimum number of quantum repeaters to deploy in large-scale networks to provide end-to-end connectivity between all end hosts. The results show that, compared to the integer linear programming approach, the heuristic methods can find near-optimal solutions while reducing the execution time from days to seconds when evaluated against several synthetic and real-world networks such as SURFnet and ESnet. As reliability is critical for any network, we demonstrate that the heuristic method can estimate deployment models to endure up to two link/node failures.
Long-distance quantum communication presents a significant challenge as maintaining the fidelity of qubits can be difficult. This issue can be addressed through the use of quantum repeaters to transmit entanglement information through Bell measurements. However, despite its necessity to enable wide-area quantum internet, the deployment cost of quantum repeaters can be prohibitively expensive, thus it is important to develop a quantum repeater deployment model that can strike a balance between cost and effectiveness. In this work, we present novel heuristic models to quickly determine a minimum number of quantum repeaters to deploy in large-scale networks to provide end-to-end connectivity between all end hosts. The results show that, compared to the linear programming approach, the heuristic methods can find near-optimal solutions while reducing the execution time from days to seconds when evaluated against several synthetic and real-world networks such as SURFnet and ESnet. As reliability is key for any network, we also demonstrate that the heuristic method can determine deployment models that can endure up to two link/node failures.
Abstract We consider the problem of deploying a quantum network on an existing fiber infrastructure, where quantum repeaters and end nodes can only be housed at specific locations. We propose a method based on integer linear programming (ILP) to place the minimal number of repeaters on such an existing network topology, such that requirements on end-to-end entanglement-generation rate and fidelity between any pair of end-nodes are satisfied. While ILPs are generally difficult to solve, we show that our method performs well in practice for networks of up to 100 nodes. We illustrate the behavior of our method both on randomly-generated network topologies, as well as on a real-world fiber topology deployed in the Netherlands.
Deploying quantum networks involves the placement of quantum repeaters, which generate entangled qubits for quantum computers to perform quantum teleportation. Besides placing repeaters on ground devices, there have been efforts towards the use of satellites or drones as repeaters. This paper considers the scenario of using drones due to their cost-efficiency and support for flexible network formation. While several issues in this scenario, such as enhancing network connectivity, have been studied, this paper addresses a new problem: how to minimize the number of drones placed in the air to cover all quantum computers on the ground and make the entire quantum network connected. Given that this problem is NP-hard, we propose a suboptimal but polynomial-time approach for it. Our approach consists of two stages. Stage 1 aims to minimize the number of drones needed to cover the ground computers, and Stage 2 aims to minimize the number of drones needed for connecting the drones returned by Stage 1. Both stages use algorithms of no more than quadratic time complexity. We conduct experiments to determine the best algorithm for the setting of quantum networks from several high-performing existing algorithms and design optimization techniques for existing algorithms. Our experiments confirm that our approach reduces the number of drones placed effectively.
Quantum networks (QNs) are a promising platform for secure communications, enhanced sensing, and efficient distributed quantum computing. However, due to the fragile nature of quantum states, these networks face significant challenges in terms of scalability. In this paper, the scaling limits of quantum repeater networks (QRNs) are analyzed. The goal of this work is to maximize the overall length, or scalability of QRNs such that long-distance quantum communications is achieved while application-specific quality-of-service (QQQoS) requirements are satisfied. In particular, a novel joint optimization framework that aims at maximizing QRN scalability, while satisfyingQQQoS constraints on the end-to-end fidelity and rate is proposed. The proposed approach optimizes the number of QRN repeater nodes, their separation distance, and the number of distillation rounds to be performed at both link and end-to-end levels. Extensive simulations are conducted to analyze the tradeoffs between QRN scalability, rate, and fidelity under gate and measurement errors. The obtained results characterize the QRN scaling limits for a given QoS requirement. The proposed approach offers a promising solution and design guidelines for future QRN deployments.