Related papers: Numerical matrix method for quantum periodic poten…
Accurate computation of multiple eigenvalues of quantum Hamiltonians is essential in quantum chemistry, materials science, and molecular spectroscopy. Estimating excited-state energies is challenging for classical algorithms due to…
Recently, three numerical methods for the computation of eigenvalues of singular matrix pencils, based on a rank-completing perturbation, a rank-projection, or an augmentation were developed. We show that all three approaches can be…
A novel quantum dynamical method to simulate vibronic reaction dynamics in molecules at metal surfaces is proposed. The method is based on the hierarchical quantum master equation approach and uses a discrete variable representation of the…
We propose the variational quantum singular value decomposition based on encoding the elements of the considered { $N\times N$} matrix into the state of a quantum system of appropriate dimension. This method doesn't use the expansion of…
In quantum theory, the so-called "spinless Salpeter equation," the relativistic generalization of the nonrelativistic Schroedinger equation, is used to describe both bound states of scalar particles and the spin-averaged spectra of bound…
The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average…
The behavior of the quantum potential is studied for a particle in a linear and a harmonic potential by means of an extended phase space technique. This is done by obtaining an expression for the quantum potential in momentum space…
Variational quantum algorithms are proposed to solve relevant computational problems on near term quantum devices. Popular versions are variational quantum eigensolvers and quantum ap- proximate optimization algorithms that solve ground…
Determining ground state energies of quantum systems by hybrid classical/quantum methods has emerged as a promising candidate application for near-term quantum computational resources. Short of large-scale fault-tolerant quantum computers,…
Quantum computation holds promise for the solution of many intractable problems. However, since many quantum algorithms are stochastic in nature they can only find the solution of hard problems probabilistically. Thus the efficiency of the…
The notion of a double well potential typically involves two regions of space separated by a repulsive potential barrier. The solution is a wave function that is suppressed in the barrier region and localized in the two surrounding regions.…
Supersymmetric solution of PT-/non-PT-symmetric and non-Hermitian Morse potential is studied to get real and complex-valued energy eigenvalues and corresponding wave functions. Hamiltonian Hierarchy method is used in the calculations
NP-hard problems are not believed to be exactly solvable through general polynomial time algorithms. Hybrid quantum-classical algorithms to address such combinatorial problems have been of great interest in the past few years. Such…
A particle confined to an impassable box is a paradigmatic and exactly solvable one-dimensional quantum system modeled by an infinite square well potential. Here we explore some of its infinitely many generalizations to two dimensions,…
Neural Network-based Quantum Monte Carlo (NNQMC), an emerging method for solving many-body quantum systems with high accuracy, has been limitedly applied to small systems due to demanding computation requirements. In this work, we introduce…
Many quantum algorithms for numerical linear algebra assume black-box access to a block-encoding of the matrix of interest, which is a strong assumption when the matrix is not sparse. Kernel matrices, which arise from discretizing a kernel…
We describe the bound state and scattering properties of a quantum mechanical particle in a scalar $N$-prong potential. Such a study is of special interest since these situations are intermediate between one and two dimensions. The energy…
We transform the problem of solving linear system of equations $A\mathbf{x}=\mathbf{b}$ to a problem of finding the right singular vector with singular value zero of an augmented matrix $C$, and present two quantum algorithms for solving…
In the paper, we introduce a matrix method to constructively determine spaces of polynomial solutions (in general, multiplied by exponentials) to a system of constant coefficient linear PDE's with polynomial (multiplied by exponentials)…
A numerical technique used to solve boundary value problems is modified to find periodic steady-state solutions of nonautonomous dynamical systems. The technique uses a matrix representation of the time derivative obtained through…