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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Malherbe, O., Scott, P., Selinger, P. (2013). Presheaf Models of Quantum Computation: An Outline. In: Coecke, B., Ong, L., Panangaden, P. (eds) Computation, Logic, Games, and Quantum Foundations. The Many Facets of Samson Abramsky. Lecture Notes in Computer Science, vol 7860. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38164-5_13
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