Аннотация:We consider the M -neighbor approximation in the problem of one-qubit pure state transfer along
the N -node zigzag and alternating spin chains governed by the XXZ-Hamiltonian with the dipole-
dipole interaction. We show that always M > 1, i.e., the nearest neighbor approximation is not
applicable to such interaction. Moreover, only all-node interaction (M = N − 1) properly describes
the dynamics in the alternating chain. We reveal the region in the parameter space characterizing
the chain geometry and orientation which provide the high-probability state-transfer. The optimal
state-transfer probability and appropriate time instant for the zigzag and alternating chains are
compared.