Trichromatic Open Digraphs for Understanding Qubits

Details Trichromatic Open Digraphs for Understanding Qubits Trichromatic Open Digraphs for Understanding Qubits

2011-10-12

arxiv.org/abs/1110.2613v2

Mathematics

Category Theory

15 pages, accepted to QPL 2011

Scientific paper

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 suplementarity 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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