  This is a comprehensive review on fault-tolerant topological quantum
computation with the surface codes. The basic concepts and useful tools
underlying fault-tolerant quantum computation, such as universal quantum
computation, stabilizer formalism, and measurement-based quantum computation,
are also provided in a pedagogical way. Topological quantum computation by
brading the defects on the surface code is explained in both circuit-based and
measurement-based models in such a way that their relation is clear. The
interdisciplinary connections between quantum error correction codes and
subjects in other fields such as topological order in condensed matter physics
and spin glass models in statistical physics are also discussed. This
manuscript will be appeared in SpringerBriefs.
