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QI: Fachverband Quanteninformation

QI 10: Quantum Machine Learning II

QI 10.4: Vortrag

Dienstag, 11. März 2025, 11:45–12:00, HS VIII

How bandwidth-tuned quantum kernels become classically tractable — •Roberto Flórez Ablan, Marco Roth, and Jan Schnabel — Fraunhofer Institute for Manufacturing Engineering and Automation IPA, Stuttgart, Germany

Quantum Kernels have been a popular approach in Quantum Machine Learning (QML). However, they have generally not been shown to outperform classical ML methods. A key reason for this is that QKs suffer from the exponential concentration problem. As the number of qubits increases, the overlap between states vanishes, preventing generalization. One strategy to mitigate this problem is to rescale the data points entering the quantum model. This technique, known as bandwidth tuning, has been shown to enable generalization in QKs. However, it has been numerically demonstrated that this method results in QKs that fail to provide a quantum advantage over classical methods in terms of generalization. Here, we propose an explanation for this phenomenon. We show that due to the size of the optimal rescaling factors, QKs become similar to classical kernels. Furthermore, we numerically demonstrate and propose an analytical toy model that captures how key quantities of the kernel in classification experiments are modified as a function of bandwidth. Our results align with recent trends in QML, which suggest that successful QML models become classically simulatable.

Keywords: Quantum Kernels; Exponential Concentration; Bandwidth Tuning