Quantum network is fragile to disturbances when qubits are transmitted through quantum channel. Reliability is an essential requirement for a quantum network and even the future quantum internet. A metric is needed to describe the reliability of a quantum network to build a robust infrastructure and communication protocols. In this work, we combined quantum physical parameters with graphic algebraic connectivity to indicate the transmission throughput of a grid quantum network. This metric can be extended to multiple equal point-to-point distance topology. This work also studies how to tune specific physical parameters to maintain or even increase connectivity when nodes or edges are removed from a network. Using this metric, resources consumption are compared.
Quantum network is fragile to disturbances when qubits are transmitted through quantum channel. Reliability is an essential requirement for a quantum network and even the future quantum internet. A metric is needed to describe the reliability of a quantum network to build a robust infrastructure and communication protocols. In this work, we combined quantum physical parameters with graphic algebraic connectivity to indicate the transmission throughput of a grid quantum network. This metric can be extended to multiple equal point-to-point distance topology. This work also studies how to tune specific physical parameters to maintain or even increase connectivity when nodes or edges are removed from a network. Using this metric, resources consumption are compared.
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.
The efficacy of a communication network hinges upon both its physical architecture and the protocols that are employed within it. In the context of quantum communications, there exists a fundamental rate-loss trade-off for point-to-point quantum channels such that the rate for distributing entanglement, secret keys, or quantum states decays exponentially with respect to transmission distance. Quantum networks are the solution to overcome point-to-point limitations, but they simultaneously invite a challenging open question: How should quantum networks be designed to effectively and efficiently guarantee high rates? Now that performance and physical topology are inexorably linked, this question is not easy, but the answer is essential for a future quantum internet to be successful. In this work, we offer crucial insight into this open question for complex optical-fiber quantum networks. Using realistic descriptions of quantum networks via random network models and practical end-to-end routing protocols, we reveal critical phenomena associated with large-scale quantum networks. Our work reveals the weaknesses of applying single-path routing protocols within quantum networks, observing an inability to achieve reliable rates over long distances. Adapting algorithms for multipath routing, we employ an efficient and practical multipath routing algorithm capable of boosting performance while minimizing costly quantum resources.
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.
Quantum networking has been attracting growing attention in both academia and industry during recent years. Although many routing protocols have been proposed to optimize the network layer of quantum networks, another key networklayer problem is under-explored: the topology design problem. Existing work is limited to using structure topologies such as a ring or grid, using randomly generated topologies, or using existing Internet backbone infrastructure. Whether these choices are desired for quantum networks is not fully explained. We propose the quantum network topology design problem, for which a set of end users are given and we need to compute a set of repeaters and their locations and connectivities while ensuring the network performance, such as throughput, is optimized under the same infrastructure cost (e.g., number of repeaters). We present the methodology of designing topologies based on the unique characteristics of entanglement distribution networks and propose an algorithm called TriPlace to compute a topology for a given set of end users in different locations of a geographic region. The simulation results show that TriPlace incurs a lower infrastructure cost than all existing solutions while achieving similar throughput performance as the best of these solutions. We believe this work will start a new research problem for quantum networks and attract more future work.
Quantum networks will rely on entanglement distribution to enable multi-user applications such as distributed quantum computing and cryptography. While multipartite entanglement distribution routing protocols have been extensively studied on idealised grid topologies, less is understood about how real network structure shapes their performance and resource requirements. We present a systematic study of four routing protocols for multipartite entanglement distribution, each characterised by the number of paths (single-path and multi-path) and routing strategy (star-based and tree-based), over 81 real network topologies. We identified four distinct topology-dependent performance regimes, where: (i) all protocols perform poorly, (ii) tree-based protocols dominate, (iii) multi-path protocols dominate, or (iv) all protocols perform well. By correlating clusters with graph metrics, we also provide structural explanations for the varied performance of specific protocols. Additionally, motivated by the anticipated high cost of repeaters, we investigated the impact of repeater trimming on the performance of multi-path protocols. Topology strongly governs how far repeater nodes can be removed from the network while maintaining a given performance (distribution rate). For instance, in networks where only 80% of nodes operate as repeaters, well-performing topologies are able to retain over 90% of the distribution rate; whereas sparse, weakly connected graphs exhibit rapid performance degradation, retaining less than half of the distribution rate. Our results provide a topology-aware framework for protocol selection and infrastructure optimisation in future quantum networks, bridging routing design with cost-aware deployment strategies.
This work studies the robustness of quantum key distribution (QKD) networks by combining graph-theoretic structure with a physics-based model of BB84 link capacity. Unlike classical optical networks, where traffic degrades gradually under link loss, QKD secret-key rates collapse exponentially due to fiber attenuation, detector inefficiency, misalignment, and dark counts. As a result, purely topological centrality measures fail to capture which nodes are truly critical for end-to-end secure connectivity. We model each fiber link using an asymptotic BB84 capacity function, convert it to bit/s, and then propagate capacities through the network using max–min (widest-path) routing via a Floyd–Warshall-style algorithm. Global robustness is quantified by the sum of all-pairs widest-path capacities under progressive node removal. We compare four adaptive attack strategies: random failure, degree-targeted removal, hop-based betweenness, and a new capacity-weighted betweenness that explicitly incorporates quantum-physical constraints. Experiments across multiple topology classes (random geometric, scale-free, star, and mesh) and many random network instances show that classical metrics such as degree and unweighted betweenness correlate only weakly with the actual loss of global capacity. In contrast, capacity-weighted betweenness consistently identifies nodes whose removal causes catastrophic collapse of the QKD backbone, especially in sparse and hub-dominated networks. The results lead to a clear design principle: topology alone is insufficient; QKD robustness is governed primarily by the physics-constrained capacity structure. The repository includes the full PDF manuscript and Python code used to generate the BB84 link capacities, widest-path capacity matrices, centrality metrics, and robustness curves. These materials are intended to support reproducibility and to provide a baseline for future work on quantum-aware network design, survivability optimization, and traffic engineering in national-scale QKD infrastructures.