  We introduce a two-parameter approximate counter-diabatic term into the
Hamiltonian of the transverse-field Ising model for quantum annealing to
accelerate convergence to the solution, generalizing an existing
single-parameter approach. The protocol is equivalent to unconventional
diabatic control of the longitudinal and transverse fields in the
transverse-field Ising model and thus makes it more feasible for experimental
realization than an introduction of new terms such as non-stoquastic catalysts
toward the same goal of performance enhancement. We test the idea for the
$p$-spin model with $p=3$, which has a first-order quantum phase transition,
and show that our two-parameter approach leads to significantly larger
ground-state fidelity and lower residual energy than those by traditional
quantum annealing as well as by the single-parameter method. We also find a
scaling advantage in terms of the time to solution as a function of the system
size in a certain range of parameters as compared to the traditional methods.
