  We introduce a hardware-specific, problem-dependent digital-analog quantum
algorithm of a counterdiabatic quantum dynamics tailored for optimization
problems. Specifically, we focus on trapped-ion architectures, taking advantage
from global M{\o}lmer-S{\o}rensen gates as the analog interactions complemented
by digital gates, both of which are available in the state-of-the-art
technologies. We show an optimal configuration of analog blocks and digital
steps leading to a substantial reduction in circuit depth compared to the
purely digital approach. This implies that, using the proposed encoding, we can
address larger optimization problem instances, requiring more qubits, while
preserving the coherence time of current devices. Furthermore, we study the
minimum gate fidelity required by the analog blocks to outperform the purely
digital simulation, finding that it is below the best fidelity reported in the
literature. To validate the performance of the digital-analog encoding, we
tackle the maximum independent set problem, showing that it requires fewer
resources compared to the digital case. This hybrid co-design approach paves
the way towards quantum advantage for efficient solutions of quantum
optimization problems.
