Related papers: Rank Reduction for the Local Consistency Problem
The quantum marginal problem asks what local spectra are consistent with a given spectrum of a joint state of a composite quantum system. This setting, also referred to as the question of the compatibility of local spectra, has several…
The low-rank approximation is a complexity reduction technique to approximate a tensor or a matrix with a reduced rank, which has been applied to the simulation of high dimensional problems to reduce the memory required and computational…
The classical low rank approximation problem is to find a rank $k$ matrix $UV$ (where $U$ has $k$ columns and $V$ has $k$ rows) that minimizes the Frobenius norm of $A - UV$. Although this problem can be solved efficiently, we study an…
It is a hard and important problem to find the criterion of the set of positive-definite matrixes which can be written as reduced density operators of a multi-partite quantum state. This problem is closely related to the study of many-body…
Matrix rank minimizing subject to affine constraints arises in many application areas, ranging from signal processing to machine learning. Nuclear norm is a convex relaxation for this problem which can recover the rank exactly under some…
We present a constructive solution to the N-representability problem---a full characterization of the conditions for constraining the two-electron reduced density matrix (2-RDM) to represent an N-electron density matrix. Previously known…
Minimization of the nuclear norm is often used as a surrogate, convex relaxation, for finding the minimum rank completion (recovery) of a partial matrix. The minimum nuclear norm problem can be solved as a trace minimization semidefinite…
We investigate the equivalence of quantum mixed states under local unitary transformations. For a class of rank-two mixed states, a sufficient and necessary condition of local equivalence is obtained by giving a complete set of invariants…
The challenge of taking many variables into account in optimization problems may be overcome under the hypothesis of low effective dimensionality. Then, the search of solutions can be reduced to the random embedding of a low dimensional…
Rank deficient Hankel matrices are at the core of several applications. However, in practice, the coefficients of these matrices are noisy due to e.g. measurements errors and computational errors, so generically the involved matrices are…
The (constrained) minimization of a ratio of set functions is a problem frequently occurring in clustering and community detection. As these optimization problems are typically NP-hard, one uses convex or spectral relaxations in practice.…
Low-rank and sparse composite approximation is a natural idea to compress Large Language Models (LLMs). However, such an idea faces two primary challenges that adversely affect the performance of existing methods. The first challenge…
Given a set of local dynamics, are they compatible with a global dynamics? We systematically formulate these questions as quantum channel marginal problems. These problems are strongly connected to the generalization of the no-signaling…
We present a random-subspace variant of cubic regularization algorithm that chooses the size of the subspace adaptively, based on the rank of the projected second derivative matrix. Iteratively, our variant only requires access to…
In this paper, we propose a novel approach to the rank minimization problem, termed rank residual constraint (RRC) model. Different from existing low-rank based approaches, such as the well-known nuclear norm minimization (NNM) and the…
In this paper, we propose a low-rank representation with symmetric constraint (LRRSC) method for robust subspace clustering. Given a collection of data points approximately drawn from multiple subspaces, the proposed technique can…
Complete characterization of a noisy multipartite quantum state in terms of entanglement requires full knowledge of how the entanglement content in the state is affected by the spatial distribution of noise in the state. Specifically, we…
Uncertainty quantification based on stochastic spectral methods suffers from the curse of dimensionality. This issue was mitigated recently by low-rank tensor methods. However, there exist two fundamental challenges in low-rank tensor-based…
In this paper, we develop a local rank correlation measure which quantifies the performance of dimension reduction methods. The local rank correlation is easily interpretable, and robust against the extreme skewness of nearest neighbor…
We introduce and study Minimum Cut Representability, a framework to solve optimization and feasibility problems over stable matchings by representing them as minimum s-t cut problems on digraphs over rotations. We provide necessary and…