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Quantum Algorithms for Some Strings Problems Based on Quantum String Comparator

Author

Listed:
  • Kamil Khadiev

    (Institute of Computational Mathematics and Information Technologies, Kazan Federal University, Kremlevskaya 18, 420008 Kazan, Russia)

  • Artem Ilikaev

    (Institute of Computational Mathematics and Information Technologies, Kazan Federal University, Kremlevskaya 18, 420008 Kazan, Russia)

  • Jevgenijs Vihrovs

    (Center for Quantum Computer Science, Faculty of Computing, University of Latvia, Raina 19, LV-1586 Riga, Latvia)

Abstract

We study algorithms for solving three problems on strings. These are sorting of n strings of length k , “the Most Frequent String Search Problem”, and “searching intersection of two sequences of strings”. We construct quantum algorithms that are faster than classical (randomized or deterministic) counterparts for each of these problems. The quantum algorithms are based on the quantum procedure for comparing two strings of length k in O ( k ) queries. The first problem is sorting n strings of length k . We show that classical complexity of the problem is Θ ( n k ) for constant size alphabet, but our quantum algorithm has O ˜ ( n k ) complexity. The second one is searching the most frequent string among n strings of length k . We show that the classical complexity of the problem is Θ ( n k ) , but our quantum algorithm has O ˜ ( n k ) complexity. The third problem is searching for an 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 show that the classical complexity of the problem is Θ ( ( n + m ) k ) , but our quantum algorithm has O ˜ ( ( n + m ) k ) complexity.

Suggested Citation

  • Kamil Khadiev & Artem Ilikaev & Jevgenijs Vihrovs, 2022. "Quantum Algorithms for Some Strings Problems Based on Quantum String Comparator," Mathematics, MDPI, vol. 10(3), pages 1-12, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:377-:d:734357
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    Citations

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    Cited by:

    1. Fernando L. Pelayo & Mauro Mezzini, 2022. "Preface to the Special Issue on “Quantum Computing Algorithms and Computational Complexity”," Mathematics, MDPI, vol. 10(21), pages 1-3, October.

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