  We investigate the energy and phase relaxation of a superconducting qubit
caused by a single quasiparticle. In our model, the qubit is an isolated system
consisting of a small island (Cooper-pair box) and a larger superconductor
(reservoir) connected with each other by a tunable Josephson junction. If such
system contains an odd number of electrons, then even at lowest temperatures a
single quasiparticle is present in the qubit. Tunneling of a quasiparticle
between the reservoir and the Cooper-pair box results in the relaxation of the
qubit. We derive master equations governing the evolution of the qubit
coherences and populations. We find that the kinetics of the qubit can be
characterized by two time scales - quasiparticle escape time from reservoir to
the box, $\Gamma^{-1}_{in}$, and quasiparticle relaxation time $\tau$. The
former is determined by the dimensionless normal-state conductance $g_T$ of the
Josephson junction and one-electron level spacing $\delta_r$ in the reservoir
($\Gamma_{in}\sim g_T\delta_r$), and the latter is due to electron-phonon
interaction. We find that phase coherence is damped on the time scale of
$\Gamma^{-1}_{in}$. The qubit energy relaxation depends on the ratio of the two
characteristic times, $\tau$ and $\Gamma^{-1}_{in}$, and also on the ratio of
temperature $T$ to the Josephson energy $E_J$.
