Y-Calculus: A Language for Real Matrices Derived from the ZX-Calculus
Quantum Physics
2018-03-05 v2 Logic in Computer Science
Abstract
We introduce a ZX-like diagrammatic language devoted to manipulating real matrices - and rebits -, with its own set of axioms. We prove the necessity of some non trivial axioms of these. We show that some restriction of the language is complete. We exhibit two interpretations to and from the ZX-Calculus, thus showing the consistency between the two languages. Finally, we derive from our work a way to extract the real or imaginary part of a ZX-diagram, and prove that a restriction of our language is complete if the equivalent restriction of the ZX-calculus is complete.
Cite
@article{arxiv.1702.00934,
title = {Y-Calculus: A Language for Real Matrices Derived from the ZX-Calculus},
author = {Emmanuel Jeandel and Simon Perdrix and Renaud Vilmart},
journal= {arXiv preprint arXiv:1702.00934},
year = {2018}
}
Comments
In Proceedings QPL 2017, arXiv:1802.09737