相关论文: Conditional Probability Distributions of Finite Ab…

We introduce quantum walks with a time-dependent coin, and show how they include, as a particular case, the generalized quantum walk recently studied by Wojcik et al. {[}Phys. Rev. Lett. \textbf{93}, 180601(2004){]} which exhibits…

It has been discovered that open quantum walks diffusively distribute in space, since they were introduced in 2012. Indeed, some limit distributions have been demonstrated and most of them are described by Gaussian distributions. We operate…

In this paper, a study on discrete-time coined quantum walks on the line is presented. Clear mathematical foundations are still lacking for this quantum walk model. As a step towards this objective, the following question is being…

The extremely fascinating behaviors of the quantum walks of particles, which differ much from the classical counterparts, have attracted many physicists. Here we investigate another interesting part of the quantum walks, that is the quantum…

We investigate quantum walks in multiple dimensions with different quantum coins. We augment the model by assuming that at each step the amplitudes of the coin state are multiplied by random phases. This model enables us to study in detail…

A continuous-time quantum walk is modelled using a graph. In this short paper, we provide lower bounds on the size of a graph that would allow for some quantum phenomena to occur. Among other things, we show that, in the adjacency matrix…

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…

Quantum recurrence theorem holds for quantum systems with discrete energy eigenvalues and fails to hold in general for systems with continuous energy. We show that during quantum walk process dominated by interference of amplitude…

We consider a new model of a branching random walk on a multidimensional lattice with continuous time and one source of particle reproduction and death, as well as an infinite number of sources in which, in addition to the walk, only…

Quantum random walks are the quantum counterpart of classical random walks, and were recently studied in the context of quantum computation. A quantum random walker is subject to self interference, leading to a remarkably different behavior…

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 study quantum walks on general graphs from the point of view of scattering theory. For a general finite graph we choose two vertices and attach one half line to each. We are interested in walks that proceed from one half line, through…

Quantum walks on graphs are ubiquitous in quantum computing finding a myriad of applications. Likewise, random walks on graphs are a fundamental building block for a large number of algorithms with diverse applications. While the…

Quantum walks and random walks bear similarities and divergences. One of the most remarkable disparities affects the probability of finding the particle at a given location: typically, almost a flat function in the first case and a…

Quantum walks are considered to be quantum counterparts of random walks.They show us impressive probability distributions which are different from those of random walks.That fact has been precisely proved in terms of mathematics and some of…

Quantum versions of random walks on the line and the cycle show a quadratic improvement over classical random walks in their spreading rates and mixing times respectively. Non-unitary quantum walks can provide a useful optimisation of these…

The propagation by continuous time quantum walks (CTQWs) on one-dimensional lattices shows structures in the transition probabilities between different sites reminiscent of quantum carpets. For a system with periodic boundary conditions, we…

We present numerical study of a model of quantum walk in periodic potential on the line. We take the simple view that different potentials affect differently the way the coin state of the walker is changed. For simplicity and definiteness,…

We investigate the ballistic spreading behavior of the one-dimensional discrete time quantum walks whose time evolution is driven by any balanced quantum coin. We obtain closed-form expressions for the long-time variance of position of…

A quantum walk model which reflects the $2$-cell embedding on the orientable closed surface of a graph in the dynamics is introduced. We show that the scattering matrix is obtained by finding the faces on the underlying surface which have…