  BosonSampling is a restricted model of quantum computation proposed recently,
where a non-adaptive linear-optical network is used to solve a sampling problem
that seems to be hard for classical computers. Here we show that, even if the
linear-optical network has a constant number (greater than four) of beam
splitter layers, the exact version of the BosonSampling problem is still
classically hard, unless the polynomial hierarchy collapses to its third level.
This is based on similar result known for constant-depth quantum circuits and
circuits of 2-local commuting gates (IQP).
