Related papers: Efficient algorithm for many-electron angular mome…
In this paper we propose a new symbolic-numeric algorithm to find positive equilibria of a n-dimensional dynamical system. This algorithm implies a symbolic manipulation of ODE in order to give a local approximation of differential…
Numerical exact diagonalization is the ultimate method of choice in order to discuss static, dynamic, and thermodynamic properties of quantum systems. In this article we consider Heisenberg spin-systems and extend the range of applicability…
Reduced-order models are central to motion planning and control of quadruped robots, yet existing templates are often hand-crafted for a specific locomotion modality. This motivates the need for automatic methods that extract task-specific,…
Although the modern shell-model picture of atomic nuclei is built from single-particle orbits with good total angular momentum $j$, leading to $j$-$j$ coupling, phenomenological models suggested decades ago that for $0p$-shell nuclides a…
Due to the exponential growth of the state space of coupled quantum systems it is not possible, in general, to numerically store the state of a very large number of quantum systems within a classical computer. We demonstrate a method for…
Quantum computing has the potential to reduce the computational cost required for quantum dynamics simulations. However, existing quantum algorithms for coupled electron-nuclear dynamics simulation either require fault-tolerant devices, or…
Magnetization dynamics in ferromagnetic materials is modeled by the Landau-Lifshitz (LL) equation, a nonlinear system of partial differential equations. Among the numerical approaches, semi-implicit schemes are widely used in the…
Traditional theory of many-electron atoms and ions is based on the coefficients of fractional parentage and matrix elements of tensorial operators, composed of unit tensors. Then the calculation of spin-angular coefficients of radial…
We present a mathematical proof of the algorithm allowing to generate all - symmetric and non-symmetric - total angular momentum eigenstates in remote matter qubits by projective measurements, proposed in Maser et al. [Phys. Rev. A 79,…
We present an efficient linear-scaling algorithm for evaluating the analytical force and stress contributions derived from the exact-exchange energy, a key component in hybrid functional calculations. The algorithm, working equally well for…
A useful finite-dimensional matrix representation of the derivative of periodic functions is obtained by using some elementary facts of trigonometric interpolation. This NxN matrix becomes a projection of the angular derivative into…
A new methodology is developed to integrate numerically the equations of motion for classical many-body systems in molecular dynamics simulations. Its distinguishable feature is the possibility to preserve, independently on the size of the…
Arrays of atoms trapped in optical tweezers combine features of programmable analog quantum simulators with atomic quantum sensors. Here we propose variational quantum algorithms, tailored for tweezer arrays as programmable quantum sensors,…
This library (collection of subroutines) is presented for calculating standard quantities in the decomposition of many-electron matrix elements in atomic structure theory. These quantities include the coefficients of fractional parentage,…
We adapt the simulated annealing algorithm to the search of periodic orbits for classical multi-electron atomic systems. This is done by minimizing the n-th return distance to the initial position on a Poincare surface of section under an…
The application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wavefunctions that are relevant in the behavior of the system under study. Hamiltonian symmetries are an important…
Recent quantum algorithms pertaining to electronic structure theory primarily focus on threshold-based dynamic construction of ansatz by selectively including important many-body operators. These methods can be made systematically more…
The present paper gives a review of our recent progress and latest results for novel linear-algebraic algorithms and its application to large-scale quantum material simulations or electronic structure calculations. The algorithms are…
Nonlinear spectroscopy is a cornerstone of quantum science, providing unique access to multi-point correlations, quantum coherence, and couplings that are invisible to linear methods. However, classical simulation of these phenomena is…
A revised program for generating the spin-angular coefficients in relativistic atomic structure calculations is presented. When compared with our previous version [G.Gaigalas, S.Fritzsche and I.P.Grant, CPC 139 (2001) 263], the new version…