Family of Grover's quantum-searching algorithms - art. no. 062303

We introduce the concepts of Grover operators and Grover kernels to systema tically analyze Grover's searching algorithms. Then we investigate a one-pa rameter family of quantum searching algorithms of Grover type and we show t hat the standard Grover algorithm is a distinguished member of this family. We show that all the algorithms of this class solve the searching problem with an efficiency of order O(rootN), with a coefficient which is class-dep endent. The analysis of this dependence is a test of the stability and robu stness of the algorithms. We show the stability of this constructions under perturbations of the initial conditions and extend them to a very general class of Grover operators.