Quantum walks (QWs) exhibit different properties compared with classical random (RWs), most notably by linear spreading and localization. In the meantime, that replicate quantum walks, which we refer to as quantum-walk-replicating (QWRWs), have been studied in literature where eventual of QWRW coincide those QWs. However, consider unique attributes QWRWs not fully utilized former studies obtain...

Motivated by the success of classical random walks and chaotic dynamical systems, we study the quantisation of the random walk over Z and its relationships with a classical chaotic system x → 2xmod1, x ∈ [0,1]. In the physics literature, quantum random walks have been studied, for instance, by Ambainis et al. [1] and Konno et al. [8, 9]. In [8], Konno shows that the quantum random walk over Z c...

Motivated by the success of classical random walks and chaotic dynamical systems, we study the quantisation of the random walk over Z and its relationships with a classical chaotic system x → 2xmod1, x ∈ [0,1]. In the physics literature, quantum random walks have been studied, for instance, by Ambainis et al. [1] and Konno et al. [8, 9]. In [8], Konno shows that the quantum random walk over Z c...

Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or discrete time. But whereas a continuous-time random walk can be obtained as the limit of a sequence of discretetime random walks, the two types of quantum w...

The development of quantum algorithms based on quantum versions of random walks is placed in the context of the emerging field of quantum computing. Constructing a suitable quantum version of a random walk is not trivial; pure quantum dynamics is deterministic, so randomness only enters during the measurement phase, i.e. when converting the quantum information into classical information. The ou...

In recent years quantum random walks have garnered much interest among quantum information researchers. Part of the reason is the prospect that many hard problems can be solved efficiently by employing algorithms based on quantum random walks, in the same way that classical random walks have played a central role in many hugely successful randomized algorithms. In this paper we introduce a new ...

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 both walks and study limit theorems and absorption problems for correlated random walks by our PQRS method, which was used in our analysis of quantum walks.