  The control of qubit states is often impeded by systematic control errors.
Compensating pulse sequences have emerged as a resource efficient method for
quantum error reduction. In this review, we discuss compensating composite
pulse methods, and introduce a unifying control-theoretic framework using a
dynamic interaction picture. This admits a novel geometric picture where
sequences are interpreted as vector paths on the dynamical Lie algebra.
Sequences for single-qubit and multi-qubit operations are described with this
method.
