  We show by direct calculation starting from a microscopic model that the
two-state system with time-dependent energy levels in the presence of fast
quantum noise obeys the master equation. The solution of master equation is
found analytically and analyzed in a broad range of parameters. The fast
transverse noise affects the transition probability during much longer time
(the accumulation time) than the longitudinal one. The action of the fast
longitudinal noise is restricted by the shorter Landau-Zener time, the same as
in the regular Landau-Zener process. The large ratio of time scales allows
solving the Landau-Zener problem with longitudinal noise only, then solving the
same problem with the transverse noise only and matching the two solutions. The
correlation of the longitudinal and transverse noise renormalizes the
Landau-Zener transition matrix element and can strongly enhance the survival
probability, whereas the transverse noise always reduces it. Both longitudinal
and transverse noise reduce the coherence. The decoherence time is inverse
proportional to the noise intensity. If the noise is fast, its intensity at
which the multi-quantum processes become essential corresponds to a deeply
adiabatic regime. We briefly discuss possible applications of the general
theory to the problem of the qubit decoherence and to the spin relaxation of
molecular magnets.
