  In this work we study a system that consists of $2M$ matter qubits that
interact through a boson sampling circuit, i.e., an $M$-port interferometer,
embedded in two different architectures. We prove that, under the conditions
required to derive a master equation, the qubits evolve according to effective
bipartite XY spin Hamiltonians, with or without local and collective
dissipation terms. This opens the door to the simulation of any bipartite spin
or hard-core boson models and exploring dissipative phase transitions as the
competition between coherent and incoherent exchange of excitations. We also
show that in the purely dissipative regime this model has a large number of
exact and approximate dark states, whose structure and decay rates can be
estimated analytically. We finally argue that this system may be used for the
adiabatic preparation of boson sampling states encoded in the matter qubits.
