文章基本信息

标题：A ZX-Calculus with Triangles for Toffoli-Hadamard, Clifford+T, and Beyond
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作者：Renaud Vilmart
期刊名称：Electronic Proceedings in Theoretical Computer Science
电子版ISSN：2075-2180
出版年度：2019
卷号：287
页码：313-344
DOI：10.4204/EPTCS.287.18
语种：English
出版社：Open Publishing Association
摘要：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-Hadamard quantum mechanics. We extend the language with arbitrary angles and show that any true equation involving linear diagrams which constant angles are multiple of Pi are derivable. We show that a single axiom is then necessary and sufficient to make the language equivalent to the ZX-calculus which is known to be complete for Clifford+T quantum mechanics. As a by-product, it leads to a new and simple complete axiomatisation for Clifford+T quantum mechanics.