Related papers: Localization of M-Particle Quantum Walks
The Hadamard walk is a typical model of the discrete-time quantum walk. We investigate sojourn times of the Hadamard walk on a line by a path counting method.
In this work we introduce the concept of a quantum walk on a hypergraph. We show that the staggered quantum walk model is a special case of a quantum walk on a hypergraph.
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 on the line with a single particle possess a classical analog. Involving more walkers opens up the possibility to study collective quantum effects, such as many particle correlations. In this context, entangled initial states…
We introduce an analytically treatable spin decoherence model for quantum walk on a line that yields the exact position probability distribution of an unbiased classical random walk at all-time scales. This spin decoherence model depicts a…
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…
Quantum walks have been shown to be fruitful tools in analysing the dynamic properties of quantum systems. This article proposes to use quantum walks as an approach to Quantum Neural Networks (QNNs). QNNs replace binary McCulloch-Pitts…
It is well known that many real world networks have the power-law degree distribution (scale-free property). However there are no rigorous results for continuous-time quantum walks on such realistic graphs. In this paper, we analyze…
We demonstrate a coined quantum walk over ten steps in a one-dimensional network of linear optical elements. By applying single-point phase defects, the translational symmetry of an ideal standard quantum walk is broken resulting in…
The parametric maximum likelihood estimation problem is addressed in the context of quantum walk theory for quantum walks on the lattice of integers. A coin action is presented, with the real parameter $\theta$ to be estimated identified…
There is a property called localization, which is essential for applications of quantum walks. From a mathematical point of view, the occurrence of localization is known to be equivalent to the existence of eigenvalues of the time evolution…
The quantum random walk is a possible approach to construct new quantum algorithms. Several groups have investigated the quantum random walk and experimental schemes were proposed. In this paper we present the experimental implementation of…
We consider discrete-time nearest-neighbor quantum walks on random environments in one dimension. Using the method based on a path counting, we present both quenched and annealed weak limit theorems for the quantum walk.
We analyze the application of the history state formalism to quantum walks. The formalism allows one to describe the whole walk through a pure quantum history state, which can be derived from a timeless eigenvalue equation. It naturally…
Quantum random walk in a two-dimensional lattice with randomly distributed traps is investigated. Distributions of quantum walkers are evaluated dynamically for the cases of Hadamard, Fourier, and Grover coins, and quantum to classical…
We study maximal coin-position entanglement generation via a discrete-time quantum walk, in which the coin operation is randomly selected from one of two coin operators set at each step. We solve maximal entanglement generation as an…
Discrete-time quantum walk in one-dimension is studied from a path-integral perspective. This enables derivation of a closed-form expression for amplitudes corresponding to any coin-position basis of the state vector of the quantum walker…
Two subjects are discussed in this work: localisation and recurrence in a model of quantum walk in a periodic potential, and a model of opinion dynamics with multiple choices of opinions.
In this paper, we consider periodicity for space-inhomogeneous quantum walks on the cycle. For isospectral coin cases, we propose a spectral analysis. Based on the analysis, we extend the result for periodicity for Hadamard walk to some…
We address the scattering of a quantum particle by a one-dimensional barrier potential over a set of discrete positions. We formalize the problem as a continuous-time quantum walk on a lattice with an impurity, and use the quantum Fisher…