# Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure

@article{Mong2013UniversalTQ, title={Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure}, author={Roger S. K. Mong and David J. Clarke and Jason Alicea and Netanel H. Lindner and Paul Fendley and C. Nayak and Yuval Oreg and Ady Stern and Erez Berg and Kirill Shtengel and Matthew P A Fisher}, journal={arXiv: Strongly Correlated Electrons}, year={2013}, pages={011036} }

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…

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## References

SHOWING 1-10 OF 208 REFERENCES

### Exotic non-Abelian anyons from conventional fractional quantum Hall states

- PhysicsNature Communications
- 2013

A device fabricated from conventional fractional quantum Hall states and s-wave superconductors that supports exotic non-defects binding parafermionic zero modes, which generalize Majorana bound states are introduced.

### Non-Abelian Anyons and Topological Quantum Computation

- Physics
- 2008

Topological quantum computation has emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of…

### Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states

- Physics
- 2012

We study the non-abelian statistics characterizing systems where counter-propagating gapless modes on the edges of fractional quantum Hall states are gapped by proximity-coupling to superconductors…

### Non-Abelian statistics and topological quantum information processing in 1D wire networks

- Physics
- 2011

The synthesis of a quantum computer remains an ongoing challenge in modern physics. Whereas decoherence stymies most approaches, topological quantum computation schemes evade decoherence at the…

### From Luttinger liquid to non-Abelian quantum Hall states

- Physics
- 2012

We formulate a theory of non-Abelian fractional quantum Hall states by considering an anisotropic system consisting of coupled, interacting one dimensional wires. We show that Abelian bosonization…

### Braiding of Abelian and Non-Abelian Anyons in the Fractional Quantum Hall Effect

- Physics
- 2011

In this paper, we report on the study of Abelian and non-Abelian statistics through Fabry-Perot interferometry of fractional quantum Hall (FQH) systems. Our detection of phase slips in quantum…

### Collective states of interacting anyons, edge states, and the nucleation of topological liquids.

- PhysicsPhysical review letters
- 2009

These results describe nucleation of different 2D topological quantum fluids within a "parent" non-Abelian quantum Hall state, arising from a macroscopic occupation with localized, interacting anyons.

### Two-dimensional quantum liquids from interacting non-Abelian anyons

- Physics
- 2011

A set of localized, non-Abelian anyons—such as vortices in a px+ipy superconductor or quasiholes in certain quantum Hall states—gives rise to a macroscopic degeneracy. Such a degeneracy is split in…

### Theory of edge states in a quantum anomalous Hall insulator/ spin-singlet s-wave superconductor hybrid system

- Physics
- 2011

We study the edge states for a quantum anomalous Hall system (QAHS) coupled with a spin-singlet s-wave superconductor through the proximity effect, and clarify the topological nature of them. When we…

### Topological Quantum Computation

- PhysicsQCQC
- 1998

The connection between fault-tolerant quantum computation and nonabelian quantum statistics in two spatial dimensions is explored and it is shown that if information is encoded in pairs of quasiparticles, then the Aharonov-Bohm interactions can be adequate for universal fault-Tolerance quantum computation.