Simple qudit ZX and ZH calculi, via integrals
Abstract
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.
Cite
@article{arxiv.2304.03310,
title = {Simple qudit ZX and ZH calculi, via integrals},
author = {Niel de Beaudrap and Richard D. P. East},
journal= {arXiv preprint arXiv:2304.03310},
year = {2024}
}
Comments
16 pages of main text, 42 pages of appendices, many equations involving diagrams. Substantially re-structured for presentation, and edited for concision and to fix minor errors. Full version of accepted submission to MFCS 2024