Quantum theory, the Church–Turing principle and the universal quantum computer

@article{Deutsch1985QuantumTT,
  title={Quantum theory, the Church–Turing principle and the universal quantum computer},
  author={D. Deutsch},
  journal={Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences},
  year={1985},
  volume={400},
  pages={117 - 97}
}
  • D. Deutsch
  • Published 1985
  • Mathematics
  • Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
It is argued that underlying the Church–Turing hypothesis there is an implicit physical assertion. Here, this assertion is presented explicitly as a physical principle: ‘every finitely realizible physical system can be perfectly simulated by a universal model computing machine operating by finite means’. Classical physics and the universal Turing machine, because the former is continuous and the latter discrete, do not obey the principle, at least in the strong form above. A class of model… Expand
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    References

    SHOWING 1-10 OF 32 REFERENCES
    Church's Thesis and Principles for Mechanisms
    TLDR
    It is argued that Turing's analysis of computation by a human being does not apply directly to mechanical devices, and it is proved that if a device satisfies the principles then its successive states form a computable sequence. Expand
    On the Einstein-Podolsky-Rosen paradox
    THE paradox of Einstein, Podolsky and Rosen [1] was advanced as an argument that quantum mechanics could not be a complete theory but should be supplemented by additional variables. These additionalExpand
    On quantum-mechanical automata
    Abstract An automaton whose states are solutions of quantum-mechanical equations of motion is described, and the capacities of such an automaton to “measure” and to “know” and to “predict” certainExpand
    Universal upper bound on the entropy-to-energy ratio for bounded systems
    We present evidence for the existence of a universal upper bound of magnitude $\frac{2\ensuremath{\pi}R}{\ensuremath{\hbar}c}$ to the entropy-to-energy ratio $\frac{S}{E}$ of an arbitrary system ofExpand
    Computation and Construction Universality of Reversible Cellular Automata
    • T. Toffoli
    • Computer Science, Mathematics
    • J. Comput. Syst. Sci.
    • 1977
    TLDR
    A way of implementing nontrivial irreversible processes in a reversible medium is explicitly shown, both in general and for reversible cellular automata. Expand
    Black holes and entropy
    There are a number of similarities between black-hole physics and thermodynamics. Most striking is the similarity in the behaviors of black-hole area and of entropy: Both quantities tend to increaseExpand
    Gödel, Escher, Bach: An Eternal Golden Braid
    From the Publisher: Winner of the Pulitzer Prize, this book applies Godel's seminal contribution to modern mathematics to the study of the human mind and the development of artificial intelligence.
    The Logic of Scientific Discovery.
    Int. J. theor. Phys
    • Int. J. theor. Phys
    • 1985
    1976Conceptual foundations of quantum mechanics (second edn)
    • 1976
    ...
    1
    2
    3
    4
    ...