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@ARTICLE{Amaro:888654,
      author       = {Amaro, David and Bennett, Jemma and Vodola, Davide and
                      Müller, Markus},
      title        = {{A}nalytical percolation theory for topological color codes
                      under qubit loss},
      journal      = {Physical review / A},
      volume       = {101},
      number       = {3},
      issn         = {2469-9926},
      address      = {Woodbury, NY},
      publisher    = {Inst.},
      reportid     = {FZJ-2020-05097},
      pages        = {032317},
      year         = {2020},
      abstract     = {Quantum information theory has shown strong connections
                      with classical statistical physics. For example, quantum
                      error correcting codes like the surface and the color code
                      present a tolerance to qubit loss that is related to the
                      classical percolation threshold of the lattices where the
                      codes are defined. Here we explore such connection to study
                      analytically the tolerance of the color code when the
                      protocol introduced in Vodola et al. [Phys. Rev. Lett. 121,
                      060501 (2018)] to correct qubit losses is applied. This
                      protocol is based on the removal of the lost qubit from the
                      code, a neighboring qubit, and the lattice edges where these
                      two qubits reside. We first obtain analytically the average
                      fraction of edges r(p) that the protocol erases from the
                      lattice to correct a fraction p of qubit losses. Then, the
                      threshold pc below which the logical information is
                      protected corresponds to the value of p at which r(p) equals
                      the bond-percolation threshold of the lattice. Moreover, we
                      prove that the logical information is protected if and only
                      if the set of lost qubits does not include the entire
                      support of any logical operator. The results presented here
                      open a route to an analytical understanding of the effects
                      of qubit losses in topological quantum error codes.},
      cin          = {PGI-2},
      ddc          = {530},
      cid          = {I:(DE-Juel1)PGI-2-20110106},
      pnm          = {144 - Controlling Collective States (POF3-144)},
      pid          = {G:(DE-HGF)POF3-144},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000519631000001},
      doi          = {10.1103/PhysRevA.101.032317},
      url          = {https://juser.fz-juelich.de/record/888654},
}