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Bulletin of the American Physical Society

Quantum classifier with tailored quantum kernel

Kyungdeock Park, Carsten Blank, June‐Koo Kevin Rhee, Francesco Petruccione

Published Mar 2, 2020• 0 citations
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This work investigates quantum kernel methods for classification on unbalanced datasets. The study considers the effect of techniques commonly used in classical machine learning, such as kernel centering and cost-sensitive learning, when applied to quantum models. Experiments are conducted on five datasets, including MNIST-1D, the real-world dataset Glass6, and synthetic datasets tailored for quantum classifiers. Results indicate that quantum kernel methods can address unbalanced classification tasks albeit none of the techniques studied showed a statistically significant improvement of the scoring metrics. Results also highlight the influence of hyperparameterization and in particular, quantum bandwidth is identified as a critical hyperparameter for the performance of quantum models.

•May 14, 2026•0 citations
Abstract 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.
This work investigates quantum kernel methods for classification on unbalanced datasets. The study considers the effect of techniques commonly used in classical machine learning, such as kernel centering and cost-sensitive learning, when applied to quantum models. Experiments are conducted on five datasets, including MNIST-1D, the real-world dataset Glass6, and synthetic datasets tailored for quantum classifiers. Results indicate that quantum kernel methods can address unbalanced classification tasks albeit none of the techniques studied showed a statistically significant improvement of the scoring metrics. Results also highlight the influence of hyperparameterization and in particular, quantum bandwidth is identified as a critical hyperparameter for the performance of quantum models.