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We consider Grover's search algorithm on a model quantum computer implementedon a chain of four or five nuclear spins with first and second neighbour Isinginteractions. Noise is introduced into the system in terms of randomfluctuations of the external fields. By averaging over many repetitions of thealgorithm, the output state becomes effectively a mixed state. We study itsoverlap with the nominal output state of the algorithm, which is calledfidelity. We find either an exponential or a Gaussian decay for the fidelity asa function of the strength of the noise, depending on the type of noise (staticor random) and whether error supression is applied (the 2pi k-method) or not.

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