Eigenvalues of Two-State Quantum Walks Induced by the Hadamard Walk
Shimpei Endo,
Takako Endo,
Takashi Komatsu,
Norio Konno
Affiliations
Shimpei Endo
Department of Physics, Frontier Research Institute for Interdisciplinary Science, Faculty of Science, Tohoku University, 6-3, Aoba, Aramaki-aza, Aobaku, Sendai, Miyagi 980-8578, Japan
Takako Endo
Department of Applied Mathematics, Faculty of Engineering, Yokohama National University, Hodogaya, Yokohama 240-8501, Japan
Takashi Komatsu
Department of Bioengineering School of Engineering, The University of Tokyo, Bunkyo, Tokyo 113-8656, Japan
Norio Konno
Department of Applied Mathematics, Faculty of Engineering, Yokohama National University, Hodogaya, Yokohama 240-8501, Japan
Existence of the eigenvalues of the discrete-time quantum walks is deeply related to localization of the walks. We revealed, for the first time, the distributions of the eigenvalues given by the splitted generating function method (the SGF method) of the space-inhomogeneous quantum walks in one dimension we had treated in our previous studies. Especially, we clarified the characteristic parameter dependence for the distributions of the eigenvalues with the aid of numerical simulation.
