Related papers: A limit theorem for a splitting distribution of a …

We consider the Grover walk as a 4-state quantum walk without memory in one dimension. The walker in our 4-state quantum walk moves to the left or right. We compute the stationary distribution of the walk, in addition, we obtain the weak…

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…

In this paper we present closed-form expressions for the wave function that governs the evolution of the discrete-time quantum walk on a line when the coin operator is arbitrary. The formulas were derived assuming that the walker can either…

Estimation of the coin parameter(s) is an important part of the problem of implementing more robust schemes for quantum simulation using quantum walks. We present the estimation of the quantum coin parameter used for one-dimensional…

The discrete-time quantum walk (QW) has been extensively and intensively investigated for the last decade, whose coin operator is defined by a unitary matrix. We extend the QW to a walk determined by a unitary matrix whose component is…

We introduce the driven discrete time quantum walk, where walkers are added during the walk instead of only at the beginning. This leads to interference in walker number and very different dynamics when compared to the original quantum…

Quantization and asymptotic behaviour of a variant of discrete random walk on integers are investigated. This variant, the $\epsilon_{V^{k}}$ walk, has the novel feature that it uses many identical quantum coins keeping at the same time…

A discrete time quantum walk is known to be the single-particle sector of a quantum cellular automaton. For a long time, these models have interested the community for their nice properties such as locality or translation invariance. This…

Randomly breaking connections in a graph alters its transport properties, a model used to describe percolation. In the case of quantum walks, dynamic percolation graphs represent a special type of imperfections, where the connections appear…

In recent years, there has been an emerging trend of combining two innovations in computer science and physics to achieve better computation capability. Exploring the potential of quantum computation to achieve highly efficient performance…

We observe that changing a phase at a single point in a discrete quantum walk results in a rather surprising localization effect. For certain values of this phase change the possibility of localization strongly depends on the internal…

Quantum walks subject to decoherence generically suffer the loss of their genuine quantum feature, a quadratically faster spreading compared to classical random walks. This intuitive statement has been verified analytically for certain…

We propose a variation of the quantum walk on a circle in phase space by conjoining the Hadamard coin flip with simultaneous displacement of the walker's location in phase space and show that this generalization is a proper quantum walk…

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…

By pursuing the deep relation between the one-dimensional Dirac equation and quantum walks, the physical role of quantum interference in the latter is explained. It is shown that the time evolution of the probability density of a quantum…

We show that probability is locally conserved in discrete time quantum walks, corresponding to a particle evolving in discrete space and time. In particular, for a spatial structure represented by an arbitrary directed graph, and any…

We consider a random walk model in a one-dimensional environment, formed by several zones of finite width with the fixed transition probabilities. It is also assumed that the transitions to the left and right neighboring points have unequal…

Quantum walk has been regarded as a primitive to universal quantum computation. By using the operations required to describe the single particle discrete-time quantum walk on a position space we demonstrate the realization of the universal…

We study the motion of two non-interacting quantum particles performing a random walk on a line and analyze the probability that the two particles are detected at a particular position after a certain number of steps (meeting problem). The…

We present the first robust implementation of a coined quantum walk over five steps using only passive optical elements. By employing a fiber network loop we keep the amount of required resources constant as the walker's position Hilbert…