Abstract Quantum networks (QNs) will play a key role in distributed quantum information processing. As the network size increases, network-level errors like random breakdown and intentional attack are inevitable; therefore, it is important to understand the robustness of large-scale QNs, similar to what has been done for the classical counterpart—the internet. For exponential networks such as Waxman networks, errors simply re-parameterize the network and lead to a linear decrease of the quantum capacity with the probability of error. The same linear decay happens for scale-free QNs under random breakdowns, despite the previously discovered robustness in terms of the connectivity. In presence of attack, however, the capacity of scale-free QNs shows a sharp exponential decay with the increasing attack fraction. Our results apply to quantum internet based on fibers for all kinds of quantum communications and provide implications for the future construction of QNs with regard to its robustness.
Abstract Quantum networks (QNs) will play a key role in distributed quantum information processing. As the network size increases, network-level errors like random breakdown and intentional attack are inevitable; therefore, it is important to understand the robustness of large-scale QNs, similar to what has been done for the classical counterpart—the internet. For exponential networks such as Waxman networks, errors simply re-parameterize the network and lead to a linear decrease of the quantum capacity with the probability of error. The same linear decay happens for scale-free QNs under random breakdowns, despite the previously discovered robustness in terms of the connectivity. In presence of attack, however, the capacity of scale-free QNs shows a sharp exponential decay with the increasing attack fraction. Our results apply to quantum internet based on fibers for all kinds of quantum communications and provide implications for the future construction of QNs with regard to its robustness.
Quantum network is the key to enable distributed quantum information processing. As the single-link communication rate decays exponentially with the distance, to enable reliable end-to-end quantum communication, the number of nodes needs to grow with the network scale. For highly connected networks, we identify a threshold transition in the capacity as the density of network nodes increases: below a critical density the rate is almost zero, while above the threshold the rate increases linearly with the density. Surprisingly, above the threshold the typical communication capacity between two nodes is independent of the distance between them, due to multipath routing enabled by the quantum network. In contrast, for less connected networks such as scale-free networks, the end-to-end capacity saturates to constants as the number of nodes increases, and always decays with the distance. Our results are based on capacity evaluations, therefore the minimum density requirement for an appreciable capacity applies to any general protocols of quantum networks.
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.
Abstract Quantum networks allow us to harness networked quantum technologies and to develop a quantum internet. But how robust is a quantum network when its links and nodes start failing? We show that quantum complex networks based on typical noisy quantum-repeater nodes are prone to discontinuous phase transitions with respect to the random loss of operating links and nodes, abruptly compromising the connectivity of the network, and thus significantly limiting the reach of its operation. Furthermore, we determine the critical quantum-repeater efficiency necessary to avoid this catastrophic loss of connectivity as a function of the network topology, the network size, and the distribution of entanglement in the network. From all the network topologies tested, a scale-free network topology shows the best promise for a robust large-scale quantum internet.
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.
Abstract The realization of a desirably functional quantum Internet is hindered by fundamental and practical challenges such as high loss during transmission of quantum systems, decoherence due to interaction with the environment, and fragility of quantum states under measurement. We study the implications of these constraints by analyzing the limitations on the scaling and robustness of the quantum Internet. Considering quantum networks, we present practical bottlenecks for secure communication, delegated computing, and resource distribution among end nodes. In particular, we show that the device-independent quantum key distribution (DI-QKD) network of isotropic states with parameter p has a finite diameter depending on p . Motivated by the power of abstraction in graph theory (in association with quantum information theory), that allows us to consider the topology of a network of users spatially separated over long distances around the globe or separated as nodes within the small space over a processor or circuit within a same framework, we consider graph-theoretic quantifiers to assess network robustness and provide critical values of communication lines for viable communication over quantum Internet. We consider some quantum networks of practical interest, ranging from satellite-based networks connecting far-off spatial locations to currently available quantum processor architectures within computers, and analyze their robustness to perform quantum information processing tasks. Some of these tasks form primitives for delegated quantum computing, e.g., entanglement distribution and quantum teleportation, that are desirable for all scale of quantum networks, be it quantum processors or quantum Internet.
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.