  In superconducting qubits the lifetime of quantum states cannot be prolonged
arbitrarily by decreasing temperature. At low temperature quasiparticles
tunneling between electromagnetic environment and superconducting islands takes
the condensate state out of equilibrium due to charge imbalance. We obtain the
tunneling rate from a phenomenological model of non-equilibrium, where
nonequilibrium quasiparticle tunnelling stimulates a temperature-dependent
chemical potential shift in superconductor. As a result we obtain a
non-monotonic behavior for relaxation rate as function of temperature.
Depending on the fabrication parameters for some qubits the lowest tunneling
rate of nonequilibrium quasiparticles can take place only near the onset
temperature below which nonequilibrium quasiparticles dominate over equilibrium
one. Our theory also indicates that such tunnelings can influence the
probability of transitions in qubits through a coupling to the zero-point
energy of phase fluctuations.
