Extraspecial Two-Groups, Generalized Yang-Baxter Equations and Braiding Quantum Gates Institutional Repository Document uri icon


  • 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.

author list (cited authors)

  • Rowell, E. C., Zhang, Y., Wu, Y., & Ge, M.

complete list of authors

  • Rowell, Eric C||Zhang, Yong||Wu, Yong-Shi||Ge, Mo-Lin

publication date

  • June 2007