Quantum technologies are nowadays at the cutting-edge of science. Much effort has been devoted to understand controlled quantum dynamics and be aware of its limits. In this context, special attention has been focused on time-optimal manipulation of quantum states. Among this kind of problems, there is an important class related to the time-optimal quantum evolution under the influence of external fields or potentials that cannot be suppressed. Such problems are really important because in real laboratories one cannot get rid of certain external influences. From a classical point of view, this problem was first posed by Zermelo. We introduce the quantum counterpart of the well known classical navigation problem stated by Zermelo for a two-level system and provide a simple resolution in terms of a control Hamiltonian. This Hamiltonian yields a time-optimal control of a general Bloch vector in a two-dimensional Hilbert space.

Time-optimal quantum evolution: The Zermelo approach

ACS Fall 2021

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