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.MFCS.2019.55
URN: urn:nbn:de:0030-drops-109999
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10999/
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Carette, Titouan ; Horsman, Dominic ; Perdrix, Simon

SZX-Calculus: Scalable Graphical Quantum Reasoning

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LIPIcs-MFCS-2019-55.pdf (0.7 MB)

Abstract

We introduce the Scalable ZX-calculus (SZX-calculus for short), a formal and compact graphical language for the design and verification of quantum computations. The SZX-calculus is an extension of the ZX-calculus, a powerful framework that captures graphically the fundamental properties of quantum mechanics through its complete set of rewrite rules. The ZX-calculus is, however, a low level language, with each wire representing a single qubit. This limits its ability to handle large and elaborate quantum evolutions. We extend the ZX-calculus to registers of qubits and allow compact representation of sub-diagrams via binary matrices. We show soundness and completeness of the SZX-calculus and provide two examples of applications, for graph states and error correcting codes.

BibTeX - Entry

@InProceedings{carette_et_al:LIPIcs:2019:10999,
  author =	{Titouan Carette and Dominic Horsman and Simon Perdrix},
  title =	{{SZX-Calculus: Scalable Graphical Quantum Reasoning}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{55:1--55:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Peter Rossmanith and Pinar Heggernes and Joost-Pieter Katoen},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10999},
  URN =		{urn:nbn:de:0030-drops-109999},
  doi =		{10.4230/LIPIcs.MFCS.2019.55},
  annote =	{Keywords: Quantum computing, categorical quantum mechanics, completeness, scalability}
}

Keywords: Quantum computing, categorical quantum mechanics, completeness, scalability
Collection: 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)
Issue Date: 2019
Date of publication: 20.08.2019

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