Heterotic quantum and classical computing on convergence spaces

D. R. Patten, D. W. Jakel, R. J. Irwin, H. A. Blair

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Category-theoretic characterizations of heterotic models of computation, introduced by Stepney et al., combine computational models such as classical/quantum, digital/analog, synchronous/asynchronous, etc. to obtain increased computational power. A highly informative classical/quantum heterotic model of computation is represented by Abramsky's simple sequential imperative quantum programming language which extends the classical simple imperative programming language to encompass quantum computation. The mathematical (denotational) semantics of this classical language serves as a basic foundation upon which formal verification methods can be developed. We present a more comprehensive heterotic classical/quantum model of computation based on heterotic dynamical systems on convergence spaces. Convergence spaces subsume topological spaces but admit finer structure from which, in prior work, we obtained differential calculi in the cartesian closed category of convergence spaces allowing us to define heterotic dynamical systems, given by coupled systems of first order differential equations whose variables are functions from the reals to convergence spaces.

Original languageEnglish (US)
Title of host publicationQuantum Information and Computation XIII
EditorsMichael Hayduk, Andrew R. Pirich, Eric Donkor
PublisherSPIE
ISBN (Electronic)9781628416169
DOIs
StatePublished - Jan 1 2015
EventQuantum Information and Computation XIII - Baltimore, United States
Duration: Apr 22 2015Apr 24 2015

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
Volume9500
ISSN (Print)0277-786X
ISSN (Electronic)1996-756X

Other

OtherQuantum Information and Computation XIII
CountryUnited States
CityBaltimore
Period4/22/154/24/15

Keywords

  • Cartesian-closed
  • category
  • convergence space
  • dynamical system
  • functor
  • heterotic
  • quantum

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering

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  • Cite this

    Patten, D. R., Jakel, D. W., Irwin, R. J., & Blair, H. A. (2015). Heterotic quantum and classical computing on convergence spaces. In M. Hayduk, A. R. Pirich, & E. Donkor (Eds.), Quantum Information and Computation XIII [950010] (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 9500). SPIE. https://doi.org/10.1117/12.2179050