Context-Dependent Phase Structure in Z-Diagonal Unitaries Detected via Plaquette Curvature Profiles

Higher-order diagonal interactions (involving three or more qubits) can make the effective two-qubit phase depend on spectator-qubit states, a form of context dependence that scalar benchmarks intentionally average away. Full tomographic reconstruction can in principle resolve such structure, but at a cost that scales exponentially with system size. We introduce a gauge-invariant plaquette curvature defined for each qubit pair and spectator configuration of a Z-diagonal unitary, and prove that strictly 2-local diagonal generators yield a flat curvature profile, whereas diagonal terms involving three or more qubits that include the diagnostic pair can break this flatness. The protocol estimates the curvature for each spectator context with a four-setting readout combining expectation values into complex phase factors (phasors), using only single-qubit Clifford gates and Z-basis measurement. Simulations (n = 2–7) demonstrate and IBM QPU experiments corroborate the scalar-versus-profile contrast: profile dispersion grows with the strength of higher-order diagonal content while context-collapsed scalar summaries remain nearly unchanged. Because spectator contexts can be sampled rather than exhaustively enumerated, measurement overhead scales with the sampling budget rather than with qubit count.