Related papers: Eigenvalue Distributions of Reduced Density Matric…
This paper aims to investigate the distributed stochastic optimization problems on compact embedded submanifolds (in the Euclidean space) for multi-agent network systems. To address the manifold structure, we propose a distributed…
Solving linear systems and computing eigenvalues are two fundamental problems in linear algebra. For solving linear systems, many efficient quantum algorithms have been discovered. For computing eigenvalues, currently, we have efficient…
Data which lie in the space $\mathcal{P}_{m\,}$, of $m \times m$ symmetric positive definite matrices, (sometimes called tensor data), play a fundamental role in applications including medical imaging, computer vision, and radar signal…
The eigenvalue density of a matrix plays an important role in various types of scientific computing such as electronic-structure calculations. In this paper, we propose a quantum algorithm for computing the eigenvalue density in a given…
We develop the basic theory of eigenvalues of $p$-adic random matrices, analogous to the classical theory for random matrices over $\mathbb{R}$ and $\mathbb{C}$. Such eigenvalue statistics were proposed as a model for the zeroes of $p$-adic…
The Gaussian and Laguerre orthogonal ensembles are fundamental to random matrix theory, and the marginal eigenvalue distributions are basic observable quantities. Notwithstanding a long history, a formulation providing high precision…
In this thesis we study the behavior of bipartite entanglement of a large quantum system, by analyzing the distribution of the Schmidt coefficients of the reduced density matrix. Applying the general methods of classical statistical…
New inequalities for tomographic probability distributions and density matrices of qutrit states are obtained by means of generalization of qubit portrait method. The approach based on the qudit portrait method to get new entropic…
We derive the hole probability and the distribution of the smallest eigenvalue of chiral hermitian random matrices corresponding to Dirac operators coupled to massive quarks in QCD. They are expressed in terms of the QCD partition function…
Conditional on the extended Riemann hypothesis, we show that with high probability, the characteristic polynomial of a random symmetric $\{\pm 1\}$-matrix is irreducible. This addresses a question raised by Eberhard in recent work. The main…
We suggest a method of studying the joint probability density (JPD) of an eigenvalue and the associated 'non-orthogonality overlap factor' (also known as the 'eigenvalue condition number') of the left and right eigenvectors for…
We propose a method for directly measuring the quantum mechanical pseudo-distribution of observable properties via its characteristic function. Vandermonde matrices of the eigenvalues play a central role in the theory. This proposal…
We propose a convex variational principle to find sparse representation of low-lying eigenspace of symmetric matrices. In the context of electronic structure calculation, this corresponds to a sparse density matrix minimization algorithm…
We study the Hilbert-Schmidt measure on the manifold of mixed Gaussian states in multi mode continuous variable quantum systems. An analytical expression for the Hilbert-Schmidt volume element is derived. Its corresponding probability…
We propose an adaptive random quantum algorithm to obtain an optimized eigensolver. Specifically, we introduce a general method to parametrize and optimize the probability density function of a random number generator, which is the core of…
We introduce a new Partition of Unity Method for the numerical homogenization of elliptic partial differential equations with arbitrarily rough coefficients. We do not restrict to a particular ansatz space or the existence of a finite…
It has been observed that the statistical distribution of the eigenvalues of random matrices possesses universal properties, independent of the probability law of the stochastic matrix. In this article we find the correlation functions of…
Complex Hermitian random matrices with a unitary symmetry can be distinguished by a weight function. When this is even, it is a known result that the distribution of the singular values can be decomposed as the superposition of two…
Non-Hermitian random matrices with statistical spectral characteristics beyond the standard Ginibre ensembles have recently emerged in the description of dissipative quantum many-body systems as well as in non-ergodic wave transport in…
Accurate computation of multiple eigenvalues of quantum Hamiltonians is essential in quantum chemistry, materials science, and molecular spectroscopy. Estimating excited-state energies is challenging for classical algorithms due to…