We have found an exact expression for the decoherence rate of a Josephson charge qubit coupled to fluctuating background charges. At low temperatures T the decoherence rate Gamma is linear in T while at high temperatures it saturates in agreement with a known classical solution which, however, reached at surprisingly high T. In contrast to the classical picture, impurity states spread in a wide interval of energies (> T) may essentially contribute to Gamma.
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