# Pivoting makes the ZX-calculus complete for real stabilizers

arXiv: https://arxiv.org/abs/1307.7048 · HTML: https://mlsanity.com/paper/1307.7048/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jul 2013.

## Built on by (most cited first, 1 of 1)

- [Kindergarden quantum mechanics graduates (...or how I learned to stop gluing LEGO together and love the ZX-calculus)](https://mlsanity.com/paper/2102.10984/) (2021)

## Abstract (arXiv)

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.