Related papers: Controlling quantum random walk with a step-depend…
We propose a scheme to implement the one-dimensional coined quantum walk with electrons transported through a two-dimensional network of spintronic semiconductor quantum rings. The coin degree of freedom is represented by the spin of the…
Quantum walks have emerged as an interesting approach to quantum information processing, exhibiting many unique properties compared to the analogous classical random walk. Here we introduce a model for a discrete-time quantum walk with…
There are presently two models for quantum walks on graphs. The "coined" walk uses discrete time steps, and contains, besides the particle making the walk, a second quantum system, the coin, that determines the direction in which the…
We advance the previous studies of quantum walks on the line with two coins. Such four-state quantum walks driven by a three-direction shift operator may have nonzero stationary distributions (localization), thus distinguishing themselves…
We consider two independent quantum walks on separate lines augmented by partial or full swapping of coins after each step. For classical random walks, swapping or not swapping coins makes little difference to the random walk…
In this study we show a way of achieving the reverse evolution of n-dimensional quantum walks by introducing interventions on the coin degree of freedom during the forward progression of the coin-walker system. Only a single intervention is…
We study the asymptotic position distribution of general quantum walks on a lattice, including walks with a random coin, which is chosen from step to step by a general Markov chain. In the unitary (i.e., non-random) case, we allow any…
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…
In this paper, we consider discrete time quantum walks on graphs with coin focusing on the decentralized model, where the coin operation is allowed to change with the vertex of the graph. When the coin operations can be modified at every…
We propose a novel implementation of discrete time quantum walks for a neutral atom in an array of optical microtraps or an optical lattice. We analyze a one-dimensional walk in position space, with the coin, the additional qubit degree of…
Quantum walks, both discrete (coined) and continuous time, form the basis of several recent quantum algorithms. Here we use numerical simulations to study the properties of discrete, coined quantum walks. We investigate the variation in the…
The dynamics of a one dimensional quantum walker on the lattice with two internal degrees of freedom, the coin states, is considered. The discrete time unitary dynamics is determined by the repeated action of a coin operator in U(2) on the…
In this Chapter, we present some interesting properties of quantum walks on the line. We concentrate our attention in the emergence of invariance and provide some insights into the ultimate origin of the observed behavior. In the first part…
Exploring the quantum walk as a tool of generating various probability distributions and quantum entanglements is a topic of current interest. In the present work, we use extensive numerical simulations to investigate the influence of…
We characterize quantumness of the so-called quantum walks (whose dynamics is governed by quantum mechanics) by introducing two computable measures which are stronger than the variance of the walker's position probability distribution. The…
We propose an implementation of a quantum walk on a circle on an optomechanical system by encoding the walker on the phase space of a radiation field and the coin on a two-level state of a mechanical resonator. The dynamics of the system is…
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 paper, we study discrete-time quantum walks on one-dimensional lattices. We find that the coherent dynamics depends on the initial states and coin parameters. For infinite size of lattice, we derive an explicit expression for the…
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 discrete-time quantum walk is a quantum counterpart of the random walk. It is expected that the model plays important roles in the quantum field. In the quantum information theory, entanglement is a key resource. We use the von Neumann…