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We introduce an exact classical algorithm for simulating Gaussian BosonSampling (GBS). The complexity of the algorithm is exponential in the number ofphotons detected, which is itself a random variable. For a fixed number ofmodes, the complexity is in fact equivalent to that of calculating outputprobabilities, up to constant prefactors. The simulation algorithm can beextended to other models such as GBS with threshold detectors, GBS withdisplacements, and sampling linear combinations of Gaussian states. In thespecific case of encoding non-negative matrices into a GBS device, our methodleads to an approximate sampling algorithm with polynomial runtime. Weimplement the algorithm, making the code publicly available as part of Xanadu'sThe Walrus library, and benchmark its performance on GBS with random Haarinterferometers and with encoded Erd\H{o}s-Renyi graphs.

Exact simulation of Gaussian Boson Sampling in polynomial space and exponential time