Related papers: Inhomogeneous Quantum Walks
Classical and quantum walks on some finite paths are introduced. It is shown that these walks have explicit solutions given in terms of exceptional Krawtchouk polynomials and their properties are explored. In particular, fractional revival…
We look at two possible routes to classical behavior for the discrete quantum random walk on the line: decoherence in the quantum ``coin'' which drives the walk, or the use of higher-dimensional coins to dilute the effects of interference.…
We present a probabilistic theory of random walks in turbid media with non-scattering regions. It is shown that important characteristics such as diffusion constants, average step lengths, crossing statistics and void spacings can be…
Anderson's nonstandard construction of brownian motion as an infinitesimal random walk on the euclidean line is generalized to an Hausdorff riemannian manifold. A nonstandard Feynman-Kac formula holding on such an Hausdorff riemannian…
This work deals with both instantaneous uniform mixing property and temporal standard deviation for continuous-time quantum random walks on circles in order to study their fluctuations comparing with discrete-time quantum random walks, and…
We present a comprehensive classification of one-dimensional coined quantum walks on the infinite line, focusing on the spatial probability distributions they induce. Building on prior results, we identify all initial coin states that lead…
We construct a renewal structure for random walks on surface groups. The renewal times are defined as times when the random walks enters a particular type of a cone and never leaves it again. As a consequence, the trajectory of the random…
Quantum walks are powerful tools not only to construct the quantum speedup algorithms but also to describe specific models in physical processes. Furthermore, the discrete time quantum walk has been experimentally realized in various…
In this work, we study open quantum random walks, as described by S. Attal et al. These objects are given in terms of completely positive maps acting on trace-class operators, leading to one of the simplest open quantum versions of the…
We characterize quantumness of the so-called quantum walks (whose dynamics is governed by quantum mechanics) by introducing two computable measures which are stronger than the variance of the walker's position probability distribution. The…
Quantum walks are recognizably useful for the development of new quantum algorithms, as well as for the investigation of several physical phenomena in quantum systems. Actual implementations of quantum walks face technological difficulties…
This work focuses on the study of quantum stochastic walks, which are a generalization of coherent, i. e. unitary quantum walks. Our main goal is to present a measure of a coherence of the walk. To this end, we utilize the asymptotic…
We introduce and analyze a one-dimensional quantum walk with two time-independent rotations on the coin. We study the influence on the property of quantum walk due to the second rotation on the coin. Based on the asymptotic solution in the…
We consider the invariant measure of homogeneous random walks in the quarter-plane. In particular, we consider measures that can be expressed as a finite linear combination of geometric terms and present conditions on the structure of these…
The classicalization of a decoherent discrete-time quantum walk on a line or an n-cycle can be demonstrated in various ways that do not necessarily provide a geometry-independent description. For example, the position probability…
Recently, it has been shown that one-dimensional quantum walks can mix more quickly than classical random walks, suggesting that quantum Monte Carlo algorithms can outperform their classical counterparts. We study two quantum walks on the…
The continuous limit of one dimensional discrete-time quantum walks with time- and space-dependent coefficients is investigated. A given quantum walk does not generally admit a continuous limit but some families (1-jets) of quantum walks…
The discrete-time quantum walk (QW) is a quantum version of the random walk (RW) and has been widely investigated for the last two decades. Some remarkable properties of QW are well known. For example, QW has a ballistic spreading, i.e., QW…
The goal of this article is two-fold: in a first part, we prove Azuma-Hoeffding type concentration inequalities around the drift for the displacement of non-elementary random walks on hyperbolic spaces. For a proper hyperbolic space $M$, we…
A discrete-time quantum walk on a graph is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. If this unitary evolution operator has an associated group of symmetries, then for certain…