  We apply the inversely-engineered control method based on Lewis-Riesenfeld
invariants to control mixed states of a two-level quantum system. We show that
the inversely-engineered control passages of mixed states - and pure states as
special cases - can be made significantly faster than the conventional
adiabatic control passages, which renders the method applicable to quantum
computation. We devise a new type of inversely-engineered control passages, to
be coined the antedated control passages, which further speed up the control
significantly. We also demonstrate that by carefully tuning the control
parameters, the inversely-engineered control passages can be optimized in terms
of speed and energy cost.
