Robust diabatic grover search by Landau-Zener-Stückelberg oscillations

Quantum computation by the adiabatic theorem requires a slowly-varying Hamiltonian with respect to the spectral gap. We show that the Landau-Zener-Stückelberg oscillation phenomenon, which naturally occurs in quantum two-level systems under non-adiabatic periodic drive, can be exploited to find the ground state of an N-dimensional Grover Hamiltonian. The total runtime of this method is O(√2ⁿ), which is equal to the computational time of the Grover algorithm in the quantum circuit model. An additional periodic drive can suppress a large subset of Hamiltonian control errors by using coherent destruction of tunneling, thus outperforming previous algorithms.