Manipulation of Majorana states in X-junction geometries

D. N. Aristov, D. B. Gutman

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Abstract

We study quantum manipulation based on four Majorana bound states in X-junction geometry. The parameter space of this setup is bigger than of the previously studied Y-junction and is described by SO(4) symmetry group. In order for quantum computation to be dephasing free, two Majorana states have to stay degenerate at all times. We find a condition necessary for that and compute the Berry's phase, , accumulated during the manipulation. We construct simple protocols for the variety of values of α, including needed for the purposes of quantum computation. Although the manipulations in general X-junction geometry are not topologically protected, they may prove to be a feasible compromise for aims of quantum computation.

Original languageEnglish
Article number315301
JournalJournal of Physics A: Mathematical and Theoretical
Volume49
Issue number31
DOIs
StatePublished - 28 Jun 2016

Bibliographical note

Publisher Copyright:
© 2016 IOP Publishing Ltd.

Keywords

  • Berry phase
  • Majorana states
  • X junction
  • dephasing
  • quantum computing
  • topological protection

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