3 citations · 5 across the 4 of their papers we have counts for
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quant-ph2014★ 2 cited
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…
quant-ph2014
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…
quant-ph2010★ 3 cited
Limit theorems for quantum walks with memory
Norio Konno, Takuya Machida
Recently Mc Gettrick [1] introduced and studied a discrete-time 2-state quantum walk (QW) with a memory in one dimension. He gave an expression for the amplitude of the QW by path…