Representation of Boolean functions in terms of quantum computation

Yu. I. Bogdanov; N. A. Bogdanova; D. V. Fastovets; V. F. Lukichev

doi:10.1117/12.2522053

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15 March 2019 Representation of Boolean functions in terms of quantum computation

Yu. I. Bogdanov, N. A. Bogdanova, D. V. Fastovets, V. F. Lukichev

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Proceedings Volume 11022, International Conference on Micro- and Nano-Electronics 2018; 110222R (2019) https://doi.org/10.1117/12.2522053
Event: The International Conference on Micro- and Nano-Electronics 2018, 2018, Zvenigorod, Russian Federation

Abstract

The relationship between quantum physics and discrete mathematics is reviewed in this article. The Boolean functions unitary representation is considered. The relationship between Zhegalkin polynomial, which defines the algebraic normal form of Boolean function, and quantum logic circuits is described. It is shown that quantum information approach provides simple algorithm to construct Zhegalkin polynomial using truth table. Developed methods and algorithms have arbitrary Boolean function generalization with multibit input and multibit output. Such generalization allows us to use many-valued logic (k-valued logic, where k is a prime number). Developed methods and algorithms can significantly improve quantum technology realization. The presented approach is the baseline for transition from classical machine logic to quantum hardware.

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Yu. I. Bogdanov, N. A. Bogdanova, D. V. Fastovets, and V. F. Lukichev "Representation of Boolean functions in terms of quantum computation", Proc. SPIE 11022, International Conference on Micro- and Nano-Electronics 2018, 110222R (15 March 2019); https://doi.org/10.1117/12.2522053

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