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 …

This paper presents a novel quantum walk approach to simulating parton showers on a
quantum computer. We demonstrate that the quantum walk paradigm offers a natural and …

The quantum walk is a powerful tool to develop quantum algorithms, which usually are
based on searching for a vertex in a graph with multiple marked vertices, with Ambainis's …

The staggered quantum-walk model makes it possible to establish an unprecedented
connection between discrete-time quantum walks and graph theory. We call attention to the …

Perfect state transfer between two marked vertices of a graph by means of a discrete-time
quantum walk is analyzed. We consider the quantum walk search algorithm with two marked …

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 …

When searching for a marked vertex in a graph, Szegedy's usual search operator is defined
by using the transition probability matrix of the random walk with absorbing barriers at the …

Szegedy's quantum walk is a quantization of a classical random walk or Markov chain,
where the walk occurs on the edges of the bipartite double cover of the original graph. To …

Szegedy's quantum walk is an algorithm for quantizing a general Markov chain. It has plenty
of applications, such as many variants of optimizations. In order to check its properties in an …