Physics – Quantum Physics
Scientific paper
2007-06-12
Quantum Inf. Comput. 10 (2010) no. 7 & 8 0685-0702
Physics
Quantum Physics
v1: Latex, 28 pages; v2: comment and references added; v3: Title and authors changed. Significantly more concise than previous
Scientific paper
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.
Ge Mo-Lin
Rowell Eric C.
Wu Yong-Shi
Zhang Yong
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