相关论文: Higher order singular value decomposition and the …

This paper proposes a method for set-valued state estimation of nonlinear, discrete-time systems. This is achieved by combining graphs of functions representing system dynamics and measurements with the hybrid zonotope set representation…

Higher Order Topological Insulators (HOTI) are $d$-spatial dimensional systems featuring topologically protected gap-less states at their $(d-n)$-dimensional boundaries. With the help of \textit{ab-initio} calculations and tight binding…

We report the derivation and implementation of orbital optimization algorithms for the active space decomposition (ASD) model, which are extensions of complete active space self-consistent field (CASSCF) and its occupation-restricted…

Exploring novel topological matters with exotic quantum states has always been a core issue in the field of condensed matter physics, which can update the understanding of topological phases and broaden the classification of topological…

For the 3-qubit UPB state, i.e., the bound entangled state constructed from an Unextendable Product Basis of Bennett et al. (Phys. Rev. Lett. 82:5385, 1999), we provide a set of violations of Local Hidden Variable (LHV) models based on the…

Given an approximation to a multiple isolated solution of a polynomial system of equations, we have provided a symbolic-numeric deflation algorithm to restore the quadratic convergence of Newton's method. Using first-order derivatives of…

A well known result from functional analysis states that any compact operator between Hilbert spaces admits a singular value decomposition (SVD). This decomposition is a powerful tool that is the workhorse of many methods both in…

This article applies low-cost singular value decomposition (lcSVD) for the first time, to the authors knowledge, on combustion reactive flow databases. The lcSVD algorithm is a novel approach to SVD, suitable for calculating high-resolution…

We devise and evaluate numerically a Hybrid High-Order (HHO) method for incremental associative plasticity with small deformations. The HHO method uses as discrete unknowns piecewise polynomials of order $k\ge1$ on the mesh skeleton,…

The tensor Singular Value Decomposition (t-SVD) for third order tensors that was proposed by Kilmer and Martin~\cite{2011kilmer} has been applied successfully in many fields, such as computed tomography, facial recognition, and video…

We propose a state-specific orbital optimization scheme for improving the accuracy of excited states of the electronic structure Hamiltonian for the use on near-term quantum computers, which can be combined with any overlap-based…

Six-qubit cluster states built on the simultaneous entanglement of two photons in three independent degrees of freedom, i.e. polarization and a double longitudinal momentum, have been recently demonstrated. We present here the peculiar…

Quantum singular value transformation (QSVT) enables the application of polynomial functions to the singular values of near arbitrary linear operators embedded in unitary transforms, and has been used to unify, simplify, and improve most…

We propose a mixed precision Jacobi algorithm for computing the singular value decomposition (SVD) of a dense matrix. After appropriate preconditioning, the proposed algorithm computes the SVD in a lower precision as an initial guess, and…

This article introduces a novel methodology that integrates singular value decomposition (SVD) with a shallow linear neural network for forecasting high resolution fluid mechanics data. The method, termed LC-SVD-DLinear, combines a low-cost…

We demonstrate a new method that yields orders-of-magnitude acceleration in inverse design (e.g. topology optimization) of high-$Q$ resonant cavities to maximize the local density of states (LDOS), and which is also applicable to other…

Quantum state tomography via local measurements is an efficient tool for characterizing quantum states. However it requires that the original global state be uniquely determined (UD) by its local reduced density matrices (RDMs). In this…

Increasing demand for practical applications is forcing deeper research into optical vortices (OVs): from the generation and measurement to shaping and multiple singularities manipulation of OVs. Herein, we propose a new type of phase…

We propose a novel variant of the Localized Orthogonal Decomposition (LOD) method for time-harmonic scattering problems of Helmholtz type with high wavenumber $\kappa$. On a coarse mesh of width $H$, the proposed method identifies local…

Higher-order topological insulators (HOTIs) have attracted much attention in photonics due to the tightly localized disorder-robust corner and hinge states. Here, we reveal an unconventional HOTI phase with vanishing dipole and quadrupole…