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The Hubbard model is one of the primary models for understanding the essential many-body physics in condensed matter systems such as Mott insulators and cuprate high-Tc superconductors. Recent advances in atomically precise fabrication in…
This is extended version of a previously submitted paper, in which special solutions of the Hartree-Fock (HF) problem for Coulomb interacting electrons, being described by a simple model of the Cu-O planes in La2CuO4, are presented. One of…
Semiconductor architectures hold promise for quantum information processing (QIP) applications due to their large industrial base and perceived scalability potential. Electron spins in silicon in particular may be an excellent architecture…
We investigate the stability of few-electron quantum phases in vertically coupled quantum dots under a magnetic field of arbitrary strength and direction. The orbital and spin stability diagrams of realistic devices containing up to five…
Self-consistent-field (SCF) approximations formulated using Hartree-Fock (HF) or Kohn-Sham Density Functional Theory (KS-DFT) both have the potential to yield multiple solutions. However, the formal relationship between multiple solutions…
We introduce an energy functional for ground-state electronic structure calculations. Its variables are the natural spin-orbitals of singlet many-body wave functions and their joint occupation probabilities deriving from controlled…
Density-functional theory (DFT) has revolutionized computer simulations in chemistry and material science. A faithful implementation of the theory requires self-consistent calculations. However, this effort involves repeatedly diagonalizing…
Quantum dots can confine single electrons or holes to define spin qubits that can be operated with high fidelity. Experimental work has progressed from linear to two-dimensional arrays of quantum dots, enabling qubit interactions that are…
Some of the most spectacular failures of density-functional and Hartree-Fock theories are related to an incorrect description of the so-called static electron correlation. Motivated by recent progress on the N-representability problem of…
For many-body methods such as MCSCF and CASSCF, in which the number of one-electron orbitals are optimized and independent of basis set used, there are no problems with using plane-wave basis sets. However, for methods currently used in…
We study the two-electron eigenspectrum of a carbon-nanotube double quantum dot with spin-orbit coupling. Exact calculation are combined with a simple model to provide an intuitive and accurate description of single-particle and interaction…
The authors report that anisotropic confining potentials in laterally-coupled semiconductor quantum dots (QDs) have large impacts in optical transitions and energies of inter-shell collective electronic excitations. The observed…
We introduce a general setup for the analog quantum simulation of the dynamics of open quantum systems based on semiconductor quantum dots electrically connected to a chain of quantum $RLC$ electronic circuits. The dots are chosen to be in…
This chapter discusses contemporary quantum chemical methods and provides general insights into modern electronic structure theory with a focus on heavy-element-containing compounds. We first give a short overview of relativistic…
Individual impurity atoms in silicon can make superb individual qubits, but it remains an immense challenge to build a multi-qubit processor: There is a basic conflict between nanometre separation desired for qubit-qubit interactions, and…
We analyzed the Hartree-Fock approximation for an electron system. The interaction between particles is modeled by a non-Coulombian potential. We analyzed both the three-dimensional and two-dimensional systems. We obtained accurate…
Quantum computational chemistry has emerged as an important application of quantum computing. Hybrid quantum-classical computing methods, such as variational quantum eigensolvers (VQE), have been designed as promising solutions to quantum…
We compute the ground state energy of atoms and quantum dots with a large number N of electrons. Both systems are described by a non-relativistic Hamiltonian of electrons in a d-dimensional space. The electrons interact via the Coulomb…
Electronic coupling and hence hybridization of atoms serve as the basis for the rich properties of the endless library of naturally occurring molecules. Colloidal quantum dots (CQDs) manifesting quantum strong confinement, possess atomic…
We present a density matrix approach for computing global solutions of restricted open-shell Hartree-Fock theory, based on semidefinite programming (SDP), that gives upper and lower bounds on the Hartree-Fock energy of quantum systems.…