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Advances in photonics require photon-number resolved simulations of quantumoptical experiments with Gaussian states. We demonstrate a simple and versatilemethod to simulate the photon statistics of general multimode Gaussian states.The derived generating functions enable simulations of the photon numberdistribution, cumulative probabilities, moments, and factorial moments of thephoton statistics of Gaussian states as well as of multimode photon-added andphoton-subtracted Gaussian states. Numerical results are obtained by automaticdifferentiation of these generating functions by employing the softwareframework PyTorch. Our approach is particularly well suited for practicalsimulations of the photon statistics of quantum optical experiments inrealistic scenarios with low photon numbers, in which various sources ofimperfections have to be taken into account. As an example, we calculate thedetection probabilities for a recent multipartite time-bin coding quantum keydistribution setup and compare them with the corresponding experimental values.

Simulating the Photon Statistics of Multimode Gaussian States by Automatic Differentiation of Generating Functions