Related papers: Quantum Reservoir Computing and Risk Bounds

We study the fundamental problem of learning with respect to the squared loss in a convex class. The state-of-the-art sample complexity estimates in this setting rely on Rademacher complexities, which are generally difficult to control. We…

While adversarial robustness and generalization have individually received substantial attention in the recent literature on quantum machine learning, their interplay is much less explored. In this chapter, we address this interplay for…

Randomized Benchmarking allows to efficiently and scalably characterize the average error of an unitary 2-design such as the Clifford group $\mathcal{C}$ on a physical candidate for quantum computation, as long as there are no…

In many quantum tasks, there is an unknown quantum object that one wishes to learn. An online strategy for this task involves adaptively refining a hypothesis to reproduce such an object or its measurement statistics. A common evaluation…

The concurrent rise of artificial intelligence and quantum information poses opportunity for creating interdisciplinary technologies like quantum neural networks. Quantum reservoir processing, introduced here, is a platform for quantum…

In this paper, we investigate the Rademacher complexity of deep sparse neural networks, where each neuron receives a small number of inputs. We prove generalization bounds for multilayered sparse ReLU neural networks, including…

Quantum reservoir computing (QRC) is a low-complexity learning paradigm that combines the inherent dynamics of input-driven many-body quantum systems with classical learning techniques for nonlinear temporal data processing. Optimizing the…

Generalization error bounds are critical to understanding the performance of machine learning models. In this work, building upon a new bound of the expected value of an arbitrary function of the population and empirical risk of a learning…

Universal fault-tolerant quantum computers require millions of qubits with low error rates. Since this technology is years ahead, noisy intermediate-scale quantum (NISQ) computation is receiving tremendous interest. In this setup, quantum…

In this paper we develop a systematic approach to determine the classical limit of periodic quantum systems and applied it successfully to the problem of the quantum bouncer. It is well known that, for periodic systems, the classical…

Reservoir computing is a machine learning framework that uses artificial or physical dissipative dynamics to predict time-series data using nonlinearity and memory properties of dynamical systems. Quantum systems are considered as promising…

This paper examines the problem of learning with a finite and possibly large set of p base kernels. It presents a theoretical and empirical analysis of an approach addressing this problem based on ensembles of kernel predictors. This…

The inevitable accumulation of errors in near-future quantum devices represents a key obstacle in delivering practical quantum advantages, motivating the development of various quantum error-mitigation methods. Here, we derive fundamental…

In statistical learning theory, a generalization bound usually involves a complexity measure imposed by the considered theoretical framework. This limits the scope of such bounds, as other forms of capacity measures or regularizations are…

Reservoir computing is a powerful machine learning paradigm for online time series processing. It has reached state-of-the-art performance in tasks such as chaotic time series prediction and continuous speech recognition thanks to its…

We study the generalization error of stochastic learning algorithms from an information-theoretic perspective, with a particular emphasis on deriving sharper bounds for differentially private algorithms. It is well known that the…

In a recent study [Rohde et al., quant-ph/0603130 (2006)] of several quantum error correcting protocols designed for tolerance against qubit loss, it was shown that these protocols have the undesirable effect of magnifying the effects of…

Quantum machine learning has received significant attention in recent years, and promising progress has been made in the development of quantum algorithms to speed up traditional machine learning tasks. In this work, however, we focus on…

This paper presents a unified approach based on Wasserstein distance to derive concentration bounds for empirical estimates for two broad classes of risk measures defined in the paper. The classes of risk measures introduced include as…

This work advances the theoretical understanding of quantum learning by establishing a new family of upper bounds on the expected generalization error of quantum learning algorithms, leveraging the framework introduced by Caro et al. (2024)…