Benchmarking Quantum Kernels Across Diverse and Complex Data

Quantum kernel methods have shown promise and are gaining growing use among quantum machine learning approaches to enhance the performance of kernel-based models, where support vector machines (SVMs) are a common example [1]. They have been applied to various machine learning tasks, such as classification of medical data or high-energy physics [2, 3]. An advanced enhancement to these kernel methods is the trainable quantum kernel, which employs a parameterized quantum circuit (PQC), often referred to as an ansatz. Here, a quantum circuit's gate operations are controlled by a set of externally optimized classical parameters [4, 5]. This enables the quantum kernel to be trained and adapted to the specific structure of a dataset [6]. However, despite theoretical promise, the practical deployment of quantum kernel methods is still in its very early stages. Many research studies focus on a single specific machine learning area with a few dataset samples, but an evaluation of the performance of a quantum kernel across diverse domains remains unverified, whereas this ability is common in classical kernel methods such as the linear kernel or Radial Basis Function (RBF) kernel [7]. This makes it difficult to understand the characteristics of the methods' performance from a comprehensive perspective. Furthermore, existing practice is primarily conducted on low-dimensional synthetic or introductory datasets like variants of MNIST or Iris, or aggressively reduced real-world data that goes from hundreds or more to around ten features [8-10], leaving a large gap in its application to real-world machine learning scenarios.