  The quantum navigation problem of finding the time-optimal control
Hamiltonian that transports a given initial state to a target state through
quantum wind, that is, under the influence of external fields or potentials, is
analysed. By lifting the problem from the state space to the space of unitary
gates realising the required task, we are able to deduce the form of the
solution to the problem by deriving a universal quantum speed limit. The
expression thus obtained indicates that further simplifications of this
apparently difficult problem are possible if we switch to the interaction
picture of quantum mechanics. A complete solution to the navigation problem for
an arbitrary quantum system is then obtained, and the behaviour of the solution
is illustrated in the case of a two-level system.
