nLab
quantum computation

Context

Constructivism, Realizability, Computability

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Contents

Idea

Quantum computation is computation in terms of quantum information theory, possibly implemented on quantum computers, hence on physical systems for which phenomena of quantum mechanics are not negligible. In terms of computational trinitarianism quantum computation is the computation corresponding to (some kind of) quantum logic.

Specifically, topological quantum computation is (or is meant to be) quantum computation implemented on physical systems governed by topological quantum field theory, such as Chern-Simons theory. A prominent example of this is the (fractional) quantum Hall effect in solid state physics.

There are arguments that a good formal context for quantum computing is (via computational trinitarianism) linear logic/linear type theory (e.g. Lago-Faffian 12). See also at quantum logic.

Programing languages

References

General

General discussions include

  • Michael A. Nielsen, Isaac L. Chuang, Quantum computation and quantum information, Cambridge University Press 2000 (pdf)

  • Greg Kuperberg, A concise introduction to quantum probability, quantum mechanics, and quantum computation, 2005 (pdf)

  • Michael Loceff, A course in quantum computing, 2013 (pdf)

  • Wikipedia, Quantum computation

  • Scott Aaronson, Lecture notes Quantum Computing Since Democritus 2006 (web)

As linear logic

Discussion of quantum computation as the internal linear logic/linear type theory of compact closed categories is in

An exposition along these lines is in

  • John Baez, Mike Stay, Physics, topology, logic and computation: a rosetta stone, arxiv/0903.0340; in “New Structures for Physics”, ed. Bob Coecke, Lecture Notes in Physics 813, Springer, Berlin, 2011, pp. 95-174

See also the references at finite quantum mechanics in terms of dagger-compact categories.

In terms of monads

Discussion of aspects of quantum computing in terms of monads in functional programming are in

Topological quantum computing

topological quantum computation is discussed in

Revised on May 25, 2015 16:38:41 by Urs Schreiber (195.113.30.252)