  As low-loss non-linear elements, Josephson junctions are the building blocks
of superconducting qubits. The interaction of the qubit degree of freedom with
the quasiparticles tunneling through the junction represent an intrinsic
relaxation mechanism. We develop a general theory for the qubit decay rate
induced by quasiparticles, and we study its dependence on the magnetic flux
used to tune the qubit properties in devices such as the phase and flux qubits,
the split transmon, and the fluxonium. Our estimates for the decay rate apply
to both thermal equilibrium and non-equilibrium quasiparticles. We propose
measuring the rate in a split transmon to obtain information on the possible
non-equilibrium quasiparticle distribution. We also derive expressions for the
shift in qubit frequency in the presence of quasiparticles.
