Measurements in Proof Nets as Higher-Order Quantum Circuits

Akira Yoshimizu 1 Ichiro Hasuo 1 Claudia Faggian 2 Ugo Dal Lago 3, 4
1 The University of Tokyo
2 PPS - Preuves, Programmes et Systèmes
3 FOCUS - Foundations of Component-based Ubiquitous Systems
CRISAM - Inria Sophia Antipolis - Méditerranée , DISI - Dipartimento di Informatica - Scienza e Ingegneria [Bologna]
4 DISI - Dipartimento di Scienze dell'Informazione [Bologna]
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).
Keywords : Linear Logic Geometry of Interaction Proof-Nets
Type de document :
Communication dans un congrès
23rd European Symposium on Programming, Apr 2014, Grenoble, France. pp.371 - 391, 2014, 〈10.1007/978-3-642-54833-8_20〉
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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, 2014, 〈10.1007/978-3-642-54833-8_20〉. 〈hal-01091582〉

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