Related papers: Random walk questions for linear quantum groups

Random walk on the set of irreducible representations of a finite group is investigated. For the symmetric and general linear groups, a sharp convergence rate bound is obtained and a cutoff phenomenon is proved. As related results, an…

In this paper we study convergence of random walks, on finite quantum groups, arising from linear combination of irreducible characters. We bound the distance to the Haar state and determine the asymptotic behavior, i.e. the limit state if…

We study the problem of convergence to the boundary in the setting of random walks on discrete quantum groups. Convergence to the boundary is established for random walks on $\hat{\textrm{SU}_q(2)}$. Furthermore, we will define the Martin…

A natural scheme is established for the approximation of quantum Levy processes on locally compact quantum groups by quantum random walks. We work in the somewhat broader context of discrete approximations of completely positive quantum…

In this paper we study continuous-time quantum walks on Cayley graphs of the symmetric group, and prove various facts concerning such walks that demonstrate significant differences from their classical analogues. In particular, we show that…

The concept of a random walk on a finite group converging to random - and a way of measuring the distance to random after $k$ transitions - is generalised from the classical case to the case of random walks on finite quantum groups. A…

Thoma's theorem states that a group algebra $C^*(\Gamma)$ is of type I if and only if $\Gamma$ is virtually abelian. We discuss here some similar questions for the quantum groups, our main result stating that, under suitable virtually…

Random walks on general graphs play an important role in the understanding of the general theory of stochastic processes. Beyond their fundamental interest in probability theory, they arise also as simple models of physical systems. A brief…

In the present paper, we study the continuous-time quantum walk on quotient graphs. On such graphs, there is a straightforward reduction of problem to a subspace that can be considerably smaller than the original one. Along the lines of…

We investigate the use of discrete-time quantum walks to sample from an almost-uniform distribution, in the absence of any external source of randomness. Integers are encoded on the vertices of a cycle graph, and a quantum walker evolves…

In quantum computation theory, quantum random walks have been utilized by many quantum search algorithms which provide improved performance over their classical counterparts. However, due to the importance of the quantum decoherence…

We address the question of symmetries of an important type of quantum walks. We introduce all the necessary definitions and provide a rigorous formulation of the problem. Using a thorough analysis, we reach the complete answer by presenting…

A classical construction associates to a transient random walk on a discrete group $\Gamma$ a compact $\Gamma$-space $\partial_M \Gamma$ known as the Martin boundary. The resulting crossed product $C^*$-algebra $C(\partial_M \Gamma)…

This paper presents a simple model that mimics quantum mechanics (QM) results in terms of probability fields of free particles subject to self-interference, without using Schr\"{o}dinger equation or wavefunctions. Unlike the standard QM…

The theory of random walks on finite graphs is well developed with numerous applications. In quantum walks, the propagation is governed by quantum mechanical rules; generalizing random walks to the quantum setting. They have been…

Let $\Gamma$ be a discrete group of finite virtual cohomological dimension with certain finiteness conditions of the type satisfied by arithmetic groups. We define a representation ring for $\Gamma$, determined on its elements of finite…

Let $\Gamma$ be a countable discrete group, $H$ a lcsc totally disconnected group and $\rho : \Gamma \rightarrow H$ a homomorphism with dense image. We develop a general and explicit technique which provides, for every compact open subgroup…

We study discrete-time quantum walks on a half line by means of spectral analysis. Cantero et al. [1] showed that the CMV matrix, which gives a recurrence relation for the orthogonal Laurent polynomials on the unit circle [2], expresses the…

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a…

We propose an experimental realization of discrete quantum random walks using neutral atoms trapped in optical lattices. The random walk is taking place in position space and experimental implementation with present day technology --even…