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A Quantum Algorithm for the Classification of Patterns of Boolean Functions

Author

Listed:
  • Theodore Andronikos

    (Department of Informatics, Ionian University, 7 Tsirigoti Square, 49100 Corfu, Greece
    These authors contributed equally to this work.)

  • Constantinos Bitsakos

    (Computing Systems Laboratory, National Technical University of Athens, Heroon Polytechniou 9, 15780 Zografou, Greece
    These authors contributed equally to this work.)

  • Konstantinos Nikas

    (Computing Systems Laboratory, National Technical University of Athens, Heroon Polytechniou 9, 15780 Zografou, Greece
    These authors contributed equally to this work.)

  • Georgios I. Goumas

    (Computing Systems Laboratory, National Technical University of Athens, Heroon Polytechniou 9, 15780 Zografou, Greece
    These authors contributed equally to this work.)

  • Nectarios Koziris

    (Computing Systems Laboratory, National Technical University of Athens, Heroon Polytechniou 9, 15780 Zografou, Greece
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Theodore Andronikos & Constantinos Bitsakos & Konstantinos Nikas & Georgios I. Goumas & Nectarios Koziris, 2025. "A Quantum Algorithm for the Classification of Patterns of Boolean Functions," Mathematics, MDPI, vol. 13(11), pages 1-23, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:11:p:1750-:d:1663960
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    References listed on IDEAS

    as
    1. Theodore Andronikos & Alla Sirokofskich, 2021. "The Connection between the PQ Penny Flip Game and the Dihedral Groups," Mathematics, MDPI, vol. 9(10), pages 1-35, May.
    2. D. Main & P. Drmota & D. P. Nadlinger & E. M. Ainley & A. Agrawal & B. C. Nichol & R. Srinivas & G. Araneda & D. M. Lucas, 2025. "Distributed quantum computing across an optical network link," Nature, Nature, vol. 638(8050), pages 383-388, February.
    3. Theodore Andronikos & Alla Sirokofskich, 2024. "A Multiparty Quantum Private Equality Comparison Scheme Relying on | GHZ 3 〉 States," Future Internet, MDPI, vol. 16(9), pages 1-27, August.
    Full references (including those not matched with items on IDEAS)

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