Related papers: One-dimensional quantum walks with absorbing bound…

Quantum walks are known to have nontrivial interactions with absorbing boundaries. In particular it has been shown that an absorbing boundary in the one dimensional quantum walk partially reflects information, as observed by absorption…

Quantum walks are known to have nontrivial interaction with absorbing boundaries. In particular, Ambainis et.\ al.\ \cite{ambainis01} showed that in the $(\Z ,C_1,H)$ quantum walk (one-dimensional Hadamard walk) an absorbing boundary…

There has recently been considerable interest in quantum walks in connection with quantum computing. The walk can be considered as a quantum version of the so-called correlated random walk. We clarify a strong structural similarity between…

This paper treats absorption problems for the one-dimensional quantum walk determined by a 2 times 2 unitary matrix U on a state space {0,1,...,N} where N is finite or infinite by using a new path integral approach based on an orthonormal…

Absorption of two-state coined quantum walks on a finite line with two sinks located at $N$ and $-N$ is investigated. Elaborating on the results of Konno et al., J. Phys. A: Math. Gen. 36 241 (2003), we derive closed formulas for the…

Quantum walks are expected to provide useful algorithmic tools for quantum computation. This paper introduces absorbing probability and time of quantum walks and gives both numerical simulation results and theoretical analyses on Hadamard…

Generating functions for asymmetric step-size paths restricted by two absorbing barriers are derived. The method begins by applying the Lagrange inversion formula to arbitrary powers of roots of the characteristic equation, that being a…

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…

We consider a discrete random walk (RW) in n dimensions . The RW is adapted with a geometric absorption process: at any discrete time there is a constant probability that absorption occurs in the current state. To model the RW with…

We consider a discrete random walk on a diagonal lattice in two and three dimensions and obtain explicit solutions of absorption probabilities and probabilities of return in several domains. In three dimensions we consider both the cube and…

In this paper we consider limit theorems, symmetry of distribution, and absorption problems for two types of one-dimensional quantum random walks determined by 2 times 2 unitary matrices using our PQRS method. The one type was introduced by…

We obtain expected number of arrivals, absorption probabilities and expected time before absorption for a discrete random walk on the integers with an infinite set of equidistant multiple function barriers

The behaviors of one-dimensional quantum random walks are strikingly different from those of classical ones. However, when decoherence is involved, the limiting distributions take on many classical features over time. In this paper, we…

The quantum walk (QW) is the term given to a family of algorithms governing the evolution of a discrete quantum system and as such has a founding role in the study of quantum computation. We contribute to the investigation of QW phenomena…

We consider discrete-time nearest-neighbor quantum walks on random environments in one dimension. Using the method based on a path counting, we present both quenched and annealed weak limit theorems for the quantum walk.

We consider a one-dimensional space-inhomogeneous discrete time quantum walk. This model is the Hadamard walk with one defect at the origin which is different from the model introduced by Wojcik et al. [14]. We obtain a stationary measure…

The aim of this article is to introduce a unified method to obtain explicit integral representations of the trivariate generating function counting the walks with small steps which are confined to a quarter plane. For many models, this…

The first general analytic solutions for the one-dimensional walk in position and momentum space are derived. These solutions reveal, among other things, new symmetry features of quantum walk probability densities and further insight into…

We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are…

We present a scheme for multi-bit quantum random number generation using a single qubit discrete-time quantum walk in one-dimensional space. Irrespective of the initial state of the qubit, quantum interference and entanglement of particle…