  This paper studies fault-tolerant quantum computation with gapped boundaries.
We first introduce gapped boundaries of Kitaev's quantum double models for
Dijkgraaf-Witten theories using their Hamiltonian realizations. We classify the
elementary excitations on the boundary, and systematically describe the
bulk-to-boundary condensation procedure. We also provide a commuting
Hamiltonian to realize defects between boundaries in any quantum double model.
Next, we present the algebraic/categorical structure of gapped boundaries and
boundary defects, which will be used to describe topologically protected
operations and obtain quantum gates. To demonstrate a potential physical
realization, we provide quantum circuits for surface codes that can perform all
basic operations on gapped boundaries. Finally, we show how gapped boundaries
of the abelian theory $\mathfrak{D}(\mathbb{Z}_3)$ can be used to perform
universal quantum computation.
