相关论文: An alternative implementation of the Lanczos algor…
Numerical simulation of individual open quantum systems has proven advantages over density operator computations. Quantum state diffusion with a moving basis (MQSD) provides a practical numerical simulation method which takes full advantage…
Common time-explicit numerical methods for kinetic simulations of plasmas in the low-collisions limit fall into two classes of algorithms: momentum conserving and energy conserving. Each has certain drawbacks. The PIC algorithm does not…
An appropriate iterative scheme for the minimization of the energy, based on the variational Monte Carlo (VMC) technique, is introduced and compared with existing stochastic schemes. We test the various methods for the 1D Heisenberg ring…
In the preceding paper [T. Fabcic et al., preprint] "restricted Gaussian wave packets" were introduced for the regularized Coulomb problem in the four-dimensional Kustaanheimo-Stiefel coordinates, and their exact time propagation was…
Due to the nonlocal feature of fractional differential operators, the numerical solution to fractional partial differential equations usually requires expensive memory and computation costs. This paper develops a fast scheme for fractional…
The split-operator technique for wave packet propagation in quantum systems is expanded here to the case of propagating wave functions describing Schr\"odinger particles, namely, charge carriers in semiconductor nanostructures within the…
Subspace diagonalisation methods have appeared recently as promising means to access the ground state and some excited states of molecular Hamiltonians by classically diagonalising small matrices, whose elements can be efficiently obtained…
An adaptive finite difference scheme for variable-order fractional-time subdiffusion equations in the Caputo form is studied. The fractional time derivative is discretized by the L1 procedure but using nonhomogeneous timesteps. The size of…
We study the quantum diffusion of an electron in a quantum chain starting from an initial state localized around a given site. As the wavepacket diffuses, the probability of reconstructing the initial state on another site diminishes…
Variational algorithms for strongly correlated chemical and materials systems are one of the most promising applications of near-term quantum computers. We present an extension to the variational quantum eigensolver that approximates the…
The variational approach is a cornerstone of computational physics, considering both conventional and quantum computing computational platforms. The variational quantum eigensolver (VQE) algorithm aims to prepare the ground state of a…
We propose a variational approach for preparing entangled quantum states on quantum computers. The methodology involves training a unitary operation to match with a target unitary using the Fubini-Study distance as a cost function. We…
Variational (Rayleigh-Ritz) methods are applied to local quantum field theory. For scalar theories the wave functional is parametrized in the form of a superposition of Gaussians and the expectation value of the Hamiltonian is expressed in…
We discuss a remarkable property of an iterative algorithm for eigenvalue problems recently advanced by Waxman that constitutes a clear advantage over other iterative procedures. In quantum mechanics, as well as in other fields, it is often…
This paper develops a high-accuracy algorithm for time fractional wave problems, which employs a spectral method in the temporal discretization and a finite element method in the spatial discretization. Moreover, stability and convergence…
We show that the time evolution operator of kicked quantum systems, although a full matrix of size NxN, can be diagonalized with the help of a new method based on a suitable combination of fast Fourier transform and Lanczos algorithm in…
We study the quantum mechanical motion of a charged particle moving in a half plane (x>0) subject to a uniform constant magnetic field B directed along the z-axis and to an arbitrary impurity potential W_B, assumed to be weak in the sense…
For a large class of variational quantum circuits, we show how arbitrary-order derivatives can be analytically evaluated in terms of simple parameter-shift rules, i.e., by running the same circuit with different shifts of the parameters. As…
We analyze the propagation properties of the numerical versions of one and two-dimensional wave equations, semi-discretized in space by finite difference schemes. We focus on high-frequency solutions whose propagation can be described, both…
We analyze the Lanczos method for matrix function approximation (Lanczos-FA), an iterative algorithm for computing $f(\mathbf{A}) \mathbf{b}$ when $\mathbf{A}$ is a Hermitian matrix and $\mathbf{b}$ is a given vector. Assuming that $f :…