相关论文: Tensor Numerical Methods in Quantum Chemistry: fro…

The Gross-Pitaevskii equation and its generalisations to dissipative and dipolar gases have been very useful in describing dynamics of cold atomic gases, as well as polaritons and other nonlinear systems. For some of these applications the…

We describe a set of techniques for performing large scale ab initio calculations using multigrid accelerations and a real-space grid as a basis. The multigrid methods provide effective convergence acceleration and preconditioning on all…

Tensor hypercontraction provides an attractive four-center two-electron repulsion integral format that can lower the scaling of many electronic structure methods while only requiring O(N^2) memory. However, in its grid-based least-squares…

In large-scale quantum-chemical calculations the electron-repulsion integral (ERI) tensor rapidly becomes the bottleneck in terms of memory and disk space. When an external finite magnetic field is employed, this problem becomes even more…

Density functional theory (DFT) has emerged as one of the most versatile and lucrative approaches in electronic structure calculations of many-electron systems in past four decades. Here we give an account of the development of a…

With the widespread use of self-consistent field methods, including Hartree-Fock and Density Functional Theory, the implications of accelerating these methods are immense. To this end, we develop a tensor hypercontraction construction with…

In this paper, we propose and analyze the numerical algorithms for fast solution of periodic elliptic problems in random media in $\mathbb{R}^d$, $d=2,3$. We consider the stochastic realizations using checkerboard configuration of the…

We introduce the tensor numerical method for solving optimal control problems that are constrained by fractional 2D and 3D elliptic operators with variable coefficients. We solve the governing equation for the control function which…

We develop a quartic-scaling implementation of coupled-cluster singles and doubles based on low-rank tensor hypercontraction (THC) factorizations of both the electron repulsion integrals (ERIs) and the doubles amplitudes. This extends our…

Achieving chemical accuracy for strongly correlated molecules is a defining milestone for first-generation, fault-tolerant quantum computers, yet the factorial growth of three, four, and six-index tensor contractions in coupled-cluster…

In this paper, we present a method for fast summation of long-range potentials on 3D lattices with multiple defects and having non-rectangular geometries, based on rank-structured tensor representations. This is a significant generalization…

We report a complete implementation of the coupled-cluster method with single, double, and triple excitations (CCSDT) where tensor decompositions are used to reduce its scaling and overall computational costs. For the decomposition of the…

We present a tensor-structured algorithm for efficient large-scale DFT calculations by constructing a Tucker tensor basis that is adapted to the Kohn-Sham Hamiltonian and localized in real-space. The proposed approach uses an additive…

Although many programs have been published for fully numerical Hartree--Fock (HF) or density functional (DF) calculations on atoms, we are not aware of any that support hybrid DFs, which are popular within the quantum chemistry community…

Calculating highly accurate thermochemical properties of condensed matter via wave function-based approaches (such as e.g. Hartree-Fock or hybrid functionals) has recently attracted much interest. We here present two strategies providing…

The energy levels of the first few low-lying states of helium and lithium atoms in intense magnetic fields up to $\approx 10^8-10^9$~T are calculated in this study. A pseudospectral method is employed for the computational procedure. The…

Different numerical approaches for the stray-field calculation in the context of micromagnetic simulations are investigated. We compare finite difference based fast Fourier transform methods, tensor grid methods and the finite-element…

Choosing a basis set is the first step of a quantum chemistry calculation and it sets its maximum accuracy. This choice of orbitals is limited by strong technical constraints as one must be able to compute a large number of six dimensional…

Verifying quantum advantage for practical problems, particularly the ground state energy estimation (GSEE) problem, is one of the central challenges in quantum computing theory. For that purpose, dequantization algorithms play a central…

Recently, we developed a mean-field-type framework which treats the correlation induced by the tensor force. To exploit the tensor correlation we introduce single-particle states with the parity and charge mixing. To make a total wave…