Unitary and anti-unitary quantum description of the classical not gate

TL;DR

This paper explores the unitary and anti-unitary quantum operators that implement fundamental quantum gates, specifically the square root of the identity and negation, highlighting their roles in quantum basis transformations.

Contribution

It provides a detailed analysis of the unitary and anti-unitary representations of key quantum gates transforming computational basis states.

Findings

Identifies the specific forms of unitary and anti-unitary operators for these gates.

Clarifies the role of anti-unitary operators in quantum gate transformations.

Enhances understanding of quantum basis transformations through these operators.

Abstract

We consider the unitary and the anti--unitary operator realizations of two important genuine quantum gates that transform elements of the computational basis of into superpositions: the square root of the identity and the square root of the negation.