Electronic Proceedings in Theoretical Computer Science (Dec 2014)

The ZX-calculus is incomplete for quantum mechanics

  • Christian Schröder de Witt,
  • Vladimir Zamdzhiev

DOI
https://doi.org/10.4204/eptcs.172.20
Journal volume & issue
Vol. 172, no. Proc. QPL 2014
pp. 285 – 292

Abstract

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We prove that the ZX-calculus is incomplete for quantum mechanics. We suggest the addition of a new 'color-swap' rule, of which currently no analytical formulation is known and which we suspect may be necessary, but not sufficient to make the ZX-calculus complete.