Characterizing Quantum Internet Using Complex Network Models

TL;DR

This work tackles the realism gap in quantum internet modeling by incorporating heterogeneity in fiber-optic connectivity. It introduces two heterogeneous network models, Brito-Soares (distance-biased preferential attachment) and Brito-Rozenfeld (scale-free with distance constraints), alongside the original homogeneous Brito et al. baseline, and validates them against ITDK fiber-topology data. The results reveal long-tailed degree distributions, a second-order phase transition at critical density $\rho_c$, and hierarchical clustering with $C(k) \propto k^{\gamma}$ ($\gamma \approx 0.76$–$0.87$), while the networks lack small-world behavior; high-degree hubs enable efficient entanglement distribution with fewer links. Overall, the heterogeneous models better capture real-world fiber networks and provide practical guidance for realistic quantum internet design and scalability.

Abstract

Quantum communication is a growing area of research, with quantum internet being one of the most promising applications. Studying the statistical properties of this network is essential to understanding its connectivity and the efficiency of the entanglement distribution. However, the models proposed in the literature often assume homogeneous distributions in the connections of the optical fiber infrastructure, without considering the heterogeneity of the network. In this work, we propose new models for the quantum internet that incorporate this heterogeneity of node connections in the optical fiber network, analyzing how this characteristic influences fundamental metrics such as the degree distribution, the average clustering coefficient, the average shortest path and assortativity. Our results indicate that, compared to homogeneous models, heterogeneous networks efficiently reproduce key structural properties of real optical fiber networks, including degree distribution, assortativity, and hierarchical behavior. These findings highlight the impact of network structure on quantum communication and can contribute to more realistic modeling of quantum internet infrastructure.

Figures (21)

• Figure 1: Degree distribution for networks with different numbers of nodes and density $\rho = 8 \times 10^{-5}$. (a) Brito-Soares model. (b) Brito-Rozenfeld model. The distributions collapse into a single curve for different values of N in both models. The dashed black curve represents the model-specific fit to the tail, using either an exponential or a power-law fit as appropriate. The fitting parameters are given in the text.
• Figure 2: Phase transition as a function of $\rho$, for different numbers of nodes. The black dashed curve indicates the critical density of the phase transition. (a) Brito-Soares model ($\rho_c \approx 7.5 \times 10^{-5}$) and (b) Brito-Rozenfeld model ($\rho_c \approx 7.8 \times 10^{-5}$).
• Figure 3: Average shortest path length as a function of the number of nodes. (a) Brito-Soares model. (b) Brito-Rozenfeld model. The dashed curves indicate fits for $\left \langle l \right \rangle = a N^{\delta} / \rho$ (black) and $\left \langle l \right \rangle \propto \ln N$ (red), showing that the networks do not have the small-world property. (c) Comparison of the average shortest path length between the three models studied, for $\rho = 1 \times 10^{-4}$.
• Figure 4: Comparison of average shortest path length as a function of the normalized number of edges ($E/N$) for the different network models. The Brito et al. model requires a higher number of connections to achieve a given value of $\left \langle l \right \rangle$.
• Figure 5: Average clustering coefficient as a function of $\rho$ for different $R$. (a) Brito-Soares model with $\alpha_A=5$. (b) Brito-Rozenfeld model with $\lambda=3$. In both, the curves collapse into a single curve with asymptotic behavior, with asymptotic values indicated in the text. (c) and (d) show $\left \langle C \right \rangle$ for different model parameters, with $R=2000$.