Related papers: Benign Overfitting with Quantum Kernels

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…

We present quantum-inspired algorithms for classification tasks inspired by the problem of quantum state discrimination. By construction, these algorithms can perform multiclass classification, prevent overfitting, and generate probability…

Kernel methods map data into high-dimensional spaces, enabling linear algorithms to learn nonlinear functions without explicitly storing the feature vectors. Quantum kernel methods promise efficient learning by encoding feature maps into…

Quantum machine learning is considered one of the current research fields with immense potential. In recent years, Havl\'i\v{c}ek et al. [Nature 567, 209-212 (2019)] have proposed a quantum machine learning algorithm with quantum-enhanced…

Using a quantum processor to embed and process classical data enables the generation of correlations between variables that are inefficient to represent through classical computation. A fundamental question is whether these correlations…

As the quantum computing community gravitates towards understanding the practical benefits of quantum computers, having a clear definition and evaluation scheme for assessing practical quantum advantage in the context of specific…

Neural networks have achieved impressive breakthroughs in both industry and academia. How to effectively develop neural networks on quantum computing devices is a challenging open problem. Here, we propose a new quantum neural network model…

This survey is an introduction to positive definite kernels and the set of methods they have inspired in the machine learning literature, namely kernel methods. We first discuss some properties of positive definite kernels as well as…

The use of quantum computing for machine learning is among the most promising applications of quantum technologies. Quantum models inspired by classical algorithms are developed to explore some possible advantages over classical approaches.…

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…

The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…

Positive definite kernels and their associated Reproducing Kernel Hilbert Spaces provide a mathematically compelling and practically competitive framework for learning from data. In this paper we take the approximation theory point of view…

Quantum kernel methods have been proposed as a promising approach for leveraging near-term quantum computers for supervised learning, yet rigorous benchmarks against strong classical baselines remain scarce. We present a comprehensive…

This paper introduces a diagonal adaptive kernel model that dynamically learns kernel eigenvalues and output coefficients simultaneously during training. Unlike fixed-kernel methods tied to the neural tangent kernel theory, the diagonal…

Characterization of quantum systems from experimental data is a central problem in quantum science and technology. But which measurements should be used to gather data in the first place? While optimal measurement choices can be worked out…

Hyperspectral imaging is a powerful technology that is plagued by large dimensionality. Herein, we explore a way to combat that hindrance via non-contiguous and contiguous (simpler to realize sensor) band grouping for dimensionality…

In recent years, research on near-term quantum machine learning has explored how classical machine learning algorithms endowed with access to quantum kernels (similarity measures) can outperform their purely classical counterparts. Although…

Owing to the computational complexity of electronic structure algorithms running on classical digital computers, the range of molecular systems amenable to simulation remains tightly circumscribed even after many decades of work. Quantum…

Introducing quantum sensors as solution to real-world problem demands reliability and controllability outside laboratory conditions. Producers and operators ought to be assumed to have limited resources ready available for calibration, and…

Building a quantum analog of classical deep neural networks represents a fundamental challenge in quantum computing. A key issue is how to address the inherent non-linearity of classical deep learning, a problem in the quantum domain due to…