Related papers: Comment on "A Recursive Parametrisation of Unitary…
Let $G$ be a Lie group, $\g$ its Lie algebra, and $U_h(\g)$ the corresponding quantum group. We consider some examples of $U_h(\g)$-invariant one and two parameter quantizations on $G$-manifolds.
We study the asymptotics of representations of a fixed compact Lie group. We prove that the limit behavior of a sequence of such representations can be described in terms of certain random matrices; in particular operations on…
Following the works by Lin et al. (Circuits Syst. Signal Process. 20(6): 601-618, 2001) and Liu et al. (Circuits Syst. Signal Process. 30(3): 553-566, 2011), we investigate how to factorize a class of multivariate polynomial matrices. The…
A problem of constructing quantum groups from classical r-matrices is discussed.
We show in this paper that, when properly rescaled in time and in space, the characteristic polynomial of a random unitary matrix converges almost surely to a random analytic function whose zeros, which are on the real line, form a…
We introduce unitary-gate randomized benchmarking (URB) for qudit gates by extending single-and multi-qubit URB to single- and multi-qudit gates. Specifically, we develop a qudit URB procedure that exploits unitary 2-designs. Furthermore,…
The problem of finding a canonical form of complex matrices up to conjugacy with the set of canonical matrices being a union of affine planes in the matrix space is considered. A solution of the problem is given producing a new canonical…
Finding the Lie-algebraic closure of a handful of matrices has important applications in quantum computing and quantum control. For most realistic cases, the closure cannot be determined analytically, necessitating an explicit numerical…
Multiparametric quantum deformations of $gl(2)$ are studied through a complete classification of $gl(2)$ Lie bialgebra structures. From them, the non-relativistic limit leading to harmonic oscillator Lie bialgebras is implemented by means…
In this paper, we consider characterisations of the class of unitary matrix integrals $\big\langle (\det U)^q {\rm e}^{s^{1/2} \operatorname{Tr}(U + U^\dagger)} \big\rangle_{U(l)}$ in terms of a first-order matrix linear differential…
In this paper, the author present a reliable symbolic computational algorithm for inverting a general comrade matrix by using parallel computing along with recursion. The computational cost of our algorithm is O(n^2). The algorithm is…
Results obtained by us are overviewed from a general set up. The universal $R$-matrix is exploited to obtain various important relations and structures involved in quantum group algebra, which are used subsequently for generating different…
Given a simple Lie algebra $\gggg$, we consider the orbits in $\gggg^*$ which are of R-matrix type, i.e., which possess a Poisson pencil generated by the Kirillov-Kostant-Souriau bracket and the so-called R-matrix bracket. We call an…
Recurrence formulae for arbitrary hydrogenic radial matrix elements are obtained in the Dirac form of relativistic quantum mechanics. Our approach is inspired on the relativistic extension of the second hypervirial method that has been…
The category $\cal{C}$ (studied by Andersen-Jantzen-Soergel) of representations of a Lusztig's small quantum group at a root of unity, together with its modular structure, is defined geometrically, using configuration spaces.
A novel algorithm for the recovery of low-rank matrices acquired via compressive linear measurements is proposed and analyzed. The algorithm, a variation on the iterative hard thresholding algorithm for low-rank recovery, is designed to…
We develop an efficient algorithm for sampling the eigenvalues of random matrices distributed according to the Haar measure over the orthogonal or unitary group. Our technique samples directly a factorization of the Hessenberg form of such…
The fractional quantization of singular systems with second order Lagrangian is examined. The fractional singular Lagrangian is presented. The equations of motion are written as total differential equations within fractional calculus. Also,…
Any technology requires precise benchmarking of its components, and the quantum technologies are no exception. Randomized benchmarking allows for the relatively resource economical estimation of the average gate fidelity of quantum gates…
Using the methods of quantisation ideals, we construct a family of quantisations corresponding to Case alpha in Sergeev's classification of solutions to the tetrahedron equation. This solution describes transformations between special…