English

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

R2 v1 2026-06-22T00:58:26.926Z