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.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1086/341843
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 47,395
Through your library

References found in this work BETA

On Computable Numbers, with an Application to the Entscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.
21 Undecidability and Intractability in Theoretical Physics.Stephen Wolfram - 2013 - Emergence: Contemporary Readings in Philosophy and Science.
[Omnibus Review].Kenneth Kunen - 1969 - Journal of Symbolic Logic 34 (3):515-516.

View all 11 references / Add more references

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.
Hypercomputation and the Physical Church‐Turing Thesis.Paolo Cotogno - 2003 - British Journal for the Philosophy of Science 54 (2):181-223.
Quantum Algorithms: Philosophical Lessons.Amit Hagar - 2007 - Minds and Machines 17 (2):233-247.

View all 11 citations / Add more citations

Similar books and articles

Analytics

Added to PP index
2009-01-28

Total views
93 ( #94,865 of 2,291,330 )

Recent downloads (6 months)
1 ( #827,672 of 2,291,330 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature