Related papers: Space Reduction in Matrix Product State
An extension of the the density matrix renormalization group (DMRG) method is presented. Besides the two groups or classes of block states considered in White's formulation, the retained $m$ states and the neglected ones, we introduce an…
In multiparametric programming an optimization problem which is dependent on a parameter vector is solved parametrically. In control, multiparametric quadratic programming (mp-QP) problems have become increasingly important since the…
We consider the problem of noisy matrix completion, in which the goal is to reconstruct a structured matrix whose entries are partially observed in noise. Standard approaches to this underdetermined inverse problem are based on assuming…
We investigate the relation between static correlation functions in the ground state of local quantum many-body Hamiltonians and the dispersion relations of the corresponding low energy excitations using the formalism of tensor network…
The study of tensor network theory is an important field and promises a wide range of experimental and quantum information theoretical applications. Matrix product state is the most well-known example of tensor network states, which…
We determine the computational difficulty of finding ground states of one-dimensional (1D) Hamiltonians which are known to be Matrix Product States (MPS). To this end, we construct a class of 1D frustration free Hamiltonians with unique MPS…
Modern approaches to generative modeling of continuous data using tensor networks incorporate compression layers to capture the most meaningful features of high-dimensional inputs. These methods, however, rely on traditional Matrix Product…
A fast algorithm for the approximate multiplication of matrices with decay is introduced; the Sparse Approximate Matrix Multiply (SpAMM) reduces complexity in the product space, a different approach from current methods that economize…
The estimation of the density matrix of a $k$-level quantum system is studied when the parametrization is given by the real and imaginary part of the entries and they are estimated by independent measurements. It is established that the…
We study the basic problem of robust subspace recovery. That is, we assume a data set that some of its points are sampled around a fixed subspace and the rest of them are spread in the whole ambient space, and we aim to recover the fixed…
In this paper, we study the problem of approximately computing the product of two real matrices. In particular, we analyze a dimensionality-reduction-based approximation algorithm due to Sarlos [1], introducing the notion of nuclear rank as…
Low-rank matrix factorizations are a class of linear models widely used in various fields such as machine learning, signal processing, and data analysis. These models approximate a matrix as the product of two smaller matrices, where the…
We introduce a structured low rank matrix completion algorithm to recover a series of images from their under-sampled measurements, where the signal along the parameter dimension at every pixel is described by a linear combination of…
Images suffer from heavy spatial redundancy because pixels in neighboring regions are spatially correlated. Existing approaches strive to overcome this limitation by reducing less meaningful image regions. However, current leading methods…
We use projection methods to construct (global) quantum states with prescribed reduced (marginal) states, and possibly with some special properties such as having specific eigenvalues, having specific rank and extreme von Neumann or Renyi…
This paper introduces matrix product state (MPS) decomposition as a computational tool for extracting features of multidimensional data represented by higher-order tensors. Regardless of tensor order, MPS extracts its relevant features to…
The problem of recovering a matrix of low rank from an incomplete and possibly noisy set of linear measurements arises in a number of areas. In order to derive rigorous recovery results, the measurement map is usually modeled…
Recent developments in engineering techniques for spatial data collection such as geographic information systems have resulted in an increasing need for methods to analyze large spatial data sets. These sorts of data sets can be found in…
This paper addresses the problem of low-rank distance matrix completion. This problem amounts to recover the missing entries of a distance matrix when the dimension of the data embedding space is possibly unknown but small compared to the…
We extend our study of Motion Planning via Manifold Samples (MMS), a general algorithmic framework that combines geometric methods for the exact and complete analysis of low-dimensional configuration spaces with sampling-based approaches…