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SZX-Calculus: Scalable Graphical Quantum Reasoning Carette, Titouan Horsman, Dominic Perdrix, Simon Quantum computing categorical quantum mechanics completeness scalability 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Titouan Carette and Dominic Horsman and Simon Perdrix 2019 Is Part Of LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.MFCS.2019.55 urn:nbn:de:0030-drops-109999 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.55 eng https://creativecommons.org/licenses/by/3.0/legalcode