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Noisy Tree Data Structures and Quantum Applications

Author

Listed:
  • Kamil Khadiev

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

  • Nikita Savelyev

    (Intel Inc., D-81671 Munich, Germany)

  • Mansur Ziatdinov

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

  • Denis Melnikov

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

Abstract

We suggest a new technique for developing noisy tree data structures. We call it a “walking tree”. As applications of the technique we present a noisy Self-Balanced Binary Search Tree (we use a Red–Black tree as an implementation) and a noisy segment tree. The asymptotic complexity of the main operations for the tree data structures does not change compared to the case without noise. We apply the data structures in quantum algorithms for several problems on strings like the string-sorting problem and auto-complete problem. For both problems, we obtain quantum speed-up. Moreover, for the string-sorting problem, we show a quantum lower bound.

Suggested Citation

  • Kamil Khadiev & Nikita Savelyev & Mansur Ziatdinov & Denis Melnikov, 2023. "Noisy Tree Data Structures and Quantum Applications," Mathematics, MDPI, vol. 11(22), pages 1-18, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4707-:d:1284060
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