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 $\phi .$ The rotation angle is given analytically to be $\phi =2\mathrm{}\arcsin \left(\sin \right[\pi /(4J+6)\mathrm{}]/\sin \beta ),$ where $\sin \beta =1/\sqrt{N},$ N is the number of items in the database, and J is any integer equal to or greater than the integer part of $\left[\right(\pi /2\left)-\beta \right]/\left(2\mathrm{}\beta \right).\mathrm{}$ Upon measurement at the $\mathrm{}(J+1\mathrm{})\mathrm{}\mathrm{th}$ iteration, the marked state is obtained with certainty.