Microscopic models for charge-noise-induced dephasing of solid-state qubits

Several experiments have shown qubit coherence decay of the form $\mathrm{exp}[-(t/T_2)^\alpha]$ due to environmental charge-noise fluctuations. We present a microscopic description for temperature dependences of the parameters $T_2$ and $\alpha$. Our description is appropriate to qubits in semiconductors interacting with spurious two-level charge fluctuators coupled to a thermal bath. We find distinct power-law dependences of $T_2$ and $\alpha$ on temperature depending on the nature of the interaction of the fluctuators with the associated bath. We consider fluctuator dynamics induced by first- and second-order tunneling with a continuum of delocalized electron states. We also study one- and two-phonon processes for fluctuators in either GaAs or Si. These results can be used to identify dominant charge-dephasing mechanisms and suppress them.