  A non-Abelian geometric method is proposed for rotating of heavy hole spins
in a singly positive charged quantum dot in Voigt geometry. The key ingredient
is the delay-dependent non-Abelian geometric phase, which is produced by the
nonadiabatic transition between the two degenerate dark states. We demonstrate,
by controlling the pump, the Stokes and the driving fields, that the rotations
about $y$- and $z$-axes with arbitrary angles can be realized with high
fidelity. Fast initialization and heavy hole spin state readout are also
possible.

Quantum Physics