Surface-Code Hardware Hamiltonian

TL;DR

This paper introduces a scalable modeling framework for surface-code quantum processors that accurately captures many-body interactions, identifies operational regimes, and guides hardware optimization to enhance quantum computing fidelity.

Contribution

It combines diagrammatic formalism with numerical methods to evaluate complex interactions and maps chip layouts onto effective Hamiltonians, revealing critical regimes and effects of qubit crosstalk.

Findings

Identifies three operational regimes: stable, error-dominated, hierarchy-inverted.

Shows residual crosstalk can invert interaction hierarchy, affecting system phase.

Provides a framework for optimizing surface-code hardware and exploring quantum phenomena.

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.