An algebraic axiomatisation of ZXcalculus
Abstract
In this paper we give an algebraic complete axiomatisation of ZXcalculus in the sense that there are only ring operations involved for phases, without any need of trigonometry functions such as sin and cos, in contrast to previous universally complete axiomatisations of ZXcalculus. With this algebraic axiomatisation of ZXcalculus, we are able to establish an invertible translation from ZHcalculus to ZXcalculus and to derive all the ZXtranslated rules of ZHcalculus. As a consequence, we have a great benefit that all techniques obtained in ZHcalculus can be transplanted to ZXcalculus.
 Publication:

arXiv eprints
 Pub Date:
 November 2019
 arXiv:
 arXiv:1911.06752
 Bibcode:
 2019arXiv191106752W
 Keywords:

 Quantum Physics
 EPrint:
 31 pages