mindpixel's Journal: Classically Controlled Quantum Turing Machines (CQTMs)

I don't think it is a coincidence the number of dimensions at which hypersurface area is maximum is about seven and that human working memory has a span of about seven digits and that the thalmocortical system is seven layered and String theory, which is really the latest and greatest in physics, postulates that every point in our observable three-dimensional space is a heptaball...quadruple coincidence? Seems unlikely.

When I wrote about classical Turing machines with quantum tape in my November 15th post, I didn't know if they existed as theoretical objects or not. Well, they do, but they are new--about five months old [Simon Perdrix, Philippe Jorrand, July 2004].

Abstract: "Quantum computations usually take place under the control of the classical world. We introduce a Classically-controlled Quantum Turing Machine (CQTM) which is a Turing Machine (TM) with a quantum tape for acting on quantum data, and a classical transition function for a formalized classical control. In CQTM, unitary transformations and measurements are allowed. We show that any classical TM is simulated by a CQTM without loss of efficiency. The gap between classical and quantum computations, already pointed out in the framework of measurement-based quantum computation is confirmed. To appreciate the similarity of programming classical TM and CQTM, examples are given."

So CQTMs are cutting edge of theoretical computer science. The polydimensional tape geometry is novel however. It does not generalize to one dimensional tape or multi-tape machines. Something is gained because of the number of dimensions in the geometry--surface area. And the larger the surface area the more complex a pattern on its surface can be. The maximum hypersurface of a seven-sphere makes it the largest possible complexity reservoir.