Related papers: The dissection algorithm for the second-Born self-…
We present a polynomial-time quantum algorithm for obtaining the energy spectrum of a physical system, i.e. the differences between the eigenvalues of the system's Hamiltonian, provided that the spectrum of interest contains at most a…
An alternative method is introduced to solve a simple two-dimensional models describing vibrational excitation and dissociation processes during the electron-molecule collisions. The model works with one electronic and one nuclear degree of…
The Kohn-Sham scheme of density functional theory is one of the most widely used methods to solve electronic structure problems for a vast variety of atomistic systems across different scientific fields. While the method is fast relative to…
Novel results for the self-consistent single-particle spectral function and self-energy are presented for non-degenerate one-component Coulomb systems at various densities and temperatures. The GW^0-method for the dynamical self-energy is…
An outstanding challenge in chemical computation is the many-electron problem where computational methodologies scale prohibitively with system size. The energy of any molecule can be expressed as a weighted sum of the energies of…
Based on the Beylkin-Cramer summation rule, we introduce a new fast algorithm that enable us to explore the high order statistics efficiently in large data sets. Central to this technique is to make decomposition both of fields and…
The ideas behind the concept of algebraic ("integration-by-parts") algorithms for multiloop calculations are reviewed. For any topology and mass pattern, a finite iterative algebraic procedure is proved to exist which transforms the…
Sequential Monte Carlo algorithms, or Particle Filters, are Bayesian filtering algorithms which propagate in time a discrete and random approximation of the a posteriori distribution of interest. Such algorithms are based on Importance…
The contour integrals, occurring in the arbitrary-order phase-integral quantization conditions given in a previous paper, are in the first- and third-order approximations expressed in terms of complete elliptic integrals in the case that…
A new method is presented that allows for efficient evaluation of spin-orbit coupling (SOC) in density-functional theory calculations. In the so-called second-variational scheme, where Kohn-Sham functions obtained in a scalar-relativistic…
We describe a rapidly converging algorithm for solving the Kohn--Sham equations and equations of similar structure that appear frequently in calculations of the structure of inhomogeneous electronic many--body systems. The algorithm has its…
We consider the problem of solving dual monotone inclusions involving sums of composite parallel-sum type operators. A feature of this work is to exploit explicitly the cocoercivity of some of the operators appearing in the model. Several…
Considering recent advancements and successes in the development of efficient quantum algorithms for electronic structure calculations --- alongside impressive results using machine learning techniques for computation --- hybridizing…
The calculation time for the energy of atoms and molecules scales exponentially with system size on a classical computer but polynomially using quantum algorithms. We demonstrate that such algorithms can be applied to problems of chemical…
In this paper, we develop two parameter-robust numerical algorithms for Biot model and applied the algorithms in brain edema simulations. By introducing an intermediate variable, we derive a multiphysics reformulation of the Biot model.…
A new integration technique for multi-loop Feynman integrals, called the matrix method, is developed and then applied to the divergent part of the overlapping two-loop quark self-energy function $\,i\Sigma\,$ in the light- cone gauge. It is…
We describe an algorithm for using a quantum computer to calculate mean values of observables and the partition function of a quantum system. Our algorithm includes two sub-algorithms. The first sub-algorithm is for calculating, with…
In this paper we show how we can compute in a deterministic way the decomposition of a multivariate rational function with a recombination strategy. The key point of our recombination strategy is the used of Darboux polynomials. We study…
Protein characterization is one of the key components for understanding the human body and advancing drug discovery processes. While the future of quantum hardware holds the potential to accurately characterize these molecules, current…
The charging energy of a quantum dot is measured through the effect of its potential on the conductance of a second dot. This technique allows a measurement of the scaling of the dot's charging energy with the conductance of the tunnel…