Church–Turing–Deutsch principle

In computer science and quantum physics, the Church–Turing–Deutsch principle (CTD principle) is a stronger, physical form of the Church–Turing thesis formulated by David Deutsch in 1985.^[1] The principle states that a universal computing device can simulate every physical process.

History

The principle was stated by Deutsch in 1985 with respect to finitary machines and processes. He observed that classical physics, which makes use of the concept of real numbers, cannot be simulated by a Turing machine, which can only represent computable reals. Deutsch proposed that quantum computers may actually obey the CTD principle, assuming that the laws of quantum physics can completely describe every physical process.

An earlier version of this thesis for classical computers was stated by Alan Turing's friend and student Robin Gandy in 1980.^[2][3]

A similar thesis was stated by Michael Freedman in an early review of topological quantum computing with Alexei Kitaev, Michael J. Larsen, and Zhenghan Wang, known as the Freedman-Church-Turing thesis^[4]:

"All 'reasonable' computational models which add the resources of quantum mechanics (or quantum field theory) to classical computation yield (efficiently) inter-simulable classes: there is one quantum theory of computation."

This thesis differs from the Church-Turing-Deutsch thesis insofar as it is a statement about computational complexity, and not computability.

See also

• Bekenstein bound
• Digital physics
• Holographic principle
• Quantum complexity theory
• Laplace's demon

Notes

1. Nielsen, Michael (16 April 2004). "Interesting problems: The Church–Turing–Deutsch Principle". Retrieved 10 May 2014.
2. Gandy, R. (1980). Church’s thesis and principles for mechanisms. Studies in Logic and the Foundations of Mathematics (101), 123–148
3. Kaznatcheev, Artem (2014). "Falsifiability and Gandy's variant of the Church-Turing thesis". Theory, Evolution, and Games Group Blog. Retrieved 23 July 2018.
4. Freedman, Michael H.; Kitaev, Alexei; Larsen, Michael J.; Wang, Zhenghan (2002-09-20). "Topological Quantum Computation". arXiv:quant-ph/0101025.

References

• Deutsch, D. (1985). "Quantum theory, the Church–Turing principle and the universal quantum computer" (PDF). Proceedings of the Royal Society. 400 (1818): 97–117. Bibcode:1985RSPSA.400...97D. CiteSeerX 10.1.1.41.2382. doi:10.1098/rspa.1985.0070. S2CID 1438116. Archived from the original (PDF) on 2016-03-09. Retrieved 2011-08-17.

Further reading

• Deutsch, D. (1997). "6: Universality and the Limits of Computation". The Fabric of Reality. New York: Allan Lane. ISBN 978-0-14-027541-4.
• Christopher G. Timpson Quantum Computers: the Church-Turing Hypothesis Versus the Turing Principle in Christof Teuscher, Douglas Hofstadter (eds.) Alan Turing: life and legacy of a great thinker, Springer, 2004, ISBN 3-540-20020-7, pp. 213–240

External links

• Nielsen, Michael (2004-04-16). "Interesting problems: The Church–Turing–Deutsch Principle".