Virus Spreading in Quantum Networks

TL;DR

It is shown that quantum networks tend to be more resilient to viral infections, exhibiting higher epidemic thresholds than classical networks with identical graph topologies, and these findings provide key insights into the security and reliability of future large-scale quantum communication systems.

Abstract

Recent advances in quantum communication have enabled long-distance secure information transfer through quantum channels, giving rise to quantum networks with unique physical and statistical properties. However, as in classical networks, the propagation of viruses in these systems could have severe consequences. Here, we investigate the critical problem of virus spreading in quantum networks. We develop quantitative tools, particularly a modified nonlinear dynamical system model, for performing epidemiological analyses on quantum networks. Our results show that quantum networks tend to be more resilient to viral infections, exhibiting higher epidemic thresholds than classical networks with identical graph topologies. This apparent robustness, however, arises primarily from the sparser connectivity inherent to the quantum networks. When the comparison is made at a fixed average connectivity, classical and quantum networks display comparable epidemic thresholds. These findings provide key insights into the security and reliability of future large-scale quantum communication systems. Our work bridges the fields of quantum information science, network theory, and epidemiology, paving the way for future studies of quantum epidemiological dynamics.

Figures (6)

• Figure 1: Network topologies and the SIS epidemiological model.(a) A classical network generated using the Erdős–Rényi graph model, where the probability that two nodes $n_i$ and $n_j$ are connected by an optical fiber is $\Pi_{ij}=p=0.01$. (b) Schematic illustration of the susceptible–infected–susceptible (SIS) model describing the infection dynamics of a single node. The two possible states, S (susceptible) and I (infected), represent recovery and reinfection processes within the network. (c) A quantum network generated using the Waxman model. Dark green lines denote optical-fiber photonic links, established by transmitting multiple single photons (depicted as glowing orange disks) between nodes, with an overall success probability $p_{ij}$.
• Figure 2: Edge distributions and epidemic thresholds of the classical and quantum networks.(a) and (b) Degree distribution $p(k)$ with varying numbers of nodes $N$ in classical and quantum networks based on the Waxman topology. (c) and (d) Epidemic thresholds $\tau_\text{KW}$, $\tau_\text{MFA}$ and $\tau_\text{AM}$ ($\tau_\text{pAM}$ for quantum case) versus $N$ , computed numerically using Monte Carlo simulations with 200 random realizations for each $N$. For large $N$, all thresholds converge and exhibit the scaling $\tau \approx c/N$, with fitted constants $c=30.51\pm0.03$ and $c=160.24\pm0.11$ for classical and quantum networks. (e) Epidemic threshold versus average connectivity in log-log scale. Both classical and quantum models approach the asymptotic relation $\log\tau = -\log\langle k\rangle$.
• Figure 3: Epidemic dynamics in the quantum network.(a) For small curing rares ($\delta=0.1\delta_c$ and $\delta=0.3\delta_c$, the quantum network remains partially infected with $\eta_\infty > \eta_0$. (b) Increasing the curing rate to $\delta=0.4\delta_c$ keeps $\eta(t)$ close to its initial value throughout the evolution, while at $\delta=0.5\delta_c$, $\eta_\infty < \eta_0$. In both cases, mNLDS and direct simulations show small discrepancies, and the latter exhibit larger run-to-run fluctuations. (c) For higher curing rates ($0.6\delta_c$ and $\delta=0.9\delta_c$), $\eta(t)$ rapidly decreases, and the two methods yield more consistent results. (d) At the critical point $\delta=\delta_c$, both approaches predict the infection vanishes asymptotically ($\eta_{\inf} \to 0$). Simulations are performed on a quantum network with 2000 nodes and an initial infection probability $p_{i,0}=0.5$. The infection rate is $\beta=0.05$, and direct simulations are averaged over 20 independent runs with random initial configurations.
• Figure A1: Thresholds from different methods. We apply the three methods discussed to compute the threshold $\tau_\text{AM}$ for quantum networks with varying numbers of nodes $N$. In Method 2, we sampled 200 instances of the Waxman graph for each size $N$ to compute the mean and variance of the threshold holds of each instance. In Method 3, we further sample 100 instances for each instance in Method 2. All parameters are the same as those used in the main text.
• Figure A2: Thresholds versus $n_p$. In each panel, the epidemic thresholds of quantum networks are computed for varying photon loss cofficients and the number of photons used in a single communication. From left to right, the panels correspond to increasing numbers of nodes in the quantum network. In all the simulations, we fix $R_\text{max} = 1600$ km, $\alpha_L = 216$ km and $\beta_L=1$. Each data point represents an average over 1000 random instances.