Geometric quantum machine learning for barcode similarity classification

We consider the problem of distinguishing two vectors (visualized as images or barcodes) and learning if they are related to one another. For this, we develop a geometric quantum machine learning (GQML) approach with embedded symmetries that allows for the classification of similar and dissimilar pairs based on global correlations, and enables generalization from just a few samples. Unlike GQML algorithms developed to date, we propose to focus on symmetry-aware measurement adaptation that outperforms unitary parametrizations. We compare GQML for similarity testing against classical deep neural networks and convolutional neural networks with Siamese architectures. We show that quantum networks demonstrate strong empirical performance gains over their classical counterparts in generalization. We explain this difference in performance by analyzing correlated distributions used for composing our dataset. We relate the similarity testing to problems that showcase a proven maximal separation between the bounded-error quantum polynomial time complexity class and the polynomial hierarchy. While the ability to achieve a formal advantage depends on how data are loaded, we discuss how similar problems can benefit from quantum machine learning. Finally, we present a 40-qubit hardware implementation of our quantum model, using a superconducting processor (IBM Kyiv), showing remarkable scalability and resilience to noise.