Quantum Zermelo problem for general energy resource bounds.

A solution to the quantum Zermelo problem for control Hamiltonians with general energy resource bounds is provided. The solution is found to be adiabatic irrespective of the energy resource, and includes as a particular case the result in [Phys. Rev. Lett. 114, 100502 (2015)] for a Hilbert-Schmidt norm equal to one. Interestingly, the energy resource of the control Hamiltonian and the control time define a pair of conjugate variables that minimize the energy-time uncertainty relation. The resulting control protocol is applied to a single qubit as well as to a two-interacting qubit system represented by a Heisenberg spin dimer. For this low-dimensional systems, it is found that physically realizable control Hamiltonians exist only for certain, quantized, energy resources.