Related papers: Lower Bounds on Coherent State Rank
Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…
We obtain upper bounds, independent of the ambient dimension, for the number of realizable zero-nonzero patterns and (over ordered fields) sign conditions of a finite family of polynomials $\mathcal P$ restricted to an algebraic subset $V$…
This paper is concerned with the analysis of the randomized subspace iteration for the computation of low-rank approximations. We present three different kinds of bounds. First, we derive both bounds for the canonical angles between the…
Intuitively, if a density operator has small rank, then it should be easier to estimate from experimental data, since in this case only a few eigenvectors need to be learned. We prove two complementary results that confirm this intuition.…
Standard variational methods tend to obtain upper bounds on the ground state energy of quantum many-body systems. Here we study a complementary method that determines lower bounds on the ground state energy in a systematic fashion, scales…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
The existence of a polynomial pivot rule for the simplex method for linear programming, policy iteration for Markov decision processes, and strategy improvement for parity games each are prominent open problems in their respective fields.…
Matrix rank minimization problems are gaining a plenty of recent attention in both mathematical and engineering fields. This class of problems, arising in various and across-discipline applications, is known to be NP-hard in general. In…
This work studies low-rank approximation of a positive semidefinite matrix from partial entries via nonconvex optimization. We characterized how well local-minimum based low-rank factorization approximates a fixed positive semidefinite…
We introduce a reliable compressive procedure to uniquely characterize any given low-rank quantum measurement using a minimal set of probe states that is based solely on data collected from the unknown measurement itself. The procedure is…
We introduce coherent-state propagation, a computational framework for simulating bosonic systems. We focus on bosonic circuits composed of displaced linear optics augmented by Kerr nonlinearities, a universal model of bosonic quantum…
The approximate degree of a Boolean function f is the least degree of a real polynomial that approximates f pointwise to error at most 1/3. Approximate degree is known to be a lower bound on quantum query complexity. We resolve or nearly…
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 consider the Moment-SOS hierarchy in polynomial optimization. We first provide a sufficient condition to solve the truncated K-moment problem associated with a given degree-$2n$ pseudo-moment sequence $\phi$ n and a semi-algebraic set $K…
We analyze connections between two low rank modeling approaches from the last decade for treating dynamical data. The first one is the coherence problem (or coherent set approach), where groups of states are sought that evolve under the…
This paper is about minimum cost constrained selection of inputs and outputs for generic arbitrary pole placement. The input-output set is constrained in the sense that the set of states that each input can influence and the set of states…
Low-rank pseudoinverses are widely used to approximate matrix inverses in scalable machine learning, optimization, and scientific computing. However, real-world matrices are often observed with noise, arising from sampling, sketching, and…
The nonnegative rank of an entrywise nonnegative matrix A of size mxn is the smallest integer r such that A can be written as A=UV where U is mxr and V is rxn and U and V are both nonnegative. The nonnegative rank arises in different areas…
We consider the problem of minimising the number of states in a multiplicity tree automaton over the field of rational numbers. We give a minimisation algorithm that runs in polynomial time assuming unit-cost arithmetic. We also show that a…
Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of…