Quantum search in structured database

This paper is mainly about methodology in designing quantum algorithm. Based on study of Graver's algorithm, we argue that it is a short cut to design and interpret quantum algorithms from the viewpoint of Householder transformation directly. We give an example for this claim, which extends Grover's quantum search algorithm to some structured database. In this example, we show how to exploit some special structure information of problem, which restricts the search in some subspace. Based on an instantiation of this framework, we show that it does can utilize the information to the full extent. This paper gives the details that produce the algorithm framework. The idea, which is simple and intelligible, is universal to some extent, and therefore can be applied to other similar situations.