Geometry-calibrated equilibrium sensing for inverse design of nonlocal topological photonic lattices

Abstract

Topological photonic lattices are commonly designed using short-range Hamiltonians, yet realistic nanophotonic structures are governed by geometry- and wavelength-dependent long-range electromagnetic interactions. Here we introduce a geometry-calibrated quantum equilibrium-propagation framework for inference and inverse design in finite nonlocal plasmonic Su-Schrieffer-Heeger lattices. A two-qubit equilibrium sensor is trained in effective-coupling space to distinguish boundary-localized from trivial finite-lattice responses. Because labels inherited from the nearest-neighbor SSH model become unreliable in the presence of nonlocal hopping, each sample is independently relabeled using nonlocal winding numbers and a finite-gap criterion. On this physics-verified evaluation set, the sensor achieves 99.8% sensitivity and 98.1% specificity. A physics-gated robustness score then ranks verified configurations by boundary response, response contrast, gap stability and compatibility with the selected nonlocality regime. Full-wave extinction spectra of isolated and paired gold nanoparticles establish a geometry-to-coupling calibration linking particle size and separation to wavelength-resolved pair couplings. Projecting this calibration onto the verified coupling landscape identifies a finite plasmonic geometry supporting spectrally distinct corner- and edge-dominated responses at 546 and 642 nm, with sector-to-bulk intensity contrasts of $2.4 \times 10^{4}$ and $1.5 \times 10^{3}$, respectively. The framework links realistic electromagnetic geometry to nonlocal topological design, moving beyond nearest-neighbor design rules with physics-verified, geometry-resolved inference.