  We propose and analyze an efficient high-dimensional quantum state transfer
scheme through an $XXZ$-Heisenberg spin chain in an inhomogeneous magnetic
field. By the use of a combination of coherent quantum coupling and free
spin-wave approximation, pure unitary evolution results in a perfect
high-dimensional swap operation between two remote quantum registers mediated
by a uniform quantum data bus, and the feasibility is confirmed by numerical
simulations. Also, we observe that either the strong $z$-directional coupling
or high quantum spin number can partly suppress the thermal excitations and
protect quantum information from the thermal noises when the quantum data bus
is in the thermal equilibrium state.
