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arXiv · 0706.1761

Extraspecial Two-Groups, Generalized Yang-Baxter Equations and Braiding Quantum Gates

Eric C. Rowell·Yong Zhang·Yong-Shi Wu·Mo-Lin Ge
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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.

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Eric C. Rowell, Yong Zhang, Yong-Shi Wu, Mo-Lin Ge. 2010-08-30. Extraspecial Two-Groups, Generalized Yang-Baxter Equations and Braiding Quantum Gates. https://arxiv.org/abs/0706.1761

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