License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2021.30
URN: urn:nbn:de:0030-drops-144701
URL: https://drops.dagstuhl.de/opus/volltexte/2021/14470/
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Chardonnet, Kostia ; Valiron, BenoƮt ; Vilmart, Renaud

Geometry of Interaction for ZX-Diagrams

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LIPIcs-MFCS-2021-30.pdf (0.8 MB)


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.

BibTeX - Entry

@InProceedings{chardonnet_et_al:LIPIcs.MFCS.2021.30,
  author =	{Chardonnet, Kostia and Valiron, Beno\^{i}t and Vilmart, Renaud},
  title =	{{Geometry of Interaction for ZX-Diagrams}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{30:1--30:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14470},
  URN =		{urn:nbn:de:0030-drops-144701},
  doi =		{10.4230/LIPIcs.MFCS.2021.30},
  annote =	{Keywords: Quantum Computation, Linear Logic, ZX-Calculus, Geometry of Interaction}
}

Keywords: Quantum Computation, Linear Logic, ZX-Calculus, Geometry of Interaction
Collection: 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)
Issue Date: 2021
Date of publication: 18.08.2021


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