The Doi formalism treats a reaction-diffusion process as a quantum many-body problem. We use this second-quantized formulation as a starting point to derive a numerical scheme for simulating X0 reaction-diffusion processes, following a well-established time discretization procedure. In the case of a reaction zone localized in the configuration space, this formulation provides also a systematic way of designing an optimized, multiple time step algorithm, spending most of the computation time to sample the configurations where the reaction is likely to occur.

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