  In this paper we describe connections among extraspecial 2-groups, unitary
representations of the braid group and multi-qubit braiding quantum gates. We
first construct new representations of extraspecial 2-groups. Extending the
latter by the symmetric group, we construct new unitary braid representations,
which are solutions to generalized Yang-Baxter equations and use them to
realize new braiding quantum gates. These gates generate the GHZ
(Greenberger-Horne-Zeilinger) states, for an arbitrary (particularly an
\emph{odd}) number of qubits, from the product basis. We also discuss the
Yang-Baxterization of the new braid group representations, which describes
unitary evolution of the GHZ states. Our study suggests that through their
connection with braiding gates, extraspecial 2-groups and the GHZ states may
play an important role in quantum error correction and topological quantum
computing.
