  Quantum information technologies demand highly accurate control over quantum
systems. Achieving this requires control techniques that perform well despite
the presence of decohering noise and other adverse effects. Here, we review a
general technique for designing control fields that dynamically correct errors
while performing operations using a close relationship between quantum
evolution and geometric space curves. This approach provides access to the
global solution space of control fields that accomplish a given task,
facilitating the design of experimentally feasible gate operations for a wide
variety of applications.
