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Semantics of higherorder quantum computation via geometry of interaction,” Extended version
, 2011
"... Abstract—While much of the current study on quantum computation employs lowlevel formalisms such as quantum circuits, several highlevel languages/calculi have been recently proposed aiming at structured quantum programming. The current work contributes to the semantical study of such languages, by ..."
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Abstract—While much of the current study on quantum computation employs lowlevel formalisms such as quantum circuits, several highlevel languages/calculi have been recently proposed aiming at structured quantum programming. The current work contributes to the semantical study of such languages, by providing interactionbased semantics of a functional quantum programming language; the latter is based on linear lambda calculus and is equipped with features like the! modality and recursion. The proposed denotational model is the first one that supports the full features of a quantum functional programming language; we also prove adequacy of our semantics. The construction of our model is by a series of existing techniques taken from the semantics of classical computation as well as from process theory. The most notable among them is Girard’s Geometry of Interaction (GoI), categorically formulated by Abramsky, Haghverdi and Scott. The mathematical genericity of these techniques—largely due to their categorical formulation—is exploited for our move from classical to quantum. Keywordsquantum computation; lambda calculus; categorical semantics; geometry of interaction; realizability I.
Linear realizability
, 2007
"... Abstract. We define a notion of relational linear combinatory algebra (rLCA) which is a generalization of a linear combinatory algebra defined by Abramsky, Haghverdi and Scott. We also define a category of assemblies as well as a category of modest sets which are realized by rLCA. This is a linear s ..."
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Abstract. We define a notion of relational linear combinatory algebra (rLCA) which is a generalization of a linear combinatory algebra defined by Abramsky, Haghverdi and Scott. We also define a category of assemblies as well as a category of modest sets which are realized by rLCA. This is a linear style of realizability in a way that duplicating and discarding of realizers is allowed in a controlled way. Both categories form linearnonlinear models and their coKleisli categories have a natural number object. We construct some examples of rLCA’s which have some relations to well known PCA’s. 1
Abstract A Type Assignment System for Game Semantics ⋆
"... dedicated to Mariangiola, Mario and Simona, on the occasion of their 60 th birthdays We present a type assignment system that provides a finitary interpretation of lambda terms in a game semantics model. Traditionally, type assignment systems describe the semantic interpretation of terms in domain t ..."
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dedicated to Mariangiola, Mario and Simona, on the occasion of their 60 th birthdays We present a type assignment system that provides a finitary interpretation of lambda terms in a game semantics model. Traditionally, type assignment systems describe the semantic interpretation of terms in domain theoretic models. Quite surprisingly, the type assignment system presented in this paper is very similar to the traditional ones, the main difference being the omission of the subtyping rules.
Quantum Programming Language
"... “when we can run a GoI business” not like “category of games” ..."