Related papers: Quantum walks in higher dimensions

Concerning a discrete-time quantum walk X^{(d)}_t with a symmetric distribution on the line, whose evolution is described by the Hadamard transformation, it was proved by the author that the following weak limit theorem holds: X^{(d)}_t /t…

The quantum walk was originally proposed as a quantum mechanical analogue of the classical random walk, and has since become a powerful tool in quantum information science. In this paper, we show that discrete time quantum walks provide a…

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…

Lazy quantum walks were presented by Andrew M. Childs to prove that the continuous-time quantum walk is a limit of the discrete-time quantum walk [Commun.Math.Phys.294,581-603(2010)]. In this paper, we discuss properties of lazy quantum…

The study of quantum walks has been shown to have a wide range of applications in areas such as artificial intelligence, the study of biological processes, and quantum transport. The quantum stochastic walk, which allows for incoherent…

Two models are first presented, of one-dimensional discrete-time quantum walk (DTQW) with temporal noise on the internal degree of freedom (i.e., the coin): (i) a model with both a coin-flip and a phase-flip channel, and (ii) a model with…

A discrete time quantum walker is considered in one dimension, where at each step, the translation can be more than one unit length chosen randomly. In the simplest case, the probability that the distance travelled is $\ell$ is taken as…

We discuss spreading estimates for dynamical systems given by the iteration of an extended CMV matrix. Using a connection due to Cantero--Gr\"unbaum--Moral--Vel\'azquez, this enables us to study spreading rates for quantum walks in one…

We propose a simulation strategy which uses a classical device of linearly coupled chain of springs to simulate quantum dynamics, in particular the quantum walks. Through this strategy, we obtain the quantum wave function from classical…

We analyze a set of discrete-time quantum walks for which the displacements on a chain follow binary aperiodic jumps according to three paradigmatic sequences: Fibonacci, Thue-Morse and Rudin-Shapiro. We use a generalized Hadamard coin…

The evolution of a walker in standard "Discrete-time Quantum Walk (DTQW)" is determined by coin and shift unitary operators. The conditional shift operator shifts the position of the walker to right or left by unit step size while the…

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…

We show that a quantum state transfer, previously studied as a continuous time process in networks of interacting spins, can be achieved within the model of discrete time quantum walks with position dependent coin. We argue that due to…

In this expository note, we discuss spatially inhomogeneous quantum walks in one dimension and describe a genre of mathematical methods that enables one to translate information about the time-independent eigenvalue equation for the unitary…

A discrete-time quantum walk (QW) is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs have familiar physics PDEs as their continuum limit. Some slight generalization of them (allowing for…

Quantum walk (QW) utilizes its internal quantum states to decide the displacement, thereby introducing single-particle entanglement between the internal and positional degrees of freedom. By simulating three variants of QW with the…

We generalize the quantum random walk protocol for a particle in a one-dimensional chain, by using several types of biased quantum coins, arranged in aperiodic sequences, in a manner that leads to a rich variety of possible wave function…

Quantum walks are versatile simulators of topological phases and phase transitions as observed in condensed matter physics. Here, we utilize a step dependent coin in quantum walks and investigate what topological phases we can simulate with…

We analyze in detail the discrete--time quantum walk on the line by separating the quantum evolution equation into Markovian and interference terms. As a result of this separation, it is possible to show analytically that the quadratic…

In this note, we discuss a general definition of quantum random walks on graphs and illustrate with a simple graph the possibility of very different behavior between a classical random walk and its quantum analogue. In this graph,…