  We study the dynamics of a non-Hermitian superconducting qubit which is
perturbed by quantum jumps between energy levels, a purely quantum effect with
no classical correspondence. The quantum jumps mix the qubit states leading to
decoherence. We observe that this decoherence rate is enhanced near the
exceptional point, owing to the cube-root topology of the non-Hermitian
eigenenergies. Together with the effect of non-Hermitian gain/loss, quantum
jumps can also lead to a breakdown of adiabatic evolution under the
slow-driving limit. Our study shows the critical role of quantum jumps in
generalizing the applications of classical non-Hermitian systems to open
quantum systems for sensing and control.
