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.

Date Published: 21 May 2015
PDF: 9 pages
Proc. SPIE 9500, Quantum Information and Computation XIII, 950010 (21 May 2015); doi: 10.1117/12.2179050

Published in SPIE Proceedings Vol. 9500:
Quantum Information and Computation XIII
Eric Donkor; Andrew R. Pirich; Michael Hayduk, Editor(s)