Geometry of Interaction for ZX-Diagrams

Kostia Chardonnet (1, 2, 3) , Benoît Valiron (1, 4, 3) , Renaud Vilmart (1, 3)

1 LMF - Laboratoire Méthodes Formelles
2 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale
3 QuaCS - Quantum Computation Structures
4 CentraleSupélec

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.

Mots clés: Quantum Computation; Linear Logic; ZX-Calculus; Geometry of Interaction

Domaines: Physique Quantique [quant-ph]; Logique en informatique [cs.LO]

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⟩