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 …

The classical random walk formalism plays an important role in a wide range of applications.
Its quantum counterpart, the quantum walk, is proposed as an important theoretical model …

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 …

Several models have been proposed to build evolution operators to perform quantum walks
in a theoretical way, although when wanting to map the resulting evolution operators into …

We consider a quantum walk with two marked vertices, sender and receiver, and analyze its
application to perfect state transfer on complete bipartite graphs. First, the situation with both …

Random walks are fundamental models of stochastic processes with applications in various
fields, including physics, biology, and computer science. We study classical and quantum …

Grover's algorithm provides a quadratic speedup over classical algorithms to search for
marked elements in an unstructured database. The original algorithm is probabilistic, and …

We introduce a family of discrete-time quantum walks, called two-partition model, based on
two equivalence-class partitions of the computational basis, which establish the notion of …

This article proposes the first discrete-time implementation of Rydberg quantum walk in multi-
dimensional spatial space that could ideally simulate different classes of topological …

It is shown that discrete-time quantum walks can be used to digitize, ie, to time discretize
fermionic models of continuous-time lattice gauge theory. The resulting discrete-time …