Related papers: A proposal to first principles electronic structur…
We develop a new numerical method to calculate the Landauer conductance through an interacting electron system in the first order perturbation or in the self-consistent Hartree-Fock approximation. It is applied to one and two dimensional…
In this paper, we present an approach to integer factorization using distributed representations formed with Vector Symbolic Architectures. The approach formulates integer factorization in a manner such that it can be solved using neural…
This paper improves and demonstrates the usefulness of the first quantized plane-wave algorithms for the quantum simulation of electronic structure, developed by Babbush et al. and Su et al. We describe the first quantum algorithm for first…
The reduced-density-matrix method is an promising candidate for the next generation electronic structure calculation method; it is equivalent to solve the Schr\"odinger equation for the ground state. The number of variables is the same as a…
Coupled cluster methods are widely regarded as the gold standard of computational quantum chemistry as they are perceived to offer the best compromise between computational cost and a high-accuracy resolution of the ground state eigenvalue…
We introduce a novel energy functional for ground-state electronic-structure calculations. Its fundamental variables are the natural spin-orbitals of the implied singlet many-body wave function and their joint occupation probabilities. The…
Machine-learning methods are gradually being adopted in a wide variety of social, economic, and scientific contexts, yet they are notorious for struggling with exact mathematics. A typical example is computer algebra, which includes tasks…
We present an algorithm to compute bases for the spaces L(G), provided G is a rational divisor over a non-singular absolutely irreducible algebraic curve, and also another algorithm to compute the Weierstrass semigroup at P together with…
We present a novel theory and implementation for computing coupled electronic and quantal nuclear subsystems on a single potential energy surface, moving beyond the standard Born-Oppenheimer (BO) separation of nuclei and electrons. We…
Symbolic Mathematical tasks such as integration often require multiple well-defined steps and understanding of sub-tasks to reach a solution. To understand Transformers' abilities in such tasks in a fine-grained manner, we deviate from…
We study primary submodules and primary decompositions from a differential and computational point of view. Our main theoretical contribution is a general structure theory and a representation theorem for primary submodules of an arbitrary…
The numerical solution of the recently formulated number-projected Hartree-Fock-Bogoliubov equations is studied in an exactly soluble cranked-deformed shell model Hamiltonian. It is found that the solution of these number-projected…
We develop a numerical approach based on the sinc basis set for first-principles electronic structure calculations in one-dimensional systems. The method exploits the inherent accuracy and non-local character of the sinc functions to handle…
A massively parallel order-N electronic structure theory was constructed by an interdisciplinary research between physics, applied mathematics and computer science. (1) A high parallel efficiency with ten-million-atom nanomaterials was…
A new scheme of first-principles computation for strongly correlated electron systems is proposed. This scheme starts from the local-density approximation (LDA) at high-energy band structure, while the low-energy effective Hamiltonian is…
Chordal structure and bounded treewidth allow for efficient computation in numerical linear algebra, graphical models, constraint satisfaction and many other areas. In this paper, we begin the study of how to exploit chordal structure in…
The implementation of discontinuous Galerkin finite element methods (DGFEMs) represents a very challenging computational task, particularly for systems of coupled nonlinear PDEs, including multiphysics problems, whose parameters may consist…
Photonic computing has recently become an interesting paradigm for high-speed calculation of computing processes using light-matter interactions. Here, we propose and study an electromagnetic wave-based structure with the ability to…
A rigorous and powerful theoretical framework is proposed to obtain systems of orthogonal functions (or shape modes) to represent optical surfaces. The method is general so it can be applied to different initial shapes and different…
An alternative methodology to evaluate two-electron-repulsion integrals based on numerical approximation is proposed. Computational chemistry has branched into two major fields with methodologies based on quantum mechanics and classical…