**7. Conclusions**

In the paper, we propose a quantum algorithm for a comparison of strings and a general idea for any algorithm that does *A* string comparison operations. Then, using these results, we construct a quantum strings sorting algorithm that works faster than the radix sort algorithm, which is the best known deterministic algorithm for sorting a sequence of strings.

We propose quantum algorithms for two problems using the sorting algorithm: the Most Frequent String Search and Intersection of Two String Sequences. These quantum algorithms are more efficient than classical (deterministic or randomized) counterparts in a case of log2(*n*) = *o*( √*k*), where *k* is the length of strings and *n* is the number of strings. In a case of the Intersection of Two String Sequences problem, the condition is log2(*n*)(log2 *m* + log2 log2 *n*) = *o*( √*k*), where *n* and *m* are the number of strings in two sequences. Note that these assumptions are reasonable.

We discussed quantum and classical lower bounds for these problems. Classical lower bounds are tight, and at the same time, there is room to improve the quantum lower bounds.

**Author Contributions:** The main idea and algorithms, K.K. and A.I.; lower bounds, J.V. and K.K.; constructions and concepts, K.K., A.I. and J.V. All authors have read and agreed to the published version of the manuscript.

**Funding:** This paper has been supported by the Kazan Federal University Strategic Academic Leadership Program ("PRIORITY-2030"). J.V. Supported by the ERDF project 1.1.1.5/18/A/020 "Quantum algorithms: from complexity theory to experiment".

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Acknowledgments:** We thank Aliya Khadieva, Farid Ablayev, Kazan Federal University quantum group and Krišjanis Pr ¯ usis from the University of Latvia for useful discussions. ¯

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.
