A Preprocessing Perspective for Quantum Machine Learning Classification Advantage in Finance Using NISQ Algorithms

Quantum Machine Learning (QML) has not yet demonstrated extensively and clearly its advantages compared to the classical machine learning approach. So far, there are only specific cases where some quantum-inspired techniques have achieved small incremental advantages, and a few experimental cases in hybrid quantum computing are promising, considering a mid-term future (not taking into account the achievements purely associated with optimization using quantum-classical algorithms). The current quantum computers are noisy and have few qubits to test, making it difficult to demonstrate the current and potential quantum advantage of QML methods. This study shows that we can achieve better classical encoding and performance of quantum classifiers by using Linear Discriminant Analysis (LDA) during the data preprocessing step. As a result, the Variational Quantum Algorithm (VQA) shows a gain of performance in balanced accuracy with the LDA technique and outperforms baseline classical classifiers.     

K-theory for rickart C*-algebras

We give an explicit index map for any properly infinite closed ideal of a Rickart C ^*-algebra. This generalizes Olsen's work on von Neumann algebras. We use our results to compute the topological and the algebraic K ₁-groups of any quotient algebra of a Rickart C ^*-algebra.     

Electronic structure of the K3Bi2 metallic phase

The electronic structure of K3Bi2 is discussed on the basis of first-principles DFT calculations. It is shown that the dimers are formally (Bi2)3-, even though this might seem to be in contradiction with the metallic character of the salt. The apparent puzzle is explained by the sizable participation of the K levels in the bonding.     

New theoretical and experimental infrared results on formaldehyde in solution

An extension of our combined procedure to determine a complete quartic force field and to resolve a vibrational problem thanks to a variational treatment is proposed for quantitative calculations of vibrational spectra in solution. Energies and gradients are obtained through a polarizable continuum model (PCM), the so-called self-consistent isodensity (SCI)-PCM. We present in this paper new experimental results dealing with formaldehyde in solution in cyclohexane, chloroform, THF, acetonitrile, DMSO and water; the obtained vibrational spectra are then compared with CCSD(T)/cc-pVQZ calculations. In addition, density functional theory (DFT) calculations have been carried out with the aim of both anticipating and positioning these approaches for larger sized molecules.     

A TDDFT study of some dinuclear compounds containing CpM(CO)3 or CpM(CO)2 groups

The electronic structure and spectroscopy of some representative dinuclear compounds containing CpM(CO)₃ and CpM(CO)₂ groups were studied using TDDFT (Time Dependent Density Functional Theory). These compounds contain Cp (cyclopentadienyl) as a ligand, and M can be Cr, Mo or W. Their main electronic transitions were calculated and the results are in good agreement with the experimental data. This allows the assignment of some bands whose origin was not clear. In all the cases, the carbonyls and Cp groups restrict the symmetry. The molecular orbitals that would be involved in M-M bonding interact strongly with the carbonyls and show unusual shapes and occupations. The strongest electronic bands are caused by σ→σ* transitions in most of the molecules containing CpM(CO)₃ groups, whereas in molecules such as Cp(CO)₂M≡M(CO)₂Cp the most intense bands are produced by π→π* transitions. The origin of other bands is now explained. The effect of the solvent on the electronic transitions and the use of EOM-CCSD method in some compounds were also checked.     

Application of a polarity parameter model to the separation of fat-soluble vitamins by reversed-phase HPLC

The retention behavior of a series of fat-soluble vitamins has been established on the basis of a polarity retention model: log k = (log k)(0) + p (P(m) (N) - P(s) (N)), with p being the polarity of the solute, P(m) (N) the mobile phase polarity, and (log k)(0) and P(m) (N) two parameters for the characterization of the stationary phase. To estimate the p-values of solutes, two approaches have been considered. The first one is based on the application of a QSPR model, derived from the molecular structure of solutes and their log P(o/w), while in the second one, the p-values are obtained from several experimental measurements. The quality of prediction of both approaches has also been evaluated, with the second one giving more accurate results for the most lipophilic vitamins. This model allows establishing the best conditions to separate and determine simultaneously some fat-soluble vitamins in dairy foods.     

Molecules and crystals with both icosahedral and cubic symmetry

Notwithstanding the apparent incompatibility between octahedral and icosahedral symmetries, fragments with the two types of symmetry coexist in many molecules and crystals, as evidenced by continuous shape and symmetry measures. A geometric analysis of Platonic and Archimedean polyhedra and of a variety of molecular and crystal structures strongly suggests that octahedral symmetry is latent in icosahedral polyhedra and vice versa. In this Feature Article, new concepts and structural data from the literature combine to offer a perspective view of complex molecular and extended structures. Its influence on the common cubic packing of icosahedral molecules is discussed for a variety of examples, including water clathrates, dodecahedrane, Buckminsterfullerene, the Pd145 and Mo132 clusters and several intermetallic phases.