Surface-Code Hardware Hamiltonian

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.

Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)

arXiv:2507.06201 [quant-ph]

(or arXiv:2507.06201v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2507.06201 Focus to learn more arXiv-issued DOI via DataCite

https://doi.org/10.1038/s41534-026-01241-y Focus to learn more DOI(s) linking to related resources

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