Pivoting makes the ZX-calculus complete for real stabilizers

Ross Duncan, Simon Perdrix

Research output: Contribution to journalConference Contribution

13 Citations (Scopus)

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.
LanguageEnglish
Pages50-62
Number of pages13
JournalElectronic Proceedings in Theoretical Computer Science
Volume171
DOIs
Publication statusPublished - 27 Dec 2014

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Quantum theory
Decomposition

Keywords

  • quantum physics
  • stabilizer quantum mechanics
  • ZX-calculus

Cite this

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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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Pivoting makes the ZX-calculus complete for real stabilizers. / Duncan, Ross; Perdrix, Simon.

In: Electronic Proceedings in Theoretical Computer Science, Vol. 171, 27.12.2014, p. 50-62.

Research output: Contribution to journalConference Contribution

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