On capabilities of quantum-mechanical computer models

Abstract

The work includes the analyses of the theoretical capabilities of quantum-mechanical versus classical computer models in terms of their universality, their application domain, their efficacy in solving the problems and their technological feasibility. The concepts of deterministic Turing machine, probabilistic Turing machine and quantum-mechanical Turing machine are exposed. The concept of basic information unit of quantum-mechanical computer modelqubit is introduced and the qubit is represented through the use of Bloch sphere. The use of Dirac's bra-ket notation in description of quantum-mechanical state is explained, and the notation is used to form state equation of a quantummechanical Turing machine cell. Especially, consequences of quantum parallelism, quantum interference and wave function collapse are studied in respect to capabilities of quantum-mechanical computer models. The interrelationship between classes of problems that can be efficiently solved by quantum mechanical and/or classical computer models is displayed.