Quantum Algorithms for the Most Frequently String Search, Intersection of Two String Sequences and Sorting of Strings Problems

Abstract

We study algorithms for solving three problems on strings. The first one is the Most Frequently String Search Problem. The problem is the following. Assume that we have a sequence of n strings of length k. The problem is finding the string that occurs in the sequence most often. We propose a quantum algorithm that has a query complexity (formula presented). This algorithm shows speed-up comparing with the deterministic algorithm that requires (formula presented) queries. The second one is searching intersection of two sequences of strings. All strings have the same length k. The size of the first set is n and the size of the second set is m. We propose a quantum algorithm that has a query complexity (formula presented). This algorithm shows speed-up comparing with the deterministic algorithm that requires (formula presented) queries. The third problem is sorting of n strings of length k. On the one hand, it is known that quantum algorithms cannot sort objects asymptotically faster than classical ones. On the other hand, we focus on sorting strings that are not arbitrary objects. We propose a quantum algorithm that has a query complexity (formula presented). This algorithm shows speed-up comparing with the deterministic algorithm (radix sort) that requires (formula presented) queries, where d is a size of the alphabet.