Pivoting makes the ZX-calculus complete for real stabilizers

Ross Duncan, Simon Perdrix

Research output: Contribution to journalConference Contributionpeer-review

20 Citations (Scopus)
185 Downloads (Pure)


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.
Original languageEnglish
Pages (from-to)50-62
Number of pages13
JournalElectronic Proceedings in Theoretical Computer Science
Publication statusPublished - 27 Dec 2014


  • quantum physics
  • stabilizer quantum mechanics
  • ZX-calculus


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