Extraspecial two-Groups, generalized Yang-Baxter equations and braiding quantum gates (pp0685-0702)
          Eric C. Rowell, Yong Zhang, Yong-Shi Wu, and Mo-Lin Ge
          doi: https://doi.org/10.26421/QIC10.7-8-8
Abstracts: 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 YangBaxter equations and use them to realize new braiding quantum gates. These gates generate the GHZ (Greenberger-Horne-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.
Key words: Yang�Baxter, Extraspecial 2-groups, GHZ State