  A method is proposed for the optical rotation of the spin of an electron in a
quantum dot using excited trion states to implement operations up to two orders
of magnitude faster than those of most existing proposals. Key ingredients are
the geometric phase induced by 2$\pi$ hyperbolic secant pulses, use of
coherently trapped states and use of naturally dark states. Our proposal covers
a wide variety of quantum dots by addressing different parameter regimes. In
one case the treatment provides an exact solution to the three-level system.
Numerical simulations with typical parameters for InAs self-assembled quantum
dots, including their dissipative dynamics, give fidelities of the operations
in excess of 99%.
