189 citations · 1.9k across the 148 of their papers we have counts for
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Limit theorems and absorption problems for quantum random walks in one dimension
Norio Konno
In this paper we consider limit theorems, symmetry of distribution, and absorption problems for two types of one-dimensional quantum random walks determined by 2 times 2 unitary ma…
Absorption problems for quantum walks in one dimension
Norio Konno, Takao Namiki, Takahiro Soshi +1
This paper treats absorption problems for the one-dimensional quantum walk determined by a 2 times 2 unitary matrix U on a state space {0,1,...,N} where N is finite or infinite by…
A New Type of Limit Theorems for the One-Dimensional Quantum Random Walk
Norio Konno
In this paper we consider the one-dimensional quantum random walk X^{varphi} _n at time n starting from initial qubit state varphi determined by 2 times 2 unitary matrix U. We give…
Quantum random walks in one dimension
Norio Konno
This letter treats the quantum random walk on the line determined by a 2 times 2 unitary matrix U. A combinatorial expression for the mth moment of the quantum random walk is prese…
Symmetry of distribution for the one-dimensional Hadamard walk
Norio Konno, Takao Namiki, Takahiro Soshi
In this paper we study a one-dimensional quantum random walk with the Hadamard transformation which is often called the Hadamard walk. We construct the Hadamard walk using a transi…