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.
Geometry of Interaction for ZX-Diagrams [link]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
}

Downloads: 0