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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).
Cited literature [21 references]
https://hal.inria.fr/hal-01091582
Contributor : Ugo Dal Lago <>
Submitted on : Friday, December 5, 2014 - 4:31:00 PM
Last modification on : Saturday, March 28, 2020 - 2:17:14 AM
Document(s) archivé(s) le : Monday, March 9, 2015 - 6:04:44 AM
Contributor : Ugo Dal Lago <>
Submitted on : Friday, December 5, 2014 - 4:31:00 PM
Last modification on : Saturday, March 28, 2020 - 2:17:14 AM
Document(s) archivé(s) le : Monday, March 9, 2015 - 6:04:44 AM
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esop14extended.pdf
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