11 citations · 21 across the 9 of their papers we have counts for
9 papers
A method of approximation of discrete Schrödinger equation with the normalized Laplacian by discrete-time quantum walk on graphs
Kei Saito, Etsuo Segawa
We propose a class of continuous-time quantum walk models on graphs induced by a certain class of discrete-time quantum walk models with the parameter . Here the graph…
Spectral Analysis of Non-unitary Two-phase Quantum Walks in One Dimension
Chusei Kiumi, Kei Saito, Yohei Tanaka
It is recently shown by Asahara-Funakawa-Seki-Tanaka that existing index theory for chirally symmetric (discrete-time) quantum walks can be extended to the setting of non-unitary q…
Strongly trapped space-inhomogeneous quantum walks in one dimension
Chusei Kiumi, Kei Saito
Localization is a characteristic phenomenon of space-inhomogeneous quantum walks in one dimension, where particles remain localized around their initial position. The existence of…
A new type of spectral mapping theorem for quantum walks with a moving shift on graphs
Sho Kubota, Kei Saito, Yusuke Yoshie
The conventional spectral mapping theorem for quantum walks can only be applied for walks employing a shift operator whose square is the identity. This theorem gives most of the ei…
Eigenvalues of two-phase quantum walks with one defect in one dimension
Chusei Kiumi, Kei Saito
We study space-inhomogeneous quantum walks (QWs) on the integer lattice which we assign three different coin matrices to the positive part, the negative part, and the origin, respe…
Spectral analysis for a multi-dimensional split-step quantum walk with a defect
Toru Fuda, Akihiro Narimatsu, Kei Saito +1
This paper studies the spectrum of a multi-dimensional split-step quantum walk with a defect that cannot be analysed in the previous papers. To this end, we have developed a new te…
Periodicity for the 3-state quantum walk on cycles
Takeshi Kajiwara, Norio Konno, Shohei Koyama +1
Dukes (2014) and Konno, Shimizu, and Takei (2017) studied the periodicity for 2-state quantum walks whose coin operator is the Hadamard matrix on cycle graph C_N with N vertices. T…
Periodicity for the Fourier quantum walk on regular graphs
Kei Saito
Quantum walks determined by the coin operator on graphs have been intensively studied. The typical examples of coin operator are the Grover and Fourier matrices. The periodicity of…
Probability distributions and weak limit theorems of quaternionic quantum walks in one dimension
Kei Saito
The discrete-time quantum walk (QW) is determined by a unitary matrix whose component is complex number. Konno (2015) extended the QW to a walk whose component is quaternion.We cal…