Traditional methods in quantum chemistry rely on Hartree-Fock-based Slater-determinant (SD) representations, whose underlying zeroth-order picture assumes separability by particle. Here, we explore a radically different approach, based on separability by Cartesian component, rather than by particle [J. Jerke and B. Poirier, J. Chem. Phys., 2018, 148, 104101]. The approach appears to be very well suited for 3D grid-based methods in quantum chemistry, and thereby also for so-called "first-quantized" quantum computing. We first present an overview of the approach as implemented on classical computers, including numerical results that justify performance claims. In particular, we perform numerical calculations with four explicit electrons that are equivalent to full-CI matrix diagonalization with nearly 1015 SDs. We then present an implementation for quantum computers for which the number of quantum gates (and to a lesser extent, the number of qubits) can be dramatically reduced, in comparison with other quantum circuitry that has been envisioned for implementing first-quantized "quantum computational chemistry" (QCC).

We present numerically exact solutions to the full-dimensional Schrodinger Equation for the few-electron gas (few-EG) model of electronic structure theory. Our core methodology uses a Sum-of-Products (SOP) representation of singular potentials to make the fully correlated multi-particle quantum mechanical problem computationally tractable. With full access to periodic wave-functions, we analyze the exchange/correlation, spin symmetry, and thermodynamic ($T = 0$K) phases for few-EG systems with up to four explicit electrons per unit cell. We also present pure-spin exchange/correlation functionals for the same few-EG solutions. Finally, we consider the family of few-EG calculations in juxtaposition with the closely related uniform electron gas (UEG) system, for which previous calculations have been performed using density functional theory and quantum Monte Carlo methods. The exact few-EG solutions all display a similar oscillatory behavior at lower densities, which is not predicted by previous UEG simulations.

We present numerically exact solutions to the full-dimensional Schrodinger Equation for the few-electron gas (few-EG) model of electronic structure theory. Our core methodology uses a Sum-of-Products (SOP) representation of singular potentials to make the fully correlated multi-particle quantum mechanical problem computationally tractable. With full access to periodic wave-functions, we analyze the exchange/correlation, spin symmetry, and thermodynamic ($T = 0$K) phases for few-EG systems with up to four explicit electrons per unit cell. We also present pure-spin exchange/correlation functionals for the same few-EG solutions. Finally, we consider the family of few-EG calculations in juxtaposition with the closely related uniform electron gas (UEG) system, for which previous calculations have been performed using density functional theory and quantum Monte Carlo methods. The exact few-EG solutions all display a similar oscillatory behavior at lower densities, which is not predicted by previous UEG simulations.

We present an input/output analysis of photon-correlation experiments whereby a quantum mechanically entangled bi-photon state interacts with a material sample placed in one arm of a Hong-Ou-Mandel (HOM) apparatus. We show that the output signal contains detailed information about subsequent entanglement with the microscopic quantum states in the sample. In particular, we apply the method to an ensemble of emitters interacting with a common photon mode within the open-system Dicke Model. Our results indicate considerable dynamical information concerning spontaneous symmetry breaking can be revealed with such an experimental system.

Using a combination of ideas, the ground and several excited electronic states of the helium atom and the hydrogen molecule are computed to chemical accuracy-i.e., to within 1-2 mhartree or better. The basic strategy is very different from the standard electronic structure approach in that the full two-electron six-dimensional (6D) problem is tackled directly, rather than starting from a single-electron Hartree-Fock approximation. Electron correlation is thus treated exactly, even though computational requirements remain modest. The method also allows for exact wave functions to be computed, as well as energy levels. From the full-dimensional 6D wave functions computed here, radial distribution functions and radial correlation functions are extracted-as well as a 2D probability density function exhibiting antisymmetry for a single Cartesian component. These calculations support a more recent interpretation of Hund's rule, which states that the lower energy of the higher spin-multiplicity states is actually due to reduced screening, rather than reduced electron-electron repulsion. Prospects for larger systems and/or electron dynamics applications appear promising.

In a manner similar to but distinct from concurrent tensor efforts in electronic structure, it is shown that the Laplace transform can serve as a generator for a sum-of-products (SOP) form that allows one to write essentially any function of distance between two particles (i.e. any central force potential) as an exact two-body matrix. In particular, exact expressions for the Coulomb, Yukawa and long-range Ewald two-body operators are evaluated in a band-limited (Sinc function) basis. The resultant exact, full-basis, SOP representations for these interaction potentials - acting in conjunction with an external harmonic confining field - are validated via comparison with energy eigenstate solutions obtained via an independent calculation based on separation of variables. The new two-body matrix representations may have substantial impact in any of the many disciplines in which pair-wise central force interactions are relevant - especially, electronic structure and dynamics. [GRAPHICS] .

A Gaussian-Sinc basis set methodology is presented for the calculation of the electronic structure of atoms and molecules at the Hartree-Fock level of theory. This methodology has several advantages over previous methods. The all-electron electronic structure in a Gaussian-Sinc mixed basis spans both the "localized" and "delocalized" regions. A basis set for each region is combined to make a new basis methodology-a lattice of orthonormal sinc functions is used to represent the "delocalized" regions and the atom-centered Gaussian functions are used to represent the "localized" regions to any desired accuracy. For this mixed basis, all the Coulomb integrals are definable and can be computed in a dimensional separated methodology. Additionally, the Sinc basis is translationally invariant, which allows for the Coulomb singularity to be placed anywhere including on lattice sites. Finally, boundary conditions are always satisfied with this basis. To demonstrate the utility of this method, we calculated the ground state Hartree-Fock energies for atoms up to neon, the diatomic systems H2, O2, and N2, and the multi-atom system benzene. Together, it is shown that the Gaussian-Sinc mixed basis set is a flexible and accurate method for solving the electronic structure of atomic and molecular species.

A novel Gaussian-Sinc mixed basis set for the calculation of the one-electron electronic structure within a uniform magnetic field in three dimensions is presented. The one-electron system is used to demonstrate the utility of this new methodology and is a first step in laying the foundation for further development of many-electron atomic and molecular methodology. It is shown in this manuscript how to effectively calculate all basis set integrals, which includes the mixed Gaussian-Sinc integrals, with a fast and accurate method. The Sinc basis is invariant to the choice of the position of the Coulomb potential, as opposed to traditional grid based methods. This invariance guarantees that the choice of the grids origin has no effect on the electronic structure calculation. This is because the Coulomb potential is treated properly in this methodology, as opposed to DVR methodologies. The off-diagonal terms are sparse but very important around the Coulomb singularity. In general, five to six significant digits of accuracy on all converged results without the linear dependency problems of the Gaussian methodologies are achievable. This methodology is applied to calculate the ground state energy of H atom, $H_2^{+}$ ion and $H_3^{2+}$ ion in magnetic fields up to a magnetic field strength of 2.35x$10^13$ G (10,000 au). From these calculations it is shown that $H_3^{2+}$ ion is unstable without relativistic considerations.

We report on the utility of using Shannons Sampling theorem to solve Quantum Mechanical systems. We show that by extending the logic of Shannons interpolation theorem we can define a Universal Lattice Basis, which has superior interpolating properties compared to traditional methods. This basis is orthonormal, semi-local, has a Euclidean norm, and a simple analytic expression for the derivatives. Additionally, we can define a bounded domain for which band-limited functions, such as Gaussians, show quadratic convergence in the representation error in respect to the sampling frequency. This theory also extends to the periodic domain and we illustrate the simple analytic forms of the periodic semi-local basis and derivatives. Additionally, we show that this periodic basis is equivalent to the space defined by the Fast Fourier Transform. This novel basis has great utility in solving quantum mechanical problems for which the wave functions are known to be naturally band-limited. Several numerical examples in single and multi-dimensions are given to show the convergence and equivalence of the periodic and bounded domains for compact states.

Accurate measurement of galaxy cluster masses is an essential component not only in studies of cluster physics but also for probes of cosmology. However, different mass measurement techniques frequently yield discrepant results. The Sloan Digital Sky Survey MaxBCG catalog's mass-richness relation has previously been constrained using weak lensing shear, Sunyaev-Zeldovich (SZ), and X-ray measurements. The mass normalization of the clusters as measured by weak lensing shear is greater than or similar to 25% higher than that measured using SZ and X-ray methods, a difference much larger than the stated measurement errors in the analyses. We constrain the mass-richness relation of the MaxBCG galaxy cluster catalog by measuring the gravitational lensing magnification of type I quasars in the background of the clusters. The magnification is determined using the quasars' variability and the correlation between quasars' variability amplitude and intrinsic luminosity. The mass-richness relation determined through magnification is in agreement with that measured using shear, confirming that the lensing strength of the clusters implies a high mass normalization and that the discrepancy with other methods is not due to a shear-related systematic measurement error. We study the dependence of the measured mass normalization on the cluster halo orientation. As expected, line-of-sight clusters yield a higher normalization; however, this minority of haloes does not significantly bias the average mass-richness relation of the catalog.

We introduce a technique to measure gravitational lensing magnification using the variability of type I quasars. Quasars' variability amplitudes and luminosities are tightly correlated, on average. Magnification due to gravitational lensing increases the quasars' apparent luminosity, while leaving the variability amplitude unchanged. Therefore, the mean magnification of an ensemble of quasars can be measured through the mean shift in the variability-luminosity relation. As a proof of principle, we use this technique to measure the magnification of quasars spectroscopically identified in the Sloan Digital Sky Survey, due to gravitational lensing by galaxy clusters in the SDSS MaxBCG catalog. The Palomar-QUEST Variability Survey, reduced using the DeepSky pipeline, provides variability data for the sources. We measure the average quasar magnification as a function of scaled distance (r/R200) from the nearest cluster; our measurements are consistent with expectations assuming NFW cluster profiles, particularly after accounting for the known uncertainty in the clusters' centers. Variability-based lensing measurements are a valuable complement to shape-based techniques because their systematic errors are very different, and also because the variability measurements are amenable to photometric errors of a few percent and to depths seen in current wide-field surveys. Given the data volume expected from current and upcoming surveys, this new technique has the potential to be competitive with weak lensing shear measurements of large scale structure.

This article reports the results of radiation resistance tests of fully depleted p-channel Charge Coupled Devices (CCDs) developed at the Lawrence Berkeley National Laboratory for imaging applications in space. Several such devices were irradiated by 12 MeV protons at the tandem accelerator at the Wright Nuclear Structure Laboratory at Yale University by doses up to 8 x 10(10) protons/cm(2). The equivalent dose at an orbit near L2 for a six year mission in space was estimated to be an equivalent 7.3 x 10(8) 12.5 MeV protons/cm(2). The performance of the CCDs was measured both before and after irradiation. The charge transfer efficiency CTE was degraded from 0.999999 before irradiation to 0.999996 after the expected six year dose. The dark current, which was 3 electrons/pixel/hour before irradiation, is degraded to an equilibrium rate of 15 electrons/pixel/hour in orbit. We conclude that the performance of these devices is quite acceptable for high precision imaging in a space mission.

The Nearby Supernova Factory has discovered and observed in detail a large sample of Type Ia supernovae using the dedicated Supernovae Integral Field Spectrograph (SNIFS). This custom-built spectrograph has been in operation since 2004 on the Univeristy of Hawaii 2.2-m telescope on Mauna Kea. To reach the targeted spectrophotometric accuracy, attention has been focused on several key aspects of the calibration procedure, including: estimating the nightly photometric quality, derivation of the nightly sky extinction over the extended optical domain (320-1000 nm), its modeling in terms of physical components (Rayleigh and aerosol scattering, ozone absorption and telluric lines) and its variability within a given night. For this purpose, an optimal algorithm has been implemented to analyze atmospheric conditions from approximately 2300 observations of spectrophotometric standard stars taken throughout the night over nearly 300 individual nights.