Related papers: Hypergroup structures of open quantum random walks…
Graph vertex embeddings based on random walks have become increasingly influential in recent years, showing good performance in several tasks as they efficiently transform a graph into a more computationally digestible format while…
We investigate invariants for random elements of different hyperbolic groups. We provide a method, using Cayley graphs of groups, to compute the probability distribution of the minimal length of a random word, and explicitly compute the…
We show that the entanglement between the internal (spin) and external (position) degrees of freedom of a qubit in a random (dynamically disordered) one-dimensional discrete time quantum random walk (QRW) achieves its maximal possible value…
We show that simple random walks on (non-trivial) relatively hyperbolic groups stay $O(\log(n))$-close to geodesics, where $n$ is the number of steps of the walk. Using similar techniques we show that simple random walks in mapping class…
We study the state transfer through quantum walks placed on a bounded one-dimensional path. We first consider continuous-time quantum walks from a Gaussian state. We find such a state when superposing centered on the starting and antipodal…
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 introduce a new type of discrete quantum walks, called vertex-face walks, based on orientable embeddings. We first establish a spectral correspondence between the transition matrix $U$ and the vertex-face incidence structure. Using the…
In this work we introduce the concept of a quantum walk on a hypergraph. We show that the staggered quantum walk model is a special case of a quantum walk on a hypergraph.
In the present paper we find necessary and sufficient conditions for recurrence of random walks on arbitrary subgroups of the group of rational numbers $\mathbb{Q}$.
Quantum walks can be used either as tools for quantum algorithm development or as entanglement generators, potentially useful to test quantum hardware. We present a novel algorithm based on a discrete Hadamard quantum walk on a line with…
We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices $x$ and $y$ are connected with probability that asymptotically behaves like $|x-y|^{-\alpha}$ with $\alpha>d$,…
Quantum and random walks have been shown to be equivalent in the following sense: a time-dependent random walk can be constructed such that its vertex distribution at all time instants is identical to the vertex distribution of any…
It is well-known that classical random walks on regular graphs converge to the uniform distribution. Quantum walks, in their various forms, are quantizations of their corresponding classical random walk processes. Gerhardt and Watrous…
Existence of the eigenvalues of the discrete-time quantum walks is deeply related to localization of the walks. We revealed the distributions of the eigenvalues given by the splitted generating function method (the SGF method) of the…
A probabilistic approach is provided to establish new hypergeometric identities. It is based on the calculation of moments of the limiting distribution of the position of the elephant random walk in the superdiffusive regime.
In the present paper, we prove that the $C_{0}$-semigroup generated by a Schr\"odinger operator with drift on a complete Riemannian manifold is approximated by the discrete semigroups associated with a family of discrete time random walks…
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…
The Poisson and Martin boundaries for invariant random walks on the dual of the orthogonal quantum groups A_o(F), are identified with higher dimensional Podles spheres that we describe in terms of generators and relations. This provides the…
We study scattering quantum walks on highly symmetric graphs and use the walks to solve search problems on these graphs. The particle making the walk resides on the edges of the graph, and at each time step scatters at the vertices. All of…
Advances in recent years have made it possible to explore quantum dots as a viable technology for scalable quantum information processing. Charge qubits for example can be realized in the lowest bound states of coupled quantum dots and the…