Representation of Boolean functions in terms of quantum computation

TL;DR

This paper explores how Boolean functions can be represented using quantum computation, introducing algorithms that connect algebraic forms with quantum logic, facilitating the transition from classical to quantum hardware.

Contribution

It presents new algorithms linking Boolean algebra with quantum logic circuits, enabling generalization to multibit and many-valued logic systems.

Findings

Quantum algorithms for Boolean functions are developed.

Methods allow generalization to multibit and k-valued logic.

Approach can improve quantum technology implementation.

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.