  State preparation plays a pivotal role in numerous quantum algorithms,
including quantum phase estimation. This paper extends and benchmarks
counterdiabatic driving protocols across three one-dimensional spin systems
characterized by phase transitions: the axial next-nearest neighbor Ising
(ANNNI), XXZ, and Haldane-Shastry (HS) models. We perform quantum optimal
control protocols by optimizing the energy cost function, which can always be
evaluated as opposed to the fidelity one requiring the exact state. Moreover,
we incorporate Bayesian optimization within a code package for computing
various adiabatic gauge potentials. This protocol consistently surpasses
standard annealing schedules, often achieving performance improvements of
several orders of magnitude. Notably, the ANNNI model stands out as a notable
example, where fidelities exceeding 0.5 are attainable in most cases.
Furthermore, the optimized paths exhibits promising generalization capabilities
to higher-dimensional systems, allowing for the extension of parameters from
smaller models. This opens up possibilities for applying the protocol to
higher-dimensional systems. However, our investigations reveal limitations in
the case of the XXZ and HS models, particularly when transitioning away from
the ferromagnetic phase. This suggests that finding optimal diabatic gauge
potentials for specific systems remains an important research direction.
