Related papers: Kernel-based optimization of measurement operators…
Kernel ridge regression is an important nonparametric method for estimating smooth functions. We introduce a new set of conditions, under which the actual rates of convergence of the kernel ridge regression estimator under both the L_2 norm…
In this paper, we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS). We propose a new randomized algorithm that has optimal generalization error bounds with respect to the square loss, closing a…
Quantum kernels quantify similarity between data points by measuring the inner product between quantum states, computed through quantum circuit measurements. By embedding data into quantum systems, quantum kernel feature maps, that may be…
We establish optimal convergence rates for a decomposition-based scalable approach to kernel ridge regression. The method is simple to describe: it randomly partitions a dataset of size N into m subsets of equal size, computes an…
Kernel quadrature is widely used to approximate integrals of smooth functions, with worst-case error typically decaying at the minimax rate $n^{-\alpha/d}$ for smoothness $\alpha$ in dimension $d$. Existing rate-optimal methods often depend…
We propose and analyse a class of analytically solvable models of quantum reinforcement learning (QRL), formulated as finite-horizon Markov decision processes in finite-dimensional Hilbert spaces. The models are built around a…
Physical reservoir computing provides a powerful machine learning paradigm that exploits nonlinear physical dynamics for efficient information processing. By incorporating quantum effects, quantum reservoir computing offers superior…
Precision measurements of molecules offer an unparalleled paradigm to probe physics beyond the Standard Model. The rich internal structure within these molecules makes them exquisite sensors for detecting fundamental symmetry violations,…
Measurement-based quantum computing uses measurement patterns on predefined quantum resource states to execute quantum logic. Quantum simulation offers an important use case on near-term devices. However, pattern optimization depends on the…
This paper introduces kernel continual learning, a simple but effective variant of continual learning that leverages the non-parametric nature of kernel methods to tackle catastrophic forgetting. We deploy an episodic memory unit that…
We demonstrate a novel approach to reservoir computation measurements using random matrices. We do so to motivate how atomic-scale devices could be used for real-world computational applications. Our approach uses random matrices to…
Parametrised quantum circuits offer expressive and data-efficient representations for machine learning. Due to quantum states residing in a high-dimensional Hilbert space, parametrised quantum circuits have a natural interpretation in terms…
Data visualization is important in understanding the characteristics of data that are difficult to see directly. It is used to visualize loss landscapes and optimization trajectories to analyze optimization performance. Popular optimization…
Bilevel optimization has emerged as a technique for addressing a wide range of machine learning problems that involve an outer objective implicitly determined by the minimizer of an inner problem. While prior works have primarily focused on…
Physical reservoir computing (RC) is a machine learning algorithm that employs the dynamics of a physical system to forecast highly nonlinear and chaotic phenomena. In this paper, we introduce a quantum RC system that employs the dynamics…
We present an operator-free, measure-theoretic approach to the conditional mean embedding (CME) as a random variable taking values in a reproducing kernel Hilbert space. While the kernel mean embedding of unconditional distributions has…
Spin squeezing is a powerful resource for quantum metrology, and recent hardware platforms based on interacting qubits provide multiple possible architectures to generate and reverse squeezing during a sensing protocol. In this work, we…
Quantum processors require rapid and high-fidelity simultaneous measurements of many qubits. While superconducting qubits are among the leading modalities toward a useful quantum processor, their readout remains a bottleneck. Traditional…
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…
The dynamical behaviour of complex quantum systems can be harnessed for information processing. With this aim, quantum reservoir computing (QRC) with Ising spin networks was recently introduced as a quantum version of classical reservoir…