  The errors caused by the transitions with large frequency offsets
(nonresonant transitions) are calculated analytically for a scalable
solid-state quantum computer based on a one-dimensional spin chain with Ising
interactions between neighboring spins. Selective excitations of the spins are
enabled by a uniform gradient of the external magnetic field. We calculate the
probabilities of all unwanted nonresonant transitions associated with the flip
of each spin with nonresonant frequency and with flips of two spins: one with
resonant and one with nonresonant frequencies. It is shown that these errors
oscillate with changing the gradient of the external magnetic field. Choosing
the optimal values of this gradient allows us to decrease these errors by 50%.
