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SZX-calculus: Scalable Graphical Quantum Reasoning

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.
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Contributor : Simon Perdrix <>
Submitted on : Monday, December 9, 2019 - 1:27:48 PM
Last modification on : Thursday, November 19, 2020 - 1:01:58 PM

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Titouan Carette, Dominic Horsman, Simon Perdrix. SZX-calculus: Scalable Graphical Quantum Reasoning. MFCS 2019 - 44th International Symposium on Mathematical Foundations of Computer Science, Aug 2019, Aachen, Germany. pp.55:1--55:15, ⟨10.4230/LIPIcs.MFCS.2019.55⟩. ⟨hal-02400070⟩



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