  Since the development of Boson sampling, there has been a quest to construct
more efficient and experimentally feasible protocols to test the computational
complexity of sampling from photonic states. In this paper we interpret and
extend the results presented in [Phys. Rev. Lett. 119, 170501 (2017)]. We
derive an expression that relates the probability to measure a specific photon
output pattern from a Gaussian state to the \textit{hafnian} matrix function
and us it to design a Gaussian Boson sampling protocol. Then, we discuss the
advantages that this protocol has relative to other photonic protocols and the
experimental requirements for Gaussian Boson Sampling. Finally, we relate it to
the previously most general protocol, Scattershot Boson Sampling [Phys. Rev.
Lett. 113, 100502 (2014)]
