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Determining ground state energies of quantum systems by hybrid classical/quantum methods has emerged as a promising candidate application for near-term quantum computational resources. Short of large-scale fault-tolerant quantum computers,…
We have applied the Finite Element Method to the self-consistent electronic structure calculations of molecules and solids for the first time. In this approach all the calculations are performed in "real space" and the use of non-uniform…
We introduce a high-performance linear-scaling electronic structure method that employs chromatic superposition states (CSS) as a low-dimensional, high-fidelity representation, which can be orders of magnitude smaller than the full Hilbert…
The ability to design the scattering properties of electromagnetic structures is of fundamental interest in optical science and engineering. While there has been great practical success applying local optimization methods to electromagnetic…
A new class of methods is introduced for solving the Kohn-Sham equations of density functional theory, based on constructing a mapping dynamically between the Kohn-Sham system and an auxiliary system. The resulting auxiliary density…
The accurate treatment of electron correlation in extended molecular systems remains computationally challenging using classical electronic structure methods. Hybrid quantum-classical algorithms offer a potential route to overcome these…
We study the general problem of mixing for ab-initio quantum-mechanical problems. Guided by general mathematical principles and the underlying physics, we propose a multisecant form of Broydens second method for solving the self-consistent…
The past years have witnessed impressive advances in electronic structure calculation, especially in the complexity and size of the systems studied, as well as in computation time. Linear scaling methods based on empirical tight-binding…
We present a computationally efficient approach to perform systematically convergent real-space all-electron Kohn-Sham DFT calculations for solids using an enriched finite element (FE) basis. The enriched FE basis is constructed by…
Classical computation of electronic properties in large-scale materials remains challenging. Quantum computation has the potential to offer advantages in memory footprint and computational scaling. However, general and practical quantum…
Recently, a new connection between density functional theory and kinetic theory has been proposed. In particular, it was shown that the Kohn-Sham (KS) equations can be reformulated as a macroscopic limit of the steady-state solution of a…
In this paper, we define new unfitted finite element methods for numerically approximating the solution of surface partial differential equations using bulk finite elements. The key idea is that the $n$-dimensional hypersurface, $\Gamma…
A surface integral representation of Maxwell's equations allows the efficient electromagnetic (EM) modeling of three-dimensional structures with a two-dimensional discretization, via the boundary element method (BEM). However, existing BEM…
We propose a novel numerical algorithm for computing the electronic structure related eigenvalue problem of incommensurate systems. Unlike the conventional practice that approximates the system by a large commensurate supercell, our…
Methods exhibiting linear scaling with respect to the size of the system, so called O(N) methods, are an essential tool for the calculation of the electronic structure of large systems containing many atoms. They are based on algorithms…
A cardinal obstacle to performing quantum-mechanical simulations of strongly-correlated matter is that, with the theoretical tools presently available, sufficiently-accurate computations are often too expensive to be ever feasible. Here we…
In this chapter we focus first on the theoretical methods and relevant computational approaches to calculate the electronic structure of atoms, molecules, and clusters containing heavy elements for which relativistic effects become…
We study layered systems and heterostructures of s-wave superconductors by means of a suitable generalization of Dynamical Mean-Field Theory. In order to reduce the computational effort, we consider an embedding scheme in which a relatively…
A many-body wave function can be factorized in Fock space into a marginal amplitude describing a set of strongly correlated orbitals and a conditional amplitude for the remaining weakly correlated part. The marginal amplitude is the…
The inclusion of the global effects of semiconductor doping poses a unique challenge for first-principles simulations, because the typically low concentration of dopants renders an explicit treatment intractable. In systems which do not…