Y-Calculus: A Language for Real Matrices Derived from the ZX-Calculus

Emmanuel Jeandel
Simon Perdrix
Renaud Vilmart

We introduce a ZX-like diagrammatic language devoted to manipulating real matrices – and rebits –, with its own set of axioms. We prove the necessity of some non trivial axioms of these. We show that some restriction of the language is complete. We exhibit two interpretations to and from the ZX-Calculus, thus showing the consistency between the two languages. Finally, we derive from our work a way to extract the real or imaginary part of a ZX-diagram, and prove that a restriction of our language is complete if the equivalent restriction of the ZX-calculus is complete.

In Bob Coecke and Aleks Kissinger: Proceedings 14th International Conference on Quantum Physics and Logic (QPL 2017), Nijmegen, The Netherlands, 3-7 July 2017, Electronic Proceedings in Theoretical Computer Science 266, pp. 23–57.
Published: 27th February 2018.

ArXived at: http://dx.doi.org/10.4204/EPTCS.266.2 bibtex PDF
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