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〉
Liste complète des métadonnées

Littérature citée [21 références]  Voir  Masquer  Télécharger
https://hal.inria.fr/hal-01091582
Contributeur : Ugo Dal Lago <>
Soumis le : vendredi 5 décembre 2014 - 16:31:00
Dernière modification le : samedi 27 janvier 2018 - 01:31:33
Document(s) archivé(s) le : lundi 9 mars 2015 - 06:04:44

Fichier

esop14extended.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

INRIA | PPS | USPC

Citation

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〉

Exporter

BibTeX TEI DC DCterms EndNote

Partager

Métriques

Consultations de la notice

242

Téléchargements de fichiers

114

Contact


archive-ouverte@inria.fr