58 citations · 195 across the 32 of their papers we have counts for
5 papers · 2 filters
Limit theorems for the interference terms of discrete-time quantum walks on the line
Takuya Machida
The probability distributions of discrete-time quantum walks have been often investigated, and many interesting properties of them have been discovered. The probability that the wa…
The Heun differential equation and the Gauss differential equation related to quantum walks
Norio Konno, Takuya Machida, Tohru Wakasa
The limit theorems of discrete- and continuous-time quantum walks on the line have been intensively studied. We show a relation among limit distributions of quantum walks, Heun dif…
Alternate two-dimensional quantum walk with a single-qubit coin
C. Di Franco, M. Mc Gettrick, T. Machida +1
We have recently proposed a two-dimensional quantum walk where the requirement of a higher dimensionality of the coin space is substituted with the alternance of the directions in…
The discrete-time Grover walk on star graphs with one loop
Takuya Machida
This paper has been withdrawn by the author because the result of this paper was already obtained.
Return probability of one-dimensional discrete-time quantum walks with final-time dependence
Yusuke Ide, Norio Konno, Takuya Machida +1
We analyze final-time dependent discrete-time quantum walks in one dimension. We compute asymptotics of the return probability of the quantum walk by a path counting approach. More…