Related papers: Localized density matrix minimization and linear s…
We study a regularization framework that combines a convex fidelity term with multiple $\ell_1$-based regularizers, each linked to a distinct linear transform. This multi-penalty model enhances flexibility in promoting structured sparsity.…
Exact diagonalization is a powerful numerical method to study isolated quantum many-body systems. This paper provides a review of numerical algorithms to diagonalize the Hamiltonian matrix. Symmetry and the conservation law help us perform…
We develop and analyze a set of new sequential simulation-optimization algorithms for large-scale multi-dimensional discrete optimization via simulation problems with a convexity structure. The "large-scale" notion refers to that the…
Decentralized optimization for non-convex problems are now demanding by many emerging applications (e.g., smart grids, smart building, etc.). Though dramatic progress has been achieved in convex problems, the results for non-convex cases,…
This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of…
The problem of the logarithmic discretization of an arbitrary positive function (such as the density of states) is studied in general terms. Logarithmic discretization has arbitrary high resolution around some chosen point (such as Fermi…
In this paper, we study extended linear regression approaches for quantum state tomography based on regularization techniques. For unknown quantum states represented by density matrices, performing measurements under certain basis yields…
A random matrix theory approach is applied in order to analyze the localization properties of local spectral density for a generic system of coupled quantum states with strong static imperfection in the unperturbed energy levels. The system…
Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…
We consider adaptive system identification problems with convex constraints and propose a family of regularized Least-Mean-Square (LMS) algorithms. We show that with a properly selected regularization parameter the regularized LMS provably…
Majorization-minimization algorithms consist of iteratively minimizing a majorizing surrogate of an objective function. Because of its simplicity and its wide applicability, this principle has been very popular in statistics and in signal…
We describe recent progress in developing practical ab initio methods for which the computer effort is proportional to the number of atoms: linear scaling or O(N) methods. It is shown that the locality property of the density matrix gives a…
We propose a density matrix renormalization group (DMRG) technique at finite temperatures. As is the case of the ground state DMRG, we use a single-target state that is calculated by making use of a regulated polynomial expansion. Both…
This paper is concerned with a priori error estimates for the local incremental minimization scheme, which is an implicit time discretization method for the approximation of rate-independent systems with non-convex energies. We first show…
Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical…
We consider the problem of approximating an affinely structured matrix, for example a Hankel matrix, by a low-rank matrix with the same structure. This problem occurs in system identification, signal processing and computer algebra, among…
We introduce an approach to compute reduced density matrices for local quantum unitary circuits of finite depth and infinite width. Suppose the time-evolved state under the circuit is a matrix-product state with bond dimension $D$; then the…
Quantum magnetism in low dimensions has been one of the central areas of theoretical research for many decades now. One of the key reasons for the long standing interest in this field has been the existence of simplified models, which serve…
It has proved difficult to extend the density matrix renormalization group technique to large two-dimensional systems. In this Communication I present a novel approach where the calculation is done directly in two dimensions. This makes it…
Linear regression is a widely used technique to fit linear models and finds widespread applications across different areas such as machine learning and statistics. In most real-world scenarios, however, linear regression problems are often…