Related papers: Schrodingerization based quantum algorithms for th…
Employing the phase-space representation of second order ordinary differential equations we developed a method to find the eigenvalues and eigenfunctions of the 1-dimensional time independent Schr\"odinger equation for quantum model…
We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap…
The physical relevance of the fractional time derivative in quantum mechanics is discussed. It is shown that the introduction of the fractional time Scr\"odinger equation (FTSE) in quantum mechanics by analogy with the fractional diffusion…
The purpose of this work is to test the application of the finite element method to quantum mechanical problems, in particular for solving the Schroedinger equation. We begin with an overview of quantum mechanics, and standard numerical…
We show that the time-dependent Schr\"odinger equation (TDSE) is the phenomenological dynamical law of evolution unraveled in the classical limit from a timeless formulation in terms of probability amplitudes conditioned by the values of…
We show that the method of splitting the operator ${\rm e}^{\epsilon(T+V)}$ to fourth order with purely positive coefficients produces excellent algorithms for solving the time-dependent Schr\"odinger equation. These algorithms require…
Simulating time evolution of generic quantum many-body systems using classical numerical approaches has an exponentially growing cost either with evolution time or with the system size. In this work, we present a polynomially scaling hybrid…
The numerical integration of the Schr\"odinger equation by discretization of time is explored for the curved manifolds arising from finite representations based on evolving basis states. In particular, the unitarity of the evolution is…
In this study,a new method was presented by developing Reduced differential transform method in order to find approximate solution of partial differential equations. Here, RDTM with fixed grid size algorithm was developed for the first time…
This paper is concerned with the efficient numerical computation of solutions to the 1D stationary Schr\"odinger equation in the semiclassical limit in the highly oscillatory regime. A previous approach to this problem based on explicitly…
The purpose of this document is to describe the solution and implementation of the time-independent and time-dependent Schr\"odinger using pseudospectral methods. Currently, the description is for single particle systems interacting with a…
Using a new state-dependent, $\lambda$-deformable, linear functional operator, ${\cal Q}_{\psi}^{\lambda}$, which presents a natural $C^{\infty}$ deformation of quantization, we obtain a uniquely selected non--linear, integro--differential…
This paper argues that the requirement of applicableness of quantum linearity to any physical level from molecules and atoms to the level of macroscopic extensional world, which leads to a main foundational problem in quantum theory…
This article explains and illustrates the use of a set of coupled dynamical equations, second order in a fictitious time, which converges to solutions of stationary Schr\"{o}dinger equations with additional constraints. We include three…
In this paper, the periodic initial-value problem for the fractional nonlinear Schr\"odinger (fNLS) equation is discretized in space by a Fourier spectral Galerkin method and in time by diagonally implicit, high-order Runge-Kutta schemes,…
Digital quantum simulation relies on Trotterization to discretize time evolution into elementary quantum gates. On current quantum processors with notable gate imperfections, there is a critical tradeoff between improved accuracy for finer…
Imaginary-time evolution plays an important role in algorithms for computing ground-state and thermal equilibrium properties of quantum systems, but can be challenging to simulate on classical computers. Many quantum algorithms for…
Applying ideas from monadic dynamics to the well-established framework of categorical quantum mechanics, we provide a novel toolbox for the simulation of finite-dimensional quantum dynamics. We use strongly complementary structures to give…
This work presents a quantum mechanical framework for analyzing quantization-based optimization algorithms. The sampling process of the quantization-based search is modeled as a gradient-flow dissipative system, leading to a…
We consider the generalized time-dependent Schr\"odinger equation on the half-axis and a broad family of finite-difference schemes with the discrete transparent boundary conditions (TBCs) to solve it. We first rewrite the discrete TBCs in a…