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An overview of quantum-mechanical methods to generate cross-section data for electron collisions with atoms and molecules is presented. Particular emphasis is placed on the time-independent close-coupling approach, since it is particularly…
Path integral-based simulation methodologies play a crucial role for the investigation of nuclear quantum effects by means of computer simulations. However, these techniques are significantly more demanding than corresponding classical…
Precise calculations of core properties in heavy-atom systems which are described by the operators heavily concentrated in atomic cores, like to hyperfine structure and P,T-parity nonconservation effects, usually require accounting for…
One of the most promising suggested applications of quantum computing is solving classically intractable chemistry problems. This may help to answer unresolved questions about phenomena like: high temperature superconductivity, solid-state…
We provide two methods for computation of continuum backstepping kernels that arise in control of continua (ensembles) of linear hyperbolic PDEs and which can approximate backstepping kernels arising in control of a large-scale, PDE system…
Catalytic processes are vital in the chemical industry, with nitrogen-to-ammonia conversion being a major industrial process. Designing catalysts relies on computational chemistry methods like Density Functional Theory (DFT), which have…
The study and prediction of chemical reactivity is one of the most important application areas of molecular quantum chemistry. Large-scale, fully error-tolerant quantum computers could provide exact or near-exact solutions to the underlying…
Computational models are an essential tool for the design, characterization, and discovery of novel materials. Hard computational tasks in materials science stretch the limits of existing high-performance supercomputing centers, consuming…
Computational techniques are required for narrowing down the vast space of possibilities to plausible prebiotic scenarios, since precise information on the molecular composition, the dominant reaction chemistry, and the conditions for that…
Three-centre nuclear attraction integrals, which arise in density functional and \textit{ab initio} calculations, are one of the most time-consuming computations involved in molecular electronic structure calculations. Even for relatively…
Owing to the computational complexity of electronic structure algorithms running on classical digital computers, the range of molecular systems amenable to simulation remains tightly circumscribed even after many decades of work. Quantum…
Significant progress in the development of efficient and fast algorithms for quantum chemical calculations has been made in the past two decades. The main focus has always been the desire to be able to treat ever larger molecules or…
Quantum computing has shown great potential in various quantum chemical applications such as drug discovery, material design, and catalyst optimization. Although significant progress has been made in quantum simulation of simple molecules,…
This paper presents a quantum algorithm for solving the fractional Poisson equation \((-\Delta)^s u = f\) with \(s \in (0,1)\) on bounded domains. The proposed approach combines rational approximation techniques with quantum linear system…
Computer model calibration is a crucial step in building a reliable computer model. In the face of massive physical observations, a fast estimation for the calibration parameters is urgently needed. To alleviate the computational burden, we…
We propose the regularized compressed double factorization (RC-DF) method to classically compute compressed representations of molecular Hamiltonians that enable efficient simulation with noisy intermediate scale (NISQ) and error corrected…
In this work, we propose efficient and accurate numerical algorithms based on Difference Potentials Method for numerical solution of chemotaxis systems and related models in 3D. The developed algorithms handle 3D irregular geometry with the…
In this paper we describe a numerical algorithm for integrating the multicomponent, reacting, compressible Navier-Stokes equations, targeted for direct numerical simulation of combustion phenomena. The algorithm addresses two shortcomings…
Choosing a basis set is the first step of a quantum chemistry calculation and it sets its maximum accuracy. This choice of orbitals is limited by strong technical constraints as one must be able to compute a large number of six dimensional…
Recent technological advances may lead to the development of small scale quantum computers capable of solving problems that cannot be tackled with classical computers. A limited number of algorithms has been proposed and their relevance to…