  I present a simple algorithm based on a type of partial reverse-engineering
that generates an unlimited number of exact analytical solutions to the
Schrodinger equation for a general time-dependent two-level Hamiltonian. I
demonstrate this method by deriving new exact solutions corresponding to fast
control pulses that contain arbitrarily many tunable parameters. It is shown
that the formalism is naturally suited to generating analytical control
protocols that perform precise non-adiabatic rapid passage and Landau-Zener
interferometry near the quantum speed limit. A general, exact formula for
Landau-Zener interference patterns is derived.
