• DOI:10.26421/QIC10.7-8-8
• Corpus ID: 2775580

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

@article{Rowell2007ExtraspecialTG,
  title={Extraspecial two-Groups, generalized Yang-Baxter equations and braiding quantum gates},
  author={Eric C. Rowell and Yong Zhang and Yong-Shi Wu and Mo-Lin Ge},
  journal={Quantum Inf. Comput.},
  year={2007},
  volume={10},
  pages={685-702}
}

• E. Rowell, Yong Zhang, +1 author M. Ge
• Published 12 June 2007
• Mathematics
• Quantum Inf. Comput.

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.