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.