  We study the hardness of classically simulating Gaussian boson sampling at
nonzero photon distinguishability. We find that similar to regular boson
sampling, distinguishability causes exponential attenuation of the many-photon
interference terms in Gaussian boson sampling. Barring an open problem in the
theory of matrix permanents, this leads to an efficient classical algorithm to
simulate Gaussian boson sampling in the presence of distinguishability. We also
study a new form of boson sampling based on photon number superposition states,
for which we also show noise sensivity. The fact that such superposition boson
sampling is not simulable with out method at zero distinguishability is the
first evidence for the computational hardness of this problem.
