Grover algorithm with zero theoretical failure rate - art. no. 022307

In a standard Grover's algorithm for quantum searching, the probability of finding the marked item is not exactly 1. In this paper we present a modifi ed version of Grover's algorithm that searches a marked state with full suc cessful rate. The modification is done by replacing the phase inversion by phase rotation through angle phi. The rotation angle is given analytically to be phi = 2 arcsin(sin [pi/(4J+6)]/sin beta), where sin beta = 1/rootN, N is the number of items in the database, and J is any integer equal to or g reater than the integer part of [(pi /2)-beta]/(2 beta). Upon measurement a t the (J+1)th iteration, the marked state is obtained with certainty.