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Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
The aim of this article is to propose a new reduced-order modelling approach for parametric eigenvalue problems arising in electronic structure calculations. Namely, we develop nonlinear reduced basis techniques for the approximation of…
In this paper, a novel augmented Lagrangian preconditioner based on global Arnoldi for accelerating the convergence of Krylov subspace methods applied to linear systems of equations with a block three-by-three structure, these systems…
Systems of linear equations are used to model a wide array of problems in all fields of science and engineering. Recently, it has been shown that quantum computers could solve linear systems exponentially faster than classical computers,…
This paper develops a new class of Rosenbrock-type integrators based on a Krylov space solution of the linear systems. The new family, called Rosenbrock-Krylov (Rosenbrock-K), is well suited for solving large scale systems of ODEs or…
In this paper, a quantum dot mathematical model based on a two-dimensional Schr\"odinger equation assuming the 1/r inter-electronic potential is revisited. Generally, it is argued that the solutions of this model obtained by solving a…
In this article, we present a parallel recursive algorithm based on multi-level domain decomposition that can be used as a precondtioner to a Krylov subspace method to solve sparse linear systems of equations arising from the discretization…
Quantum computers have long been expected to efficiently solve complex classical differential equations. Most digital, fault-tolerant approaches use Carleman linearization to map nonlinear systems to linear ones and then apply quantum…
The logarithm-determinant is an widely-present operation in many areas of physics and computer science. Derivatives of the logarithm-determinant compute physically relevant quantities in statistical physics models, quantum field theories,…
In the era of quantum computing, the emergence of quantum computers and subsequent advancements have led to the development of various quantum algorithms capable of solving linear equations and eigenvalues, surpassing the pace of classical…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
We use classes of Hilbert lattice equations for an alternative representation of Hilbert lattices and Hilbert spaces of arbitrary quantum systems that might enable a direct introduction of the states of the systems into quantum computers.…
Computing eigenvalues is a computationally intensive task central to numerous applications in the natural sciences. Toward this end, we investigate the quantum block Krylov subspace projector (QBKSP) algorithm - a multireference quantum…
The ground state energy of a many-electron system can be approximated by an variational approach in which the total energy of the system is minimized with respect to one and two-body reduced density matrices (RDM) instead of many-electron…
We present an efficient quantum algorithm to simulate nonlinear differential equations with polynomial vector fields of arbitrary degree on quantum platforms. Models of physical systems that are governed by ordinary differential equations…
We introduce a quantum algorithm to perform the Laplace transform on quantum computers. Already, the quantum Fourier transform (QFT) is the cornerstone of many quantum algorithms, but the Laplace transform or its discrete version has not…
The electronic properties of one-dimensional clusters of N atoms or molecules have been studied. The model used is similar to the Kronig-Penney model with the potential offered by each ion being approximated by an attractive delta function.…
We compare two approaches to compute a portion of the spectrum of dense symmetric definite generalized eigenproblems: one is based on the reduction to tridiagonal form, and the other on the Krylov-subspace iteration. Two large-scale…
The possibility of using quantum computers for electronic structure calculations has opened up a promising avenue for computational chemistry. Towards this direction, numerous algorithmic advances have been made in the last five years. The…
In the present paper, we present some numerical methods for computing approximate solutions to some large differential linear matrix equations. In the first part of this work, we deal with differential generalized Sylvester matrix equations…