  We study the dynamics of dephasing in a quantum two-level system by modeling
both 1/f and high-frequency noise by random telegraph processes. Our approach
is based on a so-called spin-fluctuator model in which a noisy environment is
modeled by a large number of fluctuators. In the continuous limit we obtain an
effective random process (ERP) that is described by a distribution function of
the fluctuators. In a simplified model, we reduce the ERP to the two (slow and
fast) ensembles of fluctuators. Using this model, we study decoherence in a
superconducting flux qubit and we compare our theoretical results with the
available experimental data. We demonstrate good agreement of our theoretical
predictions with the experiments. Our approach can be applied to many quantum
systems, such as biological complexes, semiconductors, superconducting and spin
qubits, where the effects of interaction with the environment are essential.
