Related papers: Applications of the Numerov method to simple quant…
In this paper it is shown how to solve numerically eigenvalue problems associated to second order linear ordinary differential equations, containing also terms which depend on the variable. A didactic presentation of the Numerov Method is…
We propose a numerical method for approximate calculations of the time evolution of point particle systems given only the system's Hamiltonian function and initial conditions. The method both generates and solves the equations of motion…
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…
We report a case study where an existing materials science course was modified to include numerical simulation projects on the micromagnetic behavior of materials. The Ubermag micromagnetic simulation software package is used in order to…
A numerical matrix methodology is applied to quantum problems with periodic potentials. The procedure consists essentially in replacing the true potential by an alternative one, restricted by an infinite square well, and in expressing the…
We present an introduction to the Quantum Toolbox in Python (QuTiP) in the context of an undergraduate quantum mechanics class and potential senior research projects. QuTiP provides ready-to-use definitions of standard quantum states and…
We present a new numerical technique to solve large-scale eigenvalue problems. It is based on the projection technique, used in strongly correlated quantum many-body systems, where first an effective approximate model of smaller complexity…
It is exponentially hard to simulate quantum systems by classical algorithms, while quantum computer could in principle solve this problem polynomially. We demonstrate such an quantum-simulation algorithm on our NMR system to simulate an…
In this educational paper, we will discuss calculations on the hydrogen molecule both on classical and quantum computers. In the former case, we will discuss the calculation of molecular integrals that can then be used to calculate…
Model calculations of nuclear properties are peformed using quantum computing algorithms on simulated and real quantum computers. The models are a realistic calculation of deuteron binding based on effective field theory, and a simplified…
We review the so-called Nikiforov-Uvarov method along with some basic results about classical orthogonal polynomials and hypergeometric functions related to the hypergeometric differential equation. The method is employed to address certain…
The Nikiforov-Uvarov method is a simple, yet elegant and powerful method for solving second-order differential equations of generalized hypergeometric type. In the past, it has been used to solve many problems in quantum mechanics and…
Quantum computing brings a promise of new approaches into computational quantum chemistry. While universal, fault-tolerant quantum computers are still not available, we want to utilize today's noisy quantum processors. One of their flagship…
Quantum-classical hybrid algorithms are emerging as promising candidates for near-term practical applications of quantum information processors in a wide variety of fields ranging from chemistry to physics and materials science. We report…
Feynmans ideas to employ quantum systems for simulating other quantum systems gave rise to quantum simulation. While current quantum computers are still prone to decoherence and rely on error correction, the development of hybrid algorithms…
We present a modification of Newton's method to restore quadratic convergence for isolated singular solutions of polynomial systems. Our method is symbolic-numeric: we produce a new polynomial system which has the original multiple solution…
Probabilistic numerical methods (PNMs) solve numerical problems via probabilistic inference. They have been developed for linear algebra, optimization, integration and differential equation simulation. PNMs naturally incorporate prior…
While quantum computing provides an exponential advantage in solving system of linear equations, there is little work to solve system of nonlinear equations with quantum computing. We propose quantum Newton's method (QNM) for solving…
We present an open-source computer program written in Python language for quantum measurement and related issues. In our program, quantum states and operators, including quantum gates, can be developed into a quantum-object function…
Quantum simulation of complex quantum systems and their properties often requires the ability to prepare initial states in an eigenstate of the Hamiltonian to be simulated. In addition, to compute the eigenvalues of a Hamiltonian is in…