Related papers: A Lower Bound for the Sturm-Liouville Eigenvalue P…
We calculate eigenvalues of one-dimensional quantum-systems by the exact numerical solution of the Lippmann-Schwinger equation, analogous to the scattering problem. To illustrate our method, we treat elementary problems: the harmonic and…
In this paper, we shall derive a spectral matrix method for the approximation of the eigenvalues of (weakly) regular and singular Sturm-Liouville problems in normal form with an unbounded potential at the left endpoint. The method is…
In this paper, we present a direct quantum adaptation of the classical shifted power method. The method is very similar to the iterative phase estimation algorithm; however, it does not require any initial estimate of an eigenvector and as…
We present a variational algorithm for solving the classical inverse Sturm-Liouville problem in one dimension when two spectra are given. All critical points of the least squares functional are at global minima, which which suggests…
Most studies of PT-symmetric quantum-mechanical Hamiltonians have considered the Schroedinger eigenvalue problem on an infinite domain. This paper examines the consequences of imposing the boundary conditions on a finite domain. As is the…
Exact solutions describing a fall of a particle to the center of a non-regularized singular potential in classical and quantum cases are obtained and compared. We inspect the quantum problem with the help of the conventional…
We use time-independent canonical transformation methods to discuss the energy eigenfunctions for the simple linear potential, pedagogically setting the stage for some field theory calculations to follow. We then discuss the Schr\"odinger…
We develop a modified semi-classical approach to the approximate solution of Schrodinger's equation for certain nonlinear quantum oscillations problems. At lowest order, the Hamilton-Jacobi equation of the conventional semi-classical…
The paper deals with Sturm-Liouville-type operators with frozen argument of the form $\ell y:=-y''(x)+q(x)y(a),$ $y^{(\alpha)}(0)=y^{(\beta)}(1)=0,$ where $\alpha,\beta\in\{0,1\}$ and $a\in[0,1]$ is an arbitrary fixed rational number. Such…
One-way quantum computing achieves the full power of quantum computation by performing single particle measurements on some many-body entangled state, known as the resource state. As single particle measurements are relatively easy to…
The query model offers a concrete setting where quantum algorithms are provably superior to randomized algorithms. Beautiful results by Bernstein-Vazirani, Simon, Aaronson, and others presented partial Boolean functions that can be computed…
The aim of this article is to analyze numerical schemes using two-layer neural networks withinfinite width for the resolution of high-dimensional Schr{\"o}dinger eigenvalue problems with smoothinteraction potentials and Neumann boundary…
A single machine total weighted tardiness minimization (TWTM) problem in operational planning is considered. The problem is formulated as an NP-hard constrained combinatorial problem, which has no known deterministic polynomial complexity…
The protocol of quantum annealing is applied to an optimization problem with a one-dimensional continuous degree of freedom, a variant of the problem proposed by Shinomoto and Kabashima. The energy landscape has a number of local minima,…
Quantum computing has attracted considerable attention in recent years because it promises speed-ups that conventional supercomputers cannot offer, at least for some applications. Though existing quantum computers are, in most cases, still…
We present a stochastic quantum computing algorithm that can prepare any eigenvector of a quantum Hamiltonian within a selected energy interval $[E-\epsilon, E+\epsilon]$. In order to reduce the spectral weight of all other eigenvectors by…
Local Search problem, which finds a local minimum of a black-box function on a given graph, is of both practical and theoretical importance to combinatorial optimization, complexity theory and many other areas in theoretical computer…
In this note we investigate the relationship between worst-case quantum query complexity and average-case classical query complexity. Specifically, we show that if a quantum computer can evaluate a total Boolean function f with bounded…
We present a simple algebraic procedure that can be applied to solve a range of quantum eigenvalue problems without the need to know the solution of the Schr\"odinger equation. The procedure, presented with a pedagogical purpose, is based…
A locally decodable code encodes n-bit strings x in m-bit codewords C(x), in such a way that one can recover any bit x_i from a corrupted codeword by querying only a few bits of that word. We use a quantum argument to prove that LDCs with 2…