Related papers: Schrodingerization based quantum algorithms for th…
Recent breakthroughs have opened the possibility to intermediate-scale quantum computing with tens to hundreds of qubits, and shown the potential for solving classical challenging problems, such as in chemistry and condensed matter physics.…
We demonstrate a method that merges the quantum filter diagonalization (QFD) approach for hybrid quantum/classical solution of the time-independent electronic Schr\"odinger equation with a low-rank double factorization (DF) approach for the…
Variational quantum algorithms are a promising tool for solving partial differential equations. The standard approach for its numerical solution are finite difference schemes, which can be reduced to the linear algebra problem. We consider…
The method of moments in the context of Nonlinear Schrodinger Equations relies on defining a set of integral quantities, which characterize the solution of this partial differential equation and whose evolution can be obtained from a set of…
The Schrodinger equation is a mathematical equation describing the wave function's behavior in a quantum-mechanical system. It is a partial differential equation that provides valuable insights into the fundamental principles of quantum…
The time-dependent Schrodinger equation is solved for two model problems for a non-Hermitian quantum system.A simple matrix model system is used to examine two critical problems for these systems: complex and non-observable energies and…
Hamiltonian diagonalization is at the heart of understanding physical properties and practical applications of quantum systems. It is highly desired to design quantum algorithms that can speedup Hamiltonian diagonalization, especially those…
Let $L=-\Delta+V$ be a Schr\"odinger operator, where the potential $V$ belongs to the reverse H\"older class. By the subordinative formula, we introduce the fractional heat semigroup $\{e^{-t{L}^\alpha}\}_{t>0}, \alpha>0$, associated with…
In this paper we introduce an alternative approach to studying the evolution of a quantum harmonic oscillator subject to an arbitrary time dependent force. With the purpose of finding the evolution operator, certain unitary transformations…
We present a novel numerical method and algorithm for the solution of the 3D axially symmetric time-dependent Schr\"odinger equation in cylindrical coordinates, involving singular Coulomb potential terms besides a smooth time-dependent…
We develop a high accuracy power series method for solving partial differential equations with emphasis on the nonlinear Schr\"odinger equations. The accuracy and computing speed can be systematically and arbitrarily increased to orders of…
We present quantum algorithms for electromagnetic fields governed by Maxwell's equations. The algorithms are based on the Schr\"odingersation approach, which transforms any linear PDEs and ODEs with non-unitary dynamics into a system…
The linear Schr\"odinger equation with piecewise constant potential in one spatial dimension is a well-studied textbook problem. It is one of only a few solvable models in quantum mechanics and shares many qualitative features with…
The Schr\"odinger equation in the presence of an external electromagnetic field is an important problem in computational quantum mechanics. It also provides a nice example of a differential equation whose flow can be split with benefit into…
The solution of option-pricing problems may turn out to be computationally demanding due to non-linear and path-dependent payoffs, the high dimensionality arising from multiple underlying assets, and sophisticated models of price dynamics.…
The time-dependent Schr\"odinger equation (TDSE) in real space is fundamental to understanding the dynamics of many-electron quantum systems, with applications ranging from quantum chemistry to condensed matter physics and materials…
This work presents a direct and highly accurate method to solve ordinary differential equations, in particular the Schr\"odinger equation in one dimension, through the direct substitution of a power series solution to obtain a purely…
Quantum stochastic methods based on effective wave functions form a framework for investigating the generally non-Markovian dynamics of a quantum-mechanical system coupled to a bath. They promise to be computationally superior to the…
The three-dimensional Schredinger's equation is analyzed with the help of the correspondence principle between classical and quantum-mechanical quantities. Separation is performed after reduction of the original equation to the form of the…
We propose a numerical scheme to solve the time dependent linear Schr\"odinger equation. The discretization is carried out by combining a Runge-Kutta time-stepping scheme with a finite element discretization in space. Since the…