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We design a novel, exactly energy-conserving implicit non-symplectic integration method for an eight-dimensional Hamiltonian system with four degrees of freedom. In our algorithm, each partial derivative of the Hamiltonian with respect to…
Methods of the explicitly correlated F12 approach are applied to the problem of calculating the uncoupled second-order dispersion energy in symmetry-adapted perturbation theory. The accuracy of the new method is tested for noncovalently…
A widely used strategy to reduce the computational cost in quantum-chemical calculations is to partition the system into an active subsystem, which is the focus of the computational efforts and an environment that is treated at a lower…
We introduce high-order dynamical decoupling strategies for open system adiabatic quantum computation. Our numerical results demonstrate that a judicious choice of high-order dynamical decoupling method, in conjunction with an encoding…
The quantum theory of coherent Ising machines, based on degenerate optical parametric oscillators and measurement-feedback circuits, is developed using the positive $P({\alpha},{\beta})$ representation of the density operator and the master…
We introduce the pCI software package for high-precision atomic structure calculations. The standard method of calculation is based on the configuration interaction (CI) method to describe valence correlations, but can be extended to attain…
We continue our analysis of the coupling between nonlinear hyperbolic problems across possibly resonant interfaces. In the first two parts of this series, we introduced a new framework for coupling problems which is based on the so-called…
In this paper we introduce a new method to design interparticle interactions to target arbitrary crystal structures via the process of self-assembly. We show that it is possible to exploit the curvature of the crystal nucleation free-energy…
Accurately describing strong electron correlation in complex systems remains a prominent challenge in computational chemistry as near-term quantum algorithms treating total correlation often require prohibitively deep circuits. Here we…
High precision atomic data is indispensable for experiments involving studies of fundamental interactions, astrophysics, atomic clocks, plasma science, and others. We develop new parallel atomic structure codes and explore the difficulties…
A new type of approximate scaling compatible with the Balitsky-Kovchegov equation with running coupling is found, which is different from the previously known running coupling geometric scaling. The corresponding asymptotic traveling wave…
In this paper we present an efficient algorithm for bivariate interpolation, which is based on the use of the partition of unity method for constructing a global interpolant. It is obtained by combining local radial basis function…
This paper presents a one-dimensional analog of the Rectangular-Polar (RP) integration strategy and its convergence analysis for weakly singular convolution integrals. The key idea of this method is to break the whole integral into integral…
The self-consistent random phase approximation (RPA) approach with the residual interaction derived from a relativistic point-coupling energy functional is applied to evaluate the isospin symmetry-breaking corrections {\delta}c for the…
The cubic spline interpolation method, the Runge--Kutta method, and the Newton-Raphson method are extended to dual versions (developed in the context of dual numbers). This extension allows the calculation of the derivatives of complicated…
The limited number of qubits per chip remains a critical bottleneck in quantum computing, motivating the use of distributed architectures that interconnect multiple quantum processing units (QPUs). However, executing quantum algorithms…
The quest for an approximate yet accurate kinetic energy density functional is central to the development of orbital-free density functional theory. While a recipe for closed-shell systems has been proposed earlier, we have shown that it…
We describe the application of a scalable algorithm for interpolating solution data in the overlapping mesh region of two solvers. This feature is essential to obtain a globally consistent solution for in-situ coupled atmospheric wave…
We study the correlation energy associated with the pair fluctuations in BCS theory. We use a schematic two-level pairing model and discuss the behavior of the correlation energy across shell closures, including the even-odd differences. It…
In the recent developments of regularization theory for inverse and ill-posed problems, a variational quasi-reversibility (QR) method has been designed to solve a class of time-reversed quasi-linear parabolic problems. Known as a PDE-based…