Basic definitions of quantum logic

Sergio Bernini

Hafiz Md. Hasan Babu

Many of the quantum gates are included in multiple chapters. Basic definitions of the different efficiency parameters of quantum logic which are needed to design quantum circuits are described in this chapter.

Ted Hurley

A unitary matrix is shown to be a product of certain {\em basic} unitary matrices and the product is unique up to order. A basic unitary matrix itself is a product of {\em minimal basic} matrices. A unitary $n\times n$ matrix can be expressed as a product of at most $n$ basic matrices. A basic matrix is defined in terms of an idempotent matrix; the idempotent matrix used in the definition of a minimal basic unitary matrix is a {\em density} matrix. This gives builders for unitary matrices. Quantum logic gates are represented by unitary matrices thus giving unique building material for quantum logic gates.

S?awomir Bugajski

Wasan Al-Shemmari, Ahmed Al-Adilee

This study is concerned with a definition of dependences on orthoalgebra. Such dependences have been illustrated via special maps that are defined on an orthoalgebra too. In fact, those dependences deals with a notion of non-compatibility which is one of the basic important issues in quantum logic studies. Several results have been presented to show various situations of each constructed dependence. Eventually, we have mentioned several notions related to the results that we have obtained and show some properties relevant to the proposed ideas.

Mladen Pavičić, Norman D. Megill