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@ARTICLE{Old:1048967,
      author       = {Old, Josias and Tasler, Stephan and Hartmann, Michael J.
                      and Müller, Markus},
      title        = {{F}ault-{T}olerant {S}tabilizer {M}easurements in {S}urface
                      {C}odes with {T}hree-{Q}ubit {G}ates},
      reportid     = {FZJ-2025-05064, arXiv:2506.09029},
      year         = {2025},
      note         = {7 pages, 6 figures},
      abstract     = {Quantum error correction (QEC) is considered a deciding
                      component in enabling practical quantum computing.
                      Stabilizer codes, and in particular topological surface
                      codes, are promising candidates for implementing QEC by
                      redundantly encoding quantum information. While it is widely
                      believed that a strictly fault-tolerant protocol can only be
                      implemented using single- and two-qubit gates, several
                      quantum computing platforms, based on trapped ions, neutral
                      atoms and also superconducting qubits support native
                      multi-qubit operations, e.g. using multi-ion entangling
                      gates, Rydberg blockade or parallelized tunable couplers,
                      respectively. In this work, we show that stabilizer
                      measurement circuits for unrotated surface codes can be
                      fault-tolerant using single auxiliary qubits and three-qubit
                      gates. These gates enable lower-depth circuits leading to
                      fewer fault locations and potentially shorter QEC cycle
                      times. Concretely, we find that in an optimistic parameter
                      regime where fidelities of three-qubit gates are the same as
                      those of two-qubit gates, the logical error rate can be up
                      to one order of magnitude lower and the threshold can be
                      significantly higher, increasing from $\approx 0.76 \\%$ to
                      $\approx 1.05 \\%$. Our results, which are applicable to a
                      wide range of platforms, thereby motivate further
                      investigation into multi-qubit gates as components for
                      fault-tolerant QEC, as they can lead to substantial
                      advantages in terms of time and physical qubit resources
                      required to reach a target logical error rate.},
      cin          = {PGI-2},
      cid          = {I:(DE-Juel1)PGI-2-20110106},
      pnm          = {5221 - Advanced Solid-State Qubits and Qubit Systems
                      (POF4-522) / BMBF 13N16073 - MUNIQC-Atoms -
                      Neutralatom-basierter Quantencomputer-Demonstrator
                      (BMBF-13N16073) / EXC 2004:  Matter and Light for Quantum
                      Computing (ML4Q) (390534769)},
      pid          = {G:(DE-HGF)POF4-5221 / G:(DE-Juel1)BMBF-13N16073 /
                      G:(BMBF)390534769},
      typ          = {PUB:(DE-HGF)25},
      eprint       = {2506.09029},
      howpublished = {arXiv:2506.09029},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2506.09029;\%\%$},
      doi          = {10.34734/FZJ-2025-05064},
      url          = {https://juser.fz-juelich.de/record/1048967},
}