  Analytical solutions to the time-dependent Schrodinger equation describing a
driven two-level system are invaluable to many areas of physics, but they are
also extremely rare. Here, we present a simple algorithm that generates an
unlimited number of exact analytical solutions. We show that a general
single-axis driving term and its corresponding evolution operator are
determined by a single real function which is constrained only by a certain
inequality and initial conditions. Any function satisfying these constraints
yields an exact analytical solution. We demonstrate this method by presenting
several new exact solutions to the time-dependent Schrodinger equation. Our
general method and many of the new solutions we present are particularly
relevant to qubit control in quantum computing applications.
