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Simulation of the statical and dynamical noise on Grover's search algorithm implemented in a Ising nuclear spin chain quantum computer

We consider Grover's quantum search algorithm on a model quantum computer implemented on a chain of four nuclear spins with first and second neighbor 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 fidelity. We find either an exponential or a Gaussian decay for the fidelity as a function of the strength of the noise, depending on the type of noise (static or dynamic) and whether the 2πk-method (a particular error suppression scheme) is applied or not. 1 Introduction It is well known that Grover's search algorithm for searching an item in a quantum data base of length N = 2 n , where n is the length of the quantum register made up of n-qubits, provides a quadratic speed up with respect any classical search algorithm [1, 2]. Some applications of this algorithm has already been done [3, 4, 5, 6, 7], and its physical implementation has been made for few qubits [8, 9, 10, 11]. Full simulations of this algorithm has also been made for 4-qubits 1