Search an unsorted database with quantum mechanics

Abstract

In this article, we review quantum search algorithms for unsorted database search problem. Unsorted database search is a very important problem in science and technology. In a quantum computer, a marked state can be found with very high probability using the Grover's algorithm, or exactly with the Long algorithm. We review the Grover algorithm and related generalizations. In particular, we review the phase matching conditions in quantum search algorithm. Several issues that may cause confusion about the quantum search algorithm are also clarified.