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@ARTICLE{Xu:1048448,
      author       = {Xu, Xuexin and Kaur, Kuljeet and Vignes, Chloé and Ansari,
                      Mohammad H. and Martinis, John M.},
      title        = {{S}urface-{C}ode {H}ardware {H}amiltonian},
      reportid     = {FZJ-2025-04654, arXiv:2507.06201},
      year         = {2025},
      note         = {18 pages, 12 figures},
      abstract     = {We present a scalable framework for accurately modeling
                      many-body interactions in surface-code quantum processor
                      units (QPUs). Combining a concise diagrammatic formalism
                      with high-precision numerical methods, our approach
                      efficiently evaluates high-order, long-range Pauli string
                      couplings and maps complete chip layouts onto exact
                      effective Hamiltonians. Applying this method to surface-code
                      architectures, such as Google's Sycamore lattice, we
                      identify three distinct operational regimes: computationally
                      stable, error-dominated, and hierarchy-inverted. Our
                      analysis reveals that even modest increases in residual
                      qubit-qubit crosstalk can invert the interaction hierarchy,
                      driving the system from a computationally favorable phase
                      into a topologically ordered regime. This framework thus
                      serves as a powerful guide for optimizing next-generation
                      high-fidelity surface-code hardware and provides a pathway
                      to investigate emergent quantum many-body phenomena.},
      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       = {2507.06201},
      howpublished = {arXiv:2507.06201},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2507.06201;\%\%$},
      url          = {https://juser.fz-juelich.de/record/1048448},
}