  We construct an effective Hamiltonian of interacting bosons, based on
scattered radiation off vibrational modes of designed molecular architectures.
Making use of the infinite yet countable set of spatial modes representing the
scattering of light, we obtain a variable photon-photon interaction in this
basis. The effective Hamiltonian hermiticity is controlled by a geometric
factor set by the overlaps of spatial modes. Using this mapping, we relate
intensity measurements of the light to correlation functions of the interacting
bosons evolving according to the effective Hamiltonian, rendering local as well
as nonlocal observables accessible. This architecture may be used to simulate
the dynamics of interacting bosons, as well as designing tool for multi-qubit
photonic gates in quantum computing applications. Variable hopping, interaction
and confinement of the active space of the bosons are demonstrated on a model
system.
