Related papers: Optimization of Fragment State Spaces within the E…
A method for deriving superintegrable Hamiltonians with a spin orbital interaction is presented. The method is applied to obtain a new superintegrable system in Euclidean space $\mathbb{E}_3$ with the following properties. It describes a…
A biorthonormal-block density-matrix renormalization group algorithm is proposed to accurately compute properties of large-scale non-Hermitian many-body systems, in which a renormalized-space partition of the non-Hermitian reduced density…
In this work we introduce and analyze a new multiscale method for strongly nonlinear monotone equations in the spirit of the Localized Orthogonal Decomposition. A problem-adapted multiscale space is constructed by solving linear local…
A variational formulation for accelerated optimization on normed vector spaces was recently introduced in Wibisono et al., and later generalized to the Riemannian manifold setting in Duruisseaux and Leok. This variational framework was…
We develop a density matrix renormalization group (DMRG) algorithm for constrained quantum lattice models that successfully {\it{implements the local constraints as symmetries in the contraction of the matrix product states and matrix…
The task of estimating the ground state of Hamiltonians is an important problem in physics with numerous applications ranging from solid-state physics to combinatorial optimization. We provide a hybrid quantum-classical algorithm for…
Training deep neural networks (DNNs) can be difficult due to the occurrence of vanishing/exploding gradients during weight optimization. To avoid this problem, we propose a class of DNNs stemming from the time discretization of Hamiltonian…
Photonic Ising Machines constitute an emergent new paradigm of computation, geared towards tackling combinatorial optimization problems that can be reduced to the problem of finding the ground state of an Ising model. Spatial Photonic Ising…
There has been recent interest in the deployment of ab initio density matrix renormalization group computations on high performance computing platforms. Here, we introduce a reformulation of the conventional distributed memory ab initio…
In this paper, we present a novel framework for deriving the evolution equation of the level set function in topology optimization, departing from conventional Hamilton-Jacobi based formulations. The key idea is the introduction of an…
The Lip-field approach is a new way to regularize softening material models. It has already been tested in 1D quasistatic and 2D quasistatic: this paper extends it to 1D dynamics, on the challenging problem of dynamic fragmentation. The…
The choice of molecular orbitals is decisive in configuration interaction calculations. In this letter, a democratic description of the ground and excited states follows an orthogonally constrained orbitals optimization to produce…
This paper is concerned with the inverse problem of reconstructing small and local perturbations of a planar surface using the field interaction between a known plasmonic particle and the planar surface. The aim is to perform a…
Variational quantum algorithms are promising applications of noisy intermediate-scale quantum (NISQ) computers. These algorithms consist of a number of separate prepare-and-measure experiments that estimate terms in a Hamiltonian. The…
In this article we study the possibilities of recovering the structure of port-Hamiltonian systems starting from ``unlabelled'' ordinary differential equations describing mechanical systems. The algorithm we suggest solves the problem in…
An effective Hamiltonian without symmetry restriction has been developed to model the rotational and fine structure of two nearly degenerate electronic states of an open-shell molecule. In addition to the rotational Hamiltonian for an…
In recent years, reduced basis methods (RBMs) have been adapted to the many-body eigenvalue problem and they have been used, largely in nuclear physics, as fast emulators able to bypass expensive direct computations while still providing…
This paper presents an adaptive discretization strategy for level set topology optimization of structures based on hierarchical B-splines. This work focuses on the influence of the discretization approach and the adaptation strategy on the…
A renormalization scheme for interacting fermionic systems is presented where the renormalization is carried out in terms of the fermionic degrees of freedom. The scheme is based on continuous unitary transformations of the hamiltonian…
This dissertation is devoted to provide advanced nonconvex nonsmooth variational models of (Magnetic Resonance Image) MRI reconstruction, efficient learnable image reconstruction algorithms and parameter training algorithms that improve the…