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Trichromatic Open Digraphs for Understanding Qubits

Author(s): Alex Lang | Bob Coecke

Journal: Electronic Proceedings in Theoretical Computer Science
ISSN 2075-2180

Volume: 95;
Issue: Proc. QPL 2011;
Start page: 193;
Date: 2012;
Original page

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.
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