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Universal expressiveness of variational quantum classifiers and quantum kernels for support vector machines

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  • Jonas Jäger

    (University of British Columbia
    Technische Universität Darmstadt)

  • Roman V. Krems

    (University of British Columbia
    Stewart Blusson Quantum Matter Institute)

Abstract

Machine learning is considered to be one of the most promising applications of quantum computing. Therefore, the search for quantum advantage of the quantum analogues of machine learning models is a key research goal. Here, we show that variational quantum classifiers and support vector machines with quantum kernels can solve a classification problem based on the k-FORRELATION problem, which is known to be PROMISEBQP-complete. Because the PROMISEBQP complexity class includes all Bounded-Error Quantum Polynomial-Time (BQP) decision problems, our results imply that there exists a feature map and a quantum kernel that make variational quantum classifiers and quantum kernel support vector machines efficient solvers for any BQP problem. Hence, this work implies that their feature map and quantum kernel, respectively, can be designed to have a quantum advantage for any classification problem that cannot be classically solved in polynomial time but contrariwise by a quantum computer.

Suggested Citation

  • Jonas Jäger & Roman V. Krems, 2023. "Universal expressiveness of variational quantum classifiers and quantum kernels for support vector machines," Nature Communications, Nature, vol. 14(1), pages 1-7, December.
    • Handle: RePEc:nat:natcom:v:14:y:2023:i:1:d:10.1038_s41467-023-36144-5
    DOI: 10.1038/s41467-023-36144-5
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    References listed on IDEAS

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    1. Maria Schuld, 2019. "Machine learning in quantum spaces," Nature, Nature, vol. 567(7747), pages 179-181, March.
    2. Jacob Biamonte & Peter Wittek & Nicola Pancotti & Patrick Rebentrost & Nathan Wiebe & Seth Lloyd, 2017. "Quantum machine learning," Nature, Nature, vol. 549(7671), pages 195-202, September.
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