The Emergence of New Models of Computing : from Digits to Quantum Computing and Beyond

We begin with a brief review of the basic notions of classical computability theory and the Turing machine. The concept of decidability and computability, as well as the Church-Turing thesis are also introduced. The recently formalized foundations of quantum computability theory are surveyed next. Included are such topics as the universal quantum computer; the use of quantum parallelism in computation; and the Church-Turing principle. We highlight some avenues of research for new computational paradigms and suggest that underlying the new advances in both the theory and practical aspects (actual devices), is a new conceptual basis for interpreting the interactions that produce complex and partially understood processe.