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.
Highlights
The emergence of anyons that exhibit richer exchange statistics than the constituent electrons and ions in a material is among the most remarkable illustrations of “more is different.” Such particles fall into two broad categories: Abelian and non-Abelian
There we show, by relating the setup to a three-state quantum clock model, that this chain can be tuned to a critical point described by a nonchiral Z3 parafermion conformal field theory
Overcoming the nontrivial fabrication challenges involved could prove enormously beneficial for quantum-information applications. In this regard, inspired by recent progress in Majorana-based systems, we are optimistic that it should be possible to distill the architecture we propose to alleviate many of the practical difficulties toward realizing Fibonacci anyons
Summary
The emergence of anyons that exhibit richer exchange statistics than the constituent electrons and ions in a material is among the most remarkable illustrations of “more is different.” Such particles fall into two broad categories: Abelian and non-Abelian. We focus on the experimentally observed spin-unpolarized ν 1⁄4 2=3 state [94]— known as the (112) state—for which superconducting islands bind Z3 generalizations of Majorana modes This phase is ideal for building in the physics of the Z3 Read-Rezayi state, since coupling to an s-wave superconductor can generate Cooper pairs built from three charge-2e=3 excitations [95]. Superconducting vortices do not lead to new quasiparticle types, in sharp contrast to a p þ ip superconductor where vortices provide the source of Ising anyons In this sense, the fact that the Fibonacci phase exhibits an order parameter is unimportant for its universal topological physics. The abundance of systems known to host Abelian fractional quantum Hall phases and the large potential payoff together provide strong motivation for further pursuit of this avenue toward universal topological quantum computation
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
