  We study the zero-temperature phase diagram of the Lechner-Hauke-Zoller
model. An analytic expression for the free-energy and critical coefficients for
finite-size systems and in the thermodynamic limit are derived and numerically
verified. With the aim to improve standard quantum annealing, we introduce an
inhomogeneously driven transverse field with an additional time-dependent
parameter that allows one to evade the first-order quantum phase transition
and, thus, improve the efficiency of the ground-state preparation considerably.
