  We propose a strategy to suppress decoherence of a solid-state qubit coupled
to non-Markovian noises by attaching the qubit to a chaotic setup with the
broad power distribution in particular in the high-frequency domain. Different
from the existing decoherence control methods such as the usual dynamics
decoupling control, high-frequency components of our control are generated by
the chaotic setup driven by a low-frequency field, and the generation of
complex optimized control pulses is not necessary. We apply the scheme to
superconducting quantum circuits and find that various noises in a wide
frequency domain, including low-frequency $1/f$, high-frequency Ohmic,
sub-Ohmic, and super-Ohmic noises, can be efficiently suppressed by coupling
the qubits to a Duffing oscillator as the chaotic setup. Significantly, the
decoherence time of the qubit is prolonged approximately $100$ times in
magnitude.
