Related papers: Two-dimensional quantum random walk

We analyze the quantum walk in higher spatial dimensions and compare classical and quantum spreading as a function of time. Tensor products of Hadamard transformations and the discrete Fourier transform arise as natural extensions of the…

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.

Quantum walks, in virtue of the coherent superposition and quantum interference, possess exponential superiority over its classical counterpart in applications of quantum searching and quantum simulation. The quantum enhanced power is…

In this paper we analyze the behavior of quantum random walks. In particular we present several new results for the absorption probabilities in systems with both one and two absorbing walls for the one-dimensional case. We compute these…

In a recent Letter Ciftci and Cakmak [EPL 87, 60003 (2009)] showed that the two dimensional random walk in a bounded domain, where walkers which cross the boundary return to a base curve near origin with deterministic rules, can produce…

We focus on a 2-period time-dependent quantum walk on the half line in this paper. The quantum walker launches at the edge of the half line in a localized superposition state and its time evolution is carried out with two unitary operations…

When random walks on a square lattice are biased horizontally to move solely to the right, the probability distribution of their algebraic area can be exactly obtained. We explicitly map this biased classical random system on a non…

A discrete-time Quantum Walk (QW) is essentially an operator driving the evolution of a single particle on the lattice, through local unitaries. Some QWs admit a continuum limit, leading to familiar PDEs (e.g. the Dirac equation). Recently…

We attempt to analyze a one-dimensional space-inhomogeneous quantum walk (QW) with one defect at the origin, which has two different quantum coins in positive and negative parts. We call the QW "the two-phase QW", which we treated…

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…

We propose a new family of discrete-spacetime quantum walks capable to propagate on any arbitrary triangulations. Moreover we also extend and generalize the duality principle introduced by one of the authors, linking continuous local…

For a continuous-time quantum walk on a line the variance of the position observable grows quadratically in time, whereas, for its classical counterpart on the same graph, it exhibits a linear, diffusive, behaviour. A quantum walk, thus,…

Open Quantum Walks (OQW) are a type of quantum walk governed by the system's interaction with its environment. We explore the time evolution and the limit behavior of the OQW framework for Quantum Computation and show how we can represent…

When confined to a topological environment consisting of a cycle coupled with a half-line, quantum walks exhibit long-term statistical tendencies which differ dramatically from the tendencies of classical random walks in the same…

Multi-dimensional quantum walks usually require large coin spaces. Here we show that the non-localized case of the spatial density probability of the two-dimensional Grover walk can be obtained using only a two-dimensional coin space and a…

Quantum walk (QW), which is considered as the quantum counterpart of the classical random walk (CRW), is actually the quantum extension of CRW from the single-coin interpretation. The sequential unitary evolution engenders correlation…

We study the dynamical localization of discrete time evolution of topological split-step quantum random walk (QRW) on a single-site defect starting from a uniform distribution. Using analytical and numerical calculations, we determine the…

Quantum walks (QWs) describe the evolution of quantum systems on graphs. An intrinsic degree of freedom---called the coin and represented by a finite-dimensional Hilbert space---is associated to each node. Scalar quantum walks are QWs with…

This work is motivated by the study of some two-dimensional random walks in random environment (RWRE) with transition probabilities independent of one coordinate of the walk. These are non-reversible models and can not be treated by…

The discrete-time quantum walk (QW) is determined by a unitary matrix whose component is complex number. Konno (2015) extended the QW to a walk whose component is quaternion.We call this model quaternionic quantum walk (QQW). The…