Related papers: Error estimates for extrapolations with matrix-pro…
In spite of their intrinsic one-dimensional nature matrix product states have been systematically used to obtain remarkably accurate results for two-dimensional systems. Motivated by basic entropic arguments favoring projected…
We derive error bounds for CUR matrix approximation using determinant-based methods that relate local projection errors to global approximation quality. For general matrices, we establish determinant identities for bordered Gramian matrices…
We theoretically derive and validate with large scale simulations a remarkably accurate power law scaling of errors for the restricted active space density matrix renormalization group (DMRG-RAS) method [arXiv:2111.06665] in electronic…
Stochastic variance-reduced gradient (SVRG) algorithms have been shown to work favorably in solving large-scale learning problems. Despite the remarkable success, the stochastic gradient complexity of SVRG-type algorithms usually scales…
We demonstrate how to parallelize the density matrix renormalization group (DMRG) algorithm in real space through a straightforward modification of serial DMRG. This makes it possible to apply at least an order of magnitude more…
We improve a recently developed expansion technique for calculating real frequency spectral functions of any one-dimensional model with short-range interactions, by postprocessing computed Chebyshev moments with linear prediction. This can…
The density matrix renormalization group (DMRG) method introduced by White for the study of strongly interacting electron systems is reviewed; the method is variational and considers a system of localized electrons as the union of two…
Ground-state preparation is a fundamental task in quantum simulation, because the overlap of the prepared state with the true ground state significantly affects the overall cost of subsequent quantum algorithms. We propose a three-stage…
The 2-Higgs-Doublet Model (2HDM) belongs to the simplest extensions of the Standard Model (SM) Higgs sector that are in accordance with theoretical and experimental constraints. In order to be able to properly investigate the experimental…
A key property of many-body localization, the localization of quantum particles in systems with both quenched disorder and interactions, is the area law entanglement of even highly excited eigenstates of many-body localized Hamiltonians.…
We propose the Deep Distance Measurement Method (DDMM) to improve retrieval accuracy in unsupervised multivariate time series similarity retrieval. DDMM enables learning of minute differences within states in the entire time series and…
We give a thorough Biorthonormal Matrix-Product-State (BMPS) analysis of the Transfer-Matrix Renormalization-Group (TMRG) for non-Hermitian matrices in the thermodynamic limit. The BMPS is built on a dual series of reduced biorthonormal…
A celebrated method for Variational Inequalities (VIs) is Extragradient (EG), which can be viewed as a standard discrete-time integration scheme. With this view in mind, in this paper we show that EG may suffer from discretization bias when…
Motivated by the Kronecker product approximation technique, we have developed a very simple method to assess the inseparability of bipartite quantum systems, which is based on a realigned matrix constructed from the density matrix. For any…
Measurement error is a pervasive challenge across many disciplines, yet its impact on sample size determination and the accuracy and precision of estimators regarding the association between an exposure and an outcome remains understudied…
The Density Matrix Renormalization Group (DMRG) method scales exponentially in the system width for models in two dimensions, but remains one of the most powerful methods for studying 2D systems with a sign problem. Reviewing past…
Density Matrix Renormalization Group (DMRG) algorithm has been extremely successful for computing the ground states of one-dimensional quantum many-body systems. For problems concerned with mixed quantum states, however, it is less…
In this paper, we consider matrix completion with absolute deviation loss and obtain an estimator of the median matrix. Despite several appealing properties of median, the non-smooth absolute deviation loss leads to computational challenge…
This paper considers the low-observability state estimation problem in power distribution networks and develops a decentralized state estimation algorithm leveraging the matrix completion methodology. Matrix completion has been shown to be…
We characterize the squared prediction risk of ensemble estimators obtained through subagging (subsample bootstrap aggregating) regularized M-estimators and construct a consistent estimator for the risk. Specifically, we consider a…