  We implement Grover's quantum search algorithm on a nuclear spin chain
quantum computer, taking into Ising type interactions between nearest and
second nearest neighbours into account. The performance of the realisation of
the algorithm is studied by numerical simulations with four spins. We determine
the temporal behaviour of the fidelity during the algorithm, and we compute the
final fidelity as a function of the Rabi frequency. For the latter, we obtained
pronounced maxima at frequencies which fulfil the condition of the (2\pi
k)-method with respect to the second nearest neighbour interactions.
