2021/06/22 by Eduardo Mizraji, Mizraji, Eduardo
Computer Science · #03G05 #15A16 #15A24 #Advanced Algebra and Logic #Emerging Technologies (cs.ET) #FOS: Computer and information sciences #FOS: Physical sciences #Matrix Theory and Algorithms #Neural Networks and Applications #Other Computer Science (cs.OH) #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2107.06067
openalex publication_date 2021/06/22 · openalex created_date 2021/07/19 · openalex updated_date 2026/07/28
The square root of Not is a logical operator of importance in quantum computing theory and of interest as a mathematical object in its own right. In physics, it is a square complex matrix of dimension 2. In the present work it is a complex square matrix of arbitrary dimension. The introduction of linear algebra into logical theory has been enhanced in recent decades by the researches in the field of neural networks and quantum computing. Here we will make a brief description of the representation of logical operations through matrices and we show how general expressions for the two square roots of the Not operator are obtained. Then, we explore two topics. First, we study an extension to a non-quantum domain of a short form of Deutsch's algorithm. Then, we assume that a root of Not is a matrix extension of the imaginary unit i, and under this idea we obtain fully matrix versions for the Euler expansions and for the representations of circular functions by complex exponentials.