The appearance of so-called exceptional points in the complex spectra of non-Hermitian systems is often associated with phenomena that contradict our physical intuition. One example of particular interest is the state-exchange process predicted for a
n adiabatic encircling of an exceptional point. In this work we analyse this and related processes for the generic system of two coupled oscillator modes with loss or gain. We identify a characteristic system evolution consisting of periods of quasi-stationarity interrupted by abrupt non-adiabatic transitions, and we present a qualitative and quantitative description of this switching behaviour by connecting the problem to the phenomenon of stability loss delay. This approach makes accurate predictions for the breakdown of the adiabatic theorem as well as the occurrence of chiral behavior observed previously in this context, and provides a general framework to model and understand quasi-adiabatic dynamical effects in non-Hermitian systems.
Topologically quantum error corrected logical gates are complex. Chains of errors can form in space and time and diagonally in spacetime. It is highly nontrivial to determine whether a given logical gate is free of low weight combinations of errors l
eading to failure. We report a new tool Nestcheck capable of analyzing an arbitrary topological computation and determining the minimum number of errors required to cause failure.
