  Adiabatic preparation of a critical ground state is hampered by the closing
of its energy gap as the system size increases. However, this gap is directly
relevant only for a uniform ramp, where a control parameter in the Hamiltonian
is tuned uniformly in space towards the quantum critical point. Here, we
consider inhomogeneous ramps in two dimensions: initially, the parameter is
made critical at the center of a lattice, from where the critical region
expands at a fixed velocity. In the 1D and 2D quantum Ising models, which have
a well-defined speed of sound at the critical point, the ramp becomes adiabatic
with a subsonic velocity. This subsonic ramp can prepare the critical state
faster than a uniform one. Moreover, in both a model of $p$-wave paired 2D
fermions and the Kitaev model, the critical dispersion is anisotropic -- linear
with a nonzero velocity in one direction and quadratic in the other -- but the
gap is still inversely proportional to the linear size of the critical region,
with a coefficient proportional to the nonzero velocity. This suffices to make
the inhomogeneous ramp adiabatic below a finite crossover velocity and superior
to the homogeneous one.
