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00925njm 22002777a 4500 dc Garcia, Lluc author Bofill i Villà, Josep M. author Moreira, Ibério de Pinho Ribeiro author Albareda, Guillermo author 2023-01-20T09:46:58Z 2023-01-20T09:46:58Z 2022-10-26 2023-01-20T09:46:58Z Time-efficient control schemes for manipulating quantum systems are of great importance in quantum technologies, where environmental forces rapidly degrade the quality of pure states over time. In this Letter, we formulate an approach to time-optimal control that circumvents the boundary-value problem that plagues the quantum brachistochrone equation at the expense of relaxing the form of the control Hamiltonian. In this setting, a coupled system of equations, one for the control Hamiltonian and another one for the duration of the protocol, realizes an ansatz-free approach to quantum control theory. We show how driven systems, in the form of a Landau-Zener type Hamiltonian, can be efficiently maneuvered to speed up a given state transformation in a highly adiabatic manner and with a low energy cost. Teoria quàntica Física Quantum theory Physics Highly Adiabatic Time-Optimal Quantum Driving at Low Energy Cost