  Geometric and holonomic quantum computation utilizes intrinsic geometric
properties of quantum-mechanical state spaces to realize quantum logic gates.
Since both geometric phases and quantum holonomies are global quantities
depending only on the evolution paths of quantum systems, quantum gates based
on them possess built-in resilience to certain kinds of errors. This review
provides an introduction to the topic as well as gives an overview of the
theoretical and experimental progress for constructing geometric and holonomic
quantum gates and how to combine them with other error-resistant techniques.
