  We show how to perfectly transfer, without state initialization and remote
collaboration, arbitrary functions in interacting boson lattices. We describe a
possible implementation of state transfer through bosonic atoms trapped in
optical lattices or polaritons in on-chip coupled cavities. Significantly, a
family of Hamiltonians, both linear and nonlinear, is found which are related
to the Bose-Hubbard model and that enable the perfect transfer of arbitrary
functions. It is shown that the state transfer between two sites in
two-dimensional lattices can result in quantum interference due to the
different numbers of intermediate sites in different paths. The signature
factor in nuclear physics can be useful to characterize this quantum
interference.
