A Note on the Spectral Mapping Theorem of Quantum Walk Models

DOI10.4036/iis.2017.A.13zbMath1470.81028arXiv1604.00581MaRDI QIDQ5147820

Osamu Ogurisu, Kaname Matsue, Etsuo Segawa

Publication date: 28 January 2021

Published in: Interdisciplinary Information Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.00581

zbMATH Keywords

spectral mapping theoremgeneralized eigenspacequantum walk model

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Quantum computation (81P68) Path integrals in quantum mechanics (81S40) Spinor and twistor methods applied to problems in quantum theory (81R25) Twisted and skew group rings, crossed products (16S35) (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces (47A70) Random walks on graphs (05C81)

Related Items (10)

A dynamical system induced by quantum walk ⋮ Partition-based discrete-time quantum walks ⋮ Phase measurement of quantum walks: application to structure theorem of the positive support of the Grover walk ⋮ Localization for a one-dimensional split-step quantum walk with bound states robust against perturbations ⋮ Supersymmetry for chiral symmetric quantum walks ⋮ Combinatorial necessary conditions for regular graphs to induce periodic quantum walks ⋮ Eigenvalues of quantum walk induced by recurrence properties of the underlying birth and death process: application to computation of an edge state ⋮ A quantum walk induced by Hoffman graphs and its periodicity ⋮ Quantum search on simplicial complexes ⋮ A new type of spectral mapping theorem for quantum walks with a moving shift on graphs

Cites Work

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• The staggered quantum walk model
• Generator of an abstract quantum walk
• Quantum walks on simplicial complexes
• Unitary equivalent classes of one-dimensional quantum walks
• Spectral and asymptotic properties of Grover walks on crystal lattices
• Quantum random walks in one dimension

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