Related papers: A gradient system on the quantum information space…

So called "analogue models" use condensed matter systems (typically hydrodynamic) to set up an "effective metric" and to model curved-space quantum field theory in a physical system where all the microscopic degrees of freedom are well…

Based on the notion of information bottleneck (IB), we formulate a quantization problem called "IB quantization". We show that IB quantization is equivalent to learning based on the IB principle. Under this equivalence, the standard neural…

Classification using variational quantum circuits is a promising frontier in quantum machine learning. Quantum supervised learning (QSL) applied to classical data using variational quantum circuits involves embedding the data into a quantum…

High-energy physics is replete with hard computational problems and it is one of the areas where quantum computing could be used to speed up calculations. We present an implementation of likelihood-based regularized unfolding on a quantum…

This is an introduction to quantum algebra, from a geometric perspective. The classical spaces $X$, such as the Lie groups, homogeneous spaces, or more general manifolds, are described by various algebras $A$, defined over various fields…

This work presents Quantum Adaptive Search (QAGS), a hybrid quantum-classical algorithm for the global optimization of multivariate functions. The method employs an adaptive mechanism that dynamically narrows the search space based on a…

Solving inverse problems, such as parameter estimation and optimal control, is a vital part of science. Many experiments repeatedly collect data and rely on machine learning algorithms to quickly infer solutions to the associated inverse…

The Alicki-Lindblad-Fannes dynamical (ALF) entropy measures the rate at which new information is gathered about a quantum system by inspecting its long-time evolution. We propose an extension of the ALF entropy to open quantum dynamics as a…

We introduce an information-theoretic framework that views learning as universal prediction under log loss, characterized through regret bounds. Central to the framework is an effective notion of architecture-based model complexity, defined…

A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective…

Without large quantum computers to empirically evaluate performance, theoretical frameworks such as the quantum statistical query (QSQ) are a primary tool to study quantum algorithms for learning classical functions and search for quantum…

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…

We provide in this paper a concrete method for training a quantum neural network to maximize the relevant information about a property that is transmitted through the network. This is significant because it gives an operationally well…

We propose a scalable preconditioned primal-dual hybrid gradient algorithm for solving partial differential equations (PDEs). We multiply the PDE with a dual test function to obtain an inf-sup problem whose loss functional involves…

In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…

Quantum machine learning algorithms are expected to play a pivotal role in quantum chemistry simulations in the immediate future. One such key application is the training of a quantum neural network to learn the potential energy surface and…

In this article we review computational aspects of Deep Learning (DL). Deep learning uses network architectures consisting of hierarchical layers of latent variables to construct predictors for high-dimensional input-output models. Training…

Quantum Information is a new area of research which has been growing rapidly since the last decade. This topic is very close to potential applications to the so called Quantum Computer. In our point of view it makes sense to develop a more…

Understanding the dynamics of large quantum systems is hindered by the curse of dimensionality. Statistical learning offers new possibilities in this regime by neural-network protocols and classical shadows, while both methods have…

In the accompanying paper of arXiv:2505.00697, we have presented a generalized scheme of adaptive quantum gradient estimation (QGE) algorithm, and further proposed two practical variants which not only achieve doubly quantum enhancement in…