Quantum speed-up of computations


Abstract
1. The Physical Church-Turing Thesis. Physicists often interpret the Church-Turing Thesis as saying something about the scope and limitations of physical computing machines. Although this was not the intention of Church or Turing, the Physical Church Turing thesis is interesting in its own right. Consider, for example, Wolfram’s formulation: One can expect in fact that universal computers are as powerful in their computational capabilities as any physically realizable system can be, that they can simulate any physical system . . . No physically implementable procedure could then shortcut a computationally irreducible process. (Wolfram 1985) Wolfram’s thesis consists of two parts: (a) Any physical system can be simulated (to any degree of approximation) by a universal Turing machine (b) Complexity bounds on Turing machine simulations have physical significance. For example, suppose that the computation of the minimum energy of some system of n particles takes at least exponentially (in n) many steps. Then the relaxation time of the actual physical system to its minimum energy state will also take exponential time.
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DOI 10.1086/341843
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References found in this work BETA

21 Undecidability and Intractability in Theoretical Physics.Stephen Wolfram - 2013 - Emergence: Contemporary Readings in Philosophy and Science.
Laplace's Demon Consults an Oracle: The Computational Complexity of Prediction.Itamar Pitowsky - 1996 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 27 (2):161-180.

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Citations of this work BETA

The Physical Church-Turing Thesis: Modest or Bold?Gualtiero Piccinini - 2011 - British Journal for the Philosophy of Science 62 (4):733-769.
On the Significance of the Gottesman–Knill Theorem.Michael E. Cuffaro - 2017 - British Journal for the Philosophy of Science 68 (1):91-121.
Quantum Algorithms: Philosophical Lessons.Amit Hagar - 2007 - Minds and Machines 17 (2):233-247.
Quantum Hypercomputation—Hype or Computation?Amit Hagar & Alex Korolev - 2007 - Philosophy of Science 74 (3):347-363.

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