  We argue that in a second order quantum phase transition driven by an
inhomogeneous quench density of quasiparticle excitations is suppressed when
velocity at which a critical point propagates across a system falls below a
threshold velocity equal to the Kibble-Zurek correlation length times the
energy gap at freeze-out divided by $\hbar$. This general prediction is
supported by an analytic solution in the quantum Ising chain. Our results
suggest, in particular, that adiabatic quantum computers can be made more
adiabatic when operated in an "inhomogeneous" way.
