  Quasiparticles are an intrinsic source of relaxation and decoherence for
superconducting qubits. Recent works have shown that normal-metal traps may be
used to evacuate quasiparticles, and potentially improve the qubit life time.
Here, we investigate how far the normal metals themselves may introduce qubit
relaxation. We identify the ohmic losses inside the normal metal and the
tunnelling current through the normal metal-superconductor interface as the
relevant relaxation mechanisms. We show that the ohmic loss contribution
depends strongly on the device and trap geometry, as a result of the
inhomogeneous electric fields in the qubit. The correction of the quality
factor due to the tunnelling current on the other hand is highly sensitive to
the nonequilibrium distribution function of the quasiparticles. Overall, we
show that even when choosing less than optimal parameters, the presence of
normal-metal traps does not affect the quality factor of state-of-the-art
qubits.
