Related papers: Reconstruction techniques for quantum trees
We consider a second order functional-differential pencil with two constant delays of the argument and study the inverse problem of recovering its coefficients from the spectra of two boundary value problems with one common boundary…
A Green's function approach is presented for the D-dimensional inverse square potential in quantum mechanics. This approach is implemented by the introduction of hyperspherical coordinates and the use of a real-space regulator in the…
In this article, we propose a non-parametric Bayesian level-set method for simultaneous reconstruction of two different piecewise constant coefficients in an elliptic partial differential equation. We show that the Bayesian formulation of…
We propose quantum methods for solving differential equations that are based on a gradual improvement of the solution via an iterative process, and are targeted at applications in fluid dynamics. First, we implement the Jacobi iteration on…
Poly-trees are singly connected causal networks in which variables may arise from multiple causes. This paper develops a method of recovering ply-trees from empirically measured probability distributions of pairs of variables. The method…
The main goal of this paper is to propose an approach to inverse spectral problems for functional-differential operators (FDO) with involution. For definiteness, we focus on the second-order FDO with involution-reflection. Our approach is…
Solving arithmetic word problems is a cornerstone task in assessing language understanding and reasoning capabilities in NLP systems. Recent works use automatic extraction and ranking of candidate solution equations providing the answer to…
With gates of a quantum computer designed to encode multi-dimensional vectors, projections of quantum computer states onto specific qubit states can produce kernels of reproducing kernel Hilbert spaces. We show that quantum kernels obtained…
Boundary value problems for Sturm-Liouville operators with potentials from the class $W_2^{-1}$ on a star-shaped graph are considered. We assume that the potentials are known on all the edges of the graph except two, and show that the…
The inverse scattering problem of the three-dimensional Schroedinger equation is considered at fixed scattering energy with spherically symmetric potentials. The phase shifts determine the potential therefore a constructive scheme for…
Quantum Computing is a rapidly developing field with the potential to tackle the increasing computational challenges faced in high-energy physics. In this work, we explore the potential and limitations of variational quantum algorithms in…
This paper studies an inverse boundary value problem for a semilinear Helmholtz equation with Neumann boundary conditions in a bounded domain $\Omega \subset \mathbb{R}^n$ ($n\ge2$). The objective is to recover the unknown linear and…
A common problem in cosmology is to integrate the product of two or more spherical Bessel functions (sBFs) with different configuration-space arguments against the power spectrum or its square, weighted by powers of wavenumber. Naively…
A new method is presented to reconstruct the potential of a quantum mechanical many-body system from observational data, combining a nonparametric Bayesian approach with a Hartree-Fock approximation. A priori information is implemented as a…
We present a novel algorithm based on the ensemble Kalman filter to solve inverse problems involving multiscale elliptic partial differential equations. Our method is based on numerical homogenization and finite element discretization and…
We study the parameterized complexity of the graph isomorphism problem when parameterized by width parameters related to tree decompositions. We apply the following technique to obtain fixed-parameter tractability for such parameters. We…
A reconstruction algorithm for unfolding the neutron energy spectrum has been developed based on the potential reduction interior point. This algorithm can be easily applied to the neutron energy spectrum reconstruction in the recoil proton…
Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer…
The nonlinear Fourier transform (NLFT) extends the classical Fourier transform by replacing addition with matrix multiplication. While the NLFT on $\mathrm{SU}(1,1)$ has been widely studied, its $\mathrm{SU}(2)$ variant has only recently…
Many interesting computational problems can be reformulated in terms of decision trees. A natural classical algorithm is to then run a random walk on the tree, starting at the root, to see if the tree contains a node n levels from the root.…