Mong, Roger S. K. and Clarke, David J. and Alicea, Jason and Lindner, Netanel H. and Fendley, Paul and Nayak, Chetan and Oreg, Yuval and Stern, Ady and Berg, Erez and Shtengel, Kirill and Fisher, Matthew P. A. (2014) Universal Topological Quantum Computation from a Superconductor-Abelian Quantum Hall Heterostructure. Physical Review X, 4 (1). Art. No. 011036. ISSN 2160-3308. http://resolver.caltech.edu/CaltechAUTHORS:20140421-104643131
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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 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.
|Additional Information:||Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Received 2 August 2013; published 12 March 2014. We are grateful to Parsa Bonderson, Alexey Gorshkov, Victor Gurarie, Roni Ilan, Lesik Motrunich, Hirosi Ooguri, John Preskill, Miles Stoudenmire, and Krysta Svore for illuminating conversations. This work was supported in part by the NSF under Grant No. PHYS-1066293 and the hospitality of the Aspen Center for Physics, where the idea for this work was conceived. We also acknowledge funding from the NSF through Grants No. DMR-1341822 (D. J. C. and J. A.), No. DMR-MPS1006549 (P. F.), No. DMR- 0748925 (K. S.), and No. DMR-1101912 (M. F.); the Alfred P. Sloan Foundation (J. A.); the Sherman Fairchild Foundation (R.M.); the DARPA QuEST program (C. N. and K. S.); the AFOSR under Grant No. FA9550-10- 1-0524 (C. N.); the Israel Science Foundation (Y. O.); the Paul and Tina Gardner Fund for the Weizmann-TAMU Collaboration (Y. O.); the U.S.–Israel Binational Science Foundation (A. S.); the Minerva Foundation (A. S.); Microsoft Research Station Q; and the Caltech Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation.|
|Group:||IQIM, Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics|
|Subject Keywords:||Condensed Matter physics; Quantum Information; Strongly Correlated Materials|
|Official Citation:||Mong, R. S. K., Clarke, D. J., Alicea, J., Lindner, N. H., Fendley, P., Nayak, C., . . . Fisher, M. P. A. (2014). Universal Topological Quantum Computation from a Superconductor-Abelian Quantum Hall Heterostructure. Physical Review X, 4(1), 011036.|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Jason Perez|
|Deposited On:||22 Apr 2014 23:14|
|Last Modified:||18 Dec 2014 19:51|
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