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Measurements in Proof Nets as Higher-Order Quantum Circuits

Abstract : We build on the series of work by Dal Lago and coauthors and identify proof nets (of linear logic) as higher-order quantum circuits. By accommodating quantum measurement using additive slices, we obtain a comprehensive frame-work for programming and interpreting quantum computation. Specifically, we introduce a quantum lambda calculus MLLqm and define its geometry of interac-tion (GoI) semantics—in the style of token machines—via the translation of terms into proof nets. Its soundness, i.e. invariance under reduction of proof nets, is es-tablished. The calculus MLLqm attains a pleasant balance between expressivity (it is higher-order and accommodates all quantum operations) and concreteness of models (given as token machines, i.e. in the form of automata).
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Submitted on : Friday, December 5, 2014 - 4:31:00 PM
Last modification on : Friday, January 21, 2022 - 4:13:06 AM
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Akira Yoshimizu, Ichiro Hasuo, Claudia Faggian, Ugo Dal Lago. Measurements in Proof Nets as Higher-Order Quantum Circuits. 23rd European Symposium on Programming, Apr 2014, Grenoble, France. pp.371 - 391, ⟨10.1007/978-3-642-54833-8_20⟩. ⟨hal-01091582⟩



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