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A First Approach to Quantum Logical Shape Classification Framework

Author

Listed:
  • Alexander Köhler

    (Institute of Mathematics, Brandenburg University of Technology (BTU) Cottbus-Senftenberg, Platz der Deutschen Einheit 1, 03046 Cottbus, Germany)

  • Marvin Kahra

    (Institute of Mathematics, Brandenburg University of Technology (BTU) Cottbus-Senftenberg, Platz der Deutschen Einheit 1, 03046 Cottbus, Germany)

  • Michael Breuß

    (Institute of Mathematics, Brandenburg University of Technology (BTU) Cottbus-Senftenberg, Platz der Deutschen Einheit 1, 03046 Cottbus, Germany)

Abstract

Quantum logic is a well-structured theory, which has recently received some attention because of its fundamental relation to quantum computing. However, the complex foundation of quantum logic borrowing concepts from different branches of mathematics as well as its peculiar settings have made it a non-trivial task to devise suitable applications. This article aims to propose for the first time an approach using quantum logic in image processing for shape classification. We show how to make use of the principal component analysis to realize quantum logical propositions. In this way, we are able to assign a concrete meaning to the rather abstract quantum logical concepts, and we are able to compute a probability measure from the principal components. For shape classification, we consider encrypting given point clouds of different objects by making use of specific distance histograms. This enables us to initiate the principal component analysis. Through experiments, we explore the possibility of distinguishing between different geometrical objects and discuss the results in terms of quantum logical interpretation.

Suggested Citation

  • Alexander Köhler & Marvin Kahra & Michael Breuß, 2024. "A First Approach to Quantum Logical Shape Classification Framework," Mathematics, MDPI, vol. 12(11), pages 1-21, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:11:p:1646-:d:1400852
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    References listed on IDEAS

    as
    1. Gil McVean, 2009. "A Genealogical Interpretation of Principal Components Analysis," PLOS Genetics, Public Library of Science, vol. 5(10), pages 1-10, October.
    2. Le, Thai-Ha & Le, Ha-Chi & Taghizadeh-Hesary, Farhad, 2020. "Does financial inclusion impact CO2 emissions? Evidence from Asia," Finance Research Letters, Elsevier, vol. 34(C).
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