基于积分的简单qudit ZX与ZH calculus
Simple qudit ZX and ZH calculi, via integrals
AI总结：
本文利用离散测度提出统一的ZXH-calculus语义映射，分析任意维度D>1的qudit酉电路与测量，并展示了ZX和ZH calculus特定片段的重写规则。
摘要：
ZX calculus和ZH calculus使用图来表示和计算量子操作的性质，通过函子语义映射，利用“重写规则”在表示同一算子的图之间进行转换。不同的语义映射产生不同的重写系统，在不同用途下可能更方便。利用离散测度，我们描述了ZX和ZH图的语义映射，非常适合将任意固定维度D>1的qudit上的酉电路和测量作为一个单一的“ZXH-calculus”来分析。我们展示了ZX calculus的“稳定子片段”和ZH calculus的“多字符片段”的重写规则。
英文摘要：
The ZX calculus and ZH calculus use diagrams to denote and compute properties of quantum operations, using `rewrite rules' to transform between diagrams which denote the same operator through a functorial semantic map. Different semantic maps give rise to different rewrite systems, which may prove more convenient for different purposes. Using discrete measures, we describe semantic maps for ZX and ZH diagrams, well-suited to analyse unitary circuits and measurements on qudits of any fixed dimension D>1 as a single `ZXH-calculus'. We demonstrate rewrite rules for the `stabiliser fragment' of the ZX calculus and a `multicharacter fragment' of the ZH calculus.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
