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The exchange statistics of Majorana fermions in quasi-one-dimensional networks

David J. Clarke, Jay Deep Sau, Sumanta Tewari

Bulletin of the American Physical SocietyMar 25, 20110 citations

Verifying non-Abelian statistics by numerical braiding Majorana fermions

Qiu-Bo Cheng, Jing He, Su-Peng Kou

arXiv:1412.2195Physics Letters ANov 26, 201511 citations

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

Jason Alicea, Yuval Oreg, Gil Refael +2 more

arXiv:1006.4395Nature PhysicsFeb 13, 20111,633 citations

Detecting non-Abelian statistics of Majorana fermions in quantum nanowire networks

Zheng‐Yuan Xue

A scheme in semiconducting quantum nanowire structure has been proposed to demonstrate the non-Abelian statistics for Majorana fermions in terms of braid group. The Majorana fermions are localized at the endpoints of semiconducting wires, which are deposited on an s -wave superconductor. The non-Abelian nature of Majorana fermion is manifested by the fact that the output of the different applied orders of two operations, constructed by the braid group elements, are different. In particular, the difference can be unambiguously imprinted on the quantum states of a superconducting flux qubit.A scheme in semiconducting quantum nanowire structure has been proposed to demonstrate the non-Abelian statistics for Majorana fermions in terms of braid group. The Majorana fermions are localized at the endpoints of semiconducting wires, which are deposited on an s -wave superconductor. The non-Abelian nature of Majorana fermion is manifested by the fact that the output of the different applied orders of two operations, constructed by the braid group elements, are different. In particular, the difference can be unambiguously imprinted on the quantum states of a superconducting flux qubit.

arXiv:1106.5091Journal of Experimental and Theoretical Physics LettersOct 1, 20114 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

Hybrid topological quantum computation with Majorana fermions: A cold-atom setup

C. Laflamme, M. A. Baranov, P. Zoller +1 more

In this paper, we present a hybrid scheme for topological quantum computation in a system of cold atoms trapped in an atomic lattice. A topological qubit subspace is defined using Majorana fermions which emerge in a network of atomic Kitaev one-dimensional wires. We show how braiding can be efficiently implemented in this setup and propose a direct way to demonstrate the non-Abelian nature of Majorana fermions via a single-parity measurement. We then introduce a proposal for the efficient, robust, and reversible mapping of the topological qubits to a conventional qubit stored in a single atom. There, well-controlled standard techniques can be used to implement the missing gates required for universal computation. Our setup is complemented with an efficient nondestructive protocol to check for errors in the mapping.In this paper, we present a hybrid scheme for topological quantum computation in a system of cold atoms trapped in an atomic lattice. A topological qubit subspace is defined using Majorana fermions which emerge in a network of atomic Kitaev one-dimensional wires. We show how braiding can be efficiently implemented in this setup and propose a direct way to demonstrate the non-Abelian nature of Majorana fermions via a single-parity measurement. We then introduce a proposal for the efficient, robust, and reversible mapping of the topological qubits to a conventional qubit stored in a single atom. There, well-controlled standard techniques can be used to implement the missing gates required for universal computation. Our setup is complemented with an efficient nondestructive protocol to check for errors in the mapping.

arXiv:1312.6583Physical Review AFeb 13, 201421 citations

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

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