
Contents
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6.1 Introduction 6.1 Introduction
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6.2 Quantum computation and containing information 6.2 Quantum computation and containing information
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6.3 The Turing Principle versus the Church–Turing Hypothesis 6.3 The Turing Principle versus the Church–Turing Hypothesis
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6.3.1 Non-Turing computability? The example of Malament–Hogarth spacetimes 6.3.1 Non-Turing computability? The example of Malament–Hogarth spacetimes
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6.3.2 Lessons 6.3.2 Lessons
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6.4 The Church–Turing Hypothesis as a constraint on physics? 6.4 The Church–Turing Hypothesis as a constraint on physics?
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6.5 Message 6.5 Message
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6 6 Quantum Computation and the Church–Turing Hypothesis
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Published:April 2013
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Abstract
Some of the philosophical questions raised by the theory of quantum computation are discussed. First it is considered whether the possibility of exponential speed-up in quantum computation provides an argument for a more substantive notion of quantum information than so far allowed. It is concluded that this is not so. Then some questions regarding the status of the Church-Turing hypothesis in the light of quantum computation are considered. In particular, Deutsch’s claim that a physical principle, the Turing Principle, underlies the Church-Turing hypothesis is rebutted. Finally, the question of whether the Church-Turing hypothesis might serve as a constraint on the laws of physics is briefly considered.
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