  The theory of quantum computation can be constructed from the abstract study
of anyonic systems. In mathematical terms, these are unitary topological
modular functors. They underlie the Jones polynomial and arise in
Witten-Chern-Simons theory. The braiding and fusion of anyonic excitations in
quantum Hall electron liquids and 2D-magnets are modeled by modular functors,
opening a new possibility for the realization of quantum computers. The chief
advantage of anyonic computation would be physical error correction: An error
rate scaling like $e^{-\a\l}$, where $\l$ is a length scale, and $\alpha$ is
some positive constant. In contrast, the $\q$presumptive" qubit-model of
quantum computation, which repairs errors combinatorically, requires a
fantastically low initial error rate (about $10^{-4}$) before computation can
be stabilized.
