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The relationship between quantum physics and discrete mathematics is reviewedin this article. The Boolean functions unitary representation is considered.The relationship between Zhegalkin polynomial, which defines the algebraicnormal form of Boolean function, and quantum logic circuits is described. It isshown that quantum information approach provides simple algorithm to constructZhegalkin polynomial using truth table. Developed methods and algorithms havearbitrary Boolean function generalization with multibit input and multibitoutput. Such generalization allows us to use many-valued logic (k-valued logic,where k is a prime number). Developed methods and algorithms can significantlyimprove quantum technology realization. The presented approach is the baselinefor transition from classical machine logic to quantum hardware.

Representation of Boolean functions in terms of quantum computation