Semantics of higher-order quantum computation via geometry of interaction

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• 作者：Ichiro Hasuo^a ; ¹ ; ^{ichiro@is.s.u-tokyo.ac.jp} ; Naohiko Hoshino^b ; ² ; ^{naophiko@kurims.kyoto-u.ac.jp}
• 关键词：03B70 ; 18C20 ; 18C50 ; 81P68
• 刊名：Annals of Pure and Applied Logic
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：168
• 期：2
• 页码：404-469
• 全文大小：1670 K
• 卷排序：168

文摘

While much of the current study on quantum computation employs low-level formalisms such as quantum circuits, several high-level languages/calculi have been recently proposed aiming at structured quantum programming. The current work contributes to the semantical study of such languages by providing interaction-based semantics of a functional quantum programming language; the latter is, much like Selinger and Valiron's, based on linear lambda calculus and 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 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.