  The one-dimensional homonuclear periodic array of nuclear spins I = 1/2,
owing to hyperfine interaction of nuclear spins with electronic magnetic
moments in antiferromagnetic structure, is considered. The neighbor nuclear
spins in such array are opposite oriented and have resonant frequencies
determined by hyperfine interaction constant, applied magnetic field value and
interaction with the left and right nuclear neighbor spins. The resonant
frequencies difference of nuclear spins, when the neighbor spins have different
and the same states, is used to control the spin dynamics by means of selective
resonant RF-pulses both for single nuclear spins and for ensemble of nuclear
spins with the same resonant frequency.
  A model for the NMR quantum computer of cellular-automata type based on an
one-dimensional homonuclear periodic array of spins is proposed. This model may
be generalized to a large ensemble of parallel working one-dimensional arrays
and to two-dimensional and three-dimensional structures.
