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 …

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 …

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 study a quantum walk (QW) whose time evolution is induced by a random walk (RW) first
introduced by Szegedy (2004). We focus on a relation between recurrent properties of the …

Given two Hilbert spaces, HH and KK, we introduce an abstract unitary operator U on HH
and its discriminant T on KK induced by a coisometry from HH to KK and a unitary involution …

We analyze the probability distributions of the quantum walks induced from Markov chains
by Szegedy (2004). The first part of this paper is devoted to the quantum walks induced from …

In this paper, we propose a new algorithm based on a quantum walk search model to
distinguish strongly similar graphs. Our algorithm computes a signature for each graph via …

We study a position-dependent discrete-time quantum walk (QW) in one dimension, whose
time-evolution operator is built up from two coin operators which are distinguished by phase …

In this paper, we consider the time averaged distribution of discrete time quantum walks on
the glued trees. In order to analyze the walks on the glued trees, we consider a reduction to …

In this paper, we consider a spectral analysis of discrete time quantum walks on the path.
For isospectral coin cases, we show that the time averaged distribution and stationary …