  We analyze the dissipative dynamics of a two-level quantum system subject to
low-frequency, e.g. 1/f noise, motivated by recent experiments with
superconducting quantum circuits. We show that the effect of transverse linear
coupling of the system to low-frequency noise is equivalent to that of
quadratic longitudinal coupling. We further find the decay law of quantum
coherent oscillations under the influence of both low- and high-frequency
fluctuations, in particular, for the case of comparable rates of relaxation and
pure dephasing.
