### 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 language | English (US) |
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Title of host publication | Quantum Information and Computation XIII |

Editors | Michael Hayduk, Andrew R. Pirich, Eric Donkor |

Publisher | SPIE |

ISBN (Electronic) | 9781628416169 |

DOIs | |

State | Published - Jan 1 2015 |

Event | Quantum Information and Computation XIII - Baltimore, United States Duration: Apr 22 2015 → Apr 24 2015 |

### Publication series

Name | Proceedings of SPIE - The International Society for Optical Engineering |
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Volume | 9500 |

ISSN (Print) | 0277-786X |

ISSN (Electronic) | 1996-756X |

### Other

Other | Quantum Information and Computation XIII |
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Country | United States |

City | Baltimore |

Period | 4/22/15 → 4/24/15 |

### 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

*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