On the Relationship between Boolean Algebra and Quantum Informatics

The fundamental relationship between quantum physics and discrete mathematics is examined. A method for representing Boolean functions in the form of unitary transformations is described. The question of the connection of Zhegalkin polynomials defining the algebraic normal form of a Boolean function with quantum circuits is considered. It is shown that the quantum information language provides a simple algorithm for constructing the Zhegalkin polynomial based on the truth table. The developed methods and algorithms are generalized to the case of an arbitrary Boolean function with a multibit domain of definition and a multibit set of values, as well as to the case of multivalued ( -value) logic when is a prime number. The developed approach is important for the implementation of quantum computer technologies and is the foundation for the transition from classical computer logic to quantum hardware.