Related papers: Full-revivals in 2-D Quantum Walks

We consider a d-dimensional random quantum walk with site-dependent random coin operators. The corresponding transition coefficients are characterized by deterministic amplitudes times independent identically distributed site-dependent…

We consider discrete spacetime models known as quantum walks, which can be used to simulate Dirac particles. In particular we look at fermion doubling in these models, in which high momentum states yield additional low energy solutions…

We look at two possible routes to classical behavior for the discrete quantum random walk on the line: decoherence in the quantum ``coin'' which drives the walk, or the use of higher-dimensional coins to dilute the effects of interference.…

Quantum walks (QWs) exhibit different properties compared with classical random walks (RWs), most notably by linear spreading and localization. In the meantime, random walks that replicate quantum walks, which we refer to as…

We investigate recurrence phenomena in coupled two degrees of freedom systems. It is shown that an initial well localized wave packet displays recurrences even in the presence of coupling in these systems. We discuss the interdependence of…

The time-evolution equation of a one-dimensional quantum walker is exactly mapped to the three-dimensional Weyl equation for a zero-mass particle with spin 1/2, in which each wave number k of walker's wave function is mapped to a point…

We propose a phenomenon of discrete-time quantum walks on graphs called the pulsation, which is a generalization of a phenomenon in the quantum searches. This phenomenon is discussed on a composite graph formed by two connected graphs…

In this paper we focus our attention on a particle that follows a unidirectional quantum walk, an alternative version of the nowadays widespread discrete-time quantum walk on a line. Here the walker at each time step can either remain in…

Coherent evolution governs the behaviour of all quantum systems, but in nature it is often subjected to influence of a classical environment. For analysing quantum transport phenomena quantum walks emerge as suitable model systems. In…

A general semiclassical method in phase space based on the final value representation of the Wigner function is considered that bypasses caustics and the need to root-search for classical trajectories. We demonstrate its potential by…

Quantum walks are known to have nontrivial interaction with absorbing boundaries. In particular, Ambainis et.\ al.\ \cite{ambainis01} showed that in the $(\Z ,C_1,H)$ quantum walk (one-dimensional Hadamard walk) an absorbing boundary…

In this paper we consider a d-dimensional scenery seen along a simple symmetric branching random walk, where at each time each particle gives the color record it is seeing. We show that we can a.s. reconstruct the scenery up to equivalence…

In a recent Letter Ciftci and Cakmak [EPL 87, 60003 (2009)] showed that the two dimensional random walk in a bounded domain, where walkers which cross the boundary return to a base curve near origin with deterministic rules, can produce…

A convergence theorem is obtained for quantum random walks with particles in an arbitrary normal state. This result unifies and extends previous work on repeated-interactions models, including that of the author (2010, J. London Math. Soc.…

Quantum walks are the quantum mechanical analogue of classical random walks and an extremely powerful tool in quantum simulations, quantum search algorithms, and even for universal quantum computing. In our work, we have designed and…

Quantum walks are known to have nontrivial interactions with absorbing boundaries. In particular it has been shown that an absorbing boundary in the one dimensional quantum walk partially reflects information, as observed by absorption…

We provide a characterization of perfect state transfer in a quantum walk whose Hamiltonian is given by the normalized Laplacian. We discuss a connection between classical random walks and quantum walks only present in this model, and we…

We survey distributional properties of $\mathbb{R}^d$-valued cocycles of finite measure preserving ergodic transformations (or, equivalently, of stationary random walks in $\mathbb{R}^d$) which determine recurrence or transience.

Multi-dimensional quantum walks can exhibit highly non-trivial topological structure, providing a powerful tool for simulating quantum information and transport systems. We present a flexible implementation of a 2D optical quantum walk on a…

Quantization of a random-walk model is performed by giving a qudit (a multi-component wave function) to a walker at site and by introducing a quantum coin, which is a matrix representation of a unitary transformation. In quantum walks, the…