TY - EJOUR AU - Xu, Xuexin AU - Kaur, Kuljeet AU - Vignes, Chloé AU - Ansari, Mohammad H. AU - Martinis, John M. TI - Surface-Code Hardware Hamiltonian IS - arXiv:2507.06201 M1 - FZJ-2025-04654 M1 - arXiv:2507.06201 PY - 2025 N1 - 18 pages, 12 figures AB - 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. LB - PUB:(DE-HGF)25 UR - https://juser.fz-juelich.de/record/1048448 ER -