Eigenvalue analysis of three-state quantum walks with general coin matrices

• URL: http://arxiv.org/abs/2311.06468v1
• Date: Sat, 11 Nov 2023 03:37:24 GMT
• Title: Eigenvalue analysis of three-state quantum walks with general coin matrices
• Authors: Jir\^o Akahori, Chusei Kiumi, Norio Konno, Takuya Watanabe
• Abstract summary: This research focuses on the transfer matrix of three-state quantum walks with a general coin matrix. We derive eigenvalues for models that were previously unanalyzable.
• Score: 0.8022222226139029
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Mathematical analysis on the existence of eigenvalues is vital, as it corresponds to the occurrence of localization, an exceptionally important property of quantum walks. Previous studies have demonstrated that eigenvalue analysis utilizing the transfer matrix proves beneficial for space inhomogeneous three-state quantum walks with a specific class of coin matrices, including Grover matrices. In this research, we turn our attention to the transfer matrix of three-state quantum walks with a general coin matrix. Building upon previous research methodologies, we dive deeper into investigating the properties of the transfer matrix and employ numerical analysis to derive eigenvalues for models that were previously unanalyzable.

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