Unpaired Majorana fermions in quantum wires

@article{Kitaev2000UnpairedMF,
  title={Unpaired Majorana fermions in quantum wires},
  author={Alexei Y. Kitaev},
  journal={Physics-Uspekhi},
  year={2000},
  volume={44},
  pages={131-136}
}
  • A. Kitaev
  • Published 27 October 2000
  • Physics
  • Physics-Uspekhi
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 exp(-L/l0) 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… 
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References

SHOWING 1-10 OF 11 REFERENCES
Midgap edge states and pairing symmetry of quasi-one-dimensional organic superconductors
The singlet s-, d- and triplet p-wave pairing symmetries in quasi-one-dimensional organic superconductors can be experimentally discriminated by probing the Andreev bound states at the sample edges.…
Fermionic quantum computation
We define a model of quantum computation with local fermionic modes (LFMs) — sites which can be either empty or occupied by a fermion. With the standard correspondence between the Foch space of m…
Non-Abelian statistics of half-quantum vortices in p-wave superconductors.
TLDR
From the properties of the solutions to Bogoliubov-de Gennes equations in the vortex core, the non-Abelian statistics of vortices are derived identical to that for the Moore-Read (Pfaffian) quantum Hall state.
A Modular Functor Which is Universal¶for Quantum Computation
Abstract:We show that the topological modular functor from Witten–Chern–Simons theory is universal for quantum computation in the sense that a quantum circuit computation can be efficiently…
P/NP, and the quantum field computer
TLDR
This work proposes that each physical theory supports computational models whose power is limited by the physical theory, and suggests that some physical system whose effective Lagrangian contains a non-Abelian topological term might be manipulated to serve as an analog computer capable of solving NP or even #P-hard problems in polynomial time.
Fault-tolerant quantum computation with constant error
TLDR
This paper shows how to perform fault tolerant quantum computation when the error probability, q, is smaller than some constant threshold, q.. the cost is polylogarithmic in time and space, and no measurements are used during the quantum computation.
Quantum computations: algorithms and error correction
TLDR
This book discusses classical models of computations, quantum formalism, symplecto-classical cases, and error correction in the computation process: general principles.
Threshold Accuracy for Quantum Computation
TLDR
A similar concatenation technique is discussed which can be used with fault tolerant networks to achieve any desired accuracy when computing with classical initial states, provided a minimum gate accuracy can be achieved.
Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetry
  • Phys. Rev. B
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