Work

The Qupit Stabiliser ZX-travaganza: Simplified Axioms, Normal Forms and Graph-Theoretic Simplification

Year: 2023

Type: article

Abstract: 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.

Source: Electronic Proceedings in Theoretical Computer Science

DOI: 10.4204/eptcs.384.13

Authors: Boldizsár Poór, Robert I. Booth, Titouan Carette, John van de Wetering, Lia Yeh

Institutions: University of Oxford, University of Edinburgh, University of Latvia, University of Amsterdam

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funders: University of Oxford, European Regional Development Fund, Clarendon Fund

Awards: G3695008590, G4495442504