Citation: Barkeshli, Maissam, and Xiao-Liang Qi. "Synthetic topological qubits in conventional bilayer quantum Hall systems." Physical Review X 4.4 (2014): 041035.
Web: https://arxiv.org/abs/1302.2673
Tags: Physical, Ising-computer, Quantum-hall-effect
This paper proposes a physical mechanism for realizing genons in bilayer quantum Hall systems. The idea is that it is clear in principle that genons should arise from some sort of coupling between bilayer topologically ordered systems. The most famous such systems are quantum Hall systems. Hence, all that's left to do is find a physical mechanism, which is exactly what this paper does!
The idea of the coupling is to apply gates to both the top and bottom layers to deplete the fluid in a small region. This is done in such a way that a distinguished edge on both sides of the depleted fluid form line junctions, which host chiral edge modes localized at their endpoints. By some general calculation of chiral Luttinger spin liquid theory these chiral edge modes will couple across layers, and this coupling will exactly form a pair of genons.
This paper is part of a general literature of people trying to realize physical mechanisms for genons, which is a utmost importance because this can mean the difference between Clifford gates and universal gates:
> Barkeshli, Maissam, and Jay D. Sau. "Physical architecture for a universal topological quantum computer based on a network of majorana nanowires." arXiv preprint arXiv:1509.07135 (2015).
> Barkeshli, Maissam, and Michael Freedman. "Modular transformations through sequences of topological charge projections." Physical Review B 94.16 (2016): 165108.
> Barkeshli, Maissam, and Xiao-Liang Qi. "Topological nematic states and non-abelian lattice dislocations." Physical Review X 2.3 (2012): 031013.