2017/05/31 by Emmanuel Jeandel, Simon Perdrix, Jeandel, Emmanuel +3 · 7 citations
Computer Science · Physics and Astronomy · #Computability, Logic, AI Algorithms #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1705.11151
openalex publication_date 2017/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the first complete and approximatively universal diagrammatic\nlanguage for quantum mechanics. We make the ZX-Calculus, a diagrammatic\nlanguage introduced by Coecke and Duncan, complete for the so-called Clifford+T\nquantum mechanics by adding four new axioms to the language. The completeness\nof the ZX-Calculus for Clifford+T quantum mechanics was one of the main open\nquestions in categorical quantum mechanics. We prove the completeness of the\nClifford+T fragment of the ZX-Calculus using the recently studied ZW-Calculus,\na calculus dealing with integer matrices. We also prove that the Clifford+T\nfragment of the ZX-Calculus represents exactly all the matrices over some\nfinite dimensional extension of the ring of dyadic rationals.\n