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Geometry of Interaction for ZX-Diagrams

Abstract : ZX-Calculus is a versatile graphical language for quantum computation equipped with an equational theory. Getting inspiration from Geometry of Interaction, in this paper we propose a token-machinebased asynchronous model of both pure ZX-Calculus and its extension to mixed processes. We also show how to connect this new semantics to the usual standard interpretation of ZX-diagrams. This model allows us to have a new look at what ZX-diagrams compute, and give a more local, operational view of the semantics of ZX-diagrams.
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https://hal.archives-ouvertes.fr/hal-03154573
Contributor : Kostia Chardonnet Connect in order to contact the contributor
Submitted on : Monday, March 1, 2021 - 9:53:55 AM
Last modification on : Thursday, April 28, 2022 - 4:12:03 PM
Long-term archiving on: : Sunday, May 30, 2021 - 7:43:09 PM

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Kostia Chardonnet, Benoît Valiron, Renaud Vilmart. Geometry of Interaction for ZX-Diagrams. MFCS 2021 - 46th International Symposium on Mathematical Foundations of Computer Science, Aug 2021, Tallinn, Estonia. pp.30:1--30:16, ⟨10.4230/LIPIcs.MFCS.2021.30⟩. ⟨hal-03154573⟩

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