Extraspecial two-Groups, generalized Yang-Baxter equations and braiding quantum gates

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 (GreenbergerHorne-Zeilinger) states, for an arbitrary (particularly an 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. PACS numbers: 02.10.Kn, 03.65.Ud, 03.67.Lx MSC 2000 numbers: 81P68 (Primary) 20F36, 20C35, 81R05 (Secondary)