Solutions to the Yang-Baxter equation - an important equation in mathematics
and physics - and their afforded braid group representations have applications
in fields such as knot theory, statistical mechanics, and, most recently,
quantum information science. In particular, unitary representations of the
braid group are desired because they generate braiding quantum gates. These are
actively studied in the ongoing research into topological quantum computing. A
generalized Yang-Baxter equation was proposed a few years ago by Eric Rowell et
al. By finding solutions to the generalized Yang-Baxter equation, we obtain new
unitary braid group representations. Our representations give rise to braiding
quantum gates and thus have the potential to aid in the construction of useful
quantum computers.