Hybrid Classical–Quantum Text Search Based on Hashing

Author:

Ablayev Farid1,Salikhova Nailya1,Ablayev Marat1

Affiliation:

1. Institute of Computational Mathematics and Information Technology, Kazan Federal University, Kazan 420008, Russia

Abstract

The paper considers the problem of finding a given substring in a text. It is known that the complexity of a classical search query in an unordered database is linear in the length of the text and a given substring. At the same time, Grover’s quantum search provides a quadratic speed-up in the complexity of the query and gives the correct result with a high probability. We propose a hybrid classical–quantum algorithm (hybrid random–quantum algorithm, to be more precise) that implements Grover’s search to find a given substring in a text. As expected, the algorithm works (a) with a high probability of obtaining the correct result and (b) with a quadratic query acceleration compared to the classical one. What is new is that our algorithm uses the uniform hash family functions technique. As a result, our algorithm is much more memory efficient (in terms of the number of qubits used) compared to previously known quantum algorithms.

Funder

Kazan Federal University Strategic Academic Leadership

Publisher

MDPI AG

Reference18 articles.

1. Grover, L.K. (1996, January 22–24). A fast quantum mechanical algorithm for database search. Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, Philadelphia, PA, USA.

2. Gilliam, A., Pistoia, M., and Gonciulea, C. (2020). Optimizing quantum search using a generalized version of grover’s algorithm. arXiv.

3. Quantum amplitude amplification and estimation;Brassard;Contemp. Math.,2002

4. Reitzner, D., Nagaj, D., and Buzek, V. (2012). Quantum walks. arXiv.

5. De Wolf, R. (2019). Quantum computing: Lecture notes. arXiv.

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