  We present a systematic study of the first excited-state population in a 3D
transmon qubit mounted in a dilution refrigerator with a variable temperature.
Using a modified version of the protocol developed by Geerlings et al. [1], we
observe the excited-state population to be consistent with a Maxwell-Boltzmann
distribution, i.e., a qubit in thermal equilibrium with the refrigerator, over
the temperature range 35-150 mK. Below 35 mK, the excited-state population
saturates to 0.1%, near the resolution of our measurement. We verified this
result using a flux qubit with ten-times stronger coupling to its readout
resonator. We conclude that these qubits have effective temperature T_{eff} =
35 mK. Assuming T_{eff} is due solely to hot quasiparticles, the inferred qubit
lifetime is 108 us and in plausible agreement with the measured 80 us.

Quantum Physics;Superconductivity