  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 $\tilde{O}(n \sqrt{k})$. This algorithm
shows speed-up comparing with the deterministic algorithm that requires
$\Omega(nk)$ 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 $\tilde{O}((n+m) \sqrt{k})$. This algorithm shows
speed-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 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 $O(n (\log n)^2 \sqrt{k})$. This algorithm shows
speed-up comparing with the deterministic algorithm (radix sort) that requires
$\Omega((n+d)k)$ queries, where $d$ is a size of the alphabet.
