Related papers: Experimental kernel-based quantum machine learning…

Kernel methods approximate nonlinear maps in a data-driven manner by projecting the target map onto a finite-dimensional Hilbert space called the solution space. Traditionally, this space is a subspace of a fixed ambient reproducing kernel…

We present a quantum kernel method for high-dimensional data analysis using Google's universal quantum processor, Sycamore. This method is successfully applied to the cosmological benchmark of supernova classification using real spectral…

We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…

Quantum kernel methods offer significant theoretical benefits by rendering classically inseparable features separable in quantum space. Yet, the practical application of Quantum Machine Learning (QML), currently constrained by the…

Representing images by compact codes has proven beneficial for many visual recognition tasks. Most existing techniques, however, perform this coding step directly in image feature space, where the distributions of the different classes are…

Quantum machine learning could possibly become a valuable alternative to classical machine learning for applications in High Energy Physics by offering computational speed-ups. In this study, we employ a support vector machine with a…

We consider the problem of operator-valued kernel learning and investigate the possibility of going beyond the well-known separable kernels. Borrowing tools and concepts from the field of quantum computing, such as partial trace and…

Nonparametric feature selection in high-dimensional data is an important and challenging problem in statistics and machine learning fields. Most of the existing methods for feature selection focus on parametric or additive models which may…

With the advent of kernel methods, automating the task of specifying a suitable kernel has become increasingly important. In this context, the Multiple Kernel Learning (MKL) problem of finding a combination of pre-specified base kernels…

Kernel methods serve as powerful tools to capture nonlinear patterns behind data in machine learning. The quantum kernel, integrating kernel theory with quantum computing, has attracted widespread attention. However, existing studies…

Face Recognition (FR) has been the interest to several researchers over the past few decades due to its passive nature of biometric authentication. Despite high accuracy achieved by face recognition algorithms under controlled conditions,…

Classical machine learning, extensively utilized across diverse domains, faces limitations in speed, efficiency, parallelism, and processing of complex datasets. In contrast, quantum machine learning algorithms offer significant advantages,…

The popular qubit framework has dominated recent work on quantum kernel machine learning, with results characterising expressivity, learnability and generalisation. As yet, there is no comparative framework to understand these concepts for…

Quantum kernels are reproducing kernel functions built using quantum-mechanical principles and are studied with the aim of outperforming their classical counterparts. The enthusiasm for quantum kernel machines has been tempered by recent…

Bilevel optimization has emerged as a technique for addressing a wide range of machine learning problems that involve an outer objective implicitly determined by the minimizer of an inner problem. While prior works have primarily focused on…

Support Vector Machines (SVMs) are a cornerstone of supervised learning, widely used for data classification. A central component of their success lies in kernel functions, which enable efficient computation of inner products in…

In this paper we combine the theory of reproducing kernel Hilbert spaces with the field of collocation methods to solve boundary value problems with special emphasis on reproducing property of kernels. From the reproducing property of…

Classification using variational quantum circuits is a promising frontier in quantum machine learning. Quantum supervised learning (QSL) applied to classical data using variational quantum circuits involves embedding the data into a quantum…

In this paper, by mapping datasets to a set of non-linear coherent states, the process of encoding inputs in quantum states as a non-linear feature map is re-interpreted. As a result of this fact that the Radial Basis Function is recovered…

The kernel matrix used in kernel methods encodes all the information required for solving complex nonlinear problems defined on data representations in the input space using simple, but implicitly defined, solutions. Spectral analysis on…