Related papers: Modified Hermite Integrators of Arbitrary Order
In this work, we develop a class of high-order multiderivative time integration methods that is able to preserve certain functionals discretely. Important ingredients are the recently developed Hermite-Birkhoff-Predictor-Corrector methods…
Recent quantum algorithms pertaining to electronic structure theory primarily focus on threshold-based dynamic construction of ansatz by selectively including important many-body operators. These methods can be made systematically more…
An attempt has been made in this paper to modify Grover's Algorithm to find the binary string solutions approximating a target cost value. In that direction, new Controlled Oracle and the Local Diffusion Operator are suggested, apart from…
Iterative decoding was not originally introduced as the solution to an optimization problem rendering the analysis of its convergence very difficult. In this paper, we investigate the link between iterative decoding and classical…
We present a new adaptive method for electronic structure calculations based on novel fast algorithms for reduction of multivariate mixtures. In our calculations, spatial orbitals are maintained as Gaussian mixtures whose terms are selected…
We construct the ($\beta$-deformed) higher order total derivative operators and analyze their remarkable properties. In terms of these operators, we derive the higher order constraints for the ($\beta$-deformed) Hermitian matrix models. We…
Based on continuously recorded beam positions and corrector excitations from, for example, a closed-orbit feedback system we describe an algorithm that continuously updates an estimate of the orbit response matrix. The speed of convergence…
The relative power of quantum algorithms, using an adaptive access to quantum devices, versus classical post-processing methods that rely only on an initial quantum data set, remains the subject of active debate. Here, we present evidence…
We present a family of high order trapezoidal rule-based quadratures for a class of singular integrals, where the integrand has a point singularity. The singular part of the integrand is expanded in a Taylor series involving terms of…
Suzuki-Trotter decompositions of exponential operators like $\exp(Ht)$ are required in almost every branch of numerical physics. Often the exponent under consideration has to be split into more than two operators $H=\sum_k A_k$, for…
We discuss systematic extensions of the standard (St{\"o}rmer-Verlet) splitting method for differential equations of Hamiltonian mechanics, with relative accuracy of order $\tau^2$ for a timestep of length $\tau$, to higher orders in…
In this paper we have considered a finite unitary matrix group with exact elements being unknown and only approximate elements available. Such a group becomes inconsistent with its own multiplication table. We found simple correction…
A new algorithm to approximate Hermitian matrices by positive semidefinite Hermitian matrices based on modified Cholesky decompositions is presented. In contrast to existing algorithms, this algorithm allows to specify bounds on the…
Memristors have recently received significant attention as ubiquitous device-level components for building a novel generation of computing systems. These devices have many promising features, such as non-volatility, low power consumption,…
Dedicated hardware accelerators are suitable for parallel computational tasks. Moreover, they have the tendency to accept inexact results. These hardware accelerators are extensively used in image processing and computer vision…
We derive efficient and reliable goal-oriented error estimations, and devise adaptive mesh procedures for the finite element method that are based on the localization of a posteriori estimates. In our previous work [SIAM J. Sci. Comput.,…
To efficiently implement many-qubit gates for use in quantum simulations on quantum computers we develop and present methods reexpressing exp[-i (H_1 + H_2 + ...) \Delta t] as a product of factors exp[-i H_1 \Delta t], exp[-i H_2 \Delta t],…
We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…
We significantly enhance the simulation accuracy of initial Trotter circuits for Hamiltonian simulation of quantum systems by integrating first-order Riemannian optimization with tensor network methods. Unlike previous approaches, our…
Conservative symmetric second-order one-step integrators are derived using the Discrete Multiplier Method for a family of vortex-blob models approximating the incompressible Euler's equations on the plane. Conservative properties and second…