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Pivoting makes the ZX-calculus complete for real stabilizers

2013/07/31 by Ross Duncan, Simon Perdrix
Physics and Astronomy · Computer Science · #quant-ph #cs.LO

paper · pdf · doi:10.4204/eptcs.171.5

published as EPTCS 171, 2014, pp. 50-62 · In Proceedings QPL 2013, arXiv:1412.7917

arxiv created 2014/12/30 · arxiv updated 2014/12/31

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.

Citations