论文标题
在量子图形语言的食谱上
On a recipe for quantum graphical languages
论文作者
论文摘要
已经提出了不同的图形计算来表示量子计算。首先，Zx-Colculus [4]，然后是ZW-Calculus [12]，然后是ZH-Calculus [1]。我们想知道，新的Z*-Calculi是否会继续提出。本文否定回答。所有这些语言共享我们称为z*-代理的共同核心结构。我们将z* - 代数分类为在二维希尔伯特空间中的同构，并表明它们都是上述结石的变化。我们对线性关系做同样的事情，并表明[2]的演算本质上是独特的。
Different graphical calculi have been proposed to represent quantum computation. First the ZX- calculus [4], followed by the ZW-calculus [12] and then the ZH-calculus [1]. We can wonder if new Z*-calculi will continue to be proposed forever. This article answers negatively. All those language share a common core structure we call Z*-algebras. We classify Z*-algebras up to isomorphism in two dimensional Hilbert spaces and show that they are all variations of the aforementioned calculi. We do the same for linear relations and show that the calculus of [2] is essentially the unique one.
