Related papers: Computing eigenpairs of quantum many-body systems …
In this work we present and evaluate an implementation of the purify-shift-and-project method [J. Chem. Phys. 128, 176101 (2008)] for linear scaling computation of multiple eigenvectors around the homo-lumo gap of the Fock/Kohn-Sham matrix.…
Shell-model calculations play a key role in elucidating various properties of nuclei. In general, those studies require a huge number of calculations to be repeated for parameter calibration and quantifying uncertainties. To reduce the…
Parallel finite element algorithms based on object-oriented concepts are presented. Moreover, the design and implementation of a data structure proposed are utilized in realizing a parallel geometric multigrid method. The ParFEMapper and…
Thermodynamic models are often vital when characterising complex systems, particularly natural gas, electrolyte, polymer, pharmaceutical and biological systems. However, their implementations have historically been abstruse and cumbersome,…
Hamiltonian diagonalization is at the heart of understanding physical properties and practical applications of quantum systems. It is highly desired to design quantum algorithms that can speedup Hamiltonian diagonalization, especially those…
Imaging Mueller polarimetry has already proved its potential for metrology, remote sensing and biomedicine. The real-time applications of this modality require both video rate image acquisition and fast data post-processing algorithms.…
We study the computational complexity of a diagonalization technique for multivariate homogeneous polynomials, that is, expressing them as sums of powers of independent linear forms. It is based on Harrison's center theory and consists of a…
We assess numerical stabilization methods employed in fermion many-body quantum Monte Carlo simulations. In particular, we empirically compare various matrix decomposition and inversion schemes to gain control over numerical instabilities…
We provide an algorithm that takes as an input a given parametric family of homogeneous polynomials, which is invariant under the action of the general linear group, and an integer $d$. It outputs the ideal of that family intersected with…
We introduce a new algorithm computing the characteristic polynomials of hyperplane arrangements which exploits their underlying symmetry groups. Our algorithm counts the chambers of an arrangement as a byproduct of computing its…
Computing the excited states of a given Hamiltonian is computationally hard for large systems, but methods that do so using quantum computers scale tractably. This problem is equivalent to the PCA problem where we are interested in…
In this work, we explore physical systems which support not only multipartite interparticle entanglement, but also intraparticle entanglement between different degrees of freedom of the constituent particles and entanglement between…
We present new exactly solvable systems of the discrete quantum mechanics with pure imaginary shifts, whose physical range of the coordinate is the whole real line. These systems are shape invariant and their eigenfunctions are described by…
We present a new implementation of the numerical integration of the classical, gravitational, N-body problem based on a high order Hermite's integration scheme with block time steps, with a direct evaluation of the particle-particle forces.…
An open-source middleware EigenKernel was developed for use with parallel generalized eigenvalue solvers or large-scale electronic state calculation to attain high scalability and usability. The middleware enables the users to choose the…
Borel-fixed ideals play a key role in the study of Hilbert schemes. Indeed each component and each intersection of components of a Hilbert scheme contains at least one Borel-fixed point, i.e. a point corresponding to a subscheme defined by…
When modeling scientific and industrial problems, geometries are typically modeled by explicit boundary representations obtained from computer-aided design software. Unfitted (also known as embedded or immersed) finite element methods offer…
This paper demonstrates how certified computational tools can be used to address various problems in control theory. In particular, we introduce PACE.jl, a Julia package that implements symbolic elimination techniques, including (among…
We study quantitative homogenization of the eigenvalues for elliptic systems with periodically distributed inclusions, where the conductivity of inclusions are strongly contrast to that of the matrix. We propose a quantitative version of…
Non-Hermitian many-body systems can be spectrally unstable, so small perturbations may induce large eigenvalue shifts. The pseudospectrum quantifies this instability and provides a perturbation-robust diagnostic. For inverse-polynomially…