Twist defects and projective non-Abelian braiding statistics

By Maissam Barkeshli, Chao-Ming Jian, Xiao-Liang Qi. 2012

183 citations recorded by the source corpus.

It has recently been realized that a general class of non-Abelian defects can be created in conventional topological states by introducing extrinsic defects, such as lattice dislocations or superconductor-ferromagnet domain walls in conventional quantum Hall states or topological insulators. In this paper, we begin by placing these defects within the broader conceptual scheme of extrinsic twist defects associated with symmetries of the topological state. We explicitly study several classes of examples, including Z2 and Z3 twist defects, where the topological state with N twist defects can be mapped to a topological state without twist defects on a genus g∝N surface. To emphasize this connection we refer to the twist defects as genons. We develop methods to compute the projective non-Abelian braiding statistics of the genons, and we find the braiding is given by adiabatic modular transformations, or Dehn twists, of the topological state on the effective genus g surface. We study the relation between this projective braiding statistics and the ordinary non-Abelian braiding statistics obtained when the genons become deconfined, finite-energy excitations. We find that the braiding is generally different, in contrast to the Majorana case, which opens the possibility for fundamentally novel behavior. We find situations where the genons have quantum dimension 2 and can be used for universal topological quantum computing (TQC), while the host topological state is by itself nonuniversal for TQC.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/c34d51d15e735bf446013765e2f39a2b77863241

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure (2013, unknown): “realized only projectively [57,58] as a result—i.”
Quantum memories at finite temperature (2014, background): “Faulttolerant computational operations are also realized by the manipulation of holes (Bombin and Martin-Delgado, 2009; Raussendorf et al., 2006; Wootton, 2012), twist defects (Barkeshli et al., 2014, 2013; Bombin, 2010a) or by other means (Wootton and Pachos, 2011b).”