Simulating virus diffusion in networks with quantum computers

We propose to use quantum mechanical tools to simulate epidemic processes in a network. We first show a systematic way to map virus population distributions to spin-lattice configurations. Then, noticing that diffusion is a classical thermal dynamic process, we can map it to the dynamics of an effective (parametrized) Hamiltonian of a quantum thermal system. To demonstrate the rationality of the Hamiltonian, we provide numerical and analytic analyses of the evolution behaviour of the Hamiltonian. We prove that the evolution could be well described by a classical stochastic Markov process, which is consistent with the well-known epidemiological susceptible and infectious model. A practical method to determine the parameters of the thermal dynamic Hamiltonian from epidemiological inputs is exhibited. As an example, we simulate the transmission process of SARS-Cov-2 variant Omicron with a given community network.