Pivoting makes the ZX-calculus complete for real stabilizers

Ross Duncan, Simon Perdrix
2014 Electronic Proceedings in Theoretical Computer Science  
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.
doi:10.4204/eptcs.171.5 fatcat:jxubdy4nnbbzhh4pimdnav6bda