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DOI: 10.4230/LIPIcs.MFCS.2019.55
URN: urn:nbn:de:0030-drops-109999
URL: https://drops.dagstuhl.de/opus/volltexte/2019/10999/
Carette, Titouan ; Horsman, Dominic ; Perdrix, Simon
SZX-Calculus: Scalable Graphical Quantum Reasoning
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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 | |
| Seminar: | 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019) | |
| Issue date: | 2019 | |
| Date of publication: | 20.08.2019 |
