Noisy Effect on Nonlinear Quantum Search Algorithm

Abstract

In this paper, we investigate the effects of three single-qubit quantum noise channels on the quantum nonlinear search algorithm proposed by Abrams and Lloyd. We focus on the gates of the nonlinear part of the algorithm and consider the case where the quantum noise channel only affects the qubit on which the gate is proceeding. Assuming that quantum noise effects occur after using the gates of the nonlinear part of the algorithm, we find that the quantum nonlinear search algorithm appears to be very resilient to the quantum noise when the desired state does not exist in the first register and is subject to the phase damping channel or the depolarising channel.