Observation of discrete charge states of a coherent two-level system in a superconducting qubit

We report observations of discrete charge states of a coherent dielectric two-level system (TLS) that is strongly coupled to an offset-charge-sensitive superconducting transmon qubit. We measure an offset charge of 0.072$e$ associated with the two TLS eigenstates, which have a transition frequency of 2.9 GHz and a relaxation time exceeding 3 ms. Combining measurements in the strong dispersive and resonant regime, we quantify both transverse and longitudinal couplings of the TLS-qubit interaction. We further perform joint tracking of TLS transitions and quasiparticle tunneling dynamics but find no intrinsic correlations. This study demonstrates microwave-frequency TLS as a source of low-frequency charge noise.