Many-body effects of two-level systems in superconducting qubits

Superconducting qubits are often adversely affected by two-level systems (TLSs) within the Josephson junction, which contribute to decoherence and subsequently limit the performance of the qubit. By treating the TLS as a soft (i.e., low-frequency) bosonic mode localized in real space, we find that a single TLS in either the amorphous oxide surface or the superconducting bulk may result in a localized "hot spot" of amplified Josephson energy. Such amplification is shown to have a non-negligible effect on the $T_1$ time of certain superconducting qubits, regardless of whether or not the TLS is on resonance with the qubit frequency. With this study, we identify sources of decoherence unique to the superconducting element of superconducting quantum devices.