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@ARTICLE{Tasler:1048969,
      author       = {Tasler, Stephan and Old, Josias and Heunisch, Lukas and
                      Feulner, Verena and Eckstein, Timo and Müller, Markus and
                      Hartmann, Michael J.},
      title        = {{O}ptimizing {S}uperconducting {T}hree-{Q}ubit {G}ates for
                      {S}urface-{C}ode {E}rror {C}orrection},
      reportid     = {FZJ-2025-05066, arXiv:2506.09028},
      year         = {2025},
      note         = {12 pages, 11 figures},
      abstract     = {Quantum error correction (QEC) is one of the crucial
                      building blocks for developing quantum computers that have
                      significant potential for reaching a quantum advantage in
                      applications. Prominent candidates for QEC are stabilizer
                      codes for which periodic readout of stabilizer operators is
                      typically implemented via successive two-qubit entangling
                      gates, and is repeated many times during a computation. To
                      improve QEC performance, it is thus beneficial to make the
                      stabilizer readout faster and less prone to
                      fault-tolerance-breaking errors. Here we design a 3-qubit
                      CZZ gate for superconducting transmon qubits that maps the
                      parity of two data qubits onto one measurement qubit in a
                      single step. We find that the gate can be executed in a
                      duration of $35\,$ns with a fidelity of F$=99.96 \, \\%$. To
                      optimize the gate, we use an error model obtained from the
                      microscopic gate simulation to systematically suppress Pauli
                      errors that are particularly harmful to the QEC protocol.
                      Using this error model, we investigate the implementation of
                      this 3-qubit gate in a surface code syndrome readout
                      schedule. We find that for the rotated surface code, the
                      implementation of CZZ gates increases the error threshold by
                      nearly 50\\% to $\approx 1.2\,\\%$ and decreases the logical
                      error rate, in the experimental relevant regime, by up to
                      one order of magnitude, compared to the standard CZ readout
                      protocol. We also show that for the unrotated surface code,
                      strictly fault-tolerant readout schedules can be found. This
                      opens a new perspective for below-threshold surface-code
                      error correction, where it can be advantageous to use
                      multi-qubit gates instead of two-qubit gates to obtain a
                      better QEC performance.},
      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)},
      pid          = {G:(DE-HGF)POF4-5221 / G:(DE-Juel1)BMBF-13N16073},
      typ          = {PUB:(DE-HGF)25},
      eprint       = {2506.09028},
      howpublished = {arXiv:2506.09028},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2506.09028;\%\%$},
      doi          = {10.34734/FZJ-2025-05066},
      url          = {https://juser.fz-juelich.de/record/1048969},
}