Numerical evidence against advantage with quantum fidelity kernels on classical data

TL;DR

This paper provides numerical evidence that current quantum kernel methods, when hyperparameter-tuned for better generalization, effectively become classical kernels, undermining their potential quantum advantage on classical data.

Contribution

The study demonstrates that hyperparameter tuning causes quantum kernels to resemble classical kernels, challenging claims of quantum advantage in machine learning.

Findings

Hyperparameter tuning makes quantum kernels classically simulable.

Quantum kernels suffer from spectral flattening with increasing qubits.

No quantum advantage is observed with current quantum kernel techniques.

Abstract

Quantum machine learning techniques are commonly considered one of the most promising candidates for demonstrating practical quantum advantage. In particular, quantum kernel methods have been demonstrated to be able to learn certain classically intractable functions efficiently if the kernel is well-aligned with the target function. In the more general case, quantum kernels are known to suffer from exponential "flattening" of the spectrum as the number of qubits grows, preventing generalization and necessitating the control of the inductive bias by hyperparameters. We show that the general-purpose hyperparameter tuning techniques proposed to improve the generalization of quantum kernels lead to the kernel becoming well-approximated by a classical kernel, removing the possibility of quantum advantage. We provide extensive numerical evidence for this phenomenon utilizing multiple previously studied quantum feature maps and both synthetic and real data. Our results show that unless novel techniques are developed to control the inductive bias of quantum kernels, they are unlikely to provide a quantum advantage on classical data.