相关论文: Return probability and self-similarity of the Ries…

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a…

Measurements on a quantum particle unavoidably affect its state, since the otherwise unitary evolution of the system is interrupted by a non-unitary projection operation. In order to probe measurement-induced effects in the state dynamics…

There has recently been considerable interest in quantum walks in connection with quantum computing. The walk can be considered as a quantum version of the so-called correlated random walk. We clarify a strong structural similarity between…

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…

Interplay between quantum interference and classical randomness can enhance performance of various quantum information tasks. In the present paper we analyze recurrence phenomena in the discrete-time quantum stochastic walk on a line, which…

We present two long-time limit theorems of a 3-state quantum walk on the line when the walker starts from the origin. One is a limit measure which is obtained from the probability distribution of the walk at a long-time limit, and the other…

We investigate a connection between a property of the distribution and a conserved quantity for the reversible cellular automaton derived from a discrete-time quantum walk in one dimension. As a corollary, we give a detailed information of…

Quantum walks can reconstruct quantum algorithms for quantum computation, where the precise controls of quantum state transfers between arbitrary distant sites are required. Here, we investigate quantum walks using a periodically…

Monitored recurrence of a one-parameter set of three-state quantum walks on a line is investigated. The calculations are considerably simplified by choosing a suitable basis of the coin space. We show that the Polya number (i.e. the site…

Quantum and random walks have been shown to be equivalent in the following sense: a time-dependent random walk can be constructed such that its vertex distribution at all time instants is identical to the vertex distribution of any…

The probability of a random walker to return to its starting point in dimensions one and two is unity, a theorem first proven by G. Polya. The recurrence probability -- the probability to be found at the origin at a time t, is a power law…

We define a discrete-time, coined quantum walk on weighted graphs that is inspired by Szegedy's quantum walk. Using this, we prove that many lackadaisical quantum walks, where each vertex has $l$ integer self-loops, can be generalized to a…

Quantum walks are quantum counterparts of random walks and their probability distributions are different from each other. A quantum walker distributes on a Hilbert space and it is observed at a location with a probability. The finding…

The P\'olya number characterizes the recurrence of a random walk. We apply the generalization of this concept to quantum walks [M. \v{S}tefa\v{n}\'ak, I. Jex and T. Kiss, Phys. Rev. Lett. \textbf{100}, 020501 (2008)] which is based on a…

We outline basic properties of a symmetric random walk in one dimension, in which the length of the nth step equals lambda^n, with lambda<1. As the number of steps N-->oo, the probability that the endpoint is at x, P_{lambda}(x;N),…

In this work, the probability of return for random walks on $\mathbb{Z}$, whose increment is given by the $k$-bonacci sequence, is determined. Also, the Hausorff, packing and box-counting dimensions of the set of these walks that return an…

We have recently proposed a two-dimensional quantum walk where the requirement of a higher dimensionality of the coin space is substituted with the alternance of the directions in which the walker can move [C. Di Franco, M. Mc Gettrick, and…

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…

Recurrence of a random walk is described by the Polya number. For quantum walks, recurrence is understood as the return of the walker to the origin, rather than the full-revival of its quantum state. Localization for two dimensional quantum…

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…