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.2022.24
URN: urn:nbn:de:0030-drops-168225
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16822/
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Booth, Robert I. ; Carette, Titouan

Complete ZX-Calculi for the Stabiliser Fragment in Odd Prime Dimensions

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Abstract

We introduce a family of ZX-calculi which axiomatise the stabiliser fragment of quantum theory in odd prime dimensions. These calculi recover many of the nice features of the qubit ZX-calculus which were lost in previous proposals for higher-dimensional systems. We then prove that these calculi are complete, i.e. provide a set of rewrite rules which can be used to prove any equality of stabiliser quantum operations. Adding a discard construction, we obtain a calculus complete for mixed state stabiliser quantum mechanics in odd prime dimensions, and this furthermore gives a complete axiomatisation for the related diagrammatic language for affine co-isotropic relations.

BibTeX - Entry

@InProceedings{booth_et_al:LIPIcs.MFCS.2022.24,
  author =	{Booth, Robert I. and Carette, Titouan},
  title =	{{Complete ZX-Calculi for the Stabiliser Fragment in Odd Prime Dimensions}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{24:1--24:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16822},
  URN =		{urn:nbn:de:0030-drops-168225},
  doi =		{10.4230/LIPIcs.MFCS.2022.24},
  annote =	{Keywords: ZX-calculus, completeness, quantum, stabiliser, qudits}
}

Keywords: ZX-calculus, completeness, quantum, stabiliser, qudits
Collection: 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)
Issue Date: 2022
Date of publication: 22.08.2022

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