An overview is presented that investigates Classical Turing Machines and their relationship to quantum computing and Quantum Turing Machines. The examination begins by exploring the original work of Alonzo Church and Alan Turing, defining what is a Turing Machine, and discussing the differences between recursion and interation and how this relates to the overall debate on comparing present day digital computing to the Turing Machine.
Because the Turing Machine is a theoretical contrivance, it still has limitations placed upon it that can be generally overcome by considering quantum computational approaches. In order to understand quantum computing, one must first become familiar with the basics of quantum mechanics as they relate to this approach.
Finally, some of the major results associated with quantum computing are examined. The presentation concludes with a summation of the technology.
In 1936, Alonzo Church (an American) and Alan Turing (from England) independently published the basics of what became a new branch of mathematics, computability or recursive functions. This later developed into what we term today as "Automata Theory" (Vaknin, 2001). Both researches confined themselves to dealing with those classes of computation involving effective or mechanical methods for obtaining results and were so named because they could theoretically be performed by simple machines. The emphasis at this stage of their research was on a finite number of instructions, a finite number of symbols in each instruction, and a finite number of steps to obtain the result. As such what Church and Turing were able to do was to construct a set of all of the functions whose values could be obtained through the use of effective or mechanical calculation method.
Church introduced partial functions as a formalization of algorithmically computable functions (Mohr, 2000). He also recognized that all formalizations of algorithms were...