Related papers: Machine learning-based compression of quantum many…
Finding collective variables to describe some important coarse-grained information on physical systems, in particular metastable states, remains a key issue in molecular dynamics. Recently, machine learning techniques have been intensively…
In this paper, we propose a low complexity quantum principal component analysis (qPCA) algorithm. Similar to the state-of-the-art qPCA, it achieves dimension reduction by extracting principal components of the data matrix, rather than all…
Probabilistic circuits (PCs) are powerful probabilistic models that enable exact and tractable inference, making them highly suitable for probabilistic reasoning and inference tasks. While dominant in neural networks, representation…
Nonlinear principal component analysis (NLPCA) via autoencoders has attracted attention in the dynamical systems community due to its larger compression rate when compared to linear principal component analysis (PCA). These model reduction…
Active flow control remains a significant challenge due to the high-dimensional, nonlinear nature of fluid dynamics. Quantum machine learning may prove effective in addressing these issues, given that quantum computing possesses superiority…
Theoretical research into many-body quantum systems has mostly focused on regular structures which have a small, simple unit cell and where a vanishingly small number of pairs of the constituents directly interact. Motivated by advances in…
Power flow analysis is a fundamental tool for power system analysis, planning, and operational control. Traditional Newton-Raphson methods suffer from limitations such as initial value sensitivity and low efficiency in batch computation,…
Principal component analysis (PCA) is perhaps the most widely used method for data dimensionality reduction. A key question in PCA is deciding how many factors to retain. This manuscript describes a new approach to automatically selecting…
Despite the rapid development of computational hardware, the treatment of large and high dimensional data sets is still a challenging problem. This paper provides a twofold contribution to the topic. First, we propose a Gaussian Mixture…
A state-of-the-art method that combines a quantum computational algorithm and machine learning, so-called quantum machine learning, can be a powerful approach for solving quantum many-body problems. However, the research scope in the field…
A quantum mechanics representation based on position ($\vec{r}$), linear momentum($\vec{p}$) and energy($E$) eigenvalues is presented here. A set of equations, explicitly independent on wave function, was derived relating these observables.…
Principal Component Analysis (PCA) is a foundational technique in machine learning for dimensionality reduction of high-dimensional datasets. However, PCA could lead to biased outcomes that disadvantage certain subgroups of the underlying…
The hydrodynamic interpretation of quantum mechanics treats a system of particles in an effective manner. In this work, we investigate squeezed coherent states within the hydrodynamic interpretation. The Hamiltonian operator in question is…
In this thesis we present new results relevant to two important problems in quantum information science: the development of a theory of entanglement and the exploration of the use of controlled quantum systems to the simulation of quantum…
In High Energy Physics experiments Particle Flow (PFlow) algorithms are designed to provide an optimal reconstruction of the nature and kinematic properties of the particles produced within the detector acceptance during collisions. At the…
Cosmic-ray acceleration processes in astrophysical plasmas are often investigated with fully-kinetic or hybrid kinetic numerical simulations, which enable us to describe a detailed microphysics of particle energization mechanisms. Tracing…
The one-body reduced density matrix (1-RDM) of a many-body system at zero temperature gives direct access to many observables, such as the charge density, kinetic energy and occupation numbers. It would be desirable to express it as a…
Big data is transforming our world, revolutionizing operations and analytics everywhere, from financial engineering to biomedical sciences. The complexity of big data often makes dimension reduction techniques necessary before conducting…
Principal Component Analysis (PCA) is the workhorse tool for dimensionality reduction in this era of big data. While often overlooked, the purpose of PCA is not only to reduce data dimensionality, but also to yield features that are…
Principal Component Analysis (PCA) is a fundamental tool for representation learning, but its global linear formulation fails to capture the structure of data supported on curved manifolds. In contrast, manifold learning methods model…