  We propose and analyze an efficient high-dimensional quantum state transfer
protocol in an XX coupling spin network with a hypercube structure or chain
structure. Under free spin wave approximation, unitary evolution results in a
perfect high-dimensional quantum swap operation requiring neither external
manipulation nor weak coupling. Evolution time is independent of either
distance between registers or dimensions of sent states, which can enable
improvements in computational efficiency. In the low temperature regime and
thermodynamic limit, the decoherence by noisy environment is studied with a
model of an antiferromagnetic spin bath coupled to quantum channels via an
Ising type interaction is studied. it is found that while the decoherence
reduces the fidelity of state transfer, increasing intra-channel coupling can
strongly suppress such effects. These observations demonstrate that robustness
of the proposed scheme.
