  Finding minimal time and establishing the structure of the corresponding
optimal controls which can transfer a given initial state of a quantum system
into a given target state is a key problem of quantum control. In this work,
this problem is solved for a basic component of various quantum technology
processes -- a qubit interacting with the environment and experiencing an
arbitrary time-dependent coherent driving. We rigorously derive both upper and
lower estimates for the minimal steering time. Surprisingly, we discover that
the optimal controls have a very special form -- they consist of two impulses,
at the beginning and at the end of the control period, which can be assisted by
a smooth time-dependent control in between. Moreover, an important for
practical applications explicit almost optimal state transfer protocol is
provided which only consists of four impulses and gives an almost optimal time
of motion. The results can be directly applied to a variety of experimental
situations for estimation of the ultimate limits of state control for quantum
technologies.
