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Historically, Turing machines have been the paradigm by which we defined computability and efficiency. This is based on Church's thesis that everything effectively computable can also be computed on a Turing machine. But since our world behaves quantum mechanically, it seems reasonable to also consider computing models that make use of quantum mechanical properties. First stated by Benioff [Ben82] and Feynman [Fey 8 2], this idea was formalized by Deutsch [Deu85] when he introduced his quantum computer and, later on, quantum gate arrays. This paper gives an introduction to quantum computing and briefly looks at a few results in quantum computation, not the least of which is Shor's polynomial time factoring algorithm.

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