Qubit decoherence by low-frequency noise

We have derived explicit non-perturbative expression for decoherence of quantum oscillations in a qubit by low-frequency noise. Decoherence strength is controlled by the noise spectral density at zero frequency while the noise correlation time $\tau$ determines the time $t$ of crossover from the $1/\sqrt{t}$ to the exponential suppression of coherence. We also performed Monte Carlo simulations of qubit dynamics with noise which agree with the analytical results and show that most of the conclusions are valid for both Gaussian and non-Gaussian noise.