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

Exponential Speedup of Quantum Annealing by Inhomogeneous Driving of the Transverse Field