Periodicity of the Discrete-time Quantum Walk on a Finite Graph

DOI10.4036/iis.2017.A.10zbMath1470.81043MaRDI QIDQ5147817

Etsuo Segawa, Iwao Sato, Norio Konno, Yusuke Higuchi

Publication date: 28 January 2021

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

zbMATH Keywords

strongly regular graphperiodicityrandom walkquantum walkcyclotomic polynomialevolution matrix

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Quantum stochastic calculus (81S25) Discrete version of topics in analysis (39A12) Random matrices (algebraic aspects) (15B52) Cyclotomic function fields (class groups, Bernoulli objects, etc.) (11R60) Graph algorithms (graph-theoretic aspects) (05C85) Spectral sets of linear operators (47A25) Random walks on graphs (05C81) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (16)

Periodicity of quantum walks defined by mixed paths and mixed cycles ⋮ Perfect state transfer in Grover walks between states associated to vertices of a graph ⋮ Periodicity of Grover walks on complete graphs with self-loops ⋮ Quantum walk and its application domains: a systematic review ⋮ Odd-periodic Grover walks ⋮ Parameterization of quantum walks on cycles ⋮ Combinatorial necessary conditions for regular graphs to induce periodic quantum walks ⋮ Periodicity of lively quantum walks on cycles with generalized Grover coin ⋮ Quantum walks defined by digraphs and generalized Hermitian adjacency matrices ⋮ Quantum search algorithm for exceptional vertexes in regular graphs and its circuit implementation ⋮ A quantum walk induced by Hoffman graphs and its periodicity ⋮ Periodicity of Grover walks on generalized Bethe trees ⋮ Periodicities of Grover walks on distance-regular graphs ⋮ Periodicity of Grover walks on bipartite regular graphs with at most five distinct eigenvalues ⋮ Quantum search on simplicial complexes ⋮ A new type of spectral mapping theorem for quantum walks with a moving shift on graphs

Cites Work

• Generator of an abstract quantum walk
• Spectra of graphs
• State transfer on graphs
• On the hitting times of quantum versus random walks
• A note on the discrete-time evolutions of quantum walk on a graph
• QUANTUM WALKS ON GENERAL GRAPHS
• On the Digraph of a Unitary Matrix
• QUANTUM WALKS AND THEIR ALGORITHMIC APPLICATIONS
• Decoherence in quantum walks – a review
• Quantum Walk Algorithm for Element Distinctness
• Quantum simulations of classical random walks and undirected graph connectivity
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