58 citations · 195 across the 32 of their papers we have counts for
27 papers · 1 filter
A simple model of quantum walk with a gap in distribution
Takuya Machida
Quantum walks are quantum counterparts of random walks and their probability distributions are different from each other. A quantum walker distributes on a Hilbert space and it is…
Phase transition of a continuous-time quantum walk on the half line
Takuya Machida
Quantum walks are referred to as quantum analogs to random walks in mathematics. They have been studied as quantum algorithms in quantum information for quantum computers. There ar…
Limit distribution of a continuous-time quantum walk with a spatially 2-periodic Hamiltonian
Takuya Machida
Focusing on a continuous-time quantum walk on , we analyze a probability distribution with which the quantum walker is observed at a…
Phase transition of an open quantum walk
Takuya Machida
It has been discovered that open quantum walks diffusively distribute in space, since they were introduced in 2012. Indeed, some limit distributions have been demonstrated and most…
Limit distribution of a time-dependent quantum walk on the half line
Takuya Machida
We focus on a 2-period time-dependent quantum walk on the half line in this paper. The quantum walker launches at the edge of the half line in a localized superposition state and i…
A limit distribution for a quantum walk driven by a five-diagonal unitary matrix
Takuya Machida
In this paper, we work on a quantum walk whose system is manipulated by a five-diagonal unitary matrix, and present long-time limit distributions. The quantum walk launches off a l…
Some limit laws for quantum walks with applications to a version of the Parrondo paradox
Takuya Machida, F. Alberto Grunbaum
A quantum walker moves on the integers with four extra degrees of freedom, performing a coin-shift operation to alter its internal state and position at discrete units of time. The…
A limit theorem for a splitting distribution of a quantum walk
Takuya Machida
Discrete-time quantum walks are considered a counterpart of random walks and the study for them has been getting attention since around 2000. In this paper, we focus on a quantum w…
A quantum walk on the half line with a particular initial state
Takuya Machida
Quantum walks are considered to be quantum counterparts of random walks.They show us impressive probability distributions which are different from those of random walks.That fact h…
Localization and limit laws of a three-state alternate quantum walk on a two-dimensional lattice
Takuya Machida, C. M. Chandrashekar
A two-dimensional discrete-time quantum walk (DTQW) can be realized by alternating a two-state DTQW in one spatial dimension followed by an evolution in the other dimension. This w…
A localized quantum walk with a gap in distribution
Takuya Machida
Quantum walks behave differently from what we expect and their probability distributions have unique structures. They have localization, singularities, a gap, and so on. Those feat…
A limit law of the return probability for a quantum walk on a hexagonal lattice
Takuya Machida
A return probability of random walks is one of the interesting subjects. As it is well known, the return probability strongly depends on the structure of the space where the random…
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…
Self-avoiding quantum walks: realisations in subspaces and limit theorems
Takuya Machida, C. M. Chandrashekar, Norio Konno +1
While completely self-avoiding quantum walks have the distinct property of leading to a trivial unidirectional transport of a quantum state, an interesting and non-trivial dynamics…
Realization of the probability laws in the quantum central limit theorems by a quantum walk
Takuya Machida
Since a limit distribution of a discrete-time quantum walk on the line was derived in 2002, a lot of limit theorems for quantum walks with a localized initial state have been repor…
A quantum walk with a delocalized initial state: contribution from a coin-flip operator
Takuya Machida
A unit evolution step of discrete-time quantum walks is determined by both a coin-flip operator and a position-shift operator. The behavior of quantum walkers after many steps deli…
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…
Entanglement for discrete-time quantum walks on the line
Yusuke Ide, Norio Konno, Takuya Machida
The discrete-time quantum walk is a quantum counterpart of the random walk. It is expected that the model plays important roles in the quantum field. In the quantum information the…
Limit distribution with a combination of density functions for a 2-state quantum walk
Takuya Machida
We consider 2-state quantum walks (QWs) on the line, which are defined by two matrices. One of the matrices operates the walk in certain intervals. In the usual QWs starting from t…