Related papers: Solving two-dimensional quantum eigenvalue problem…
We derive the Schroedinger equation for a spinless charged particle constrained to a curved surface with electric and magnetics fields applied. The particle is confined on the surface using a thin-layer procedure, giving rise to the…
One examines the infinitely deep quantum cavity, also known as the quantum infinite square well, within the framework of the real Hilbert space. The solutions are considered in terms of complex wave functions, and also in terms of…
An outstanding problem in quantum computing is the calculation of entanglement, for which no closed-form algorithm exists. Here we solve that problem, and demonstrate the utility of a quantum neural computer, by showing, in simulation, that…
Neural networks are a promising tool for characterizing intermediate-scale quantum devices from limited amounts of measurement data. A challenging problem in this area is to learn the action of an unknown quantum process on an ensemble of…
The Einstein equations are non-linear and the particles of which the gravitational effect is described by these equations are lastly unknown. If renormalizable fields are assumed, then results are obtained only in the case of a at space.…
The objective of this paper is to investigate the ability of physics-informed neural networks to learn the magnetic field response as a function of design parameters in the context of a two-dimensional (2-D) magnetostatic problem. Our…
Physics-informed neural networks (PINNs) have emerged as a transformative framework for addressing operator learning and inverse problems involving the Korteweg-de Vries (KdV) equation for internal solitary waves. By integrating physical…
When numerically simulating the unitary time evolution of an infinite-dimensional quantum system, one is usually led to treat the Hamiltonian $H$ as an "infinite-dimensional matrix" by expressing it in some orthonormal basis of the Hilbert…
Physics-informed neural networks offered an alternate way to solve several differential equations that govern complicated physics. However, their success in predicting the acoustic field is limited by the vanishing-gradient problem that…
Chebyshev polynomials have shown significant promise as an efficient tool for both classical and quantum neural networks to solve linear and nonlinear differential equations. In this work, we adapt and generalize this framework in a quantum…
The resemblance between the methods used in quantum-many body physics and in machine learning has drawn considerable attention. In particular, tensor networks (TNs) and deep learning architectures bear striking similarities to the extent…
Solving the wave equation is one of the most (if not the most) fundamental problems we face as we try to illuminate the Earth using recorded seismic data. The Helmholtz equation provides wavefield solutions that are dimensionally reduced,…
The homogeneous Lippmann-Schwinger integral equation is solved in momentum space by using confining potentials. Since the confining potentials are unbounded at large distances, they lead to a singularity at small momentum. In order to…
In a previous article we have shown how one can employ Artificial Neural Networks (ANNs) in order to solve non-homogeneous ordinary and partial differential equations. In the present work we consider the solution of eigenvalue problems for…
We analyze the non-relativistic problem of a quantum particle that bounces back and forth between two moving walls. We recast this problem into the equivalent one of a quantum particle in a fixed box whose dynamics is governed by an…
Physics-informed neural networks (PINNs) effectively embed physical principles into machine learning, but often struggle with complex or alternating geometries. We propose a novel method for integrating geometric transformations within…
We consider one particle confined to a deformed one-dimensional wire. The quantum mechanical equivalent of the classical problem is not uniquely defined. We describe several possible hamiltonians and corresponding solutions for a finite…
Many types of physics-informed neural network models have been proposed in recent years as approaches for learning solutions to differential equations. When a particular task requires solving a differential equation at multiple…
The full spectrum and eigenfunctions of the quantum version of a nonlinear oscillator defined on an N-dimensional space with nonconstant curvature are rigorously found. Since the underlying curved space generates a position-dependent…
This paper introduces a deep learning system based on a quantum neural network for the binary classification of points of a specific geometric pattern (Two-Moons Classification problem) on a plane. We believe that the use of hybrid deep…