相关论文: Applications of the Numerov method to simple quant…
Quantum computers have the potential to transform the ways in which we tackle some important problems. The efforts by companies like Google, IBM and Microsoft to construct quantum computers have been making headlines for years. Equally…
Variational quantum algorithms exploit the features of superposition and entanglement to optimize a cost function efficiently by manipulating the quantum states. They are suitable for noisy intermediate-scale quantum (NISQ) computers that…
In this paper we focus on energy flows in simple quantum systems. This is achieved by concentrating on the quantum Hamilton-Jacobi equation. We show how this equation appears in the standard quantum formalism in essentially three different…
In this article, we discuss how a kind of hybrid computation, which employs symbolic, numeric, classic, and quantum algorithms, allows us to conduct Hartree-Fock electronic structure computation of molecules. In the proposed algorithm, we…
Lie-algebraic and quantum-algebraic techniques are used in the analysis of thermodynamic properties of molecules and solids. The local anharmonic effects are described by a Morse-like potential associated with the $su(2)$ algebra. A…
A self-contained and tutorial presentation of the diffusion Monte Carlo method for determining the ground state energy and wave function of quantum systems is provided. First, the theoretical basis of the method is derived and then a…
The matrix Numerov method provides an efficient framework for solving the time-independent Schr\"odinger equation as a matrix eigenvalue problem. However, for singular potentials such as the Coulomb interaction, the expected fourth-order…
We discuss an algorithm for the numerical evaluation of NLO multiparton processes. We focus hereby on the virtual part of the NLO calculation, i.e. on evaluating the one-loop integration numerically. We employ and extend the ideas of the…
Reducing the complexity of quantum algorithms to treat quantum chemistry problems is essential to demonstrate an eventual quantum advantage of Noisy-Intermediate Scale Quantum (NISQ) devices over their classical counterpart. Significant…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
Quantum computers have been shown to have tremendous potential in solving difficult problems in quantum chemistry. In this paper, we propose a new classical quantum hybrid method, named as power of sine Hamiltonian operator (PSHO), to…
We propose a quantum-classical hybrid algorithm of the power method, here dubbed as quantum power method, to evaluate $\hat{\cal H}^n |\psi\rangle$ with quantum computers, where $n$ is a nonnegative integer, $\hat{\cal H}$ is a…
Using the Nikiforov-Uvarov (NU) method, the energy levels and the wave functions of an electron confined in a two-dimensional (2D) pseudoharmonic quantum dot are calculated under the influence of temperature and an external magnetic field…
We describe a new polynomial time quantum algorithm that uses the quantum fast fourier transform to find eigenvalues and eigenvectors of a Hamiltonian operator, and that can be applied in cases (commonly found in ab initio physics and…
A two-dimensional hydrogen atom offers a promising alternative for describing the quantum interaction between an electron and a proton in the presence of a straight cosmic string. Reducing the hydrogen atom to two dimensions enhances its…
Harmonic polylogarithms $\H(\vec{a};x)$, a generalization of Nielsen's polylogarithms ${S}_{n,p}(x)$, appear frequently in analytic calculations of radiative corrections in quantum field theory. We present an algorithm for the numerical…
In this study, we apply the parametric Nikiforov-Uvarov method to obtain the bound state solution of Schrodinger wave equation in the presence of Kratzer plus generalized Morse potential (KPGM). The energy eigen equation and the…
Calculating the observable properties of chemical systems is often classically intractable and is widely viewed as a promising application of quantum information processing. Yet one of the most common and important chemical systems in…
This paper offers a review of numerical methods for computation of the eigenvalues of Hermitian matrices and the singular values of general and some classes of structured matrices. The focus is on the main principles behind the methods that…
Quantum computers can be used to address molecular structure, materials science and condensed matter physics problems, which currently stretch the limits of existing high-performance computing resources. Finding exact numerical solutions to…