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@ARTICLE{Colmenarez:1038535,
      author       = {Colmenarez, Luis and Kim, Seyong and Müller, Markus},
      title        = {{F}undamental thresholds for computational and erasure
                      errors via the coherent information},
      reportid     = {FZJ-2025-01520, arXiv:2412.16727},
      year         = {2025},
      note         = {31 pages, 14 figures},
      abstract     = {Quantum error correcting (QEC) codes protect quantum
                      information against environmental noise. Computational
                      errors caused by the environment change the quantum state
                      within the qubit subspace, whereas quantum erasures
                      correspond to the loss of qubits at known positions.
                      Correcting either type of error involves different
                      correction mechanisms, which makes studying the interplay
                      between erasure and computational errors particularly
                      challenging. In this work, we propose a framework based on
                      the coherent information (CI) of the mixed-state density
                      operator associated to noisy QEC codes, for treating both
                      types of errors together. We show how to rigorously derive
                      different families of statistical mechanics mappings for
                      generic stabilizer QEC codes in the presence of both types
                      of errors. We observe that the erasure errors enter as a
                      classical average over fully depolarizing channels. Further,
                      we show that computing the CI for erasure errors only can be
                      done efficiently upon sampling over erasure configurations.
                      We then test our approach on the 2D toric and color codes
                      and compute optimal thresholds for erasure errors only,
                      finding a $50\\%$ threshold for both codes. This strengthens
                      the notion that both codes share the same optimal
                      thresholds. When considering both computational and erasure
                      errors, the CI of small-size codes yields thresholds in very
                      accurate agreement with established results that have been
                      obtained in the thermodynamic limit. We thereby further
                      establish the CI as a practical tool for studying optimal
                      thresholds under realistic noise and as a means for
                      uncovering new relations between QEC codes and statistical
                      physics models.},
      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       = {2412.16727},
      howpublished = {arXiv:2412.16727},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2412.16727;\%\%$},
      url          = {https://juser.fz-juelich.de/record/1038535},
}