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@ARTICLE{Kirchhoff:1040960,
      author       = {Kirchhoff, Susanna and Wilhelm, Frank K. and Motzoi, Felix},
      title        = {{C}orrection {F}ormulas for the {M}ølmer-{S}ørensen
                      {G}ate {U}nder {S}trong {D}riving},
      journal      = {PRX quantum},
      volume       = {6},
      number       = {1},
      issn         = {2691-3399},
      address      = {College Park, MD},
      publisher    = {American Physical Society},
      reportid     = {FZJ-2025-02082},
      pages        = {010328},
      year         = {2025},
      note         = {HelmholtzValidation Fund - Project No. HVF-00096},
      abstract     = {The Mølmer-Sørensen gate is a widely used entangling gate
                      for ion platforms with inherent robustness to trap heating.
                      The gate performance is limited by coherent errors, arising
                      from the Lamb-Dicke (LD) approximation and sideband errors.
                      Here, we provide explicit analytical formulas for errors up
                      to fourth order in the LD parameter, by using the Magnus
                      expansion to match numerical precision, and overcome
                      significant orders-of-magnitude underestimation of errors by
                      previous theory methods. We show that fourth-order Magnus
                      expansion terms are unavoidable, being in fact leading order
                      in LD, and are therefore critical to include for typical
                      experimental fidelity ranges. We show how these errors can
                      be dramatically reduced compared to previous theory by using
                      analytical renormalization of the drive strength, by
                      calibration of the Lamb-Dicke parameter, and by the use of
                      smooth pulse shaping.},
      cin          = {PGI-12 / PGI-8},
      ddc          = {530},
      cid          = {I:(DE-Juel1)PGI-12-20200716 / I:(DE-Juel1)PGI-8-20190808},
      pnm          = {5221 - Advanced Solid-State Qubits and Qubit Systems
                      (POF4-522) / PASQuanS2.1 - Programmable Atomic Large-scale
                      Quantum Simulation 2 - SGA1 (101113690) / QCFD - Quantum
                      Computational Fluid Dynamics (101080085)},
      pid          = {G:(DE-HGF)POF4-5221 / G:(EU-Grant)101113690 /
                      G:(EU-Grant)101080085},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:001432392800001},
      doi          = {10.1103/PRXQuantum.6.010328},
      url          = {https://juser.fz-juelich.de/record/1040960},
}