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We study algorithms for solving three problems on strings. The first one isthe Most Frequently String Search Problem. The problem is the following. Assumethat we have a sequence of $n$ strings of length $k$. The problem is findingthe string that occurs in the sequence most often. We propose a quantumalgorithm that has a query complexity $\tilde{O}(n \sqrt{k})$. This algorithmshows speed-up comparing with the deterministic algorithm that requires$\Omega(nk)$ queries. The second one is searching intersection of two sequencesof 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 thathas a query complexity $\tilde{O}((n+m) \sqrt{k})$. This algorithm showsspeed-up comparing with the deterministic algorithm that requires$\Omega((n+m)k)$ queries. The third problem is sorting of $n$ strings of length$k$. On the one hand, it is known that quantum algorithms cannot sort objectsasymptotically faster than classical ones. On the other hand, we focus onsorting strings that are not arbitrary objects. We propose a quantum algorithmthat has a query complexity $O(n (\log n)^2 \sqrt{k})$. This algorithm showsspeed-up comparing with the deterministic algorithm (radix sort) that requires$\Omega((n+d)k)$ queries, where $d$ is a size of the alphabet.

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