Group theoretical formulation of a quantum partial search algorithm

Searching and sorting are used as a subroutine in many important algorithms. Quantum algorithm can find a target item in a database faster than any classical algorithm. One can trade accuracy for speed and find a part of the database (a block) containing the target item even faster; this is a partial search. For example, an exact address of the target item is given by a sequence of many bits, but we need to know only some of them. More generally, a partial search considers the problem in which a database is separated into several blocks and we want to find a block with the target item, not the target item itself. In this paper, we reformulate a quantum partial search algorithm in terms of group theory.