Related papers: Decomposing Finite Abelian Groups
A geometrical approach to quantum computation is presented, where a non-abelian connection is introduced in order to rewrite the evolution operator of an energy degenerate system as a holonomic unitary. For a simple geometrical model we…
We give an algorithm for solving equations and inequations with rational constraints in virtually free groups. Our algorithm is based on Rips classification of measured band complexes. Using canonical representatives, we deduce an algorithm…
In this paper, we introduce a new function related to the sum of element orders of finite groups. It is used to give some criteria for a finite group to be cyclic, abelian, nilpotent, supersolvable and solvable, respectively.
The question of computing the group complexity of finite semigroups and automata was first posed in K. Krohn and J. Rhodes, \textit{Complexity of finite semigroups}, Annals of Mathematics (2) \textbf{88} (1968), 128--160, motivated by the…
In this paper, we give a detailed account of the algorithm outlined in [1] for Feynman integral reduction and $\varepsilon$-factorised differential equations. The algorithm consists of two steps. In the first step, we use a new geometric…
The Gauss decomposition of quantum groups and supergroups are considered. The main attention is paid to the R-matrix formulation of the Gauss decomposition and its properties as well as its relation to the contraction procedure. Duality…
The affine Grassmannian is a noncompact smooth manifold that parameterizes all affine subspaces of a fixed dimension. It is a natural generalization of Euclidean space, points being zero-dimensional affine subspaces. We will realize the…
This paper is an attempt to solve an important class of hypersingular integral equations of the second kind. To this end, we apply a new weighted and modified perturbation method which includes some special cases of the Adomian…
We give a survey of the theory of finite quantum groupoids (weak Hopf algebras), including foundations of the theory and applications to finite depth subfactors, dynamical deformations of quantum groups, and invariants of knots and…
This is a survey on the state-of-the-art of the classification of finite-dimensional complex Hopf algebras. This general question is addressed through the consideration of different classes of such Hopf algebras. Pointed Hopf algebras…
The quantum algorithms of Deutsch, Simon and Shor are described in a way which highlights their dependence on the Fourier transform. The general construction of the Fourier transform on an Abelian group is outlined and this provides a…
In this paper we apply decomposition to orbifolds with quantum symmetries to resolve anomalies. Briefly, it has been argued by e.g. Wang-Wen-Witten, Tachikawa that an anomalous orbifold can sometimes be resolved by enlarging the orbifold…
The quantum Fourier transform (QFT) has emerged as the primary tool in quantum algorithms which achieve exponential advantage over classical computation and lies at the heart of the solution to the abelian hidden subgroup problem, of which…
We introduce a notion of a group-partition for a finite Abelian group, which is a generalized notion of the standard partition. To obtain asymptoticdistributions of group-partition, we study the Dirichlet series for group-partitions by…
This work presents a precise connection between Clifford circuits, Shor's factoring algorithm and several other famous quantum algorithms with exponential quantum speed-ups for solving Abelian hidden subgroup problems. We show that all…
Feynman's prescription for a quantum simulator was to find a hamitonian for a system that could serve as a computer. P\'olya and Hilbert conjecture was to demonstrate Riemann's hypothesis through the spectral decomposition of hermitian…
Renormalization group procedure for effective particles (RGPEP) is applied in terms of a second-order perturbative computation to an Abelian gauge theory, as an example of application worth studying on the way toward derivation of a…
A polynomial-time algorithm is produced which, given generators for a group of permutations on a finite set, returns a direct product decomposition of the group into directly indecomposable subgroups. The process uses bilinear maps and…
Recently, we have endowed various categories of groups with topologies. The purpose of this paper is to introduce on these categories others topologies which are statistically more suitable to study well-known problems in groups theory. We…
Hidden Subgroup Problem(HSP) seeks to identify an unknown subgroup H of a group G for a given injective function f defined on cosets of H. Here we present an initialization-free quantum algorithm for solving HSP in the case where G is a…