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… Expand

Measurements of the thermal Hall conductance in the first excited Landau level of the quantum Hall effect show the existence of a state with non-Abelian excitations and perform topological unitary transformations when braided, which can be useful for topological quantum computation.Expand

We consider a two-dimensional electron gas with strong spin-orbit coupling contacted by two superconducting leads, forming a Josephson junction. We show that in the presence of an in-plane Zeeman… Expand

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… Expand

The non-Abelian nature of quasiparticles in the fractional quantum Hall state at nu = 5/2 is tested and analogous effects in the thermodynamic properties of closed systems are found.Expand

Generalizations of two-dimensional topological insulators which can be realized in interacting, time reversal invariant electron systems, which contain excitations with fractional charge and statistics in addition to protected edge modes are analyzed.Expand

Data is reported on shot noise generated by partitioning edge currents in the ν = 5/2 state, consistent with the charge of the quasiparticle being e/4, and inconsistent with other possible values, such as e/2 and e.Expand

We analyze interference phenomena in the quantum-Hall analog of the Fabry-Perot interferometer, exploring the roles of the Aharonov-Bohm effect, Coulomb interactions, and fractional statistics on the… Expand

Experimental studies attempt to identify non-Abelian states in systems that manifest the fractional quantum Hall effect, if such states can be identified, they may become useful for quantum computation.Expand