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Article

A Quantum Algorithm for the Classification of Patterns of Boolean Functions

by
Theodore Andronikos
1,*,†,
Constantinos Bitsakos
2,†,
Konstantinos Nikas
2,†,
Georgios I. Goumas
2,† and
Nectarios Koziris
2,†
1
Department of Informatics, Ionian University, 7 Tsirigoti Square, 49100 Corfu, Greece
2
Computing Systems Laboratory, National Technical University of Athens, Heroon Polytechniou 9, 15780 Zografou, Greece
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2025, 13(11), 1750; https://doi.org/10.3390/math13111750
Submission received: 12 March 2025 / Revised: 14 May 2025 / Accepted: 19 May 2025 / Published: 25 May 2025
(This article belongs to the Special Issue Quantum Computing and Networking)

Abstract

This paper introduces a novel quantum algorithm that is able to classify a hierarchy of classes of imbalanced Boolean functions. The fundamental characteristic of imbalanced Boolean functions is that the proportion of elements in their domain that take the value 0 is not equal to the proportion of elements that take the value 1. For every positive integer, n, the hierarchy contains a class of n-ary Boolean functions defined according to their behavioral pattern. The common trait of all the functions belonging to the same class is that they possess the same imbalance ratio. Our algorithm achieves classification in a straightforward manner as the final measurement reveals the unknown function with a probability of 1.0. Let us also note that the proposed algorithm is an optimal oracular algorithm because it can classify the aforementioned functions with just a single query to the oracle. At the same time, we explain in detail the methodology we followed to design this algorithm in the hope that it will prove general and fruitful, given that it can be easily modified and extended to address other classes of imbalanced Boolean functions that exhibit different behavioral patterns.
Keywords: quantum algorithm; Boolean function; pattern; oracle; the Deutsch–Jozsa algorithm; classification quantum algorithm; Boolean function; pattern; oracle; the Deutsch–Jozsa algorithm; classification

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MDPI and ACS Style

Andronikos, T.; Bitsakos, C.; Nikas, K.; Goumas, G.I.; Koziris, N. A Quantum Algorithm for the Classification of Patterns of Boolean Functions. Mathematics 2025, 13, 1750. https://doi.org/10.3390/math13111750

AMA Style

Andronikos T, Bitsakos C, Nikas K, Goumas GI, Koziris N. A Quantum Algorithm for the Classification of Patterns of Boolean Functions. Mathematics. 2025; 13(11):1750. https://doi.org/10.3390/math13111750

Chicago/Turabian Style

Andronikos, Theodore, Constantinos Bitsakos, Konstantinos Nikas, Georgios I. Goumas, and Nectarios Koziris. 2025. "A Quantum Algorithm for the Classification of Patterns of Boolean Functions" Mathematics 13, no. 11: 1750. https://doi.org/10.3390/math13111750

APA Style

Andronikos, T., Bitsakos, C., Nikas, K., Goumas, G. I., & Koziris, N. (2025). A Quantum Algorithm for the Classification of Patterns of Boolean Functions. Mathematics, 13(11), 1750. https://doi.org/10.3390/math13111750

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