Presheaf Models of Quantum Computation: An Outline [chapter]

Octavio Malherbe, Philip Scott, Peter Selinger
2013 Lecture Notes in Computer Science  
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
more » ... n 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.
doi:10.1007/978-3-642-38164-5_13 fatcat:vphga3zfbfa35kyhrhziem7bzi