  Although the Gaussian-noise assumption is widely adopted in the study of
qubit decoherence, non-Gaussian noise sources, especially the strong discrete
fluctuators, have been detected in many qubits. It remains an important task to
further understand and mitigate the distinctive decoherence effect of the
non-Gaussian noise. Here, we study the qubit dephasing caused by the
non-Gaussian fluctuators, and predict a symmetry-breaking effect that is unique
to the non-Gaussian noise. This broken symmetry results in an experimentally
measurable mismatch between the extremum points of the dephasing rate and qubit
frequency, which demands extra carefulness in characterizing the noise and
locating the optimal working point. To further enhance the coherence time at
the sweet spot, we propose to suppress the second-order derivative of the qubit
frequency by the Floquet engineering. Our simulation with a heavy fluxonium
shows an order of magnitude improvement of the dephasing time, even after
including the noise introduced by the drive.
