Second-order decoherence mechanisms of a transmon qubit probed with thermal microwave states

Thermal microwave states are omnipresent noise sources in superconducting quantum circuits covering all relevant frequency regimes. We use them as a probe to identify three second-order decoherence mechanisms of a superconducting transmon. First, we quantify the efficiency of a resonator filter in the dispersive Jaynes-Cummings regime and find evidence for parasitic loss channels. Second, we probe second-order noise in the low-frequency regime and demonstrate the expected $T^{3}$ temperature dependence of the qubit dephasing rate. Finally, we show that qubit parameter fluctuations due to two-level states are enhanced under the influence of thermal microwave states. In particular, we experimentally confirm the $T^{2}$-dependence of the fluctuation spectrum expected for noninteracting two-level states.