  Amorphous dielectric materials have been known to host two-level systems
(TLSs) for more than four decades. Recent developments on superconducting
resonators and qubits enable detailed studies on the physics of TLSs. In
particular, measuring the loss of a device over long time periods (a few days)
allows us to investigate stochastic fluctuations due to the interaction between
TLSs. We measure the energy relaxation time of a frequency-tunable planar
superconducting qubit over time and frequency. The experiments show a variety
of stochastic patterns that we are able to explain by means of extensive
simulations. The model used in our simulations assumes a qubit interacting with
high-frequency TLSs, which, in turn, interact with thermally activated
low-frequency TLSs. Our simulations match the experiments and suggest the
density of low-frequency TLSs is about three orders of magnitude larger than
that of high-frequency ones.
