Related papers: Parameterizing density operators with arbitrary sy…
Estimation of quantum states is one of the most important steps in any quantum information processing experiment. A naive reconstruction of the density matrix from experimental measurements can often give density matrices which are not…
We give an exact solution to the nonlinear optimization problem of approximating a Hermitian matrix by positive semi-definite matrices. Our algorithm was then used to judge whether a quantum state is entangled or not. We show that the exact…
Maximizing the precision in estimating parameters in a quantum system subject to instrumentation constraints is cast as a convex optimization problem. We account for prior knowledge about the parameter range by developing a worst-case and…
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…
We address a broad class of optimization problems of finding quantum measurements, which includes the problems of finding an optimal measurement in the Bayes criterion and a measurement maximizing the average success probability with a…
We develop a density matrix renormalization group (DMRG) algorithm for constrained quantum lattice models that successfully {\it{implements the local constraints as symmetries in the contraction of the matrix product states and matrix…
Constraining Beyond the Standard Model theories usually involves scanning highly multi-dimensional parameter spaces and check observable predictions against experimental bounds and theoretical constraints. Such task is often timely and…
Quantum state tomography aims to determine the state of a quantum system as represented by a density matrix. It is a fundamental task in modern scientific studies involving quantum systems. In this paper, we study estimation of…
We provide an efficient method for computing the maximum likelihood mixed quantum state (with density matrix $\rho$) given a set of measurement outcome in a complete orthonormal operator basis subject to Gaussian noise. Our method works by…
This paper studies the parameter tuning problem of positive linear systems for optimizing their stability properties. We specifically show that, under certain regularity assumptions on the parametrization, the problem of finding the…
Path integral techniques for the density matrix of a one-dimensional statistical system near a boundary previously employed in black-hole physics are applied to providing a new interpretation of the density matrix renormalization group: its…
Variational quantum algorithms use non-convex optimization methods to find the optimal parameters for a parametrized quantum circuit in order to solve a computational problem. The choice of the circuit ansatz, which consists of…
In this survey the possible approaches to the description of the evolution of states of quantum many-particle systems by means of the possible modifications of the density operator which kernel known as density matrix are considered. In…
Any given density matrix can be represented as an infinite number of ensembles of pure states. This leads to the natural question of how to uniquely select one out of the many, apparently equally suitable, possibilities. Following Jaynes'…
Quantum state tomography provides a fundamental framework for reconstructing quantum states. When the measurement data are not informationally complete, the observed statistics admit multiple compatible density matrices, making the…
A characterization of the general linear equation in standard form admitting a maximal symmetry algebra is obtained in terms of a simple set of conditions relating the coefficients of the equation. As a consequence, it is shown that in its…
A system of PDE describing bilayers amphiphilic membranes is studied by Lie group analysis. This algorithmic approach allows us to show all the symmetries of the system, to determine all possible symmetry reductions, to recover the…
Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…
This paper is a study of the Lie groups of point symmetries admitted by a system describing a non-stationary planar flow of an ideal plastic material. For several types of forces involved in the system, the infinitesimal generators which…
The density matrix renormalization group (DMRG) algorithm was originally designed to efficiently compute the zero temperature or ground-state properties of one dimensional strongly correlated quantum systems. The development of the…