Pivoting Makes the ZX-Calculus Complete for Real Stabilizers

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.
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Contributor : Nicolas Peltier <>
Submitted on : Thursday, January 23, 2014 - 11:15:30 AM
Last modification on : Friday, October 25, 2019 - 2:01:26 AM

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  • HAL Id : hal-00935185, version 1
  • ARXIV : 1307.7048

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Ross Duncan, Simon Perdrix. Pivoting Makes the ZX-Calculus Complete for Real Stabilizers. QPL 2013 - 10th Workshop on Quantum Physics and Logic, Jul 2013, Castelldefels, Barcelona, Spain. ⟨hal-00935185⟩

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