2011/10/31 by Alex Lang, Bob Coecke
Mathematics · Computer Science · Physics and Astronomy · #math.CT #cs.LO #math.QA #quant-ph
paper · pdf · doi:10.4204/eptcs.95.14
published as EPTCS 95, 2012, pp. 193-209 · In Proceedings QPL 2011, arXiv:1210.0298
arxiv created 2012/10/02 · arxiv updated 2012/10/03
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.