Trichromatic Open Digraphs for Understanding Qubits

Alex Lang
(University of Oxford)
Bob Coecke
(University of Oxford)

We introduce a trichromatic graphical calculus for quantum computing. The generators represent three complementary observables that are treated on equal footing, hence reflecting the symmetries of the Bloch sphere. We derive the Euler angle decomposition of the Hadamard gate within it as well as the so-called supplementary relationships, which are valid equations for qubits that were not derivable within Z/X-calculus of Coecke and Duncan. More specifically, we have: dichromatic Z/X-calculus + Euler angle decomposition of the Hadamard gate = trichromatic calculus.

In Bart Jacobs, Peter Selinger and Bas Spitters: Proceedings 8th International Workshop on Quantum Physics and Logic (QPL 2011), Nijmegen, Netherlands, October 27-29, 2011, Electronic Proceedings in Theoretical Computer Science 95, pp. 193–209.
Published: 1st October 2012.

ArXived at: http://dx.doi.org/10.4204/EPTCS.95.14 bibtex PDF
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