Skip to main content
Log in

Local Approach to Quantum-inspired Classification

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

In the context of quantum-inspired machine learning, remarkable mathematical tools for solving classification problems are given by some methods of quantum state discrimination. In this respect, quantum-inspired classifiers based on nearest centroid and Helstrom discrimination have been efficiently implemented on classical computers. We present a local approach combining the kNN algorithm to some quantum-inspired classifiers.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Algorithm 1
Algorithm 2
Algorithm 3

Similar content being viewed by others

References

  1. Leporini, R., Pastorello, D.: An efficient geometric approach to quantum-inspired classifications. Scientific Reports 12(1). https://doi.org/10.1038/s41598-022-12392-1 (2022)

  2. Blanzieri, E., Melgani, F.: An Adaptive Svm Nearest Neighbor Classifier for Remotely Sensed Imagery. In: 2006 IEEE International Symposium on Geoscience and Remote Sensing, pp. 3931–3934. https://doi.org/10.1109/IGARSS.2006.1008 (2006)

  3. Leporini, R., Pastorello, D.: Support vector machines with quantum state discrimination. Quantum Reports 3(3). https://doi.org/10.3390/quantum3030032 (2021)

  4. Leporini, R., Pastorello, D.: Quantum-inspired classification based on voronoi tessellation and pretty-good measurements. Quantum Reports 4(4). https://doi.org/10.3390/quantum4040031 (2022)

  5. Helstrom, C. W.: Quantum detection and estimation theory. J. Stat. Phys. 1, 231–252 (1969). https://doi.org/10.1007/BF01007479

    Article  ADS  Google Scholar 

  6. Mochon, C.: Family of generalized pretty good measurements and the minimal-error pure-state discrimination problems for which they are optimal. Physical Review A 93(3). https://doi.org/10.1103/PhysRevA.73.032328https://doi.org/10.1103/PhysRevA.73.032328 (2006)

  7. Bae, J.: Structure of minimum-error quantum state discrimination. New Journal of Physics 96(7). https://doi.org/10.1088/1367-2630/15/7/073037 (2013)

  8. Kimura, G., Kossakowski, A.: The bloch-vector space for n-level systems: the spherical-coordinate point of view. Open Systems & Information Dynamics 12(3). https://doi.org/10.1007/s11080-005-0919-y (2005)

  9. Sergioli, G., Giuntini, R., Freytes, H.: A new quantum approach to binary classification. PLoS ONE 14(5), 0216224 (2019). https://doi.org/10.1371/journal.pone.0216224

    Article  Google Scholar 

  10. Giuntini, R., Freytes, H., Park, D. K., Blank, C., Holik, F., Chow, K. L., Sergioli, G.: Quantum state discrimination for supervised classification. arXiv:2104.00971v1 (2021)

  11. Fix, E., Hodges, J.L.: Discriminatory Analysis, Nonparametric Discrimination: Consistency Properties. Technical Report 4, USAF School of Aviation Medicine, Randolph Field (1951)

Download references

Acknowledgements

This work was supported by Q@TN, the joint lab between University of Trento, FBK- Fondazione Bruno Kessler, INFN- National Institute for Nuclear Physics and CNR- National Research Council.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Davide Pastorello.

Ethics declarations

Conceptualization, E.B, R.L. and D.P.; validation, E.B., D.P.; formal analysis, D.P.; writing—original draft preparation, R.L. and D.P.; writing—review and editing, E.B, D.P. All authors have read and agreed to this version of the manuscript.

Conflict of Interests

The authors declare no conflict of interest.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Enrico Blanzieri, Roberto Leporini and Davide Pastorello are contributed equally to this work.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Blanzieri, E., Leporini, R. & Pastorello, D. Local Approach to Quantum-inspired Classification. Int J Theor Phys 62, 4 (2023). https://doi.org/10.1007/s10773-022-05263-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10773-022-05263-y

Keywords

Navigation