Power-Law Scaling of Relaxation Time Fluctuations in Transmon Qubits

We have measured temporal fluctuations in the energy relaxation time
T
₁
of a series of 3D transmon qubits. At 20 mK, the relaxation times of the devices have average values between 2 and 190 μs, with standard deviations as large as 20% of the averages. Over the different devices, this fluctuation magnitude roughly scales as a power law in the average
T
₁
, with an exponent near 1.5. With increasing temperature,
T
₁
decreases due to a higher density of thermally-generated quasiparticles. For an individual device measured up to 250 mK, the fluctuation magnitude appears to be proportional to
T
₁
. We present a model of quasiparticle dissipation channels that reproduces both of the observed scaling relationships.