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 …

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 …

Quantum computation, one of the latest joint ventures between physics and the theory of
computation, is a scientific field whose main goals include the development of hardware and …

Shenvi, Kempe, and Whaley's quantum random-walk search (SKW) algorithm [Phys. Rev. A
67, 052307 (2003)] is known to require O (N) number of oracle queries to find the marked …

The Pólya number characterizes the recurrence of a random walk. We apply the
generalization of this concept to quantum walks [M. Štefaňák, Phys. Rev. Lett. 100, 020501 …

Quantum walks on a line with a single particle possess a classical analogue. Involving more
walkers opens up the possibility of studying collective quantum effects, such as many …

The Pólya number of a classical random walk on a regular lattice is known to depend solely
on the dimension of the lattice. For one and two dimensions it equals one, meaning unit …

We examine the physical implementation of a discrete time quantum walk with a four-
dimensional coin. Our quantum walker is a photon moving repeatedly through a time delay …

Recurrence of a random walk is described by the Pólya number. For quantum walks,
recurrence is understood as the return of the walker to the origin, rather than the full revival …