Related papers: Evanescence in Coined Quantum Walks
We address the question of symmetries of an important type of quantum walks. We introduce all the necessary definitions and provide a rigorous formulation of the problem. Using a thorough analysis, we reach the complete answer by presenting…
The continuous-time quantum walk is a particle evolving by Schr\"odinger's equation in discrete space. Encoding the space as a graph of vertices and edges, the Hamiltonian is proportional to the discrete Laplacian. In some physical systems,…
The "quantum walk" has emerged recently as a paradigmatic process for the dynamic simulation of complex quantum systems, entanglement production and quantum computation. Hitherto, photonic implementations of quantum walks have mainly been…
We propose a general framework for quantum walks on d-dimensional spaces. We investigate asymptotic behavior of these walks. Among them, existence of limit distribution of homogeneous walks is proved. In this theorem, the support of the…
We make and generalize the observation that summing of probability amplitudes of a discrete-time quantum walk over partitions of the walking graph consistent with the step operator results in a unitary evolution on the reduced graph which…
We explore a discrete-time, coined quantum walk on a quantum network where the coherent superposition of walker-moves originates from the unitary interaction of the walker-coin with the qubit degrees of freedom in the quantum network. The…
We perform the scattering analysis of the evolution operator of quantum walks with an anisotropic coin, and we prove a weak limit theorem for their asymptotic velocity. The quantum walks that we consider include one-defect models, two-phase…
We re-use some original ideas of de~Broglie, Schr\"odiger, Dirac and Feynman to revise the ensemble interpretation of wave function in quantum mechanics. To this end we introduce coherence (auto-concordance) of ensembles of quantum…
The quantum walk is the quantum analogue of the well-known random walk, which forms the basis for models and applications in many realms of science. Its properties are markedly different from the classical counterpart and might lead to…
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 present an introduction to coined quantum walks on regular graphs, which have been developed in the past few years as an alternative to quantum Fourier transforms for underpinning algorithms for quantum computation. We then describe our…
In this paper, a study on discrete-time coined quantum walks on the line is presented. Clear mathematical foundations are still lacking for this quantum walk model. As a step towards this objective, the following question is being…
The quantum walk differs fundamentally from the classical random walk in a number of ways, including its linear spreading and initial condition dependent asymmetries. Using stationary phase approximations, precise asymptotics have been…
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…
This work focuses on the study of quantum stochastic walks, which are a generalization of coherent, i. e. unitary quantum walks. Our main goal is to present a measure of a coherence of the walk. To this end, we utilize the asymptotic…
We present analytical treatment of quantum walks on a cycle graph. The investigation is based on a realistic physical model of the graph in which decoherence is induced by continuous monitoring of each graph vertex with nearby quantum point…
Quantum random walks use interference to obtain faster state space exploration, which can be used for algorithmic purposes. Photonic technologies provide a natural platform for many recent experimental demonstrations. Here we analyze…
We study a class of discrete-time quantum walks with inhomogeneous coins defined in [Y. Shikano and H. Katsura, Phys. Rev. E {\bf 82}, 031122 (2010)]. We establish symmetry properties of the spectrum of the evolution operator, which…
We propose a class of continuous-time quantum walk models on graphs induced by a certain class of discrete-time quantum walk models with the parameter $\epsilon\in [0,1]$. Here the graph treated in this paper can be applied both finite and…
The quantum random walk has been much studied recently, largely due to its highly nonclassical behavior. In this paper, we study one possible route to classical behavior for the discrete quantum walk on the line: the presence of decoherence…