  A general theory is presented for the treatment of decoherence of a
multilevel quantum system (with many degrees of freedom) interacting with
multi-bath reservoir and driven by ac fields. In this approach, the system is
described by a reduced density operator and the multi-bath reservoir is
characterized by a number of spectral densities. The reduced density operator
is governed by the master equation in which the effect of ac driving fields and
the leakage to non-computational states are included. The theory is applied to
the study of decoherence of a two-dimensional (2D) SQUID flux qubit coupled to
control and readout circuits. The predicted results are in very good agreement
with available experimental results in the absence of driving fields and with
the analytic results of a dissipative two-level system in the presence of weak
driving fields. The relaxation and decoherence times versus the parameters and
temperature of the control and readout circuits are also explored in details to
facilitate the optimization of the 2D SQUID qubit.
