Related papers: Benign Overfitting with Quantum Kernels
Invariance to nuisance transformations is one of the desirable properties of effective representations. We consider transformations that form a \emph{group} and propose an approach based on kernel methods to derive local group invariant…
Quantum state tomography is a daunting challenge of experimental quantum computing even in moderate system size. One way to boost the efficiency of state tomography is via local measurements on reduced density matrices, but the…
Quantum measurement is a physical process. What physical resources and constraints does quantum mechanics require for measurement to produce the classical world we observe? Treating measurement as a fully unitary quantum process, our goal…
Kernel approximation is widely used to scale up kernel SVM training and prediction. However, the memory and computation costs of kernel approximation models are still too high if we want to deploy them on memory-limited devices such as…
Quantum computing leverages quantum effects to build algorithms that are faster then their classical variants. In machine learning, for a given model architecture, the speed of training the model is typically determined by the size of the…
These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing…
Quantum annealing is a promising technique which leverages quantum mechanics to solve hard optimization problems. Considerable progress has been made in the development of a physical quantum annealer, motivating the study of methods to…
The integration of quantum computing into classical machine learning architectures has emerged as a promising approach to enhance model efficiency and computational capacity. In this work, we introduce the Quantum Kernel-Based Long…
We show that kernel-based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels, for a particular decomposition that always exists for such kernels. We provide a…
Quantum tomography is the main method used to assess the quality of quantum information processing devices, but its complexity presents a major obstacle for the characterization of even moderately large systems. The number of experimental…
We present a unified framework for quantum sensitivity sampling, extending the advantages of quantum computing to a broad class of classical approximation problems. Our unified framework provides a streamlined approach for constructing…
Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used…
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…
Kernel $k$-means clustering is a powerful tool for unsupervised learning of non-linearly separable data. Since the earliest attempts, researchers have noted that such algorithms often become trapped by local minima arising from…
We consider the problem of distinguishing two vectors (visualized as images or barcodes) and learning if they are related to one another. For this, we develop a geometric quantum machine learning (GQML) approach with embedded symmetries…
Enhancing classical machine learning (ML) algorithms through quantum kernels is a rapidly growing research topic in quantum machine learning (QML). A key challenge in using kernels -- both classical and quantum -- is that ML workflows…
Quantum correlations exhibit behaviour that cannot be resolved with a local hidden variable picture of the world. In quantum information, they are also used as resources for information processing tasks, such as Measurement-based Quantum…
In quantum kernel learning, the primary method involves using a quantum computer to calculate the inner product between feature vectors, thereby obtaining a Gram matrix used as a kernel in machine learning models such as support vector…
Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…
The instantaneous quantum polynomial (IQP) quantum circuit Born machine (QCBM) has been proposed as a promising quantum generative model over bitstrings. Recent works have shown that the training of IQP-QCBM is classically tractable w.r.t.…