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Conference Papers Year : 2019

SZX-calculus: Scalable Graphical Quantum Reasoning


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.

Dates and versions

hal-02400070 , version 1 (09-12-2019)



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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