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Related papers: On the expressivity of embedding quantum kernels

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A Hilbert space embedding for probability measures has recently been proposed, wherein any probability measure is represented as a mean element in a reproducing kernel Hilbert space (RKHS). Such an embedding has found applications in…

Machine Learning · Statistics 2010-03-04 Bharath K. Sriperumbudur , Kenji Fukumizu , Gert R. G. Lanckriet

We study the expressive power of kernel methods and the algorithmic feasibility of multiple kernel learning for a special rich class of kernels. Specifically, we define \emph{Euclidean kernels}, a diverse class that includes most, if not…

Machine Learning · Computer Science 2019-02-14 Pravesh K. Kothari , Roi Livni

Quantum kernel methods leverage a kernel function computed by embedding input information into the Hilbert space of a quantum system. However, large Hilbert spaces can hinder generalization capability, and the scalability of quantum kernels…

Quantum Physics · Physics 2024-04-16 Rodrigo Martínez-Peña , Miguel C. Soriano , Roberta Zambrini

Quantum machine learning is often motivated by the idea that quantum systems can expose useful high-dimensional structure that is difficult to access with classical models. We isolate one central component of this claim: the fixed…

Quantum Physics · Physics 2026-05-26 Toheeb Ogunade , Taofeek Kassim , Etinosa Osaro

The kernel mean embedding of probability distributions is commonly used in machine learning as an injective mapping from distributions to functions in an infinite dimensional Hilbert space. It allows us, for example, to define a distance…

Quantum Physics · Physics 2019-12-24 Jonas M. Kübler , Krikamol Muandet , Bernhard Schölkopf

Quantum computing has been revolutionizing the development of algorithms. However, only noisy intermediate-scale quantum devices are available currently, which imposes several restrictions on the circuit implementation of quantum…

Quantum Physics · Physics 2023-09-29 Jonathan H. A. de Carvalho , Fernando M. de Paula Neto

Categorical data plays an important part in machine learning research and appears in a variety of applications. Models that can express large classes of real-valued functions on the Boolean cube are useful for problems involving…

Quantum Physics · Physics 2023-04-25 Dylan Herman , Rudy Raymond , Muyuan Li , Nicolas Robles , Antonio Mezzacapo , Marco Pistoia

Quantum bits can be isolated to perform useful information-theoretic tasks, even though physical systems are fundamentally described by very high-dimensional operator algebras. This is because qubits can be consistently embedded into…

Quantum Physics · Physics 2023-10-04 Andrew J. P. Garner , Markus P. Mueller

Quantum embedding is a fundamental prerequisite for applying quantum machine learning techniques to classical data, and has substantial impacts on performance outcomes. In this study, we present Neural Quantum Embedding (NQE), a method that…

Quantum Physics · Physics 2024-08-12 Tak Hur , Israel F. Araujo , Daniel K. Park

Quantum kernels (QK) are widely used in quantum machine learning applications; yet, their potential to surpass classical machine learning methods on classical datasets remains uncertain. This limitation can be attributed to the exponential…

Quantum Physics · Physics 2025-07-29 Roberto Flórez-Ablan , Marco Roth , Jan Schnabel

The use of kernels for nonlinear prediction is widespread in machine learning. They have been popularized in support vector machines and used in kernel ridge regression, amongst others. Kernel methods share three aspects. First, instead of…

Machine Learning · Statistics 2025-08-25 Patrick J. F. Groenen , Michael Greenacre

Recently, machine learning had a remarkable impact, from scientific to everyday-life applications. However, complex tasks often imply unfeasible energy and computational power consumption. Quantum computation might lower such requirements,…

Kernel mean embeddings -- integrals of a kernel with respect to a probability distribution -- are essential in Bayesian quadrature, but also widely used in other computational tools for numerical integration or for statistical inference…

Machine Learning · Statistics 2025-04-29 François-Xavier Briol , Alexandra Gessner , Toni Karvonen , Maren Mahsereci

The study of classical algorithms is supported by an immense understructure, founded in logic, type, and category theory, that allows an algorithmist to reason about the sequential manipulation of data irrespective of a computation's…

Quantum Physics · Physics 2023-04-28 Zane M. Rossi , Isaac L. Chuang

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…

Quantum Physics · Physics 2007-05-23 Rolando D. Somma

Kernel methods give powerful, flexible, and theoretically grounded approaches to solving many problems in machine learning. The standard approach, however, requires pairwise evaluations of a kernel function, which can lead to scalability…

Machine Learning · Computer Science 2021-04-08 Danica J. Sutherland , Jeff Schneider

We present a quantum-in-quantum embedding strategy coupled to machine learning potentials to improve on the accuracy of quantum-classical hybrid models for the description of large molecules. In such hybrid models, relevant structural…

Quantum neuromorphic computing (QNC) is a sub-field of quantum machine learning (QML) that capitalizes on inherent system dynamics. As a result, QNC can run on contemporary, noisy quantum hardware and is poised to realize challenging…

Quantum Physics · Physics 2024-02-22 Rodrigo Araiza Bravo , Khadijeh Najafi , Taylor L. Patti , Xun Gao , Susanne F. Yelin

Quantum computing opens exciting opportunities for kernel-based machine learning methods, which have broad applications in data analysis. Recent works show that quantum computers can efficiently construct a model of a classifier by…

We build a framework allowing for a systematic investigation of the issue: "Which quantum states are universal resources for one-way quantum computation?" We start by re-examining what is exactly meant by "universality" in quantum…

Quantum Physics · Physics 2007-07-31 M. Van den Nest , W. Dür , A. Miyake , H. J. Briegel
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