  Non-Hermitian physics predicts open quantum system dynamics with unique
topological features such as exceptional points and the non-Hermitian skin
effect. We show that this new paradigm of topological systems can serve as
probes for bulk Hamiltonian parameters with quantum-enhanced sensitivity
reaching Heisenberg scaling. Such enhancement occurs close to a spectral
topological phase transition, where the entire spectrum undergoes a
delocalization transition. We provide an explanation for this enhanced
sensitivity based on the closing of point gap, which is a genuinely
non-Hermitian energy gap with no Hermitian counterpart. This establishes a
direct connection between energy-gap closing and quantum enhancement in the
non-Hermitian realm. Our findings are demonstrated through several paradigmatic
non-Hermitian topological models in various dimensions and potential
experimental implementations.
