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Quantum computing holds the potential for quantum advantage in optimizationproblems, which requires advances in quantum algorithms and hardwarespecifications. Adiabatic quantum optimization is conceptually a valid solutionthat suffers from limited hardware coherence times. In this sense,counterdiabatic quantum protocols provide a shortcut to this process, steeringthe system along its ground state with fast-changing Hamiltonian. In this work,we take full advantage of a digitized-counterdiabatic quantum optimization(DCQO) algorithm to find an optimal solution of the $p$-spin model up to4-local interactions. We choose a suitable scheduling function and initialHamiltonian such that a single-layer quantum circuit suffices to produce a goodground-state overlap. By further optimizing parameters using variationalmethods, we solve with unit accuracy 2-spin, 3-spin, and 4-spin problems for$100\%$, $93\%$, and $83\%$ of instances, respectively. As a particular case ofthe latter, we also solve factorization problems involving 5, 9, and 12 qubits.Due to the low computational overhead, our compact approach may become avaluable tool towards quantum advantage in the NISQ era.

Single-Layer Digitized-Counterdiabatic Quantum Optimization for $p$-spin Models