Simulation of Grover's quantum search algorithm in a Ising nuclear spin chain quantum computer with first and second nearest neighbour couplings

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.