论文标题
ZX-Calculus的代数完全公理化，并通过基本基质操作正常形式
Algebraic complete axiomatisation of ZX-calculus with a normal form via elementary matrix operations
论文作者
论文摘要
在本文中，我们通过基本变换为Qubit ZX-Calculus提供了完整的公理化，这是线性代数中的基本操作。这种形式主义具有两个主要优势。首先，所有阶段的操作都是代数的操作，而无需涉及三角学函数，因此为将Qubit ZX-Calculus的完全公理化铺平了道路，以使其在交换性半径上对Qudit ZX-Calculus和ZX-Calculus进行Qudit ZX-Calculus和ZX-Calculus。其次，我们用ZX图来表征基本变换，因此可以纯粹地将许多线性代数内容进行。
In this paper we give a complete axiomatisation of qubit ZX-calculus via elementary transformations which are basic operations in linear algebra. This formalism has two main advantages. First, all the operations of the phases are algebraic ones without trigonometry functions involved, thus paved the way for generalising complete axiomatisation of qubit ZX-calculus to qudit ZX-calculus and ZX-calculus over commutative semirings. Second, we characterise elementary transformations in terms of ZX diagrams, so a lot of linear algebra stuff can be done purely diagrammatically.
