2026-07-24T14:56:13Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:20576 2024-08-23T05:50:28Z ddc:004 open_access

Simple Qudit ZX and ZH Calculi, via Integrals de Beaudrap, Niel East, Richard D. P. ZX-calculus ZH-calculus qudits string diagrams discrete integrals 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Niel de Beaudrap and Richard D. P. East 2024 Is Part Of LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.MFCS.2024.20 urn:nbn:de:0030-drops-205761 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.20 eng https://creativecommons.org/licenses/by/4.0/legalcode