Quantum random walk is the quantum counterpart of a classical random walk. The classical
random walk concept has long been used as a computational framework for designing …

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 …

This is a textbook about quantum walks and quantum search algorithms. The readers will
take advantage of the pedagogical aspects and learn the topics faster and make less effort …

The development of quantum walks in the context of quantum computation, as
generalisations of random walk techniques, has led rapidly to several new quantum …

In discrete time, coined quantum walks, the coin degrees of freedom offer the potential for a
wider range of controls over the evolution of the walk than are available in the continuous …

In this paper we consider the one-dimensional quantum random walk Xϕ n at time n starting
from initial qubit state ϕ determined by 2× 2 unitary matrix U. We give a combinatorial …

Quantum walks can be considered as a generalized version of the classical random walk.
There are two classes of quantum walks, that is, the discrete-time (or coined) and the …

We formulate and prove a general weak limit theorem for quantum random walks in one and
more dimensions. With X n denoting position at time n, we show that X n/n converges weakly …

We study a generalized Hadamard walk in one dimension with three inner states. The
particle governed by the three-state quantum walk moves, in superposition, both to the left …

Recently, quantized versions of random walks have been explored as effective elements for
quantum algorithms. In the simplest case of one dimension, the theory has remained divided …