17 citations · 40 across the 23 of their papers we have counts for
23 papers
Spectral characterization of the uniform theta graph and classification of 6-periodic Grover walks
Sho Kubota
We characterize the uniform theta graph by the spectrum of its normalized adjacency matrix, or equivalently, by the spectrum of its normalized Laplacian matrix. We also in…
Entanglement entropy in two-particle Grover walks on graphs
Sho Kubota, Haruhiko Matsubara, Etsuo Segawa
We define a two-particle quantum walk of identical particles on a graph via the one-particle Grover walk on the Kronecker product , and call it the two-particle Gr…
Regular graphs to induce even periodic Grover walks
Sho Kubota, Hiroto Sekido, Kiyoto Yoshino
The interest of this paper is a characterization of graphs that induce periodic Grover walks with given periods. In previous studies, Yoshie has shown that the only graphs that ind…
Periodic solutions to Kobayashi--Warren--Carter systems
Shodai Kubota, Ken Shirakawa
In this paper, a system of parabolic PDEs, called the Kobayashi--Warren--Carter system, is considered as a possible phase-field model of planar grain boundary motion. The Main Theo…
On symmetric spectra of Hermitian adjacency matrices for non-bipartite mixed graphs
Yusuke Higuchi, Sho Kubota, Etsuo Segawa
We study the equivalence between bipartiteness and symmetry of spectra of mixed graphs, for -Hermitian adjacency matrices defined by an angle . We show that this eq…
A convergence time of Grover walk on regular graph to stationary state
Ayaka Ishikawa, Sho Kubota, Etsuo Segawa
We consider a quantum walk model on a finite graph which has an interaction with the outside. Here a quantum walker from the outside penetrates the graph and also a quantum walker…
Mutually orthogonal Sudoku Latin squares and their graphs
Sho Kubota, Sho Suda, Akane Urano
We introduce a graph attached to mutually orthogonal Sudoku Latin squares. The spectra of the graphs obtained from finite fields are explicitly determined. As a corollary, we then…
Periodicity of Grover walks on bipartite regular graphs with at most five distinct eigenvalues
Sho Kubota
We determine connected bipartite regular graphs with four distinct adjacency eigenvalues that induce periodic Grover walks, and show that it is only . We also show that there…
One-dimensional optimal control problems for time-discrete constrained quasilinear diffusion equations of Allen--Cahn types
Shodai Kubota
In this paper, we consider a class of optimal control problems for a one-dimensional time-discrete constrained quasilinear diffusion state-systems of singular Allen--Cahn types and…
Perfect state transfer in Grover walks between states associated to vertices of a graph
Sho Kubota, Etsuo Segawa
We study perfect state transfer in Grover walks, which are typical discrete-time quantum walk models. In particular, we focus on states associated to vertices of a graph. We call s…
Temperature Control of PDE Constrained Optimization Problems Governed by Kobayashi--Warren--Carter Type Models of Grain Boundary Motions
Harbir Antil, Shodai Kubota, Ken Shirakawa +1
In this paper, we consider a class of optimal control problems governed by state-equations of Kobayashi--Warren--Carter type. The control is given by physical temperature. The focu…
Combinatorial necessary conditions for regular graphs to induce periodic quantum walks
Sho Kubota
We derive combinatorial necessary conditions for discrete-time quantum walks defined by regular mixed graphs to be periodic. If the quantum walk is periodic, all the eigenvalues of…
The trace formula with respect to the twisted Grover matrix of a mixed digraph
Takashi Komatsu, Sho Kubota, Norio Konno +1
We define a zeta function woth respect to the twisted Grover matrix of a mixed digraph, and present an exponential expression and a determinant expression of this zeta function. As…
Subdifferential decomposition of 1D-regularized total variation with nonhomogeneous coefficients
Shodai Kubota
In this paper, we consider a convex function defined as a 1D-regularized total variation with nonhomogeneous coefficients, and prove the Main Theorem concerned with the decompositi…
Periodicity of quantum walks defined by mixed paths and mixed cycles
Sho Kubota, Hiroto Sekido, Harunobu Yata
In this paper, we determine periodicity of quantum walks defined by mixed paths and mixed cycles. By the spectral mapping theorem of quantum walks, consideration of periodicity is…
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…
Optimal control problems for 1D parabolic state-systems of KWC types with dynamic boundary conditions
Shodai Kubota, Ryota Nakayashiki, Ken Shirakawa
In this paper, we consider a class of optimal control problems governed by 1D parabolic state-systems of KWC types with dynamic boundary conditions. The state-systems are based on…
Optimal Control Problems Governed by 1-D Kobayashi-Warren-Carter Type Systems
Harbir Antil, Shodai Kubota, Ken Shirakawa +1
This paper is devoted to the study of a class of optimal control problems governed by 1-D Kobayashi-Warren-Carter type systems, which are based on a phase-field model of grain boun…
The uniqueness of covers for widely generalized line graphs
Michitaka Furuya, Sho Kubota, Tetsuji Taniguchi +1
As a natural generalization of line graphs, Hoffman line graphs were defined by Woo and Neumaier. Especially, Hoffman line graphs are closely related to the smallest eigenvalue of…
Quantum walks defined by digraphs and generalized Hermitian adjacency matrices
Sho Kubota, Etsuo Segawa, Tetsuji Taniguchi
We propose a quantum walk defined by digraphs (mixed graphs). This is like Grover walk that is perturbed by a certain complex-valued function defined by digraphs. The discriminant…
Periodicity of Grover walks on generalized Bethe trees
S. Kubota, E. Segawa, T. Taniguchi +1
This paper explains the perfect characterization of the generalized Bethe trees by analyzing the spectrum of its transition matrix.
Unification of graph products and compatibility with switching
Sho Kubota
We define the type of graph products, which enable us to treat many graph products in a unified manner. These unified graph products are shown to be compatible with Godsil--McKay s…
Strongly regular graphs with the same parameters as the symplectic graph
Sho Kubota
We consider orbit partitions of groups of automorphisms for the symplectic graph and apply Godsil-McKay switching. As a result, we find four families of strongly regular graphs wit…