  We show, for quantum annealing, that a certain type of inhomogeneous driving
of the transverse field erases first-order quantum phase transitions in the
p-body interacting mean-field-type model with and without longitudinal random
field. Since a first-order phase transition poses a serious difficulty for
quantum annealing (adiabatic quantum computing) due to the exponentially small
energy gap, the removal of first-order transitions means an exponential speedup
of the annealing process. The present method may serve as a simple protocol for
the performance enhancement of quantum annealing, complementary to
non-stoquastic Hamiltonians.
