Geometry of Interaction for ZX-Diagrams. Chardonnet, K., Valiron, B., & Vilmart, R. In Bonchi, F. & Puglisi, S. J., editors, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021), volume 202, of Leibniz International Proceedings in Informatics (LIPIcs), pages 30:1–30:16, Dagstuhl, Germany, August, 2021. Schloss Dagstuhl – Leibniz-Zentrum für Informatik. Paper doi abstract bibtex 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-machine-based 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.
@inproceedings{Chardonnet2021,
title = {{Geometry of Interaction for ZX-Diagrams}},
author = {Chardonnet, Kostia and Valiron, Beno{\^i}t and Vilmart, Renaud},
year = {2021},
month = aug,
booktitle = {46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
editor = {Bonchi, Filippo and Puglisi, Simon J.},
publisher = dagstuhl,
address = {Dagstuhl, Germany},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
volume = {202},
eid = {30},
pages = {30:1--30:16},
doi = {10.4230/LIPIcs.MFCS.2021.30},
url = {https://hal.archives-ouvertes.fr/hal-03154573/},
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-machine-based 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.},
keywords = {quantum computation, linear logic, zx-calculus, geometry of interaction},
bibsource = qplbib
}
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