  We analyze the decay of Rabi oscillations in a charge qubit consisting of a
Cooper pair box connected to a finite-size superconductor by a Josephson
junction. We concentrate on the contribution of quasiparticles in the
superconductors to the decay rate. Passing of a quasiparticle through the
Josephson junction tunes the qubit away from the charge degeneracy, thus
spoiling the Rabi oscillations. We find the temperature dependence of the
quasiparticle contribution to the decay rate for open and isolated systems. The
former case is realized if a normal-state trap is included in the circuit, or
if just one vortex resides in the qubit; the decay rate has an activational
temperature dependence with the activation energy equal to the superconducting
gap $\Delta$. In a superconducting qubit isolated from the environment, the
activation energy equals $2\Delta$ if the number of electrons is even, while
for an odd number of electrons the decay rate of an excited qubit state remains
finite in the limit of zero temperature. We estimate the decay rate for
realistic parameters of a qubit.
