Related papers: On the expressivity of embedding quantum kernels
Machine learning is a fascinating and exciting field within computer science. Recently, this excitement has been transferred to the quantum information realm. Currently, all proposals for the quantum version of machine learning utilize the…
A quantum neural network (QNN) is a method to find patterns in quantum data and has a wide range of applications including quantum chemistry, quantum computation, quantum metrology, and quantum simulation. Efficiency and universality are…
Quantum reservoir computing offers a promising route for time series learning by modelling sequential data via rich quantum dynamics while the only training required happens at the level of a lightweight classical readout. However, studies…
Contrary to the classical case, the relation between quantum programming languages and quantum Turing Machines (QTM) has not being fully investigated. In particular, there are features of QTMs that have not been exploited, a notable example…
Quantum kernel methods have emerged as a promising approach for leveraging high-dimensional feature spaces in machine learning, particularly in domains where classical kernel methods face scalability limitations. In this work, we present…
Quantum mechanics requires the operation of quantum computers to be unitary, and thus makes it important to have general techniques for developing fast quantum algorithms for computing unitary transforms. A quantum routine for computing a…
A central task in the field of quantum computing is to find applications where quantum computer could provide exponential speedup over any classical computer. Machine learning represents an important field with broad applications where…
Ascertaining whether a classical model can efficiently replace a given quantum model -- dequantization -- is crucial in assessing the true potential of quantum algorithms. In this work, we introduced the dequantizability of the function…
Quantum Machine Learning (QML) has emerged as a promising framework for exploring how quantum dynamics may enhance data processing tasks. Here we investigate Quantum Extreme Learning Machines (QELMs), a quantum analogue of classical Extreme…
The expressive power of Gaussian processes depends heavily on the choice of kernel. In this work we propose the novel harmonizable mixture kernel (HMK), a family of expressive, interpretable, non-stationary kernels derived from mixture…
We introduce a quantum data embedding protocol based on the preparation of a ground state of a parameterized Hamiltonian. We analyze the corresponding quantum feature map, recasting it as an adiabatic state preparation procedure with…
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…
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…
Quantum Machine Learning (QML) is considered one of the most promising applications of Quantum Computing in the Noisy Intermediate Scale Quantum (NISQ) era for the impact it is thought to have in the near future. Although promising…
This work concerns the construction and characterization of product kernels for multivariate approximation from a finite set of discrete samples. To this end, we consider composing different component kernels, each acting on a…
Kernel methods are a highly effective and widely used collection of modern machine learning algorithms. A fundamental limitation of virtually all such methods are computations involving the kernel matrix that naively scale quadratically…
We propose digital-analog quantum kernels for enhancing the detection of complex features in the classification of images. We consider multipartite-entangled analog blocks, stemming from native Ising interactions in neutral-atom quantum…
Kernel methods are among the most popular techniques in machine learning. From a frequentist/discriminative perspective they play a central role in regularization theory as they provide a natural choice for the hypotheses space and the…
Dynamical quantum phase transition is a critical phenomenon involving out-of-equilibrium states and broken symmetries without classical analogy. However, when finite-sized systems are analyzed, dynamical singularities of the rate function…
The kernel trick is a widely applicable technique in machine learning domains that maps datasets that are difficult to classify into a computationally friendly feature space. As the dimension of the dataset scales, these kernel calculations…