  We consider a two-level quantum system prepared in an arbitrary initial state
and relaxing to a steady state due to the action of a Markovian dissipative
channel. We study how optimal control can be used for speeding up or slowing
down the relaxation towards the fixed point of the dynamics. We analytically
derive the optimal relaxation times for different quantum channels in the ideal
ansatz of unconstrained quantum control (a magnetic field of infinite
strength). We also analyze the situation in which the control Hamiltonian is
bounded by a finite threshold. As byproducts of our analysis we find that: (i)
if the qubit is initially in a thermal state hotter than the environmental
bath, quantum control cannot speed up its natural cooling rate; (ii) if the
qubit is initially in a thermal state colder than the bath, it can reach the
fixed point of the dynamics in finite time if a strong control field is
applied; (iii) in the presence of unconstrained quantum control it is possible
to keep the evolved state indefinitely and arbitrarily close to special initial
states which are far away from the fixed points of the dynamics.
