Extraspecial two-groups, generalized yang-baxter equations and braiding quantum gates

  • Authors:

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

  • Affiliations:

  • Department of Mathematics, Texas A&M University, College Station, TX;Department of Physics and Astronomy, University of Utah, Salt Lake City, UT;Department of Physics and Astronomy, University of Utah, Salt Lake City, UT;Chern Institute of Mathematics, Nankai University, Tianjin, China

  • Venue:
  • Quantum Information & Computation
  • Year:
  • 2010

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Abstract

In this paper we describe connections among extraspecial 2-groups, unitary representa-tions of the braid group and multi-qubit braiding quantum gates. We first construct newrepresentations 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 gen-erate the GHZ (Greenberger-Horne-Zeilinger) states, for an arbitrary (particularly anodd) number of qubits, from the product basis. We also discuss the Yang-Baxterizationof the new braid group representations, which describes unitary evolution of the GHZstates. Our study suggests that through their connection with braiding gates, extraspe-cial 2-groups and the GHZ states may play an important role in quantum error correctionand topological quantum computing.