Nonequilibrium Quasiparticles in Superconducting Circuits: Energy Relaxation, Charge and Flux Noise

The quasiparticle density observed in low-temperature superconducting circuits is several orders of magnitude larger than the value expected at thermal equilibrium. The tunneling of this excess of quasiparticles across Josephson junctions is recognized as one of the main loss and decoherence mechanisms in superconducting qubits. Here we present a unified impedance theory that accounts for quasiparticle energy loss in circuit regions both far and near (across) junctions. Our theory leverages the recent experimental demonstration that the excess quasiparticles are in \emph{quasiequilibrium} [T. Connolly et al., Phys. Rev. Lett. $\textbf{132}$, 217001 (2024)] and uses a generalized fluctuation-dissipation theorem to predict the amount of charge and flux noise generated by them. We compute the resulting energy relaxation time $T_1$ in transmon qubits with and without junction asymmetric gap engineering, and show that quasiparticles residing away from junctions can play a dominant role in the former case. They also may provide an upper limit for resonator quality factors if the density of amorphous two-level systems is reduced. In addition, we show that charge noise from quasiparticles leads to flux noise that is logarithmic-in-frequency, giving rise to a ``nearly white" contribution that is comparable to the flux noise observed in flux qubits. This contrasts with amorphous two-level systems, whose associated flux noise is shown to be superOhmic. \Addition{We discuss how this quasiparticle flux noise can limit $T_2^{*}$ coherence times in flux-tunable qubits. The final conclusion is that asymmetric gap engineering can greatly reduce noise and increase coherence times in superconducting qubits.