Quantum Walks on Necklaces and Mixing

Kieferova, M; Nagaj, D

Quantum Walks on Necklaces and Mixing

Kieferova, M

Nagaj, D

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Publication Type:: Journal Article
Citation:: Issue, 2 pp. 1250025 - ?

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Field	Value	Language
dc.contributor.author	Kieferova, M https://orcid.org/0000-0002-0749-8126	en_US
dc.contributor.author	Nagaj, D	en_US
dc.identifier.citation	Issue, 2 pp. 1250025 - ?	en_US
dc.identifier.uri	http://hdl.handle.net/10453/135293
dc.description.abstract	We analyze continuous-time quantum walks on necklace graphs - cyclical graphs consisting of many copies of a smaller graph (pearl). Using a Bloch-type ansatz for the eigenfunctions, we block-diagonalize the Hamiltonian, reducing the effective size of the problem to the size of a single pearl. We then present a general approach for showing that the mixing time scales (with growing size of the necklace) similarly to that of a simple walk on a cycle. Finally, we present results for mixing on several necklace graphs.	en_US
dc.relation.ispartof	Issue	en_US
dc.rights	info:eu-repo/semantics/openAccess
dc.title	Quantum Walks on Necklaces and Mixing	en_US
dc.type	Journal Article
utslib.citation.volume	2	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Computer Science
pubs.organisational-group	/University of Technology Sydney/Strength - QSI - Centre for Quantum Software and Information
utslib.copyright.status	open_access	*
pubs.volume	2	en_US

Abstract:

We analyze continuous-time quantum walks on necklace graphs - cyclical graphs consisting of many copies of a smaller graph (pearl). Using a Bloch-type ansatz for the eigenfunctions, we block-diagonalize the Hamiltonian, reducing the effective size of the problem to the size of a single pearl. We then present a general approach for showing that the mixing time scales (with growing size of the necklace) similarly to that of a simple walk on a cycle. Finally, we present results for mixing on several necklace graphs.

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http://hdl.handle.net/10453/135293