An efficient quantum search engine on unsorted database

We consider the problem of finding one or more desired items out of an unsorted database. Patel has shown that if the database permits quantum queries, then mere digitization is sufficient for efficient search for one desired item. The algorithm, called factorized quantum search algorithm, presented by him can locate the desired item in an unsorted database using O(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$log_4N$$\end{document}) queries to factorized oracles. But the algorithm requires that all the attribute values must be distinct from each other. In this paper, we discuss how to make a database satisfy the requirements, and present a quantum search engine based on the algorithm. Our goal is achieved by introducing auxiliary files for the attribute values that are not distinct, and converting every complex query request into a sequence of calls to factorized quantum search algorithm. The query complexity of our algorithm is O(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$log_4N$$\end{document}) for most cases.