  At first, we generally investigate the short-time decoherence of a qubit
nonlinearly coupling with a bath. The measure of the decoherence is chosen as
the maximum norm of the deviation density operator. Then we concretely
investigate the Josephson charge qubit (JCQ) model. It is shown that at the
temperature T=30mK, the loss of fidelity (due to decoherence) of the JCQ is
bigger than the DiVincenzo low decoherence criterion. The decoherence will
decrease with the decrease of the experimental temperature. When the
temperature decreases to T=0.3mK the DiVincenzo low decoherence criterion can
be satisfied.
