Simulation of static and random errors on Grover's search algorithm implemented in an Ising nuclear spin chain quantum computer with a few qubits

We consider Grover's search algorithm on a model quantum computer implemented on a chain of four or five nuclear spins with first- and second-neighbour Ising interactions. Noise is introduced into the system in terms of random fluctuations of the external fields. By averaging over many repetitions of the algorithm, the output state becomes effectively a mixed state. We study its overlap with the nominal output state of the algorithm, which is called the fidelity. We analyse the behaviour of the fidelity as a function of the noise intensity for static and random noise on either the Larmor frequencies or the Rabi frequency, and we compare our results to theoretical predictions and numerical simulations which are based on more abstract quantum computer models.