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Non-abelian anyons and topological quantum information processing in 1D wire networks

Jason Alicea

Bulletin of the American Physical SocietyFeb 27, 20122 citations

Controlling non-Abelian statistics of Majorana fermions in quasi-one-dimensional wire networks

Jay Deep Sau, David J. Clarke, Sumanta Tewari

arXiv:1012.0561Dec 2, 20100 citations

Topological Quantum Computation via Non-Abelian Statistics

Roderich Moessner, Joel E. Moore

Cambridge University Press eBooksApr 9, 20210 citations

Correlated parity measurements as a probe of non-Abelian statistics in one-dimensional superconducting wires

F. J. Burnell

We propose a method to detect a signature of non-Abelian statistics in a one-dimensional (1D) superconducting wire by tuning the effective coupling between a pair of Majorana particles. Our experiment requires a single wire with two segments in the topological superconducting phase and a total of four Majorana particles. We show that an appropriately timed ``pulse'' in the coupling between the two middle Majoranas leads to a coherent rotation of the two qubits associated with the pairs of Majoranas in the two topological superconducting segments, in much the same way that an appropriate-length pulse of a transverse magnetic field can be used to rotate spins in nuclear magnetic resonance. This can be exploited both to probe the correlations of the Majoranas and to manipulate the Majorana qubits in these 1D wires. We discuss the experimental requirements for such a coherent rotation to be observable when the wire system is coupled to a fermionic bath.We propose a method to detect a signature of non-Abelian statistics in a one-dimensional (1D) superconducting wire by tuning the effective coupling between a pair of Majorana particles. Our experiment requires a single wire with two segments in the topological superconducting phase and a total of four Majorana particles. We show that an appropriately timed ``pulse'' in the coupling between the two middle Majoranas leads to a coherent rotation of the two qubits associated with the pairs of Majoranas in the two topological superconducting segments, in much the same way that an appropriate-length pulse of a transverse magnetic field can be used to rotate spins in nuclear magnetic resonance. This can be exploited both to probe the correlations of the Majoranas and to manipulate the Majorana qubits in these 1D wires. We discuss the experimental requirements for such a coherent rotation to be observable when the wire system is coupled to a fermionic bath.

arXiv:1307.0839Physical Review BJun 17, 201412 citations

Topological aspects of quantum information processing

Ville Lahtinen, Jiannis K. Pachos

Texts and readings in physical sciencesJan 1, 20170 citations

Non-Abelian Fermions from Linked Vortex Networks in a 3+1D Quantized Superfluid (v5) Part II

Alex Smith

We extend the emergent hydrodynamic framework for fermionic statistics in a 3+1D quantized superfluid to include non-Abelian topological excitations.Single framed vortex loops reproduce the familiar Abelian π Berry phase corresponding to fermionic exchange. Multi-component vortex networks exhibit matrix-valuednon-Abelian holonomies associated with internal symmetry groups G. Linked and knotted vortices provide a mechanical realization of both fermionic statistics andinternal quantum numbers. We discuss how effective gauge interactions emerge from topological constraints, provide energy scale estimates, and present a roadmapconnecting vortex network structures to Standard Model-like particles and forces.We extend the emergent hydrodynamic framework for fermionic statistics in a 3+1D quantized superfluid to include non-Abelian topological excitations.Single framed vortex loops reproduce the familiar Abelian π Berry phase corresponding to fermionic exchange. Multi-component vortex networks exhibit matrix-valuednon-Abelian holonomies associated with internal symmetry groups G. Linked and knotted vortices provide a mechanical realization of both fermionic statistics andinternal quantum numbers. We discuss how effective gauge interactions emerge from topological constraints, provide energy scale estimates, and present a roadmapconnecting vortex network structures to Standard Model-like particles and forces.

Feb 7, 20260 citations

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

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