Pivoting makes the ZX-calculus complete for real stabilizers

Ross Duncan
(University of Strathclyde)
Simon Perdrix
(CNRS)

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.

In Bob Coecke and Matty Hoban: Proceedings of the 10th International Workshop on Quantum Physics and Logic (QPL 2013), Castelldefels (Barcelona), Spain, 17th to 19th July 2013, Electronic Proceedings in Theoretical Computer Science 171, pp. 50–62.
Published: 27th December 2014.

ArXived at: http://dx.doi.org/10.4204/EPTCS.171.5 bibtex PDF
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