Related papers: Spectral parameterization for the power sums of qu…
First some old as well as new results about P.I. algebras, Ore extensions, and degrees are presented. Then quantized $n\times r$ matrices as well as quantized factor algebras of $M_q(n)$ are analyzed. The latter are the quantized function…
The quantum singular value transformation has revolutionised quantum algorithms. By applying a polynomial to an arbitrary matrix, it provides a unifying picture of quantum algorithms. However, polynomials are restricted to definite parity…
In the present paper we are dealing with reflection equation algebras ${\cal L}(R)$ corresponding to even skew-invertible Hecke symmetries. Our main result consists in computing the characters of the spectral values of the generating matrix…
The classical Cayley-Hamilton identities are generalized to quantum matrix algebras of the GL(m|n) type.
Turull has described the fields of values for characters of $SL_n(q)$ in terms of the parametrization of the characters of $GL_n(q)$. In this article, we extend these results to the case of $SU_n(q)$.
We obtain sequences of inclusion sets for the spectrum, essential spectrum, and pseudospectrum of banded, in general non-normal, matrices of finite or infinite size. Each inclusion set is the union of the pseudospectra of certain…
In this manuscript, a parametrization of positive matrices together with some of its many applications in quantum information theory is given.
We propose new quantum algorithms for estimating spectral sums of positive semi-definite (PSD) matrices. The spectral sum of an PSD matrix $A$, for a function $f$, is defined as $ \text{Tr}[f(A)] = \sum_j f(\lambda_j)$, where $\lambda_j$…
We show that a quantum super matrix in standard format is invertible if and only if its block matrices of even entries are invertible. We prove the q-analog of the well-known formula for the Berezinian.
In this note, we present a generalization of some results concerning the spectral properties of a certain class of block matrices. As applications, we study some of its implications on nonnegative matrices, doubly stochastic matrices and…
Quantum light is described not only by a quantum state but also by the shape of the electromagnetic modes on which the state is defined. Optical precision measurements often estimate a ``mode parameter'' that determines properties such as…
We use renormalization group summed perturbation theory (RGSPT) to improve perturbation series in quantum chromodynamics in the determination of some of the standard model parameters.
The characteristic identity formalism discussed in our recent articles is further utilized to derive matrix elements of type 2 unitary irreducible $gl(m|n)$ modules. In particular, we give matrix element formulae for all gl(m|n) generators,…
We give an algorithm for computing matrix corepresentations for special linear and special unitary quantum groups using a combinatorial re-indexing of basis elements.
The supersymmetric standard model with supergravity-inspired soft breaking terms predicts a rich pectrum of sparticles to be discovered at the SSC, LHC and NLC. Because there are more supersymmetric particles than unknown parameters, one…
In this paper, we consider the parameterized quantum query complexity for graph problems. We design parameterized quantum query algorithms for $k$-vertex cover and $k$-matching problems, and present lower bounds on the parameterized quantum…
In the overview, a generic mathematical object (mapping) is introduced, and its relation to model physics parameterization is explained. Machine learning (ML) tools that can be used to emulate and/or approximate mappings are introduced.…
We give the characteristic polynomial of the distance or adjacency matrix of the strong power graph of a finite group, and compute its distance and adjacency spectrum.
Full generalization of Kasner metric for the case of $n+1$ dimensions and $m\le n+1$ essential variables is obtained. Any solution is defined by the corresponding constant matrix of Kasner parameters. This parameters form in euclidian space…
The formalism of Supersymmetric Quantum Mechanics provides us the eigenfunctions to be used in the variational mathod to obtain the eigenvalues for the Hulth\'en Potential.