Extraspecial Two-Groups, Generalized Yang-Baxter Equations and Braiding Quantum Gates
Abstract
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.
Cite
@article{arxiv.0706.1761,
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= {arXiv preprint arXiv:0706.1761},
year = {2014}
}