Related papers: Algorithmic constructions of unitary matrices and …

In a recent paper, an algorithm has been presented for determining implications between a particular kind of category theoretic property represented by matrices -- the so called `matrix properties'. In this paper we extend this algorithm to…

The problem of constructing maximal equiangular tight frames or SICs was raised by Zauner in 1998. Four years ago it was realized that the problem is closely connected to a major open problem in number theory. We discuss why such a…

Unknown unitary inversion is a fundamental primitive in quantum computing and physics. Although recent work has demonstrated that quantum algorithms can invert arbitrary unknown unitaries without accessing their classical descriptions,…

We present further properties of a previously proposed recursive scheme for parameterisation of n-by-n unitary matrices. We show that the factors in the recursive formula may be introduced in any desired order. The method is used to study…

Wavelet frames for $L^2({\mathbb R})$ can be characterized by means of spectral techniques. This work uses spectral formulas to determine all the tight wavelet frames for $L^2({\mathbb R})$ with a fixed finite number of generators of…

Random matrices now play a role in many parts of computational mathematics. To advance these applications, it is desirable to have tools that are flexible, easy to use, and powerful. Over the last 25 years, researchers have developed a…

Given a quantum algorithm, it is highly nontrivial to devise an efficient sequence of physical gates implementing the algorithm on real hardware and incorporating topological quantum error correction. In this paper, we present a first step…

We show that much of the theory of finite tight frames can be generalised to vector spaces over the quaternions. This includes the variational characterisation, group frames, and the characterisations of projective and unitary equivalence.…

As a generalization of orthonormal wavelets in $L_2(R)$, tight framelets (also called tight wavelet frames) are of importance in wavelet analysis and applied sciences due to their many desirable properties in applications such as image…

We will show that tight frames satisfying the restricted isometry property give rise to nearly tight fusion frames which are nearly orthogonal and hence are nearly equi-isoclinic. We will also show how to replace parts of the RIP frame with…

Coupled matrix and tensor factorizations (CMTF) are frequently used to jointly analyze data from multiple sources, also called data fusion. However, different characteristics of datasets stemming from multiple sources pose many challenges…

Inspired by previous work of Shoup, Lenstra-De Smit and Couveignes-Lercier, we give fast algorithms to compute in (the first levels of) the ell-adic closure of a finite field. In many cases, our algorithms have quasi-linear complexity.

This paper is dedicated to the problem of verification of matrices for unitary similarity. For the case of nonderogatory matrices, we have been able to present the new solution for this problem based on geometric approach. The main…

Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which…

Since simulating quantum computers requires exponentially more classical resources, efficient algorithms are extremely helpful. We analyze algorithms that create single qubit and specific controlled qubit matrix representations of gates.…

The evolution of previous Click-Through Rate (CTR) models has mainly been driven by proposing complex components, whether shallow or deep, that are adept at modeling feature interactions. However, there has been less focus on improving…

Girth-regular graphs with equal girth, regular degree and chromatic index are studied for the determination of 1-factorizations with each 1-factor intersecting every girth cycle. Applications to hamiltonian decomposability and to…

In order to solve the problem of non-ideal training sets (i.e., the less-complete or over-complete sets) and implement one-iteration learning, a novel efficient quantum perceptron algorithm based on unitary weights is proposed, where the…

We present a uniform methodology for computing with finitely generated matrix groups over any infinite field. As one application, we completely solve the problem of deciding finiteness in this class of groups. We also present an algorithm…

Bridging logical and algorithmic reasoning with modern machine learning techniques is a fundamental challenge with potentially transformative impact. On the algorithmic side, many NP-hard problems can be expressed as integer programs, in…