  In this paper we investigate the short-time decoherence from Ohmic and 1/f
noise of single Josephson charge qubit (JCQ). At first, we use the short-time
approximation to obtain the dynamics of the open JCQ. Then we calculate the
decoherence the measure of which is chosen as the maximum norm of the deviation
density operator. It is shown that the decoherence from 1/f noise plays the
central role. The total decoherence from Ohmic and 1/f noise is serious at
present experiential conditions according to the DiVincenzo criterion.
