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Strong approximation errors of both finite element semi-discretization and spatio-temporal full discretization are analyzed for the stochastic Allen-Cahn equation driven by additive noise in space dimension $d \leq 3$. The full…
We provide a priori error estimates for the spectral and pseudospectral Fourier (also called planewave) discretizations of the periodic Thomas-Fermi-von Weizs\"{a}cker (TFW) model and for the spectral discretization of the Kohn-Sham model,…
Quantum error correction protects quantum information against environmental noise. When using qubits, a measure of quality of a code is the maximum number of errors that it is able to correct. We show that a suitable notion of ``number of…
We investigate the basis-set convergence of electronic correlation energies calculated using coupled cluster theory and a recently proposed finite basis-set correction technique. The correction is applied to atomic and molecular systems and…
In this article, we consider the extended Kohn-Sham model for atoms subjected to cylindrically-symmetric external potentials. The variational approximation of the model and the construction of appropriate discretization spaces are detailed…
In this work we propose a new, arbitrary order space-time finite element discretisation for Hamiltonian PDEs in multisymplectic formulation. We show that the new method which is obtained by using both continuous and discontinuous…
Quantum annealing (QA) is one of the efficient methods to calculate the ground-state energy of a problem Hamiltonian. In the absence of noise, QA can accurately estimate the ground-state energy if the adiabatic condition is satisfied.…
Symmetry-preserving (mimetic) discretization aims to preserve certain properties of a continuous differential operator in its discrete counterpart. For these discretizations, stability and (discrete) conservation of mass, momentum and…
Computational models in chemistry rely on a number of approximations. The effect of such approximations on observables derived from them is often unpredictable. Therefore, it is challenging to quantify the uncertainty of a computational…
Noise is typically treated as the adversary of quantum information processing. For open quantum dynamics, however, dissipation is part of the target physics, creating a tension with fault-tolerant architectures designed to suppress…
Error-correcting codes were invented to correct errors on noisy communication channels. Quantum error correction (QEC), however, may have a wider range of uses, including information transmission, quantum simulation/computation, and…
We provide {\it a priori} error estimates for the spectral and pseudospectral Fourier (also called planewave) discretizations of the periodic Thomas-Fermi-von Weizs\"acker (TFW) model and of the Kohn-Sham model, within the local density…
Coupled cluster methods are widely regarded as the gold standard of computational quantum chemistry as they are perceived to offer the best compromise between computational cost and a high-accuracy resolution of the ground state eigenvalue…
In backward error analysis, an approximate solution to an equation is compared to the exact solution to a nearby modified equation. In numerical ordinary differential equations, the two agree up to any power of the step size. If the…
A procedure for obtaining a "minimal" discretization of a partial differential equation, preserving all of its Lie point symmetries is presented. "Minimal" in this case means that the differential equation is replaced by a partial…
We decompose the energy error of any variational DFT calculation into a contribution due to the approximate functional and that due to the approximate density. Typically, the functional error dominates, but in many interesting situations,…
By taking into account the physical nature of quantum errors it is possible to improve the efficiency of quantum error correction. Here we consider an optimisation to conventional quantum error correction which involves exploiting…
Quantum defect embedding theory (QDET) is a many-body embedding method designed to describe condensed systems with correlated electrons localized within a given region of space, for example spin defects in semiconductors and insulators.…
Data scarcity, bias, and experimental noise are all frequently encountered problems in the application of deep learning to chemical and material science disciplines. Transfer learning has proven effective in compensating for the lack in…
This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…