Nonequilibrium quasiparticle relaxation in superconducting qubits

In a superconducting qubit the lifetime of qubit state is restricted by nonequilibrium quasiparticle tunneling. We calculate the rate of these tunnelings using the nonequilibrium effects they induce on the condensate chemical potential of leads and islands. We show that by decreasing temperature below a crossover, the quasiparticle relaxation rate changes from exponential to much slower suppression and saturates to a finite value at zero temperature. This prediction is consistent with recent experiments. Our model also indicates a striking modification to qubit transitions: the matrix element of an energy transition in qubit strongly depends on coupling between tunneling quasiparticles and the environment. This features important fabrication hints to improve quantum state efficiency.