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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.
Cited literature [20 references]
https://hal.archives-ouvertes.fr/hal-01529623
Contributor : Renaud Vilmart Connect in order to contact the contributor
Submitted on : Friday, February 23, 2018 - 4:46:54 PM
Last modification on : Thursday, April 28, 2022 - 4:12:03 PM
Long-term archiving on: : Friday, May 25, 2018 - 9:54:14 AM
Contributor : Renaud Vilmart Connect in order to contact the contributor
Submitted on : Friday, February 23, 2018 - 4:46:54 PM
Last modification on : Thursday, April 28, 2022 - 4:12:03 PM
Long-term archiving on: : Friday, May 25, 2018 - 9:54:14 AM
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pi_4-completeness-arxiv-v2.pdf
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