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<p>We present a scalable framework for accurately modeling many-body interactions in surface-code quantum processing units. 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 <i>Sycamore</i> lattice, we identify three distinct interaction regimes: computationally stable phase, error-dominated phase, and hierarchy-inverted phase. 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.</p>

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Surface-code hardware Hamiltonian

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年4月22日

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

摘要

We present a scalable framework for accurately modeling many-body interactions in surface-code quantum processing units. 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 interaction regimes: computationally stable phase, error-dominated phase, and hierarchy-inverted phase. 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.