Related papers: Continuous Unitary Transformations
The one-way measurement model is a framework for universal quantum computation, in which algorithms are partially described by a graph G of entanglement relations on a collection of qubits. A sufficient condition for an algorithm to perform…
In this paper we will present some alternative types of discretization methods (discrete approximation) for the fractional-order (FO) differentiator and their application to the FO dynamical system described by the FO differential equation…
Stochastic differential equations for processes with values in Hilbert spaces are now largely used in the quantum theory of open systems. In this work we present a class of such equations and discuss their main properties; moreover, we…
The general conditions under which the quadratic, uniform and monotonic convergence in the quasilinearization method of solving nonlinear ordinary differential equations could be proved are formulated and elaborated. The generalization of…
A method of representation of a solution as segments of the series in powers of the step of the independent variable is expanded for solving complex systems of ordinary differential equations (ODE): the Lorenz system and other systems. A…
Motivated by the contemporary advances in quantum implementation of non-unitary operations, we propose a new dilation method based on the biorthogonal representation of the non-unitary operator, mapping it to an isomorphic unitary matrix in…
This work introduces a Hamiltonian approach to regularization and linearization of central-force particle dynamics through a new canonical extension of the so-called "projective decomposition". The regularization scheme is formulated within…
We demonstrate the use of the Unified Transform Method or Method of Fokas for boundary value problems for systems of constant-coefficient linear partial differential equations. We discuss how the apparent branch singularities typically…
This paper addresses the problems of disparity and optical flow partitioning based on the brightness invariance assumption. We investigate new variational approaches to these problems with Potts priors and possibly box constraints. For the…
Continuous normalizing flows (CNFs) construct invertible mappings between an arbitrary complex distribution and an isotropic Gaussian distribution using Neural Ordinary Differential Equations (neural ODEs). It has not been tractable on…
Log-homotopy particle flow filters realize nonlinear Bayesian estimation by continuously migrating samples from the prior to the posterior distribution. This transport is governed by a pseudo-time ordinary differential equation (ODE). A…
In this article I present a fast and direct method for solving several types of linear finite difference equations (FDE) with constant coefficients. The method is based on a polynomial form of the translation operator and its inverse, and…
The nonlinear Fourier transform, which is also known as the forward scattering transform, decomposes a periodic signal into nonlinearly interacting waves. In contrast to the common Fourier transform, these waves no longer have to be…
Neural ordinary differential equations describe how values change in time. This is the reason why they gained importance in modeling sequential data, especially when the observations are made at irregular intervals. In this paper we propose…
We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the…
We introduce stochastic normalizing flows, an extension of continuous normalizing flows for maximum likelihood estimation and variational inference (VI) using stochastic differential equations (SDEs). Using the theory of rough paths, the…
Motivated by the viewpoint of integrable systems, we study commuting flows of 2-component quasilinear equations, reducing to investigate the solutions of the wave equation with non-constant speed. In this paper, we apply the reduction…
Based on the concept of manifold valued generalized functions we initiate a study of nonlinear ordinary differential equations with singular (in particular: distributional) right hand sides in a global setting. After establishing several…
By means of the continuous unitary transformation similar to a general scheme of the Renormalization Group (RG) procedure we study the issue of symmetry breaking and pairing instability in the system of interacting fermions. Constructing a…
The problem of diagonalization of Hamiltonians of N-dimensional boson systems by means of time-dependent canonical transformations (CT) is considered, the case of quadratic Hamiltonians being treated in greater detail. The unitary generator…