  We have investigated the driven dynamics of a superconducting flux qubit that
is tunably coupled to a microwave resonator. We find that the qubit experiences
an oscillating field mediated by off-resonant driving of the resonator, leading
to strong modifications of the qubit Rabi frequency. This opens an additional
noise channel, and we find that low-frequency noise in the coupling parameter
causes a reduction of the coherence time during driven evolution. The noise can
be mitigated with the rotary-echo pulse sequence, which, for driven systems, is
analogous to the Hahn-echo sequence.
