Semistochastic Quadratic Bound Methods

Partition functions arise in a variety of settings, including conditional random fields, logistic regression, and latent gaussian models. In this paper, we consider semistochastic quadratic bound (SQB) methods for maximum likelihood inference based on partition function optimization. Batch methods based on the quadratic bound were recently proposed for this class of problems, and performed favorably in comparison to state-of-the-art techniques. Semistochastic methods fall in between batch algorithms, which use all the data, and stochastic gradient type methods, which use small random selections at each iteration. We build semistochastic quadratic bound-based methods, and prove both global convergence (to a stationary point) under very weak assumptions, and linear convergence rate under stronger assumptions on the objective. To make the proposed methods faster and more stable, we consider inexact subproblem minimization and batch-size selection schemes. The efficacy of SQB methods is demonstrated via comparison with several state-of-the-art techniques on commonly used datasets.Comment: 11 pages, 1 figur

Electronic Structure of Excited States with Configuration Interaction Methods

Computational chemistry is routinely applied to ground state molecular systems to provide chemical insights. Accurate excited state calculations, however, still typically require carefully tailored calculations and sizeable computational resources. This work focuses on the development of methods and strategies that enable the calculation of excited state properties with more accuracy and on larger systems than ever before. The first two Chapters focus on the spin-flip configuration interaction family of methods. Chapter 2 introduces us to the quantities one can obtain with excited state methods, with a challenging example being the electronic structure of a possible intramolecular singlet fission system, a quinoidal bithiophene. The study assigns an experimentally observed long-lived exciton to a long-lived singlet multiexciton state with a combination of energetic and transition dipole moment quantities. The spin-flip methodology is extended in Chapter 3 to provide more insight into the energetic orderings of the multiexciton states of a tetracene dimer, a model singlet fission system, showing that triplet decoupling should occur spontaneously upon population of the intermediate multiexciton state, 1(TT). However, this extension enlarged the configuration spaces to the point that they became a limiting factor in the calculation of larger systems. Therefore, the latter two Chapters focus on investigating new strategies for identifying and eliminating unneeded configurations. Chapter 4 presents iterative submatrix diagonalization, a procedure for converging the Davidson diagonalization procedure with a reduced set of active orbitals. This is accomplished by generating a systematic series of submatrix approximations to the full configuration space and solving for eigenpairs within the series until convergence of eigenpairs is achieved. The method shows promise, converging eigenvalues with a considerable reduction in orbitals and total computational time. Chapter 5 applies heat-bath configuration interaction towards obtaining exact excitation energies and examines various ways in which convergence is signified. A new convergence metric based on the magnitude of the perturbative correction is developed and converged excitation energies are obtained for systems as large as hexatriene. These results involved treating configuration spaces with as many as 1038 configurations, a full 29 orders of magnitude over what is achievable with conventional configuration interaction methods and 10 orders beyond results reported by other recent state-of-art solvers. While there is still a great deal of work to be done before excited state computational chemistry will be routinely applicable to a wide variety of systems, the various methods investigated and extended here show significant promise, especially those presented in the latter Chapters as these are generally applicable to any configuration interaction method.PHDChemistryUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/140821/1/alandc_1.pd

Radical Artificial Intelligence: A Postmodern Approach

The dynamic response of end-clamped monolithic beams and sandwich beams has been measured by loading the beams at mid-span using metal foam projectiles. The AISI 304 stainless-steel sandwich beams comprise two identical face sheets and either prismatic Y-frame or corrugated cores. The resistance to shock loading is quantified by the permanent transverse deflection at mid-span of the beams as a function of projectile momentum. The prismatic cores are aligned either longitudinally along the beam length or transversely. It is found that the sandwich beams with a longitudinal core orientation have a higher shock resistance than the monolithic beams of equal mass. In contrast, the performance of the sandwich beams with a transverse core orientation is very similar to that of the monolithic beams. Three-dimensional finite element (FE) simulations are in good agreement with the measured responses. The FE calculations indicate that strain concentrations in the sandwich beams occur at joints within the cores and between the core and face sheets; the level of maximum strain is similar for the Y-frame and corrugated core beams for a given value of projectile momentum. The experimental and FE results taken together reveal that Y-frame and corrugated core sandwich beams of equal mass have similar dynamic performances in terms of rear-face deflection, degree of core compression and level of strain within the beam

Methods for variational computation of molecular properties on near term quantum computers

In this thesis we explore the near term applications of quantum computing to Quantum Chemistry problems, with a focus on electronic structure calculations. We begin by discussing the core subroutine of near-term quantum computing methods: the variational quantum eigensolver (VQE). By drawing upon the literature, we discuss the relevance of the method in computing electronic structure properties, compare it to alternative conventional or quantum methods and outline best practices. We then discuss the key limitations of this method, namely: the exploding number of measurements required, showing that parallelisation will be relevant for VQE to compete with conventional methods; the barren plateau problem; and the management of errors through error mitigation - we present a light touch error mitigation technique which is used to improve the results of experiments presented later in the thesis. From this point, we propose three methods for near term applications of quantum computing, with a focus on limiting the requirements on quantum resources. The first two methods concern the computation of ground state energy. We adapt the conventional methods of complete active space self consistent field (CASSCF) and energy-weighted density matrix embedding theory (EwDMET) by integrating a VQE subroutine to compute the electronic wavefunctions from which reduced density matrices are sampled. These method allow recovering additional electron correlation energy for a given number of qubits and are tested on quantum devices. The last method is focused on computing excited electronic states and uses techniques inspired from the generative adversarial machine learning literature. It is a fully variational method, which is shown to work on current quantum devices

Quantum chemistry of the excited state: recent trends in methods developments and applications

Advances (2016–2017) in Quantum Chemistry of the Excited State (QCEX) are presented in this book chapter focusing firstly on developments of methodology and excited-state reaction-path computational strategies and secondly on the applications of QCEX to study light–matter interaction in distinct fields of biology, (nano)-technology, medicine and the environment. We highlight in this contribution developments of static and dynamic electron-correlation methods and methodological approaches to determine dynamical properties, recent examples of the roles of conical intersections, novel DNA spectroscopy and photochemistry findings, photo-sensitisation mechanisms in biological structures and the current knowledge on chemi-excitation mechanisms that give rise to light emission (in the chemiluminescence and bioluminescence phenomena)

Quantum Monte Carlo simulations of warm dense matter

Recent experimental progress in laser technology has led to renewed interest in warm dense matter. Found in the interiors of gas giants and in inertial confinement fusion experiments, warm dense matter is relevant to problems of fundamental and technological importance but is a challenge to create experimentally and describe theoretically. Modern electronic structure theory, in the form of density functional theory coupled with molecular dynamics, in principle offers a route to describing realistic warm dense matter. However, until quite recently, no accurate exchange correlation free energy functionals existed and the accuracy of existing fits was largely unknown. %Moreover, existing accurate quantum Monte Carlo data for the exchange correlation energy of the warm dense electron gas differ substantially. In this thesis we extend the independent, systematically exact, density matrix quantum Monte Carlo method, to address these issues. Focussing on the warm dense uniform electron gas, we first outline how sampling issues present in the original formulation can be overcome and how numerical basis set corrections can significantly reduce the computational burden at high electronic temperatures. We next introduce a systematic approximation allowing larger system sizes to be tackled. In the process we resolve a controversy present between two competing path integral Monte Carlo methods, whose results for the exchange correlation energy of the uniform electron gas differ substantially in the warm dense regime. Finally, we develop a general procedure for deriving analytic finite size corrections in the warm dense regime, thus removing the final barrier to reaching the thermodynamic limit.Open Acces

Postmodern Electronic Structure Theory

This dissertation is concerned with the development and applications of approaches to the electron correlation problem. We start with an introduction that summarizes modern approaches to the electron correlation problem. In our view, there are two remaining challenges that modern density functional theory cannot satisfactorily solve. The first challenge is due to self-interaction error and the second is due to strong correlation. We discuss two methods developed by the author that attempt to make progress to address the second challenge.The first approach is useful in distinguishing strong and weak correlation in a computationally economical way. It is based on orbital optimization in the presence of regularized second-order Moller-Plesset perturbation theory (k-OOMP2), which is an approximate method to obtain Brueckner orbitals. k-OOMP2 includes weak correlation while attenuating strong correlation. As such, it distinguishes artificial and essential symmetry breaking which occur at the Hartree-Fock (HF) level. Artificial symmetry breaking appears due to the lack of weak correlation, not due to the lack of strong correlation. Therefore, the common wisdom in quantum chemistry, which equates symmetry breaking at the HF level and strong correlation, can result in a wrong understanding of the system. Essential symmetry breaking, on the other hand, signals strong correlation that is beyond the scope of simple perturbation theory. k-OOMP2 has been shown to reliably distinguish these two: symmetry breaking in the k-OOMP2 orbitals is essential. This has been applied to a recent controversy about whether C60 is strongly correlated. Starting from a broken-symmetry HF solution, k-OOMP2 restores every symmetry. As such, C60 is not strongly correlated. Moreover, k-OOMP2 successfully predicts strong correlation for a known biradicaloid, C36, by showing essential symmetry breaking in its orbitals. We also exploited essential symmetry breaking in singlet biradicaloids using k-OOMP2 and showed quantitative accuracy in obtaining singlet-triplet gaps of various molecules. This new approach should be helpful for redefining the common wisdom in quantum chemistry.The second method is an exact, spin-pure, polynomial-scaling way to describe strong spin-correlation (SSC). SSC is present when there are many spatially separate open-shell electrons with small spin-flip energy cost. Describing SSC exactly requires the inclusion of all essential spin-couplings. The number of such spin-couplings scales exponentially with the number of electrons. Because of this, SSC was thought to require an exponential number of wavefunction parameters in general. However, new development suggests that there is an efficient way to obtain all these spin-couplings with only a quadratic number of wavefunction parameters, which is called the coupled-cluster valence-bond (CCVB) method. We discuss different challenges in CCVB: (1) its non-black-box nature and (2) its inability to describe SSC in spin-frustrated systems. We present two improved CCVB approaches that address these two challenges. These approaches were applied to describe emergent strong correlation in oligoacenes and SSC in spin-frustrated systems such as single molecular magnets and metalloenzymes. The remaining challenges in CCVB are the inclusion of ionic excitations which are not relevant for SSC, but crucial for obtaining quantitative accuracy