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Quantum computing


Unpaired Majorana fermions in quantum wires

 a, b
a Microsoft Research, United States of America
b Landau Institute for Theoretical Physics, Russian Academy of Sciences, prosp. Akademika Semenova 1A, Chernogolovka, Moscow Region, 142432, Russian Federation

Certain one-dimensional Fermi systems have an energy gap in the bulk spectrum while boundary states are described by one Majorana operator per boundary point. A finite system of length $L$ possesses two ground states with an energy difference proportional to $\mathrm{exp}(-L/l_0)$ and different fermionic parities. Such systems can be used as qubits since they are intrinsically immune to decoherence. The property of a system to have boundary Majorana fermions is expressed as a condition on the bulk electron spectrum. The condition is satisfied in the presence of an arbitrary small energy gap induced by proximity of a three-dimensional p-wave superconductor, provided that the normal spectrum has an odd number of Fermi points in each half of the Brillouin zone (each spin component counts separately).

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Fulltext is also available at DOI: 10.1070/1063-7869/44/10S/S29
PACS: 71.10.+Pm, 73.22.Dj, 85.25.−j, 73.40.Gk (all)
DOI: 10.1070/1063-7869/44/10S/S29
URL: https://ufn.ru/en/articles/2001/13/ac/
Citation: Kitaev A Yu "Unpaired Majorana fermions in quantum wires" Phys. Usp. 44 131–136 (2001)
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Îðèãèíàë: Kitaev A Yu «Unpaired Majorana fermions in quantum wires» ÓÔÍ 171 131–136 (2001); DOI: 10.1070/1063-7869/44/10S/S29

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