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SZX-Calculus: Scalable Graphical Quantum Reasoning

Authors Titouan Carette , Dominic Horsman, Simon Perdrix



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Titouan Carette
  • CNRS, LORIA, Inria Mocqua, Université de Lorraine, F 54000 Nancy, France
Dominic Horsman
  • LIG, Université Grenoble Alpes, France
Simon Perdrix
  • CNRS, LORIA, Inria Mocqua, Université de Lorraine, F 54000 Nancy, France

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Titouan Carette, Dominic Horsman, and Simon Perdrix. SZX-Calculus: Scalable Graphical Quantum Reasoning. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 55:1-55:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.MFCS.2019.55

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum computation theory
Keywords
  • Quantum computing
  • categorical quantum mechanics
  • completeness
  • scalability

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