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

Nature Physics volume 7, pages 412–417 (2011)Cite this article

Abstract

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 hardware level by storing quantum information non-locally. Here we establish that a key operation—braiding of non-Abelian anyons—can be implemented using one-dimensional semiconducting wires. Such wires can be driven into a topological phase supporting long-sought particles known as Majorana fermions that can encode topological qubits. We show that in wire networks, Majorana fermions can be meaningfully braided by simply adjusting gate voltages, and that they exhibit non-Abelian statistics like vortices in a p+i p superconductor. We propose experimental set-ups that enable probing of the Majorana fusion rules and the efficient exchange of arbitrary numbers of Majorana fermions. This work should open a new direction in topological quantum computation that benefits from physical transparency and experimental feasibility.

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Figure 1: Majorana fermions appear at the ends of a 1D ‘spinless’ p-wave superconductor, which can be experimentally realized in semiconducting wires21,22.
Figure 2: Applying a ‘keyboard’ of individually tunable gates to the wire allows local control of which regions are topological (dark blue) and non-topological (light blue), and hence manipulate Majorana fermions while maintaining the bulk gap.
Figure 3: A T-junction provides the simplest wire network that enables meaningful adiabatic exchange of Majorana fermions.
Figure 4: Experimental set-ups that allow the probing of non-Abelian statistics and Majorana-fermion fusion rules.

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Acknowledgements

We have benefited greatly from stimulating conversations with P. Bonderson, S. Das Sarma, L. Fidkowski, E. Henriksen, A. Kitaev, P. Lee, X. Qi and A. Stern. We also gratefully acknowledge support from the Lee A. DuBridge Foundation, ISF, BSF, DIP and SPP 1285 grants, Packard and Sloan fellowships, the Institute for Quantum Information under NSF grants PHY-0456720 and PHY-0803371, and the National Science Foundation through grant DMR-0529399.

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Authors and Affiliations

  1. Department of Physics and Astronomy, University of California, Irvine, California 92697, USA

    Jason Alicea

  2. Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 76100, Israel

    Yuval Oreg

  3. Department of Physics, California Institute of Technology, Pasadena, California 91125, USA

    Gil Refael & Matthew P. A. Fisher

  4. Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany

    Felix von Oppen

  5. Department of Physics, University of California, Santa Barbara, California 93106, USA

    Matthew P. A. Fisher

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  1. Jason Alicea
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All authors contributed to the inception of the ideas in the manuscript, design of networks and proposed experimental setups, and proof of non-Abelian statistics.

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Correspondence to Jason Alicea.

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Alicea, J., Oreg, Y., Refael, G. et al. Non-Abelian statistics and topological quantum information processing in 1D wire networks. Nature Phys 7, 412–417 (2011). https://doi.org/10.1038/nphys1915

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