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Proceedings of the AAAI Symposium Series

Quantum Network Science: Linking Graph Structure to Entanglement Performance

Rawan AlMakinah, Muhammed Abdullah Canbaz

Published Nov 23, 2025• 0 citations
Publisher

Abstract

Quantum communication networks—the substrate of a future quantum Internet—demand analytical tools that account for entanglement, fidelity, and quantum-specific constraints absent from classical models. In this paper, we introduce the Quantum Network Science (QNS) framework that adapts core network metrics to the quantum setting through fidelity-, success-probability-, and capacity-aware weighting. We formalize centrality (including Quantum PageRank and continuous-time quantum-walk variants), community structure on entanglement graphs, and robustness/percolation with fidelity thresholds. The framework is validated via analytic motifs and controlled simulations on Erdős–Rényi, scale-free, and small-world topologies, as well as satellite-assisted versus fiber-only designs. Our results show that (i) fidelity weighting reorders structural importance and can reconnect networks that appear fragmented classically; (ii) heavy-tailed degree patterns improve tolerance to random failures but heighten vulnerability to targeted hub attacks; (iii) small-world shortcuts induced by long-range quantum links shrink path lengths; and (iv) overlapping “connected components” emerge from entanglement swapping, motivating revised connectivity baselines. We also discuss design implications—degree caps and hub hardening, link-type diversity, multipath routing, and buffering policies—and outline extensions to temporal and multilayer modeling that couple the quantum plane with its classical control layer. QNS thus offers a principled, measurement-oriented foundation for analyzing, comparing, and engineering resilient, high-capacity quantum networks.

DOI
10.1609/aaaiss.v7i1.36900

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Quantum communication networks—the substrate of a future quantum Internet—demand analytical tools that account for entanglement, fidelity, and quantum-specific constraints absent from classical models. In this paper, we introduce the Quantum Network Science (QNS) framework that adapts core network metrics to the quantum setting through fidelity-, success-probability-, and capacity-aware weighting. We formalize centrality (including Quantum PageRank and continuous-time quantum-walk variants), community structure on entanglement graphs, and robustness/percolation with fidelity thresholds. The framework is validated via analytic motifs and controlled simulations on Erdős–Rényi, scale-free, and small-world topologies, as well as satellite-assisted versus fiber-only designs. Our results show that (i) fidelity weighting reorders structural importance and can reconnect networks that appear fragmented classically; (ii) heavy-tailed degree patterns improve tolerance to random failures but heighten vulnerability to targeted hub attacks; (iii) small-world shortcuts induced by long-range quantum links shrink path lengths; and (iv) overlapping “connected components” emerge from entanglement swapping, motivating revised connectivity baselines. We also discuss design implications—degree caps and hub hardening, link-type diversity, multipath routing, and buffering policies—and outline extensions to temporal and multilayer modeling that couple the quantum plane with its classical control layer. QNS thus offers a principled, measurement-oriented foundation for analyzing, comparing, and engineering resilient, high-capacity quantum networks.
The realization of a large-scale Quantum Internet is a long-term objective of quantum information science, aiming to interconnect quantum devices through the reliable distribution of entanglement across long distances. Unlike classical networks, quantum networks are constrained by decoherence, probabilistic operations, and the no-cloning theorem, which fundamentally alter network design principles. This paper presents a new simulation-driven study of a scalable and resilient Quantum Internet architecture based on adaptive, entanglement-centric networking. A detailed system model is developed, incorporating realistic quantum channel noise, memory decoherence, and repeater-assisted communication. Novel fidelity-aware routing and resource-adaptive entanglement management strategies are evaluated through extensive simulations. Mathematical models, algorithmic pseudocode, and performance analysis demonstrate how adaptive control significantly improves end-to-end fidelity and network throughput under non-ideal conditions. The results provide actionable design insights for future experimental and large-scale quantum networking deployments.
The recent development of small-scale quantum networks poses the question of which network-level mechanisms could enable quantum communication to operate at scale in a future Quantum Internet. The question can be answered within a well-established framework where a quantum network is mapped into a classical weighted graph, and communication reliability is assessed using methods from network theory. Previous work relied on this framework to determine sufficient conditions for viable network-wide communication only on special network topologies, such as regular lattices, and to devise communication protocols applicable only to small- and moderate-sized real networks. Here, we overcome both limitations by introducing a family of quantum communication protocols that scale to networks with hundreds of millions of nodes. We show that the competition between increasing communication distance and path redundancy determines their large-scale behavior, and that degree heterogeneity can provide sufficient redundancy to sustain communication in small-world networks. These conclusions are supported by a systematic analysis of both real network topologies and synthetic networks, and an analytical treatment in the limit of infinitely large random scale-free graphs.
Imagine a Quantum Internet where people can freely establish physically secure communication channels or migrate quantum programs between anywhere in the world. What would it look like? Despite the very exciting recent advances around building prototypes of quantum networks, little is known about how lab-scale prototypes can be expanded into a global infrastructure that is as capacitated, robust, and cost-efficient as the digital Internet right now. Part of the difficulty lies in our lack of understanding of how the structure of a quantum network affects its capacity and performance when serving multi-commodity quantum communication demands. This article studies the problem of designing high-performance network topologies for the quantum Internet. Utilizing abstract models of the basic quantum network operations and an optimal entanglement distribution protocol, we characterize the capacity and performance of various candidate topologies for the quantum Internet, in terms of the rate of entanglement distribution between source-destination pairs and the fidelity of entangled pairs, respectively. We discuss the implications of our preliminary results, and propose directions for further investigation. As the feasibility of largescale quantum network deployment continues to increase, we hope this article can draw attention to these macroscopic design problems, such as topology design, which potentially have a profound influence on how the entire technology evolves, just as we have observed with the digital Internet in the past decades.
As quantum networks move toward multi-user architectures, a central question is how the performance of entanglement distribution scales with the numbers of network nodes NNN and active users MMM, yet existing studies use different objectives, resource assumptions, and normalizations. To account for delivery distance under multi-user demand, we define entanglement transport, which weights each delivered Bell pair meeting a fixed fidelity threshold by its endpoint separation. In a two-layer framework, (i) a resource layer measures capacity per activation slot under different aggregation regimes, and (ii) a physical layer measures service per second under implementation constraints. For matched implementations with a bounded number of activation slots per second, asymptotic-aggregation capacity sets a service ceiling, whereas achievable service must be established separately. On expanding honeycomb lattices with one random session, fixed-window entanglement-percolation constructions achieve Θ(N−1)Θ(N^{-1})Θ(N−1) entanglement transport per activation slot below their thresholds and Θ(N)Θ(\sqrt N)Θ(N​) above them. For homogeneous chains, asymptotic aggregation exceeds fixed-window capacity by a factor Θ(N2/M)Θ(N^2/M)Θ(N2/M), and in spatial expansion a noisy physical implementation achieves Θ(M/N)Θ(M/N)Θ(M/N) service per second. These examples show that entanglement-transport scaling depends not only on connectivity but also on resource aggregation and physical implementation. The framework provides a common basis on which quantum-network scaling laws can be established.
Future quantum networks will be hybrid structures, constructed from complex architectures of quantum repeaters interconnected by quantum channels that describe a variety of physical domains; predominantly optical-fiber and free-space links. In this hybrid setting, the interplay between the channel quality within network substructures must be carefully considered, and is pivotal for ensuring high-rate end-to-end quantum communication. In this work, we combine recent advances in the theory of point-to-point free-space channel capacities and end-to-end quantum network capacities in order to develop critical tools for the study of hybrid, free-space quantum networks. We present a general formalism for studying the capacities of arbitrary, hybrid quantum networks, before specifying to the regime of atmospheric and space-based quantum channels. We then introduce a class of modular quantum network architectures, which offer a realistic and readily analyzable framework for hybrid quantum networks. By considering a physically motivated, highly connected modular structure we are able to idealize network performance and derive channel conditions for which optimal performance is guaranteed. This allows us to reveal vital properties for which distance-independent rates are achieved, so that the end-to-end capacity has no dependence on the physical separation between users. Our analytical method elucidates key infrastructure demands for a future satellite-based global quantum internet, and for hybrid wired and wireless metropolitan quantum networks.
The practical utility of a quantum network depends on its ability to establish entanglement between arbitrary node pairs with quality sufficient to execute entanglement enabled tasks. This capability can be assessed globally, through aggregate performance over all node pairs, as well as locally, at the level of individual nodes. Since entanglement-based connections form a layer above the underlying physical topology, quantum connectivity is not adequately captured by classical topological connectivity metrics. To enable characterisation of the quantum connectivity at the level of the network (or its subnetworks), we introduce the quantum connectivity measure (QCM), which quantifies the average connection quality between pairs of network nodes. Further, we describe two quantities, the quantum-connected fraction (QCF) and the quantum clustering coefficient (QCC), naturally derived from the QCM, which capture important features of the functional connectivity of the quantum network at the level of the network and an individual node, respectively. These metrics of quantum connectivity depend crucially on the entanglement distribution protocol and the quantum network parameters in addition to its physical topology. We demonstrate the crucial distinction between topological and quantum connectivity, showing that even a fully connected graph can be functionally disconnected for quantum tasks if average network edge-concurrence falls below a critical threshold. These quantum connectivity metrics thus provide important tools for the design, optimization, and benchmarking of future quantum networks.