  Boson Sampling represents a promising approach to obtain an evidence of the
supremacy of quantum systems as a resource for the solution of computational
problems. The classical hardness of Boson Sampling has been related to the so
called Permanent-of-Gaussians Conjecture and has been extended to some
generalizations such as Scattershot Boson Sampling, approximate and lossy
sampling under some reasonable constraints. However, it is still unclear how
demanding these techniques are for a quantum experimental sampler. Starting
from a state of the art analysis and taking account of the foreseeable
practical limitations, we evaluate and discuss the bound for quantum supremacy
for different recently proposed approaches, accordingly to today's best known
classical simulators.
