Quantum tangent kernel

TL;DR

This paper introduces the quantum tangent kernel, a new approach that extends quantum kernel methods using deep parameterized quantum circuits, showing improved performance and theoretical insights into quantum machine learning.

Contribution

It proposes the quantum tangent kernel, a novel kernel derived from deep quantum circuits, enabling enhanced representation power beyond traditional quantum kernel methods.

Findings

Quantum tangent kernel outperforms conventional quantum kernel on generated datasets.

Deep quantum circuits exhibit minimal parameter change during training, enabling first-order analysis.

The work links deep quantum models to classical neural tangent kernel concepts.

Abstract

Quantum kernel method is one of the key approaches to quantum machine learning, which has the advantages that it does not require optimization and has theoretical simplicity. By virtue of these properties, several experimental demonstrations and discussions of the potential advantages have been developed so far. However, as is the case in classical machine learning, not all quantum machine learning models could be regarded as kernel methods. In this work, we explore a quantum machine learning model with a deep parameterized quantum circuit and aim to go beyond the conventional quantum kernel method. In this case, the representation power and performance are expected to be enhanced, while the training process might be a bottleneck because of the barren plateaus issue. However, we find that parameters of a deep enough quantum circuit do not move much from its initial values during training, allowing first-order expansion with respect to the parameters. This behavior is similar to the neural tangent kernel in the classical literatures, and such a deep variational quantum machine learning can be described by another emergent kernel, quantum tangent kernel. Numerical simulations show that the proposed quantum tangent kernel outperforms the conventional quantum kernel method for an ansatz-generated dataset. This work provides a new direction beyond the conventional quantum kernel method and explores potential power of quantum machine learning with deep parameterized quantum circuits.