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

Abstract

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 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 random) and whether error supression is applied (the 2πk-method) or not. PACS IntroductionIt 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 have already been done [3,4,5,6,7,8], and its physical implementation has been made for few qubits [9,10,11,12]. Numerical simulations of this algorithm have also been made for a 4-qubits solid state quantum computer which is made up of a chain of 1