Related papers: Advantages in Choosing Real Generators for SU(N)
We reduce the problem of integer quantum Hall transition to a random rotation of an N-dimensional vector by an su(N) algebra, where only N specially selected generators of the algebra are nonzero. The group-theoretical structure revealed in…
Quantum kernel methods offer significant theoretical benefits by rendering classically inseparable features separable in quantum space. Yet, the practical application of Quantum Machine Learning (QML), currently constrained by the…
We present a general construction of pseudo-hermitian matrices in an arbitrary large, but finite dimensional vector space. The positive-definite metric which ensures reality of the entire spectra of a pseudo-hermitian operator, and is used…
As the quantum computing community gravitates towards understanding the practical benefits of quantum computers, having a clear definition and evaluation scheme for assessing practical quantum advantage in the context of specific…
The generators of the algebra $gl_{n+1}$ in a form of differential operators of the first order acting on ${\bf R}^n$ with matrix coefficients are explicitly written. The algebraic Hamiltonians for a matrix generalization of $3-$body…
We give an algorithm for computing matrix corepresentations for special linear and special unitary quantum groups using a combinatorial re-indexing of basis elements.
We present experimental results on the effects of using quantum or 'truly' random numbers, as opposed to pseudorandom numbers, in a system that exhibits computational creativity (given its ability to compose original chess problems). The…
Generators of the quantum $SU_q(2)$ algebra are obtained in the explicit form in the basis where the operator $\exp {J_z\over 2} J_x \exp {J_z\over 2}$ is diagonal. It is shown that the solution of this problem is related to the…
Field-theoretic models for fields taking values in quantum groups are investigated. First we consider $SU_q(2)$ $\sigma$ model ($q$ real) expressed in terms of basic notions of noncommutative differential geometry. We discuss the case in…
This paper collects miscellaneous results about the group SU(1,1) that are helpful in applications in quantum optics. Moreover, we derive two new results, the first is about the approximability of SU(1,1) elements by a finite set of…
We obtain a presentation of Schur algebras (and q-Schur algebras) by generators and relations which is compatible with the usual presentation of the enveloping algebra (quantized enveloping algebra) corresponding to the Lie algebra gl(n) of…
Quantum generative modeling is a growing area of interest for industry-relevant applications. With the field still in its infancy, there are many competing techniques. This work is an attempt to systematically compare a broad range of these…
The problem of construction of irreducible representations of quantum $A^q_n$ algebras is solved at the level of explicit integration of the linear (inhomogeneous) system in finite differences in the n-dimensional space. The general…
Type A N-fold supersymmetry of one-dimensional quantum mechanics can be constructed by using sl(2) generators represented on a finite dimensional functional space. Using this sl(2) formalism we show a general method of constructing Type A…
In this paper we present experiments in order to show how some pseudo random number generators can improve the effectiveness of a statistical cryptanalysis algorithm. We deduce mainly that a better generator enhance the accuracy of the…
Quantum random sampling is the leading proposal for demonstrating a computational advantage of quantum computers over classical computers. Recently, first large-scale implementations of quantum random sampling have arguably surpassed the…
Demonstrating quantum advantage in machine learning tasks requires navigating a complex landscape of proposed models and algorithms. To bring clarity to this search, we introduce a framework that connects the structure of parametrized…
A new set of polynomial states (to be called character states) are derived for $Sp(4)$ reduced to its $SU(2) \times U(1)$ subgroup, and the relevant generator matrix elements are evaluated for generic representations $(a,b)$ of $Sp(4)$.…
We analyze the structure of the group of (local) non-linear canonical transformations that exist in a system with n fermionic modes. To perform our study we develop an alternative framework to represent the generators of these canonical…
We construct a special principal series representation for the modular double $U_{q\tilde{q}}(g_R)$ of type $A_r$ representing the generators by positive essentially self-adjoint operators satisfying the transcendental relations that also…