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

Counterdiabatic optimized driving in quantum phase sensitive models