The Turing Machine and Quantum Computing

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 finit

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d the thermodynamic limits to energy dissipation. Parallel computing applications where processors are randomly accessing a similar large number of other processors will naturally have a latency problem associated with their efficiency. Similarly longer wires need larger drivers that will encompass larger volume that will put limitations on packaging as well as thermodynamics. Quantum computing can potentially eliminate these challenges associated with computers used in a parallel processing type of architecture. Thus is opened the door to literally unlimited use of parallelism for those applications (like factoring) where classical methods utilize exponentially exploding time (Vitany, et al, 1996). Additionally, quantum-based search algorithms for use with unstructured databases are much faster (by a quadratic factor) than classical approaches. In order to better understand how quantum computers work, one must first better understand quantum mechanics. Quantum mechanics represents that branch of physics providing description to the microcosmic portion of the world in which we live. As such, quantum mechanics is governed by the Schroedinger Wave Equation. This fundamental law in quantum theory represents a collation of sma
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