Chapter 1 Quantum Computing Basics and Concepts

Chapter 1 Quantum Computing Basics IntroductionThis book is for researchers and students of computational intelligence as well as forengineers interested in designing Quantum algorithms in the circuit content of this book is presented as a set of design methods of Quantum circuitswith the focus on evolutionary algorithm; however some heuristic algborithms aswell as a wide range of application of Quantum circuits are general idea behind this book is to represent every computational problemas a Quantum circuit and then to use some classical synthesisapproach to designthe circuit. The goal of such approach is to describe and illustrate the use of clas-sical design methods and their extension into Quantum logicsynthesis. The reasonof using the circuit representation is that in classical logic synthesis various algo-rithms exist for the design of both combinatorial and sequential circuits and thusdesigning Quantum algorithms in the circuit representation provides a good basisfor comparison.

The information in quantum computation is represented by a qubit that in the Dirac notation can be written in the form of a characteristic equation. For instance a qubit with two possible orthonormal states |0iand |1iis described by eq. 1.2. The

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