Analysis of Quantum Machine Learning Methods for Geochemical Pattern Recognition

Abstract

Geochemical data analysis presents challenges due to multi-element interactions and non-linear spatial patterns that classical methods struggle to capture. This study compares quantum machine learning (QML) clustering methods applied to geochemical data from the Antofagasta region of Chile, introducing a methodological framework using database independence constraints to validate that identified patterns reflect geochemical variation rather than sampling artifacts. Preliminary comparison of four quantum approaches—the Quantum Approximate Optimization Algorithm (QAOA), amplitude embedding, angle embedding, and the Quantum Boltzmann Machine (QBM)—identified QBM as achieving the best clustering quality with superior computational efficiency. We then systematically explored 150 QBM configurations varying qubit count (2–6), feature aggregation, principal component analysis (PCA) preprocessing, and training steps, evaluating clustering performance on 643 multi-element samples. A two-stage selection framework combining domain constraints ( $K \geq 4$ ) with Jensen-Shannon Divergence filtering (max JSD < 0.20) ensures identified patterns reflect geochemical variation rather than database artifacts. To ensure a fair comparison, the best QBM configuration was benchmarked against a broad, comparably tuned panel of classical clustering methods (1,900 configurations spanning $K$ -means, Gaussian mixtures, agglomerative, spectral, and density-based clustering over linear, kernel, and manifold representations) and against the other three quantum methods, all evaluated under the identical protocol. Scored on common geochemical ground, the best QBM configuration attained a silhouette of 0.476 versus 0.262 for the strongest classical method (0.722 versus 0.539 in each method’s own feature space); the advantage was positive across all bootstrap resamples (95% confidence interval $[+0.145, +0.275]$ ) and persisted under a compositional (centered-log-ratio) transform, while a subsample-refit estimate places the de-biased QBM silhouette at $0.42 \pm 0.08$ . The JSD filter rejected 49% of QBM configurations that would have produced database-dominated clusters, demonstrating the importance of this validation step. The optimal four-cluster solution ( $K=4$ ) identified interpretable geochemical populations: a regional background (88.5%) and three small anomaly clusters—arsenic-enriched (7.0%), boron-rich (1.2%), and a multi-metal Cu–Pb–Zn cluster reaching 8,131 mg/kg Cu (3.3%)—whose signatures are consistent with a mixture of natural mineralization/alteration and anthropogenic, mining-related contamination. Cross-database validation confirmed statistically significant convergence (Jaccard similarity = 0.702, random subset permutation $p = 0.028$ ; Spearman $\rho = 0.566$ ), with seven core signature elements (B, Cd, Co, Cr, Fe, Mn, Ni) converging across all three independent surveys. These results indicate that, for this multi-source geochemical dataset and under database independence constraints, QBM yields better-separated, anomaly-sensitive clusters than a broad classical baseline and the other quantum methods tested, with the advantage arising from its isolation of small, geochemically coherent anomaly populations; given the limited qubit counts and the small, noiseless simulations used here, this should not be read as evidence of a general quantum advantage. We provide guidelines for applying QBM to multi-source geoscientific datasets. INDEX TERMS Quantum machine learning, geochemical clustering, pattern recognition, unsupervised learning, quantum Boltzmann machines, Antofagasta region.