Quantum classifier with tailored quantum kernel

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

Research output: Contribution to journalArticlepeer-review

88 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

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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