Grover algorithm with zero theoretical failure rate

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 modified version of Grover's algorithm that searches a marked state with full successful rate. The modification is done by replacing the phase inversion by phase rotation through angle φ. The rotation angle is given analytically to be φ=2 arcsin(sin [π/(4J+6)]/sin β), where sin β=1/N, N is the number of items in the database, and J is any integer equal to or greater than the integer part of [(π/2)-β]/(2β). Upon measurement at the (J+1)th iteration, the marked state is obtained with certainty.