Thermal and Residual Excited-State Population in a 3D Transmon Qubit
  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. 
X. Y. Jin, A. Kamal, A. P. Sears, T. Gudmundsen, D. Hover, J. Miloxi,   R. Slattery, F. Yan, J. Yoder, T. P. Orlando, S. Gus...
quant-ph cond-mat.supr-con