Robust Diabatic Quantum Search by Landau-Zener-Stückelberg Oscillations

Abstract

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, that 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 $O(\sqrt{2^n})$ 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 using coherent destruction of tunneling, providing superior performance compared to standard algorithms.

10 pages, 5 figures

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Cited by in corpus (3)

• Nonadiabatic Landau-Zener-Stückelberg-Majorana transitions, dynamics, and interference
• Reservoir-engineering shortcuts to adiabaticity
• Tuning the initial phase to control the final state of a driven qubit