Related papers: Large Qudit Limit of One-dimensional Quantum Walks
In this paper, we study the properties of lackadaisical quantum walks on a line. This model is first proposed in~\cite{wong2015grover} as a quantum analogue of lazy random walks where each vertex is attached $\tau$ self-loops. We derive an…
We offer theoretical explanations for some recent observations in numerical simulations of quantum random walks (QRW). Specifically, in the case of a QRW on the line with one particle (walker) and two entangled coins, we explain the…
We consider the dynamical properties of Quantum Walks defined on the d-dimensional cubic lattice, or the homogeneous tree of coordination number 2d, with site dependent random phases, further characterised by transition probabilities…
We study time-dependent discrete-time quantum walks on the one-dimensional lattice. We compute the limit distribution of a two-period quantum walk defined by two orthogonal matrices. For the symmetric case, the distribution is determined by…
A particular family of time- and space-dependent discrete-time quantum walks (QWs) is considered in one dimensional physical space. The continuous limit of these walks is defined through a new procedure and computed in full detail. In this…
We study the discrete-time quantum walk in one-dimension governed by the Fibonacci transformation .We show localization does not occur for the Fibonacci quantum walk by investigating the stationary distribution of the walk, in addition, we…
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…
An algebraic structure for one-dimensional quantum walks is introduced. This structure characterizes, in some sense, one-dimensional quantum walks. A natural computation using this algebraic structure leads us to obtain an effective formula…
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 walks, both discrete (coined) and continuous time, form the basis of several quantum algorithms and have been used to model processes such as transport in spin chains and quantum chemistry. The enhanced spreading and mixing…
We investigate the use of discrete-time quantum walks to sample from an almost-uniform distribution, in the absence of any external source of randomness. Integers are encoded on the vertices of a cycle graph, and a quantum walker evolves…
We study the dynamics given by the iteration of a (half-line) CMV matrix with sparse, high barriers. Using an approach of Tcheremchantsev, we are able to explicitly compute the transport exponents for this model in terms of the given…
We investigate continuous-time quantum walks of two indistinguishable particles (bosons, fermions or hard-core bosons) in one-dimensional lattices with nearest-neighbour interactions. The two interacting particles can undergo independent-…
We introduce and study a class of discrete-time quantum walks on a one-dimensional lattice. In contrast to the standard homogeneous quantum walks, coin operators are inhomogeneous and depend on their positions in this class of models. The…
This paper studies particle propagation in a one-dimensional inhomogeneous medium where the laws of motion are generated by chaotic and deterministic local maps. Assuming that the particle's initial location is random and uniformly…
While completely self-avoiding quantum walks have the distinct property of leading to a trivial unidirectional transport of a quantum state, an interesting and non-trivial dynamics can be constructed by restricting the self-avoidance to a…
We show that particle transport in a uniform, quantum multi-baker map, is generically ballistic in the long time limit, for any fixed value of Planck's constant. However, for fixed times, the semi-classical limit leads to diffusion. Random…
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…
The one-dimensional elephant random walk is a typical model of discrete-time random walk with step-reinforcement, and is introduced by Sch\"{u}tz and Trimper (2004). It has a parameter $\alpha \in (-1,1)$: The case $\alpha=0$ corresponds to…
We consider a discrete-time 2-state quantum walk on the line. The state of the quantum walker evolves according to a rule which is determined by a coin-flip operator and a position-shift operator. In this paper we take a 3-periodic time…