License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2020.118
URN: urn:nbn:de:0030-drops-125250
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12525/
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Carette, Titouan ; Jeandel, Emmanuel

A Recipe for Quantum Graphical Languages

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LIPIcs-ICALP-2020-118.pdf (0.6 MB)

Abstract

Different graphical calculi have been proposed to represent quantum computation. First the ZX-calculus [Coecke and Duncan, 2011], followed by the ZW-calculus [Hadzihasanovic, 2015] and then the ZH-calculus [Backens and Kissinger, 2018]. We can wonder if new ZX-like calculi will continue to be proposed forever. This article answers negatively. All those language share a common core structure we call Z^*-algebras. We classify Z^*-algebras up to isomorphism in two dimensional Hilbert spaces and show that they are all variations of the aforementioned calculi. We do the same for linear relations and show that the calculus of [Bonchi et al., 2017] is essentially the unique one.

BibTeX - Entry

@InProceedings{carette_et_al:LIPIcs:2020:12525,
  author =	{Titouan Carette and Emmanuel Jeandel},
  title =	{{A Recipe for Quantum Graphical Languages}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{118:1--118:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Artur Czumaj and Anuj Dawar and Emanuela Merelli},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12525},
  URN =		{urn:nbn:de:0030-drops-125250},
  doi =		{10.4230/LIPIcs.ICALP.2020.118},
  annote =	{Keywords: Categorical Quantum Mechanics, Quantum Computing, Category Theory}
}

Keywords: Categorical Quantum Mechanics, Quantum Computing, Category Theory
Collection: 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)
Issue Date: 2020
Date of publication: 29.06.2020

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