58 citations · 195 across the 32 of their papers we have counts for
4 papers · 1 filter
Trapping and spreading properties of quantum walk in homological structure
Takuya Machida, Etsuo Segawa
We attempt to extract a homological structure of two kinds of graphs by the Grover walk. The first one consists of a cycle and two semi-infinite lines and the second one is assembl…
Turing instability in Reaction-Diffusion models on complex networks
Yusuke Ide, Hirofumi Izuhara, Takuya Machida
In this paper, the Turing instability in reaction-diffusion models defined on complex networks is studied. Here, we focus on three types of models which generate complex networks,…
Limit theorems of a 3-state quantum walk and its application for discrete uniform measures
Takuya Machida
We present two long-time limit theorems of a 3-state quantum walk on the line when the walker starts from the origin. One is a limit measure which is obtained from the probability…
A limit theorem for a 3-period time-dependent quantum walk
F. Alberto Grünbaum, Takuya Machida
We consider a discrete-time 2-state quantum walk on the line. The state of the quantum walker evolves according to a rule which is determined by a coin-flip operator and a position…