A Complete Axiomatisation of the ZX-Calculus for Clifford+T Quantum Mechanics - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year :

A Complete Axiomatisation of the ZX-Calculus for Clifford+T Quantum Mechanics

Abstract

We introduce the first complete and approximatively universal diagrammatic language for quantum mechanics. We make the ZX-Calculus, a diagrammatic language introduced by Coecke and Duncan, complete for the so-called Clifford+T quantum mechanics by adding four new axioms to the language. The completeness of the ZX-Calculus for Clifford+T quantum mechanics was one of the main open questions in categorical quantum mechanics. We prove the completeness of the π/4-fragment of the ZX-Calculus using the recently studied ZW-Calculus, a calculus dealing with integer matrices. We also prove that the π/4-fragment of the ZX-Calculus represents exactly all the matrices over some finite dimensional extension of the ring of dyadic rationals.
Fichier principal
Vignette du fichier
pi_4-completeness-arxiv-v2.pdf (837.97 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01529623 , version 1 (31-05-2017)
hal-01529623 , version 2 (23-02-2018)

Identifiers

Cite

Emmanuel Jeandel, Simon Perdrix, Renaud Vilmart. A Complete Axiomatisation of the ZX-Calculus for Clifford+T Quantum Mechanics. The 33rd Annual {ACM/IEEE} Symposium on Logic in Computer Science, {LICS} 2018, Jul 2018, Oxford, United Kingdom. pp.559--568, ⟨10.1145/3209108.3209131⟩. ⟨hal-01529623v2⟩
532 View
504 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More