Kernel method based on non-linear coherent states in quantum feature space

Prayag Tiwari, Shahram Dehdashti, Abdul Karim Obeid, Pekka Marttinen, Peter Bruza*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)


In this paper, by mapping datasets to a set of non-linear coherent states, the process of encoding inputs in quantum states as a non-linear feature map is re-interpreted. As a result of the fact that the radial basis function is recovered when data is mapped to a complex Hilbert state represented by coherent states, non-linear coherent states can be considered as a natural generalisation of the associated kernels. In this paper, as an example of kernels based on non-linear coherent states, we propose kernel functions based on generalized hypergeometric functions, as orthogonal polynomial functions. The suggested kernel is implemented with the support vector machine (SVM) on two well known datasets (make_circles, and make_moons) and outperforms the baselines, even when the level of noise is high. In addition, we study the impact of the geometrical properties of the feature space, obtained by the non-linear coherent states, on the SVM classification task, by considering the Fubini-Study metric of the associated coherent states.

Original languageEnglish
Article number355301
JournalJournal of Physics A: Mathematical and Theoretical
Issue number35
Publication statusPublished - 2 Sep 2022
MoE publication typeA1 Journal article-refereed


  • coherent
  • feature
  • kerneling
  • non-linear
  • quantum
  • states


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