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Descripción

Recent completeness results on the ZX-Calculus used a third-party language, namely the ZW-Calculus. As a consequence, these proofs are elegant, but sadly non-constructive. We address this issue in the following. To do so, we first describe a generic normal form for ZX-diagrams in any fragment that contains Clifford+T quantum mechanics. We give sufficient conditions for an axiomatisation to be complete, and an algorithm to reach the normal form. Finally, we apply these results to the Clifford+T fragment and the general ZX-Calculus – for which we already know the completeness–, but also for any fragment of rational angles: we show that the axiomatisation for Clifford+T is also complete for any fragment of dyadic angles, and that a simple new rule (called cancellation) is necessary and sufficient otherwise.

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Autor(es)

Jeandel , Emmanuel -  Perdrix , Simon -  Vilmart , Renaud - 

Id.: 71314929

Idioma: inglés  - 

Versión: 1.0

Estado: Final

Palabras clave[ INFO.INFO -  LO ] Computer Science [cs]/Logic in Computer Science [cs.LO] - 

Tipo de recurso: info:eu-repo/semantics/preprint  -  Preprints, Working Papers, ...  - 

Tipo de Interactividad: Expositivo

Nivel de Interactividad: muy bajo

Audiencia: Estudiante  -  Profesor  -  Autor  - 

Estructura: Atomic

Coste: no

Copyright: sí

: info:eu-repo/semantics/OpenAccess

Requerimientos técnicos:  Browser: Any - 

Fecha de contribución: 17-may-2018

Contacto:

Localización:
* hal-01791791

Otros recursos del mismo autor(es)

  1. A ZX-Calculus with Triangles for Toffoli-Hadamard, Clifford+T, and Beyond We consider a ZX-calculus augmented with triangle nodes which is well-suited to reason on the so-cal...
  2. Structural aspects of tilings 11 pages
  3. Tilings and model theory ISBN 978-5-94057-377-7
  4. Subshifts, Languages and Logic International audience
  5. Tilings robust to errors We study the error robustness of tilings of the plane. The fundamental question is the following: gi...

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