  Quantum scars are non-thermal eigenstates characterized by low entanglement
entropy, initially detected in systems subject to nearest-neighbor Rydberg
blockade, the so called PXP model. While most of these special eigenstates
elude an analytical description and seem to hybridize with nearby thermal
eigenstates for large systems, some of them can be written as matrix product
states (MPS) with size-independent bond dimension. We study the response of
these exact quantum scars to perturbations by analysing the scaling of the
fidelity susceptibility with system size. We find that some of them are
anomalously stable at first order in perturbation theory, in sharp contrast to
the eigenstate thermalization hypothesis. However, this stability seems to
breakdown when all orders are taken into account. We further investigate models
with larger blockade radius and find a novel set of exact quantum scars, that
we write down analytically and compare with the PXP exact eigenstates. We show
that they exhibit the same robustness against perturbations at first order.
