  We consider the initialization of the spin-state of a single electron trapped
in a self-assembled quantum dot via optical pumping of a trion level. We show
that with a magnetic field applied perpendicular to the growth direction of the
dot, a near-unity fidelity can be obtained in a time equal to a few times the
inverse of the spin-conserving trion relaxation rate. This method is several
orders-of-magnitude faster than with the field aligned parallel, since this
configuration must rely on a slow hole spin-flip mechanism. This increase in
speed does result in a limit on the maximum obtainable fidelity, but we show
that for InAs dots, the error is very small.
