2 research outputs found
Trichromatic Open Digraphs for Understanding Qubits
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.Comment: In Proceedings QPL 2011, arXiv:1210.029
Pivoting makes the ZX-calculus complete for real stabilizers
We show that pivoting property of graph states cannot be derived from the
axioms of the ZX-calculus, and that pivoting does not imply local
complementation of graph states. Therefore the ZX-calculus augmented with
pivoting is strictly weaker than the calculus augmented with the Euler
decomposition of the Hadamard gate. We derive an angle-free version of the
ZX-calculus and show that it is complete for real stabilizer quantum mechanics.Comment: In Proceedings QPL 2013, arXiv:1412.791