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We show how to perfectly transfer, without state initialization and remotecollaboration, arbitrary functions in interacting boson lattices. We describe apossible implementation of state transfer through bosonic atoms trapped inoptical lattices or polaritons in on-chip coupled cavities. Significantly, afamily of Hamiltonians, both linear and nonlinear, is found which are relatedto the Bose-Hubbard model and that enable the perfect transfer of arbitraryfunctions. It is shown that the state transfer between two sites intwo-dimensional lattices can result in quantum interference due to thedifferent numbers of intermediate sites in different paths. The signaturefactor in nuclear physics can be useful to characterize this quantuminterference.

Perfect function transfer and interference effects in interacting boson lattices