Quantum adiabatic brachistochrone for open systems

We propose a variational principle to compute quantum adiabatic brachistochrone (QAB) for open systems. Using the notion of ``adiabatic speed'' based on energy gaps, we derive Lagrangian associated functional measuring time spent achieve behavior, which in turn allows us perform optimization. The QAB is illustrated nonunitary dynamics stimulated Raman passage process, Deutsch-Jozsa computing algorithm, and transmon qutrit. A numerical protocol devised, one arbitrary systems exact simulations can be afforded. also establish sufficient conditions equivalence between Lagrangians, thus QAB, closed