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arXiv · 2507.06201

Surface-Code Hardware Hamiltonian

Xuexin Xu·Kuljeet Kaur·Chloé Vignes·John M. Martinis·Mohammad H. Ansari
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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.

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Xuexin Xu, Kuljeet Kaur, Chloé Vignes, John M. Martinis, Mohammad H. Ansari. 2025-07-08. Surface-Code Hardware Hamiltonian. https://doi.org/10.1038/s41534-026-01241-y

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