Summary
Following the development of quantum computers, a question has arisen regarding the relation between the basis of the classical theory of computation and the quantum theory. Here I argue against Deutsch’s claim that a physical principle, the Turing principle, underlies the famous Church-Turing hypothesis. I also discuss the computational analogy and emphasize a certain line of argument suggesting it may be misplaced. Finally, I assess Deutsch’s claims for the dependence of mathematics upon empirical science, claims that arise as a consequence of his conception of computation and his adherence to the computational analogy.
Thanks are due to Harvey Brown and David Corfield for useful discussion. This work was supported by a studentship from the UK Arts and Humanities Research Board.
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Timpson, C.G. (2004). Quantum Computers: the Church-Turing Hypothesis Versus the Turing Principle. In: Teuscher, C. (eds) Alan Turing: Life and Legacy of a Great Thinker. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05642-4_9
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