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We find analytic models that can perfectly transfer, without stateinitializati$ or remote collaboration, arbitrary functions in two- andthree-dimensional interacting bosonic and fermionic networks. We elaborate on apossible implementation of state transfer through bosonic or fermionic atomstrapped in optical lattices. A significant finding is that the state of a spinqubit can be perfectly transferred through a fermionic system. Families ofHamiltonians, both linear and nonlinear, are described which are related to thelinear Boson model and that enable the perfect transfer of arbitrary functions.This includes entangled states such as decoherence-free subsystems enablingnoise protection of the transferred state.

Perfect Function Transfer in two- and three- dimensions without initialization