  We study the Josephson junction between two d-wave superconductors, which is
discussed as an implementation of a qubit. We propose an approach that allows
to calculate the decoherence time due to an intrinsic dissipative process:
quantum tunneling between the two minima of the double-well potential excites
nodal quasiparticles which lead to incoherent damping of quantum oscillations.
The decoherence is weakest in the mirror junction, where the contribution of
nodal quasiparticles corresponds to the superohmic dissipation and becomes
small at small tunnel splitting of the energy level in the double-well
potential. For available experimental data, we estimate the quality factor.
