  Topological quantum computation may provide a robust approach for encoding
and manipulating information utilizing the topological properties of anyonic
quasi-particle excitations. We develop an efficient means to map between dense
and sparse representations of quantum information (qubits) and a simple
construction of multi-qubit gates, for all anyon models from
Chern-Simons-Witten SU(2)$_k$ theory that support universal quantum computation
by braiding ($k\geq 3,\ k \neq 4$). In the process, we show how the
constructions of topological quantum memory and gates for $k=2,4$ connect
naturally to those for $k\geq 3,\ k \neq 4$, unifying these concepts in a
simple framework. Furthermore, we illustrate potential extensions of these
ideas to other anyon models outside of Chern-Simons-Witten field theory.
