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In this paper we describe connections among extraspecial 2-groups, unitaryrepresentations of the braid group and multi-qubit braiding quantum gates. Wefirst construct new representations of extraspecial 2-groups. Extending thelatter by the symmetric group, we construct new unitary braid representations,which are solutions to generalized Yang-Baxter equations and use them torealize 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 theYang-Baxterization of the new braid group representations, which describesunitary evolution of the GHZ states. Our study suggests that through theirconnection with braiding gates, extraspecial 2-groups and the GHZ states mayplay an important role in quantum error correction and topological quantumcomputing.

Extraspecial Two-Groups, Generalized Yang-Baxter Equations and Braiding Quantum Gates