Efficient characterization methods for coherent TLSs with sub-MHz swapping frequencies.

An outstanding challenge in building superconducting quantum circuits is mitigating the loss and dephasing due to two-level systems (TLS) defects. SWAP spectroscopy with frequency-tunable qubits is the standard technique to detect TLSs as coherent swapping, a phenomenon almost exclusively found in literature for fast swapping frequencies ~10 MHz.

Here we introduce characterization methods that help understand the properties of TLSs showing slow swapping frequencies ~0.1 - 1 MHz, which become more prominent with increasingly coherent qubits. In order to meet the higher sensitivity required to detect these TLSs, we use a new pulse sequence that minimizes qubit dephasing during the SWAP interaction. This advancement makes it suitable to perform SWAP spectroscopy with sub-MHz frequency resolution and long SWAP interaction times. We put forward an interacting qubit-TLS model from literature that can quantitatively describe a coherent swapping and allow us to extract the qubit-TLS decoherence rates. Additionally, we find qubit-TLS swapping decay rates much slower than the individual, non-interacting qubit and TLS decoherence rates. This provides an alternative interpretation for the observed long swapping decay times that previously have been attributed to TLSs close to their symmetry points.