The Qupit Stabiliser ZX-travaganza: Simplified Axioms, Normal Forms and Graph-Theoretic Simplification
Boldizsár Poór, Robert I. Booth, Titouan Carette, John van de Wetering, Lia Yeh · Electronic Proceedings in Theoretical Computer Science · 2023
We present a smorgasbord of results on the stabiliser ZX-calculus for odd prime-dimensional qudits (i.e.qupits).We derive a simplified rule set that closely resembles the original rules of qubit ZX-calculus.Using these rules, we demonstrate analogues of the spider-removing local complementation and pivoting rules.This allows for efficient reduction of diagrams to the affine with phases normal form.We also demonstrate a reduction to a unique form, providing an alternative and simpler proof of completeness.Furthermore, we introduce a different reduction to the graph state with local Cliffords normal form, which leads to a novel layered decomposition for qupit Clifford unitaries.Additionally, we propose a new approach to handle scalars formally, closely reflecting their practical usage.Finally, we have implemented many of these findings in DiZX, a new open-source Python library for qudit ZX-diagrammatic reasoning.