Quantum state tomography is a key technique for quantum information processing but challenging due to the exponential growth of its complexity with system size. In this work we propose an algorithm which iteratively finds best non-negative matrix product approximation based on set measurement outcomes whose size does not necessarily grow exponentially. Compared method neural network states, our...

Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In t...

Precomputed Radiance Transfer (PRT) aims at computing global illumination effects such as soft shadows and object interreflection in realtime. This is accomplished by precomputing the factors of the Rendering Equation and projecting them into a suitable basis which allows to combine them efficiently at runtime. Several basis function have been proposed for PRT. Recently, Haar wavelets have been...

Abstract. This note presents some equalities in law for ZN := det(Id− G), where G is an element of a subgroup of the set of unitary matrices of size N , endowed with its unique probability Haar measure. Indeed, under some general conditions, ZN can be decomposed as a product of independent random variables, whose laws are explicitly known. Our results can be obtained in two ways : either by a r...

A new way to discretize the filtered back-projection (FBP) algorithm is presented. The function basis is the Haar system (2D product of rectangular windows). This scheme allows one to derive the optimal shape of the apodisation window, which is angle varying, and the oversampling ratio between the pixel and the projection cell size. The discrete equivalent filter is also derived. The comparison...

LetMn be a random n n unitary matrix with distribution given by Haar measure on the unitary group. Using explicit moment calculations, a general criterion is given for linear combinations of traces of powers of Mn to converge to a Gaussian limit as n ! 1. By Fourier analysis, this result leads to central limit theorems for the measure on the circle that places a unit mass at each of the eigenva...

This paper deals with the wavelet-based performance analysis of the safety barrier for use in a full-scale test. The test involves a vehicle, a Ford Fiesta, which strikes the safety barrier at a prescribed angle and speed. The vehicle speed before the collision was measured. Vehicle accelerations in three directions at the centre of gravity were measured during the collision. The yaw rate was m...

Abstract—The system is designed to show images which are related to the query image. Extracting color, texture, and shape features from an image plays a vital role in content-based image retrieval (CBIR). Initially RGB image is converted into HSV color space due to its perceptual uniformity. From the HSV image, Color features are extracted using block color histogram, texture features using Haa...