{"id":89,"date":"2014-04-06T08:43:57","date_gmt":"2014-04-06T06:43:57","guid":{"rendered":"http:\/\/phsites.technion.ac.il\/lindner\/?page_id=89"},"modified":"2020-08-10T12:28:35","modified_gmt":"2020-08-10T09:28:35","slug":"non-abelian-topological-systems","status":"publish","type":"page","link":"https:\/\/phsites.technion.ac.il\/lindner\/non-abelian-topological-systems\/","title":{"rendered":"Non Abelian Topological Systems"},"content":{"rendered":"\n

Non Abelian Topological Systems<\/h1>\n\n\n\n
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A fascinating property of many topological phases are collective fractionalized excitations which are highly
\nnon-local in nature. These carry fractions of the quantum numbers of the underlying microscopic degrees of freedom; e.g., they can carry fractions of the electron charge. In two spatial dimensions, such emergent excitations can have exotic exchange rules, which are different from those of either bosons or fermions. Most intriguingly, certain topological systems can support \u201cnon-Abelian\u201d excitations, whose exchange rules are described by non-commuting matrices. In the presence of such excitations, the many-body ground state is multiply degenerate; this degeneracy is topological, in the sense that it cannot be lifted by any local perturbation. The degenerate ground states encode quantum information in a non-local way. The information is therefore immune to decoherence – the destructive effect of the noisy environment. Thus, non-Abelian systems may hold the key for overcoming one of greatest challenges in contemporary physics and engineering: the realization of a fault-tolerant quantum computer.<\/p>\n

Selected Work<\/h3>\n
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Universal topological quantum computation from a superconductor-Abelian quantum Hall heterostructure<\/h4>\n

\"prx4_011036_2014\"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\u2019s 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 Z3 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\u2014unlike Ising anyons\u2014allow for universal topological quantum computation solely through braiding. Using a variant of Teo and Kane\u2019s 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 twofold ground-state degeneracy on a torus. In contrast to a p+ip superconductor, vortices do not yield additional particle types, yet depending on nonuniversal 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.<\/p>\n