Presheaf models of quantum computation: an outline
release_xv4rzpvw4bdlro6eun33wetnoi
by
Octavio Malherbe, Philip Scott, Peter Selinger
2013
Abstract
This paper outlines the construction of categorical models of higher-order
quantum computation. We construct a concrete denotational semantics of Selinger
and Valiron's quantum lambda calculus, which was previously an open problem. We
do this by considering presheaves over appropriate base categories arising from
first-order quantum computation. The main technical ingredients are Day's
convolution theory and Kelly and Freyd's notion of continuity of functors. We
first give an abstract description of the properties required of the base
categories for the model construction to work. We then exhibit a specific
example of base categories satisfying these properties.
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