  Adiabatic time evolution of quantum systems is a widely used tool with
applications ranging from state preparation through simplifications of
computations and topological transformations to optimization and quantum
computing. Adiabatic time evolution generally works well for gapped ground
states, but not for thermal states in the middle of the spectrum that lack a
protecting energy gap. Here we show that quantum many-body scars -- a
particular type of highly excited states -- are suitable for adiabatic time
evolution despite the absence of a protecting energy gap. Considering two
rather different models, namely a one-dimensional model constructed from tensor
networks and a two-dimensional fractional quantum Hall model with anyons, we
find that the quantum scars perform similarly to gapped ground states with
respect to adiabatic dynamics when the required final adiabatic fidelity is
around 0.99. The maximum speed at which the scar state of the one-dimensional
model can be adiabatically transformed decreases as a power law with system
size, as opposed to exponentially for both generic thermal and disorder-driven
localized states. At constant and very low ramp speed, we find that the
deviation of the fidelity from unity scales linearly with ramp speed for scar
states, but quadratically for gapped ground states. The gapped ground states
hence perform better when the required adiabatic fidelities are very high, such
as 0.9999 and above. We identify two mechanisms for leakage out of the scar
state and use them to explain our results. While manipulating a single,
isolated ground state is common in quantum applications, adiabatic evolution of
scar states provides the flexibility to manipulate an entire tower of
ground-state-like states simultaneously in a single system.
