Quantum-Kernel Benchmark for Isotopic Provenance Clustering in the Andes Region

Lead isotope ratios are frequently used in archaeometric provenance analysis; however, the overlap of isotopic fields within the Andean metallogenic belt complicates reliable provenance determination. This study presents a reproducible fidelity-based kernel method for the unsupervised clustering of Andean lead-isotope data and investigates whether a quantum-mechanical similarity space can reveal geologically significant structures beyond the classical Euclidean partition. A dataset of 1522 measurements of 206Pb/204Pb, 207Pb/204Pb, and 208Pb/204Pb was analyzed using a fidelity-based quantum kernel based on a three-qubit Pauli feature map and compared with classical K-means clustering, Gaussian mixture models, and Ward’s agglomerative clustering under various preprocessing strategies and cluster counts. The optimal quantum kernel setup achieved the highest silhouette score at k = 2. However, because analytical uncertainties were not consistently reported across all the compiled sources, an uncertainty-weighted similarity could not be applied. Geological insights indicate that this binary division separates less radiogenic, arc-related compositions from more radiogenic and thorogenic crustal signatures, a contrast that broadly follows the west-to-east crustal-contamination gradient across the Andes. Conversely, the traditional four-cluster approach provides more detailed subdivisions that align with the previously identified isotopic provinces. The reported separation reflects the geometry of the quantum feature space rather than any hardware-level speed-up, as this work represents only a simulation approach. Overall, these findings support a hierarchical and complementary approach to analyzing Pb isotope origins, in which quantum kernel clustering provides robust large-scale separation and classical clustering enhances regional understanding.