Boson Sampling for Generalized Bosons

We generalized the standard Boson sampling task including Linear Boson Sampling the Gaus- sian Boson Sampling from photons to what we call generalized boson system which the computation relation between the creation and annihilation operators is not a constant. We showed that in such a system, one still has the standard hardness results including Hafnian and Permanents. We also use the spin system as our example and provide an experimental setup.