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@ARTICLE{Pedrocchi:276259,
      author       = {Pedrocchi, Fabio L. and Bonesteel, N. E. and DiVincenzo,
                      David},
      title        = {{M}onte {C}arlo studies of the self-correcting properties
                      of the {M}ajorana quantum error correction code under
                      braiding},
      journal      = {Physical review / B},
      volume       = {92},
      number       = {11},
      issn         = {1098-0121},
      address      = {College Park, Md.},
      publisher    = {APS},
      reportid     = {FZJ-2015-06722},
      pages        = {115441},
      year         = {2015},
      note         = {Main text: 20 pages, Supplementary Material: 66 pages.
                      Short version: arXiv:1505.03712},
      abstract     = {The Majorana code is an example of a stabilizer code where
                      the quantum information is stored in a system supporting
                      well-separated Majorana Bound States (MBSs). We focus on
                      one-dimensional realizations of the Majorana code, as well
                      as networks of such structures, and investigate their
                      lifetime when coupled to a parity-preserving thermal
                      environment. We apply the Davies prescription, a standard
                      method that describes the basic aspects of a thermal
                      environment, and derive a master equation in the Born-Markov
                      limit. We first focus on a single wire with immobile MBSs
                      and perform error correction to annihilate thermal
                      excitations. In the high-temperature limit, we show both
                      analytically and numerically that the lifetime of the
                      Majorana qubit grows logarithmically with the size of the
                      wire. We then study a trijunction with four MBSs when
                      braiding is executed. We study the occurrence of dangerous
                      error processes that prevent the lifetime of the Majorana
                      code from growing with the size of the trijunction. The
                      origin of the dangerous processes is the braiding itself,
                      which separates pairs of excitations and renders the noise
                      nonlocal; these processes arise from the basic constraints
                      of moving MBSs in 1D structures. We confirm our predictions
                      with Monte Carlo simulations in the low-temperature regime,
                      i.e. the regime of practical relevance. Our results put a
                      restriction on the degree of self-correction of this
                      particular 1D topological quantum computing architecture.},
      cin          = {IAS-3 / PGI-2},
      ddc          = {530},
      cid          = {I:(DE-Juel1)IAS-3-20090406 / I:(DE-Juel1)PGI-2-20110106},
      pnm          = {144 - Controlling Collective States (POF3-144)},
      pid          = {G:(DE-HGF)POF3-144},
      typ          = {PUB:(DE-HGF)16},
      eprint       = {1507.00892},
      howpublished = {arXiv:1507.00892},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:1507.00892;\%\%$},
      UT           = {WOS:000361802100003},
      doi          = {10.1103/PhysRevB.92.115441},
      url          = {https://juser.fz-juelich.de/record/276259},
}