  We have studied decoherence in a system where two Josephson-junction flux
qubits share a part of their superconducting loops and are inductively coupled.
By tuning the flux bias condition, we control the sensitivities of the energy
levels to flux noises in each qubit. The dephasing rate of the first excited
state is enhanced or suppressed depending on the amplitudes and the signs of
the sensitivities. We have quantified the $1/f$ flux noises and their
correlations and found that the dominant contribution is by local fluctuations.
