Between the Turing machine and the Church-Turing Thesis a strong foundation was made for study of that what was computable and uncomputable. Complexity analysis allows for a more granular distinction between the tractability of any particular problem on a Turing machine.
The components in classical computers are rapidly shrinking to a size where quantum behavior is inevitable. Through the principle of superposition in quantum systems we can create useful memory components that are on the scale of an atom or smaller. These quantum memory registers may facilitate exponential computational speed increases by taking advantage of quantum parallelism.
Peter Shor has provided an algorithm which makes factoring large numbers tractable, and in doing so has drawn great attention to the field of quantum computing. Due to Shor's algorithm, we may someday have to turn to other means of encrypting data than currently employed. L. K. Grover's database search algorithm shows another noteworthy task that a quantum computer can perform faster than any classical computer.(Brassard) The efforts to build a functional quantum memory register are in the most preliminary stages.
Operational quantum computers are by no means an inevitable consequence of this research. It may be that the problems surrounding keeping a quantum memory register isolated from any disturbance long enough for a calculation to take place will be insurmountable. In any case, quantum computing will remain an exciting topic for experimentalists and theorists alike for years to come. Hopefully this paper, and the simulation of Shor's algorithm have been as enlightening and fun for the reader as they were for the author.