Quantum classifier with tailored quantum kernel

Carsten Blank, Daniel K. Park, June Koo Kevin Rhee, Francesco Petruccione

Research output: Contribution to journalArticlepeer-review

46 Citations (Scopus)


Kernel methods have a wide spectrum of applications in machine learning. Recently, a link between quantum computing and kernel theory has been formally established, opening up opportunities for quantum techniques to enhance various existing machine-learning methods. We present a distance-based quantum classifier whose kernel is based on the quantum state fidelity between training and test data. The quantum kernel can be tailored systematically with a quantum circuit to raise the kernel to an arbitrary power and to assign arbitrary weights to each training data. Given a specific input state, our protocol calculates the weighted power sum of fidelities of quantum data in quantum parallel via a swap-test circuit followed by two single-qubit measurements, requiring only a constant number of repetitions regardless of the number of data. We also show that our classifier is equivalent to measuring the expectation value of a Helstrom operator, from which the well-known optimal quantum state discrimination can be derived. We demonstrate the performance of our classifier via classical simulations with a realistic noise model and proof-of-principle experiments using the IBM quantum cloud platform.

Original languageEnglish
Article number41
Journalnpj Quantum Information
Issue number1
Publication statusPublished - 2020 Dec 1

Bibliographical note

Funding Information:
This research is supported by the National Research Foundation of Korea (Grant No. 2019R1I1A1A01050161 and 2018K1A3A1A09078001), by the Ministry of Science and ICT, Korea, under an ITRC Program, IITP-2019-2018-0-01402, and by the South African Research Chair Initiative of the Department of Science and Technology and the National Research Foundation. We thank Spiros Kechrimparis for stimulating discussions on the Helstrom measurement. We acknowledge use of the IBM Q for this work. The views expressed are those of the authors and do not reflect the official policy or position of IBM or the IBM Q team.

Publisher Copyright:
© 2020, The Author(s).

All Science Journal Classification (ASJC) codes

  • Computer Science (miscellaneous)
  • Statistical and Nonlinear Physics
  • Computer Networks and Communications
  • Computational Theory and Mathematics


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