Related papers: Gaussian Kernel in Quantum Learning

Forecasting in probabilistic time series is a complex endeavor that extends beyond predicting future values to also quantifying the uncertainty inherent in these predictions. Gaussian process regression stands out as a Bayesian machine…

In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…

Quantum computers are next-generation devices that hold promise to perform calculations beyond the reach of classical computers. A leading method towards achieving this goal is through quantum machine learning, especially quantum generative…

In this note, we introduce a family of "power sum" kernels and the corresponding Gaussian processes on symmetric groups $\mathrm{S}_n$. Such processes are bi-invariant: the action of $\mathrm{S}_n$ on itself from both sides does not change…

This paper introduces a method for the nonparametric Bayesian learning of nonlinear operators, through the use of the Volterra series with kernels represented using Gaussian processes (GPs), which we term the nonparametric Volterra kernels…

Convolutional Neural Network (CNN) is a popular model in computer vision and has the advantage of making good use of the correlation information of data. However, CNN is challenging to learn efficiently if the given dimension of data or…

Quantum neural networks (QNNs) and quantum kernels stand as prominent figures in the realm of quantum machine learning, poised to leverage the nascent capabilities of near-term quantum computers to surmount classical machine learning…

With gates of a quantum computer designed to encode multi-dimensional vectors, projections of quantum computer states onto specific qubit states can produce kernels of reproducing kernel Hilbert spaces. We show that quantum kernels obtained…

We show that Gaussian process regression (GPR) allows representing multivariate functions with low-dimensional terms via kernel design. When using a kernel built with HDMR (High-dimensional model representation), one obtains a similar type…

Support vector data description (SVDD) is a popular technique for detecting anomalies. The SVDD classifier partitions the whole space into an inlier region, which consists of the region near the training data, and an outlier region, which…

Kernel methods are a cornerstone of classical machine learning. The idea of using quantum computers to compute kernels has recently attracted attention. Quantum embedding kernels (QEKs) constructed by embedding data into the Hilbert space…

Quantum support vector machines employ quantum circuits to define the kernel function. It has been shown that this approach offers a provable exponential speedup compared to any known classical algorithm for certain data sets. The training…

Support Vector Machines (SVMs) are well-established Machine Learning (ML) algorithms. They rely on the fact that i) linear learning can be formalized as a well-posed optimization problem; ii) non-linear learning can be brought into linear…

Gaussian processes (GP) for machine learning have been studied systematically over the past two decades and they are by now widely used in a number of diverse applications. However, GP kernel design and the associated hyper-parameter…

Currently, quantum hardware is restrained by noises and qubit numbers. Thus, a quantum virtual machine that simulates operations of a quantum computer on classical computers is a vital tool for developing and testing quantum algorithms…

In this paper, we explore the potential of quantum computing in enhancing malware detection through the application of Quantum Machine Learning (QML). Our main objective is to investigate the performance of the Quantum Support Vector…

Variational quantum circuits are used in quantum machine learning and variational quantum simulation tasks. Designing good variational circuits or predicting how well they perform for given learning or optimization tasks is still unclear.…

The expressive power of Bayesian kernel-based methods has led them to become an important tool across many different facets of artificial intelligence, and useful to a plethora of modern application domains, providing both power and…

Classical machine learning has succeeded in the prediction of both classical and quantum phases of matter. Notably, kernel methods stand out for their ability to provide interpretable results, relating the learning process with the physical…

Kernel methods are ubiquitous in classical machine learning, and recently their formal similarity with quantum mechanics has been established. To grasp the potential advantage of quantum machine learning, it is necessary to understand the…