Related papers: Accelerating Eigenvalue Computation for Nuclear St…
We propose a nonlinear model predictive control (NMPC) framework based on a direct optimal control method that ensures continuous-time constraint satisfaction and accurate evaluation of the running cost, without compromising computational…
We present high-precision quantum computing simulations of three-body atoms (He, H$^-$) and molecules (H$_2^+$, HD$^+$), the latter being studied beyond the Born-Oppenheimer approximation. The Non-Iterative Disentangled Unitary Coupled…
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…
We propose a novel parallel numerical algorithm for calculating the smallest eigenvalues of highly ill-conditioned matrices. It is based on the {\it LDLT} decomposition and involves finding a $k \times k$ sub-matrix of the inverse of the…
We propose a general way to construct an effective Hamiltonian in the Self-learning Monte Carlo method (SLMC), which speeds up Monte Carlo simulations by training an effective model to propose uncorrelated configurations in the Markov…
The generator coordinate method (GCM) is an important tool of choice for modeling large-amplitude collective motion in atomic nuclei. The computational complexity of the GCM increases rapidly with the number of collective coordinates. It…
A method to accelerate the matrix-vector products of j-scheme nuclear Shell-Model Configuration Interaction (SMCI) calculations is presented. The method takes advantage of the matrix product form of the j-scheme proton-neutron Hamiltonian…
This paper presents a new approach to solve linear and nonlinear model predictive control (MPC) problems that requires small memory footprint and throughput and is particularly suitable when the model and/or controller parameters change at…
One of the most challenging problems in solid state systems is the microscopic analysis of electronic correlations. A paramount minimal model that encodes correlation effects is the Hubbard Hamiltonian, which -- albeit its simplicity -- is…
We introduce the pCI software package for high-precision atomic structure calculations. The standard method of calculation is based on the configuration interaction (CI) method to describe valence correlations, but can be extended to attain…
We analyse the effects that different nuclear structure approximations associated with the short range correlations (SRC), finite nucleon size (FNS), higher order terms in the nucleon currents (HOC) and with some nuclear input parameters,…
Construction and diagonalization of the Hamiltonian matrix is the rate-limiting step in most low-energy electron -- molecule collision calculations. Tennyson (J Phys B, 29 (1996) 1817) implemented a novel algorithm for Hamiltonian…
Large-scale eigenvalue problems pose a significant challenge to classical computers. While there are efficient quantum algorithms for unitary or Hermitian matrices, eigenvalue problems for non-normal matrices remain open in quantum…
In this paper, a parallel structured divide-and-conquer (PSDC) eigensolver is proposed for symmetric tridiagonal matrices based on ScaLAPACK and a parallel structured matrix multiplication algorithm, called PSMMA. Computing the eigenvectors…
In Parts I and II of this series of papers, three new methods for the computation of eigenvalues of singular pencils were developed: rank-completing perturbations, rank-projections, and augmentation. It was observed that a straightforward…
Perturbation theory is used systematically to investigate the symmetries of the Dirac Hamiltonian and their breaking in atomic nuclei. Using the perturbation corrections to the single-particle energies and wave functions, the link between…
This paper offers a review of numerical methods for computation of the eigenvalues of Hermitian matrices and the singular values of general and some classes of structured matrices. The focus is on the main principles behind the methods that…
We introduce a multi-modal, multi-level quantum complex exponential least squares (MM-QCELS) method to simultaneously estimate multiple eigenvalues of a quantum Hamiltonian on early fault-tolerant quantum computers. Our theoretical analysis…
The recently introduced coupled cluster (CC) downfolding techniques for reducing the dimensionality of quantum many-body problems recast the CC formalism in the form of the renormalization procedure allowing, for the construction of…
Neutrino mass constraints are a primary focus of current and future large-scale structure (LSS) surveys. Non-linear LSS models rely heavily on cosmological simulations -- the impact of massive neutrinos should therefore be included in these…