Algebraic complete axiomatisation of ZX-calculus with a normal form via elementary matrix operations
Quantum Physics
2022-01-26 v3 Category Theory
Abstract
In this paper we give a complete axiomatisation of qubit ZX-calculus via elementary transformations which are basic operations in linear algebra. This formalism has two main advantages. First, all the operations of the phases are algebraic ones without trigonometry functions involved, thus paved the way for generalising complete axiomatisation of qubit ZX-calculus to qudit ZX-calculus and ZX-calculus over commutative semirings. Second, we characterise elementary transformations in terms of ZX diagrams, so a lot of linear algebra stuff can be done purely diagrammatically.
Keywords
Cite
@article{arxiv.2007.13739,
title = {Algebraic complete axiomatisation of ZX-calculus with a normal form via elementary matrix operations},
author = {Quanlong Wang},
journal= {arXiv preprint arXiv:2007.13739},
year = {2022}
}
Comments
99 pages, many diagrams, added another normal form. arXiv admin note: substantial text overlap with arXiv:1912.01003