  We consider the problem of stochastic averaging of a quantum two-state
dynamics driven by non-Markovian, discrete noises of the continuous time random
walk type (multistate renewal processes). The emphasis is put on the proper
averaging over the stationary noise realizations corresponding, e.g., to a
stationary environment. A two state non-Markovian process with an arbitrary
non-exponential distribution of residence times (RTDs) in its states with a
finite mean residence time provides a paradigm. For the case of a two-state
quantum relaxation caused by such a classical stochastic field we obtain the
explicit exact, analytical expression for the averaged Laplace-transformed
relaxation dynamics. In the limit of Markovian noise (implying an exponential
RTD), all previously known results are recovered. We exemplify new more general
results for the case of non-Markovian noise with a biexponential RTD. The
averaged, real-time relaxation dynamics is obtained in this case by numerically
exact solving of a resulting algebraic polynomial problem. Moreover, the case
of manifest non-Markovian noise with an infinite range of temporal
autocorrelation (which in principle is not accessible to any kind of
perturbative treatment) is studied, both analytically (asymptotic long-time
dynamics) and numerically (by a precise numerical inversion of the
Laplace-transformed averaged quantum relaxation).
