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 …

There are at least three models of discrete-time quantum walks (QWs) on graphs currently
under active development. In this work, we focus on the equivalence of two of them, known …

We review various unitary network models used in quantum computing, spectral analysis or
condensed matter physics and establish relationships between them. We show that …

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 …

Many systems such as social networks and biological networks take the form of complex
networks, which have a community structure. Community detection in complex networks is of …

We consider the Grover walk model on a connected finite graph with two infinite length tails
and we set an-infinite external source from one of the tails as the initial state. We show that …

We give an explicit formula of the generator of an abstract Szegedy evolution operator in
terms of the discriminant operator of the evolution. We also characterize the asymptotic …

In this paper, we introduce a multi-dimensional generalization of Kitagawa's split-step
discrete-time quantum walk, study the spectrum of its evolution operator for the case of one …

We establish the theory for pretty good state transfer in discrete-time quantum walks. For a
class of walks, we show that pretty good state transfer is characterized by the spectrum of …

In this paper, we determine periodicity of quantum walks defined by mixed paths and mixed
cycles. By the spectral mapping theorem of quantum walks, consideration of periodicity is …