A ZX-Calculus with Triangles for Toffoli-Hadamard, Clifford+T, and Beyond

We consider a ZX-calculus augmented with triangle nodes which is well-suited to reason on the so-called Toffoli-Hadamard fragment of quantum mechanics. We precisely show the form of the matrices it represents, and we provide an axiomatisation which makes the language complete for the Toffoli-Hadamar...

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Bibliographic Details
Main Author: Renaud Vilmart
Format: Article
Language:English
Published: Open Publishing Association 2019-01-01
Series:Electronic Proceedings in Theoretical Computer Science
Online Access:http://arxiv.org/pdf/1804.03084v3