Perfect quantum state transfer in two- and three-dimensional structures

We introduce a scheme for perfect state transfer in regular two- and three-dimensional structures. The interactions on the lattices are of the XX spin type with uniform couplings. In two dimensions, the structure is a hexagonal lattice, and in three dimensions, it consists of hexagonal planes joined to each other at arbitrary points. We will show that compared to other schemes, much less control is needed for routing, the algebra of global control is quite simple, and the same kind of control can upload and download qubit states to or from built-in read-write heads.