A Simplified Stabilizer ZX-calculus
A Simplified Stabilizer ZX-calculus
复制标题
DOI：
10.4204/eptcs.236.1
复制
发表时间：
2016-02
期刊：
影响因子：
--
通讯作者：
Miriam Backens;S. Perdrix;Quanlong Wang
中科院分区：
文献类型：
--
作者：
Miriam Backens;S. Perdrix;Quanlong Wang
稳定器ZX演算是一种严格的用于量子力学推理的图形语言。该语言是健全和完整的：当且仅当这两个图表示相同的量子演化或量子态时，稳定器ZX图可以转换为另一个图。我们证明了稳定器ZX演算可以被简化，去掉不必要的方程，同时只保留可能捕捉到量子力学基本结构的基本公理。因此，我们给出了一组小得多的公理，并证明了像“颜色对称”和“倒置对称”这样的元规则，在以前的语言版本中被认为是公理，实际上可以推导出来。特别是，我们证明了附加符号和最近为跟踪标量(没有输入或输出的图)而引入的规则之一是不必要的。
The stabilizer ZX-calculus is a rigorous graphical language for reasoning about quantum mechanics.The language is sound and complete: a stabilizer ZX-diagram can be transformed into another one if and only if these two diagrams represent the same quantum evolution or quantum state. We show that the stabilizer ZX-calculus can be simplified, removing unnecessary equations while keeping only the essential axioms which potentially capture fundamental structures of quantum mechanics. We thus give a significantly smaller set of axioms and prove that meta-rules like 'colour symmetry' and 'upside-down symmetry', which were considered as axioms in previous versions of the language, can in fact be derived. In particular, we show that the additional symbol and one of the rules which had been recently introduced to keep track of scalars (diagrams with no inputs or outputs) are not necessary.