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Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
- Source :
- Phys. Rev. X 4, 011036 (2014)
- Publication Year :
- 2013
-
Abstract
- Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. A key breakthrough in the pursuit of these exotic particles originated from Read and Green's observation that the Moore-Read quantum Hall state and a (relatively simple) two-dimensional p+ip superconductor both support so-called Ising non-Abelian anyons. Here we establish a similar correspondence between the Z_3 Read-Rezayi quantum Hall state and a novel two-dimensional superconductor in which charge-2e Cooper pairs are built from fractionalized quasiparticles. In particular, both phases harbor Fibonacci anyons that---unlike Ising anyons---allow for universal topological quantum computation solely through braiding. Using a variant of Teo and Kane's construction of non-Abelian phases from weakly coupled chains, we provide a blueprint for such a superconductor using Abelian quantum Hall states interlaced with an array of superconducting islands. Fibonacci anyons appear as neutral deconfined particles that lead to a two-fold ground-state degeneracy on a torus. In contrast to a p+ip superconductor, vortices do not yield additional particle types yet depending on non-universal energetics can serve as a trap for Fibonacci anyons. These results imply that one can, in principle, combine well-understood and widely available phases of matter to realize non-Abelian anyons with universal braid statistics. Numerous future directions are discussed, including speculations on alternative realizations with fewer experimental requirements.<br />Comment: 37 pages. v2 fixed typos and clarified some issue
Details
- Database :
- arXiv
- Journal :
- Phys. Rev. X 4, 011036 (2014)
- Publication Type :
- Report
- Accession number :
- edsarx.1307.4403
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1103/PhysRevX.4.011036