We consider dissipative dynamics of a flux qubit caused by 1/f noises, which act both on the shunting LC-contour and on the SQUID loop. These classical Gaussian noises modulate of the level splitting and of the tunnel coupling, respectively, and they are partially correlated. The transient evolution of qubit has been studied for the regimes: (a) the interwell incoherent tunneling, (b) the relaxation of interlevel population, and (c) the decoherence of the off-diagonal part of a density matrix. For all regimes, the relaxation rates and the frequency renormalization [for the case (c)] are analyzed versus the parameters of qubit and couplings to the noises applied. The fluctuation effects give a dominant contribution at tails of relaxation, so that the averaged dissipative dynamics is not valid there. The results obtained open a way for verification of the parameters of qubit-noise interaction and for minimization of coupling between qubit and environment. Under typical level of noises, the results are comparable to the recent experimental data on the population relaxation and on the incoherent interwell tunneling.
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