We propose to use quantum computers to simulate infection spreading in networks. We first show the analogy between the infection distribution and spin-lattice configurations with Ising-type interactions. Then, since the spreading process can be modeled as a classical Markovian process, we show that the spreading process can be simulated using the evolution of a quantum thermal dynamic model with a parameterized Hamiltonian. In particular, we analytically and numerically analyze the evolution behavior of the Hamiltonian, and prove that the evolution simulates a classical Markovian process, which describes the well-known epidemiological stochastic susceptible and infectious (SI) model. A practical method to determine the parameters of the thermal dynamic Hamiltonian from epidemiological inputs is exhibited. As an example, we simulate the infection spreading process of the SARS-Cov-2 variant Omicron in a small-world network.
We propose to use quantum computers to simulate infection spreading in networks. We first show the analogy between the infection distribution and spin-lattice configurations with Ising-type interactions. Then, since the spreading process can be modeled as a classical Markovian process, we show that the spreading process can be simulated using the evolution of a quantum thermal dynamic model with a parameterized Hamiltonian. In particular, we analytically and numerically analyze the evolution behavior of the Hamiltonian, and prove that the evolution simulates a classical Markovian process, which describes the well-known epidemiological stochastic susceptible and infectious (SI) model. A practical method to determine the parameters of the thermal dynamic Hamiltonian from epidemiological inputs is exhibited. As an example, we simulate the infection spreading process of the SARS-Cov-2 variant Omicron in a small-world network.
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.
We introduce a discrete-time quantum random walk (QRW) framework for spatial epidemic modelling on a two-dimensional square lattice and compare its dynamics to classical random-walk SIR models. In our model, each infected site spawns a quantum walker whose coherent evolution (controlled by an amplitude-splitting coin and conditional shifts) can infect visited susceptible sites with probability p and persists for a lifetime of τ steps. We perform extensive quantum simulations on finite lattices and compute the basic reproduction number R0 across a broad grid of (p,τ) values. Results show that QRW dynamics interpolate between diffusive and super-diffusive regimes: at low p the QRW reproduces classical-like R0, while at higher p and τ ballistic propagation and interference produce markedly larger R0 and non-Gaussian spatial profiles. We compare the QRW R0 range to empirical estimates from historical outbreaks and discuss parameter regimes where QRW offers a closer qualitative match than classical diffusion. We conclude that QRWs provide a flexible, conceptually novel toy model for exploring rapid or heavy-tailed epidemic spread.
In this work, we introduce a quantum-inspired epidemic model to study the dynamics of an infectious disease in a population divided into compartments. By treating the healthy population as a large reservoir, we construct a framework based on open quantum systems and a Hilbert space formalism to model the spread of the infection. This approach allows for a mathematical framework that captures both Markovian and semi-Markovian dynamics in the evolution equations. Through numerical experiments, we examine the effect of varying memory parameters on the epidemic evolution, focusing in particular on the conditions under which the model remains physically admissible.This article is part of the theme issue 'Quantum theory and topology in models of decision making (Part 1)'.
Processes of viral diffusion are important in biological, technological, and social systems alike. Several mathematical models of infection have been developed to predict diffusion through networks, such as nonlinear dynamical systems (NLDSs). Such models generally offer accurate representations of real-world diffusion, particularly for networks with static topologies. However, simulations of viral diffusion are computationally expensive, rendering them infeasible for large-scale networks. Here, a new approach is shown that leverages quantum computing to make viral diffusion simulations feasible for large networks, independent of network topology. Simulations of an error-free quantum circuit accurately modeled viral diffusion, with multivariate Euclidean distances from predicted infection probabilities capped near 8% for a network with N = 5 nodes and t = 20 time-steps. This is sufficient accuracy to distinguish the relative susceptibility of nodes and to identify significant changes, such as periods of especially high susceptibility. The results illustrate the potential for quantum computational network simulation to provide accurate models of diffusion through large networks, an important real-world application of quantum computing. The ability to simulate viral diffusion is invaluable for researchers across disciplines who aim to understand, anticipate, prepare for, and intervene in ongoing diffusion processes.
Effective epidemic control is crucial for mitigating the spread of infectious diseases, particularly when pharmaceutical interventions such as vaccines or treatments are limited. Nonpharmaceutical strategies, including mobility restrictions, are key in reducing transmission rates but require careful optimization to balance public health benefits and socioeconomic costs. Quantum computing is emerging as a powerful tool for solving complex optimization problems that are intractable for classical methods and can thus be leveraged to handle mobility restrictions. This article presents a new approach to optimizing epidemic control strategies using quantum computing techniques. We focus on non-pharmaceutical interventions, particularly mobility restriction, modeled as a discrete-time network epidemic process based on the susceptible-infected-susceptible and sus-ceptible-infected-removed frameworks. The control problem is formulated as a combinatorial optimization task, inherently NPhard due to the binary nature of intervention decisions. To tackle this computational complexity, we derive a Quadratic Unconstrained Binary Optimization representation of the control problem, enabling its efficient solution via quantum computing resources. Our methodology is validated through numerical simulations on realistic case studies, showcasing the potential of quantum algorithms for enhancing epidemic control strategies. These findings pave the way for leveraging quantum optimization in broader applications of networked dynamical systems, demonstrating its viability for complex decision-making processes in public health management.
Random walks are fundamental models of stochastic processes with applications in various fields, including physics, biology, and computer science. We study classical and quantum random walks under the influence of stochastic resetting on arbitrary networks. Based on the mathematical formalism of quantum stochastic walks, we provide a framework of classical and quantum walks whose evolution is determined by graph Laplacians. We study the influence of quantum effects on the stationary and long-time average probability distribution by interpolating between the classical and quantum regime. We compare our analytical results on stationary and long-time average probability distributions with numerical simulations on different networks, revealing differences in the way resets affect the sampling properties of classical and quantum walks.