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Entanglement routing in large-scale quantum networks with ground-space interconnection

Agathe Blaise, Luca Paccard, Fabrice Arnal, Laurent de Forges de Parny, S. Molin

Published Dec 1, 2025• 0 citations
OpenAlex

Abstract

Quantum Information networks (QIN) aim to interconnect quantum systems via quantum repeaters through end-to-end entanglement of qubits. The integration of both satellites and ground segments is essential to provide global connectivity, even over large distances. In this paper, we study the problem of entanglement routing in large-scale quantum networks -i.e., with a large number of nodes, with a hybrid space-ground architecture. We decompose the routing problem into two subcomponents: request scheduling and path selection, and structure our approach around two phases: a proactive and a reactive step. We design and implement an entanglement routing strategy in an emulated European quantum network, first in a custom Python-based simulator for performance forecasting, and then into the NetSquid quantum network simulator. Our work thus provides a tool allowing for a comparison between terrestrial and satellite segments in terms of successful end-to-end entanglement in a large-scale network and shows that both segments are required for optimal service. Our results indicate that, within the emulated European topology, terrestrial networks can support end-toend entanglement for approximately 35% of user pairs -the remaining pairs are too distant and suffer from prohibitive losses. In contrast, the satellite-based network achieves connectivity for up to 91% of user pairs, although some pairs remain unreachable due to a lack of simultaneous satellite visibility. However, while satellites can outperform terrestrial networks in total photon distribution, they may not be suitable for lowlatency requests if out of visibility, making ground networks essential. This highlights the complementary roles of space and terrestrial segments in quantum networking.

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Quantum Information networks (QIN) aim to interconnect quantum systems via quantum repeaters through end-to-end entanglement of qubits. The integration of both satellites and ground segments is essential to provide global connectivity, even over large distances. In this paper, we study the problem of entanglement routing in large-scale quantum networks -i.e., with a large number of nodes, with a hybrid space-ground architecture. We decompose the routing problem into two subcomponents: request scheduling and path selection, and structure our approach around two phases: a proactive and a reactive step. We design and implement an entanglement routing strategy in an emulated European quantum network, first in a custom Python-based simulator for performance forecasting, and then into the NetSquid quantum network simulator. Our work thus provides a tool allowing for a comparison between terrestrial and satellite segments in terms of successful end-to-end entanglement in a large-scale network and shows that both segments are required for optimal service. Our results indicate that, within the emulated European topology, terrestrial networks can support end-toend entanglement for approximately 35% of user pairs -the remaining pairs are too distant and suffer from prohibitive losses. In contrast, the satellite-based network achieves connectivity for up to 91% of user pairs, although some pairs remain unreachable due to a lack of simultaneous satellite visibility. However, while satellites can outperform terrestrial networks in total photon distribution, they may not be suitable for lowlatency requests if out of visibility, making ground networks essential. This highlights the complementary roles of space and terrestrial segments in quantum networking.
A large scale quantum network requires the distribution of high-fidelity end-to-end entanglement. To overcome the range limitations inherent to terrestrial fiber, a leading architecture has emerged: satellite-based sources transmitting entanglement to quantum repeaters on the ground. By bridging the gap between abstract analytical frameworks and computationally heavy numerical simulations, this paper provides the first quantitative answer to the question of such a network's achievable performance with current and near-term space technology, while accounting for entanglement swapping and purification. This is achieved by integrating a detailed physical model of a satellite-to-ground link into an analytical entanglement resource estimation framework for quantum repeaters, enabling an optimization of the end-to-end entanglement rate. Our analysis, performed across leading quantum hardware platforms, shows that Low Earth Orbit satellite constellations combined with quantum repeaters employing Neutral Atom or Nitrogen and Silicon Vacancy qubits, could enable a global quantum network, distributing entanglement over distances up to 20,000 km, sufficient for connecting any two points on Earth. This work highlights the major bottlenecks in space and quantum hardware technologies, which need to be addressed, thereby guiding informed investments necessary for enabling a large scale quantum network.
In the era of 6G and beyond, space-aerial-terrestrial quantum networks (SATQNs) are poised to advance the development of a global-scale quantum Internet. These networks leverage free space optical satellite and aerial quantum networks to complement optical fiber-based terrestrial quantum networks to enable the distribution of high-fidelity quantum entanglement over long distances. However, establishing multi-hop end-to-end quantum entanglement remains highly challenging, not only due to time-varying link conditions and structural heterogeneity inherent in SATQNs, but also because noise in quantum channels and imperfections in quantum operations can degrade the quality of entanglement. To address this challenge, we formulate an optimization problem that maximizes SATQN throughput by jointly optimizing routing path selection and entanglement generation rates (PS-EGR) while ensuring high entanglement fidelity. The resulting problem is a mixed-integer linear programming (MILP) formulation, which is NP-hard. We propose a Benders’ decomposition (BD)-based approach to solve this problem efficiently. Specifically, the MILP is decomposed into a master problem for binary routing path selection and a subproblem for continuous entanglement generation rate optimization. Numerical results validate the effectiveness of the proposed PS-EGR scheme, offering critical insights into the optimization and deployment of SATQNs.
In this article, we present SPARQ: A SPace- Air-gRound Quantum network that supports longrange quantum teleportation and superdense coding in the quantum Internet. SPARQ integrates satellites (space layer), unmanned aerial vehicles (air layer), and remote end users (ground layer) to perform end-to-end entanglement distribution. We first present the architecture of SPARQ, followed by a discussion of its potential applications as well as the challenges facing SPARQ. Next, we investigate one of SPARQ's challenges, the need for efficient routing algorithms. This challenge is particularly significant for SPARQ because of the presence of three layers with diverse distances and capabilities among the nodes, which makes the existing routing algorithms inefficient. Hence, we propose a routing strategy that adopts entanglement fidelity as a routing metric and specifies optimal end-to-end entangled paths while avoiding intensive resource usage. Experimental results demonstrate the superiority of the SPARQ architecture and the proposed routing algorithm. Specifically, SPARQ achieves up to a 5.5% improvement in entanglement fidelity, a 49% increase in entanglement distribution efficiency, and a 10-fold increase in the average number of served requests. The proposed routing algorithm also achieves up to a 7% improvement in entanglement fidelity and a 9-fold increase in the average number of served requests. Finally, we present the conclusion and future directions.
The advancement of satellite-based quantum networks shows promise in transforming global communication infrastructure by establishing a secure and reliable quantum Internet. These networks use optical signals from satellites to ground stations to distribute high-fidelity quantum entanglements over long distances, overcoming the limitations of traditional terrestrial systems. However, the complexity of satellite-based entanglement distribution and terrestrial quantum swapping in the integrated network requires joint optimization with satellite assignment, resource allocation, and path selection. To address this challenge, we introduce a hybrid quantum-classical algorithm to solve the optimization problem by leveraging the strengths of both quantum and classical computing. The original problem is decomposed into a master problem and several subproblems using Dantzig-Wolfe decomposition and linearization techniques. Through experiments, this study demonstrates the effectiveness and reliability of the proposed methods in optimizing large-scale networks and managing qubit usage compared to the classical optimization techniques. The findings provide valuable insights for designing and implementing satellite-based entanglement distribution in quantum networks, paving the way for a secure global quantum communication infrastructure.
Satellite-based quantum networks leverage the advantageous properties of optical signals from satellites to ground stations, to enable the distribution of high-fidelity quantum entanglements over vast distances, thus circumventing the limitations of traditional terrestrial-based systems. However, the satellite-based entanglement distribution coupled with terrestrial quantum swapping in the space-terrestrial integrated network becomes very complex when considering the joint optimization with satellite assignment, resource allocation, and path selections. To tackle this issue, we introduce a hybrid quantum-classical Dantzig-Wolfe decomposition technique by leveraging the strengths of both quantum and classical computing, to solve the joint optimization problem. Through a series of experiments, the paper demonstrates the efficiency and robustness of the proposed methods in addressing large-scale network optimization and balancing qubit usage. The insights generated by this work offer valuable guidance for the design and implementation of satellite-based entanglement distribution for quantum networks, thereby laying the groundwork for the realization of a secure quantum communication infrastructure on a global scale.
Quantum networks emerge as fundamental frameworks for addressing various large-scale problems. There are two primary architectures: space-based quantum networks, which deploy satellites with free space channels to interconnect users, and ground-based quantum networks, which utilize optical fibers to interconnect users. In this paper, we explore space-ground integrated quantum networks that incorporate both satellites and optical fibers into the infrastructure. This integrated network features three forms of communication: using only free space links, only ground links, or a hybrid usage of free space and ground links. We formulate the routing problem in space-ground integrated quantum networks as an integer programming and propose two solutions: using linear relaxation or a greedy algorithm. The linear relaxation method allows timely scheduling of additional entanglement purification, whereas the greedy method enables quick scheduling. Simulation results demonstrate their effective balancing between network throughput and communication fidelity.