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.
- Quantum complexity theory
- Digital physics
- Holographic principle and Bekenstein bound, which prohibit unlimited precision real numbers in the physical universe
- Nielsen, Michael. "Interesting problems: The Church–Turing–Deutsch Principle". Retrieved 10 May 2014.
- Gandy, R. (1980). Church’s thesis and principles for mechanisms. Studies in Logic and the Foundations of Mathematics (101), 123–148
- Kaznatcheev, Artem. "Falsifiability and Gandy's variant of the Church-Turing thesis". Retrieved 23 July 2018.
- Deutsch, D. (1985). "Quantum theory, the Church–Turing principle and the universal quantum computer" (PDF). Proceedings of the Royal Society. 400 (1818): 97–117. CiteSeerX 10.1.1.41.2382. doi:10.1098/rspa.1985.0070.
- 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