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We have derived explicit non-perturbative expression for decoherence ofquantum oscillations in a qubit by low-frequency noise. Decoherence strength iscontrolled by the noise spectral density at zero frequency while the noisecorrelation time $\tau$ determines the time $t$ of crossover from the$1/\sqrt{t}$ to the exponential suppression of coherence. We also performedMonte Carlo simulations of qubit dynamics with noise which agree with theanalytical results and show that most of the conclusions are valid for bothGaussian and non-Gaussian noise.Comment: 4 pages, 2 figure

Qubit decoherence by Gaussian low-frequency noise