Related papers: Uniform error bounds for quantized dynamical model…

This paper presents a sampled-data approach for the robust control of a single qubit (quantum bit). The required robustness is defined using a sliding mode domain and the control law is designed offline and then utilized online with a…

Uniform stability of a learning algorithm is a classical notion of algorithmic stability introduced to derive high-probability bounds on the generalization error (Bousquet and Elisseeff, 2002). Specifically, for a loss function with range…

Data-driven methods for modeling dynamic systems have received considerable attention as they provide a mechanism for control synthesis directly from the observed time-series data. In the absence of prior assumptions on how the time-series…

This article deals with the computation of guaranteed lower bounds of the error in the framework of finite element (FE) and domain decomposition (DD) methods. In addition to a fully parallel computation, the proposed lower bounds separate…

Calculating bounds of properties of many-body quantum systems is of paramount importance, since they guide our understanding of emergent quantum phenomena and complement the insights obtained from estimation methods. Recent semidefinite…

Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…

We derive a tight generalization bound for quantum machine learning that is applicable to a wide range of supervised tasks, data, and models. Our bound is both efficiently computable and free of big-O notation. Furthermore, we point out…

There is a growing interest in building autonomous systems that interact with complex environments. The difficulty associated with obtaining an accurate model for such environments poses a challenge to the task of assessing and guaranteeing…

Upper Confidence Bound (UCB) is arguably the most commonly used method for linear multi-arm bandit problems. While conceptually and computationally simple, this method highly relies on the confidence bounds, failing to strike the optimal…

Quantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring…

The aim in model order reduction is to approximate an input-output map described by a large-scale dynamical system with a low-dimensional and cheaper-to-evaluate reduced order model. While high fidelity can be achieved by a variety of…

Seeking the available precision limit of unknown parameters is a significant task in quantum parameter estimation. One often resorts to the widely utilized quantum Cramer-Rao bound (QCRB) based on unbiased estimators to finish this task.…

We demonstrate that the dynamics of an open quantum system can be calculated efficiently and with predefined error, provided a basis exists in which the system-environment interactions are local and hence obey the Lieb-Robinson bound. We…

Gaussian processes have become a promising tool for various safety-critical settings, since the posterior variance can be used to directly estimate the model error and quantify risk. However, state-of-the-art techniques for safety-critical…

Network quantization generally converts full-precision weights and/or activations into low-bit fixed-point values in order to accelerate an inference process. Recent approaches to network quantization further discretize the gradients into…

Understanding the theoretical capabilities and limitations of quantum machine learning (QML) models to solve machine learning tasks is crucial to advancing both quantum software and hardware developments. Similarly to the classical setting,…

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

Local decision rules are commonly understood to be more explainable, due to the local nature of the patterns involved. With numerical optimization methods such as gradient boosting, ensembles of local decision rules can gain good predictive…

Studies on simulation input uncertainty often built on the availability of input data. In this paper, we investigate an inverse problem where, given only the availability of output data, we nonparametrically calibrate the input models and…

Obtaining predictive low-order models is a central challenge in fluid dynamics. Data-driven frameworks have been widely used to obtain low-order models of aerodynamic systems; yet, resulting models tend to yield predictions that grow…