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@ARTICLE{Botzung:1038568,
      author       = {Botzung, Thomas and Buchhold, Michael and Diehl, Sebastian
                      and Müller, Markus},
      title        = {{R}obustness and measurement-induced percolation of the
                      surface code},
      reportid     = {FZJ-2025-01551, arXiv:2311.14338},
      year         = {2025},
      note         = {18 pages, 11 figures},
      abstract     = {We examine the robustness of a logical qubit in the planar
                      surface code subject to 'measurement-errors', i.e., to local
                      Pauli measurements at known positions. This yields a
                      measurement-only dynamics, which is driven by the
                      competition between local Pauli measurements and stabilizer
                      measurements. The setup differs from the conventional
                      surface code for which errors are caused by decoherence and
                      their positions are unknown. Yet, our setting allows us to
                      examine the dynamics of the encoded logical qubit by using a
                      combination of analytical arguments based on percolation
                      theory and numerical simulations. Firstly, we show that for
                      a single round of Pauli measurements only, the threshold
                      corresponding to the irreversible loss of the logical qubit
                      depends only on the rate of $ \hat X$- and $\hat
                      Z$-measurements, and that this loss of logical quantum
                      information is equivalent to the bond percolation transition
                      in a 2D square lattice. Local $\hat Y$-measurements, which
                      affect both $X$ and $Z$ stabilizers, erase the logical qubit
                      only if all physical qubits along one of the diagonals are
                      measured, and are thus negligible at large code distance.
                      Secondly, we examine the dynamics in the code by considering
                      the interplay between rounds of Pauli measurements and
                      rounds of stabilizer measurements. Focusing on the lifetime
                      of the logical qubit, we obtain a rich phase diagram
                      featuring different dynamical regimes. We argue that the
                      loss of the logical qubit in this setting can still be
                      understood by percolation theory and underpin our arguments
                      with numerical simulations.},
      cin          = {PGI-2},
      cid          = {I:(DE-Juel1)PGI-2-20110106},
      pnm          = {5221 - Advanced Solid-State Qubits and Qubit Systems
                      (POF4-522)},
      pid          = {G:(DE-HGF)POF4-5221},
      typ          = {PUB:(DE-HGF)25},
      eprint       = {2311.14338},
      howpublished = {arXiv:2311.14338},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2311.14338;\%\%$},
      url          = {https://juser.fz-juelich.de/record/1038568},
}