Quantum implementation of circulant matrices and its use in quantum string processing

Abstract

String problems in general can be solved faster by using special data structures such as suffixes in many cases structured as trees and arrays. In this paper, we show that suffixes used in those data structures can be obtained by using circulant matrices as a quantum operator which can be implemented in logarithmic time. Hence, if the strings are given as quantum states, using the presented circuit implementation one can do string processing efficiently on quantum computers.