Quantum Geometry of Data

Alexander G. Abanov, Luca Candelori, Harold C. Steinacker, Martin T. Wells, Jerome R. Busemeyer +7 more
7/22/2025
cs.LGquant-phstat.ML

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Abstract

We demonstrate how Quantum Cognition Machine Learning (QCML) encodes data as quantum geometry. In QCML, features of the data are represented by learned Hermitian matrices, and data points are mapped to states in Hilbert space. The quantum geometry description endows the dataset with rich geometric and topological structure - including intrinsic dimension, quantum metric, and Berry curvature - derived directly from the data. QCML captures global properties of data, while avoiding the curse of dimensionality inherent in local methods. We illustrate this on a number of synthetic and real-world examples. Quantum geometric representation of QCML could advance our understanding of cognitive phenomena within the framework of quantum cognition.

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Cite this paper

@article{abanov2025quantum,
  title  = {Quantum Geometry of Data},
  author = {Alexander G. Abanov and Luca Candelori and Harold C. Steinacker and Martin T. Wells and Jerome R. Busemeyer and Cameron J. Hogan and Vahagn Kirakosyan and Nicola Marzari and Sunil Pinnamaneni and Dario Villani and Mengjia Xu and Kharen Musaelian},
  year   = {2025},
  eprint = {2507.21135},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2507.21135v1}
}

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