45 citations · 107 across the 17 of their papers we have counts for
17 papers
Categories of quantum walks
Hiroki Sako
We propose categories of -dimensional and multi-dimensional quantum walks. In the categories, an object is a quantum walk, and a morphism is an intertwining operator between two…
Convergence theorems on multi-dimensional homogeneous quantum walks
Hiroki Sako
We propose a general framework for quantum walks on d-dimensional spaces. We investigate asymptotic behavior of these walks. Among them, existence of limit distribution of homogene…
Intertwining operators between one-dimensional homogeneous quantum walks
Hiroki Sako
The subject of this paper is a kind of dynamical systems called quantum walks. We study one-dimensional homogeneous analytic quantum walks U. We explain how to identify the space o…
Group approximation in Cayley topology and coarse geometry, Part II: Fibered coarse embeddings
Masato Mimura, Hiroki Sako
The objective of this series is to study metric geometric properties of disjoint unions of amenable Cayley graphs by group properties of the Cayley accumulation points in the space…
Space-homogeneous quantum walks on Z from the viewpoint of complex analysis
Hayato Saigo, Hiroki Sako
The subject of this paper is quantum walks, which are expected to simulate several kinds of quantum dynamical systems. In this paper, we define analyticity for quantum walks on Z.…
On a property of the simple random walk on
Norio Konno, Hayato Saigo, Hiroki Sako
The subject of this paper is the simple random walk on . We give a very simple answer to the following problem: under the condition that a random walk has already spent…