Eigenvalues of two-state quantum walks induced by the Hadamard walk
arXiv:1909.08226 · doi:10.3390/e22010127
Abstract
Existence of the eigenvalues of the discrete-time quantum walks is deeply related to localization of the walks. We revealed the distributions of the eigenvalues given by the splitted generating function method (the SGF method) of the quantum walks we had treated in our previous studies. In particular, we focused on two kinds of the Hadamard walk with one defect models and the two-phase QWs that have phases at the non-diagonal elements of the unitary transition operators. As a result, we clarified the characteristic parameter dependence for the distributions of the eigenvalues with the aid of numerical simulation.
arXiv comment9 pages, 4 figures
References in corpus (7)
- Quantum random walks - an introductory overview
- Quantum walks: a comprehensive review
- Decoherence in quantum walks - a review
- Localization of Two-Dimensional Quantum Walks
- Trapping a particle of a quantum walk on the line
- Detection of edge defects by embedded eigenvalues of quantum walks
- Localization of discrete time quantum walks on the glued trees
Cited by in corpus (6)
- Eigenvalues of two-phase quantum walks with one defect in one dimension
- Coin dimensionality as a resource in quantum metrology involving discrete-time quantum walks
- Localization of space-inhomogeneous three-state quantum walks
- Strongly trapped space-inhomogeneous quantum walks in one dimension
- Localization in quantum walks with periodically arranged coin matrices
- Spectral analysis of three-state quantum walks with general coin matrices