  Non-Hermitian systems have attracted much interest in recent decades, driven
partly by the existence of exotic spectral singularities, known as exceptional
points (EPs), where the dimensionality of the system evolution operator is
reduced. Among various intriguing applications, the discovery of EPs has
suggested the potential for implementing a symmetric mode switch, when
encircling them in a system parameter space. However, subsequent theoretical
and experimental works have revealed that {\it dynamical} encirclement of EPs
invariably results in asymmetric mode conversion; namely, the mode switching
depends only on the winding direction but not on the initial state. This
chirality arises from the failure of adiabaticity due to the complex spectrum
of non-Hermitian systems. Although the chirality revealed has undoubtedly made
a significant impact in the field, a realization of the originally sought
symmetric adiabatic passage in non-Hermitian systems with EPs has since been
elusive. In this work, we bridge this gap and theoretically demonstrate that
adiabaticity, and therefore a symmetric state transfer, is achievable when
dynamically winding around an EP. This becomes feasible by specifically
choosing a trajectory in the system parameter space along which the
corresponding evolution operator attains a real spectrum. Our findings, thus,
offer a promise for advancing various wave manipulation protocols in both
quantum and classical domains.
