Pivoting makes the ZX-calculus complete for real stabilizers
Quantum Physics
2014-12-31 v2 Logic in Computer Science
Abstract
We show that pivoting property of graph states cannot be derived from the axioms of the ZX-calculus, and that pivoting does not imply local complementation of graph states. Therefore the ZX-calculus augmented with pivoting is strictly weaker than the calculus augmented with the Euler decomposition of the Hadamard gate. We derive an angle-free version of the ZX-calculus and show that it is complete for real stabilizer quantum mechanics.
Cite
@article{arxiv.1307.7048,
title = {Pivoting makes the ZX-calculus complete for real stabilizers},
author = {Ross Duncan and Simon Perdrix},
journal= {arXiv preprint arXiv:1307.7048},
year = {2014}
}
Comments
In Proceedings QPL 2013, arXiv:1412.7917